XIX. GEOLOGICAL TIME.—PROBABLE DATE OF THE GLACIAL EPOCH
Geological Time measurable from Astronomical Data.—M. Leverrier’s Formulæ.—Tables of Eccentricity for 3,000,000 Years in the Past and 1,000,000 Years in the Future.—How the Tables have been computed.—Why the Glacial Epoch is more recent than had been supposed.—Figures convey a very inadequate Conception of immense Duration.—Mode of representing a Million of Years.—Probable Date of the Glacial Epoch.
If those great Secular variations of climate which we have been considering be indirectly the result of changes in the eccentricity of the earth’s orbit, then we have a means of determining, at least so far as regards recent epochs, when these variations took place. If the glacial epoch be due to the causes assigned, we have a means of ascertaining, with tolerable accuracy, not merely the date of its commencement, but the length of its duration. M. Leverrier has not only determined the superior limit of the eccentricity of the earth’s orbit, but has also given formulæ by means of which the extent of the eccentricity for any period, past or future, may be computed.
A well-known astronomer and mathematician, who has specially investigated the subject, is of opinion that these formulæ give results which may be depended upon as approximately correct for four millions of years past and future. An eminent physicist has, however, expressed to me his doubts as to whether the results can be depended on for a period so enormous. M. Leverrier in his Memoir has given a table of the eccentricity for 100,000 years before and after 1800 A.D., computed for intervals of 10,000 years. This table, no doubt, embraces a period sufficiently great for ordinary astronomical purposes, but it is by far too limited to afford information in regard to geological epochs.
With the view of ascertaining the probable date of the glacial epoch, as well as the character of the climate for a long course of ages, Table I. was computed from M. Leverrier’s formulæ.[194] It shows the eccentricity of the earth’s orbit and longitude of the perihelion for 3,000,000 of years back, and 1,000,000 of years to come, at periods 50,000 years apart.
On looking over the table it will be seen that there are three principal periods when the eccentricity rose to a very high value, with a few subordinate maxima between. It will be perceived also that during each of those periods the eccentricity does not remain at the same uniform value, but rises and falls, in one case twice, and in the other two cases three times. About 2,650,000 years back we have the eccentricity almost at its inferior limit. It then begins to increase, and fifty thousand years afterwards, namely at 2,600,000 years ago, it reaches ·0660; fifty thousand years after this period it has diminished to ·0167, which is about its present value. It then begins to increase, and in another fifty thousand years, namely at 2,500,000 years ago, it approaches to almost the superior limit, its value being then ·0721. It then begins to diminish, and at 2,450,000 years ago it has diminished to ·0252. These two maxima, separated by a minimum and extending over a period of 200,000 years, constitute the first great period of high eccentricity. We then pass onwards for upwards of a million and a half years, and we come to the second great period. It consists of three maxima separated by two minima. The first maximum occurred at 950,000 years ago, the second or middle one at 850,000 years ago, and the third and last at 750,000 years ago—the whole extending over a period of nearly 300,000 years. Passing onwards for another million and half years, or to about 800,000 years in the future, we come to the third great period. It also consists of three maxima one hundred thousand years apart. Those occur at the periods 800,000, 900,000, and 1,000,000 years to come, respectively, separated also by two minima. Those three great periods, two of them in the past and one of them in the future, included in the Table, are therefore separated from each other by an interval of upwards of 1,700,000 years.
In this Table there are seven periods when the earth’s orbit becomes nearly circular, four in the past and three in the future.
The Table shows also four or five subordinate periods of high eccentricity, the principal one occurring 200,000 years ago.
The variations of eccentricity during the four millions of years, are represented to the eye diagrammatically in Plate IV.
In order to determine with more accuracy the condition of the earth’s orbit during the three periods of great eccentricity included in Table I., I computed the values for periods of ten thousand years apart, and the results are embodied in Tables II., III., and IV.
There are still eminent astronomers and physicists who are of opinion that the climate of the globe never could have been seriously affected by changes in the eccentricity of its orbit. This opinion results, no doubt, from viewing the question as a purely astronomical one. Viewed from an astronomical standpoint, as has been already remarked, there is actually nothing from which any one could reasonably conclude with certainty whether a change of eccentricity would seriously affect climate or not. By means of astronomy we ascertain the extent of the eccentricity at any given period, how much the winter may exceed the summer in length (or the reverse), how much the sun’s heat is increased or decreased by a decrease or an increase of distance, and so forth; but we obtain no information whatever regarding how these will actually affect climate. This, as we have already seen, must be determined wholly from physical considerations, and it is an exceedingly complicated problem. An astronomer, unless he has given special attention to the physics of the question, is just as apt to come to a wrong conclusion as any one else. The question involves certain astronomical elements; but when these are determined everything then connected with the matter is purely physical. Nearly all the astronomical elements of the question are comprehended in the accompanying Tables.
TABLE I.
THE ECCENTRICITY AND LONGITUDE OF THE PERIHELION OF THE EARTH’S ORBIT FOR 3,000,000 YEARS IN THE PAST AND 1,000,000 YEARS IN THE FUTURE, COMPUTED FOR INTERVALS OF 50,000 YEARS.
+---------------------------------------------+ | PAST TIME. | +------------------+-------------+------------+ | Number of years |Eccentricity.|Longitude of| |before epoch 1800.| |perihelion. | +------------------+-------------+------------+ | | | ° ′ | | −3,000,000 | 0·0365 | 39 30 | | −2,950,000 | 0·0170 | 210 39 | | −2,900,000 | 0·0442 | 200 52 | | −2,850,000 | 0·0416 | 0 18 | | −2,800,000 | 0·0352 | 339 14 | | −2,750,000 | 0·0326 | 161 22 | | −2,700,000 | 0·0330 | 65 37 | | −2,650,000 | 0·0053 | 318 40 | | −2,600,000 | 0·0660 | 190 4 | | −2,550,000 | 0·0167 | 298 34 | | −2,500,000 | 0·0721 | 338 36 | | −2,450,000 | 0·0252 | 109 33 | | −2,400,000 | 0·0415 | 116 40 | | −2,350,000 | 0·0281 | 308 23 | | −2,300,000 | 0·0238 | 195 25 | | −2,250,000 | 0·0328 | 141 18 | | −2,200,000 | 0·0352 | 307 6 | | −2,150,000 | 0·0183 | 307 5 | | −2,100,000 | 0·0304 | 98 40 | | −2,050,000 | 0·0170 | 334 46 | | −2,000,000 | 0·0138 | 324 4 | | −1,950,000 | 0·0427 | 120 32 | | −1,900,000 | 0·0336 | 188 31 | | −1,850,000 | 0·0503 | 272 14 | | −1,800,000 | 0·0334 | 354 52 | | −1,750,000 | 0·0350 | 65 25 | | −1,700,000 | 0·0085 | 95 13 | | −1,650,000 | 0·0035 | 168 23 | | −1,600,000 | 0·0305 | 158 42 | | −1,550,000 | 0·0239 | 225 57 | | −1,500,000 | 0·0430 | 303 29 | | −1,450,000 | 0·0195 | 57 11 | | −1,400,000 | 0·0315 | 97 35 | | −1,350,000 | 0·0322 | 293 38 | | −1,300,000 | 0·0022 | 0 48 | | −1,250,000 | 0·0475 | 105 50 | | −1,200,000 | 0·0289 | 239 34 | | −1,150,000 | 0·0473 | 250 27 | | −1,100,000 | 0·0311 | 55 24 | | −1,050,000 | 0·0326 | 4 8 | | −1,000,000 | 0·0151 | 248 22 | | −950,000 | 0·0517 | 97 51 | | −900,000 | 0·0102 | 135 2 | | −850,000 | 0·0747 | 239 28 | | −800,000 | 0·0132 | 343 49 | | −750,000 | 0·0575 | 27 18 | | −700,000 | 0·0220 | 208 13 | | −650,000 | 0·0226 | 141 29 | | −600,000 | 0·0417 | 32 34 | | −550,000 | 0·0166 | 251 50 | | −500,000 | 0·0388 | 193 56 | | −450,000 | 0·0308 | 356 52 | | −400,000 | 0·0170 | 290 7 | | −350,000 | 0·0195 | 182 50 | | −300,000 | 0·0424 | 23 29 | | −250,000 | 0·0258 | 59 39 | | −200,000 | 0·0569 | 168 18 | | −150,000 | 0·0332 | 242 56 | | −100,000 | 0·0473 | 316 18 | | −50,000 | 0·0131 | 50 14 | +------------------+-------------+------------+
+---------------------------------------------+ | FUTURE TIME. | +------------------+-------------+------------+ | Number of years |Eccentricity.|Longitude of| |before epoch 1800.| |perihelion. | +------------------+-------------+------------+ | | | ° ′ | | A.D. 1800 | 0·0168 | 99 30 | | +50,000 | 0·0173 | 38 12 | | +100,000 | 0·0191 | 114 50 | | +150,000 | 0·0353 | 201 57 | | +200,000 | 0·0246 | 279 41 | | +250,000 | 0·0286 | 350 54 | | +300,000 | 0·0158 | 172 29 | | +350,000 | 0·0098 | 201 40 | | +400,000 | 0·0429 | 6 9 | | +450,000 | 0·0231 | 98 37 | | +500,000 | 0·0534 | 157 26 | | +550,000 | 0·0259 | 287 31 | | +600,000 | 0·0395 | 285 43 | | +650,000 | 0·0169 | 144 3 | | +700,000 | 0·0357 | 17 12 | | +750,000 | 0·0195 | 0 53 | | +800,000 | 0·0639 | 140 38 | | +850,000 | 0·0144 | 176 41 | | +900,000 | 0·0659 | 291 16 | | +950,000 | 0·0086 | 115 13 | | +1,000,000 | 0·0528 | 57 31 | +------------------+-------------+------------+
TABLE II.
ECCENTRICITY, LONGITUDE OF THE PERIHELION, &C., &C., FOR INTERVALS OF 10,000 YEARS, FROM 2,650,000 TO 2,450,000 YEARS AGO.
THE GLACIAL EPOCH OF THE Eocene period IS PROBABLY COMPREHENDED WITHIN THIS TABLE.
+---------+------------+-----------+-----------+-------------------------------------------+ | I. | II. | III. | IV. | Winter occurring in aphelion. | | | | | +---------+---------+-----------+-----------+ | | | | | V. | VI. | VII. | VIII. | |Number of|Eccentricity|Longitude | Number of |Excess of|Midwinter|Number of | Midwinter | | years | of orbit. | of | degrees | winter |intensity|degrees by |temperature| | before | |perihelion.| passed | over | of the | which the | of Great | | A.D. | | |over by the| summer, | sun’s | midwinter | Britain. | | 1800. | | |perihelion.|in days. | heat. |temperature| | | | | | Motion | | Present |is lowered | | | | | |retrograde | |intensity| | | | | | |at periods | | =1000. | | | | | | | marked R. | | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+ | | | ° | | | | | | |2,650,000| 0·0053 | 318 40 | ° ′ | | | F. | F. | |2,640,000| 0·0173 | 54 25 | 95 45 | | | ° | ° | |2,630,000| 0·0331 | 93 37 | 39 12 | 15·4 | 906 | 26·2 | 12·8 | |2,620,000| 0·0479 | 127 12 | 33 35 | 22·2 | 884 | 33·3 | 5·7 | |2,610,000| 0·0591 | 158 36 | 31 24 | 27·4 | 862 | 38·3 | 0·7 | |2,600,000| 0·0660 | 190 4 | 31 28 | 30·6 | 851 | 41·5 | −2·5 | |2,590,000| 0·0666 | 220 28 | 30 24 | 30·9 | 850 | 41·8 | −2·8 | |2,580,000| 0·0609 | 249 56 | 29 28 | 28·3 | 859 | 39·2 | −0·2 | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+ |2,570,000| 0·0492 | 277 24 | 27 28 | 22·9 | 878 | 33·9 | 5·1 | |2,560,000| 0·0350 | 305 2 | 27 38 | 16·2 | 902 | 27·1 | 11·9 | |2,550,000| 0·0167 | 298 34 | R 6 28 | | | | | |2,540,000| 0·0192 | 253 58 | R 44 36 | | | | | |2,530,000| 0·0369 | 259 19 | 5 21 | 17·1 | 899 | 28·0 | 11·0 | |2,520,000| 0·0537 | 283 7 | 23 48 | 25·0 | 871 | 35·9 | 3·1 | |2,510,000| 0·0660 | 310 4 | 26 57 | 30·6 | 851 | 41·5 | −2·5 | |2,500,000| 0·0721 | 338 36 | 28 32 | 33·5 | 841 | 44·2 | −5·2 | |2,490,000| 0·0722 | 7 36 | 29 0 | 33·6 | 841 | 44·3 | −5·3 | |2,480,000| 0·0662 | 35 46 | 28 10 | 30·8 | 850 | 41·7 | −2·7 | |2,470,000| 0·0553 | 63 26 | 27 40 | 25·7 | 868 | 36·6 | 2·4 | |2,460,000| 0·0410 | 89 13 | 25 47 | 19·1 | 892 | 30·0 | 9·0 | |2,450,000| 0·0252 | 109 33 | 20 20 | 11·7 | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+
TABLE III.
ECCENTRICITY, LONGITUDE OF THE PERIHELION, &C., &C., FOR INTERVALS OF 10,000 YEARS, FROM 1,000,000 TO 750,000 YEARS AGO.
THE GLACIAL EPOCH OF THE Miocene period IS PROBABLY COMPREHENDED WITHIN THIS TABLE.
+---------+------------+-----------+-----------+-------------------------------------------+ | I. | II. | III. | IV. | Winter occurring in aphelion. | | | | | +---------+---------+-----------+-----------+ | | | | | V. | VI. | VII. | VIII. | |Number of|Eccentricity|Longitude | Number of |Excess of|Midwinter|Number of | Midwinter | | years | of orbit. | of | degrees | winter |intensity|degrees by |temperature| | before | |perihelion.| passed | over | of the | which the | of Great | | A.D. | | |over by the| summer, | sun’s | midwinter | Britain. | | 1800. | | |perihelion.|in days. | heat. |temperature| | | | | | Motion | | Present |is lowered | | | | | |retrograde | |intensity| | | | | | |at periods | | =1000. | | | | | | | marked R. | | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+ | | | ° ′ | | | | | | |1,000,000| 0·0151 | 248 22 | ° ′ | | | F. | F. | | 990,000| 0·0224 | 313 50 | 65 28 | | | ° | ° | | 980,000| 0·0329 | 358 2 | 44 12 | 15·3 | 906 | 26·1 | 12·9 | | 970,000| 0·0441 | 32 40 | 34 38 | 20·5 | 887 | 31·5 | 7·5 | | 960,000| 0·0491 | 66 49 | 34 9 | 22·8 | 878 | 33·8 | 5·2 | | 950,000| 0·0517 | 97 51 | 31 2 | 24·0 | 874 | 35·0 | 4·0 | | 940,000| 0·0495 | 127 42 | 29 51 | 23·0 | 878 | 34·0 | 5·0 | | 930,000| 0·0423 | 156 11 | 28 29 | 19·7 | 890 | 30·6 | 8·4 | | 920,000| 0·0305 | 181 40 | 25 29 | 14·2 | 910 | 25·0 | 14·0 | | 910,000| 0·0156 | 194 15 | 12 35 | | | | | | 900,000| 0·0102 | 135 2 | R 59 13 | | | | | | 890,000| 0·0285 | 127 1 | R 8 1 | | | | | | 880,000| 0·0456 | 152 33 | 25 32 | 21·2 | 884 | 32·2 | 6·8 | | 870,000| 0·0607 | 180 23 | 27 50 | 28·2 | 859 | 39·0 | 0·0 | | 860,000| 0·0708 | 209 41 | 29 18 | 32·9 | 843 | 43·6 | −4·6 | | 850,000| 0·0747 | 239 28 | 29 47 | 34·7 | 837 | 45·3 | −6·3 | | 840,000| 0·0698 | 269 14 | 29 46 | 32·4 | 845 | 43·2 | −4·2 | | 830,000| 0·0623 | 298 28 | 29 14 | 29·0 | 857 | 40·0 | −1·0 | | 820,000| 0·0476 | 326 4 | 27 36 | 22·1 | 881 | 33·1 | 5·9 | | 810,000| 0·0296 | 348 30 | 22 26 | | | | | | 800,000| 0·0132 | 343 49 | R 4 41 | | | | | | 790,000| 0·0171 | 293 19 | R 50 30 | | | | | | 780,000| 0·0325 | 303 37 | 10 18 | 15·2 | 907 | 26·0 | 13·0 | | 770,000| 0·0455 | 328 38 | 25 1 | 21·2 | 884 | 32·2 | 6·8 | | 760,000| 0·0540 | 357 12 | 28 34 | 25·1 | 870 | 36·0 | 3·0 | | 750,000| 0·0575 | 27 18 | 30 6 | 26·7 | 864 | 37·7 | 1·3 | | 740,000| 0·0561 | 58 30 | 31 12 | 26·1 | 867 | 37·0 | 2·0 | | 730,000| 0·0507 | 90 55 | 32 25 | 23·6 | 876 | 34·6 | 4·4 | | 720,000| 0·0422 | 125 14 | 34 19 | 19·6 | 890 | 30·6 | 8·4 | | 710,000| 0·0307 | 177 26 | 52 12 | 14·3 | 910 | 25·0 | 14·0 | | 700,000| 0·0220 | 208 13 | 30 47 | | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+
TABLE IV.
ECCENTRICITY, LONGITUDE OF THE PERIHELION, &C., &C., FOR INTERVALS OF 10,000 YEARS, FROM 250,000 YEARS AGO TO THE PRESENT DATE.
THE Glacial epoch IS PROBABLY COMPREHENDED WITHIN THIS TABLE.
+---------+------------+-----------+-----------+-------------------------------------------+ | I. | II. | III. | IV. | Winter occurring in aphelion. | | | | | +---------+---------+-----------+-----------+ | | | | | V. | VI. | VII. | VIII. | |Number of|Eccentricity|Longitude | Number of |Excess of|Midwinter|Number of | Midwinter | | years | of orbit. | of | degrees | winter |intensity|degrees by |temperature| | before | |perihelion.| passed | over | of the | which the | of Great | | A.D. | | |over by the| summer, | sun’s | midwinter | Britain. | | 1800. | | |perihelion.|in days. | heat. |temperature| | | | | | Motion | | Present |is lowered | | | | | |retrograde | |intensity| | | | | | |at periods | | =1000. | | | | | | | marked R. | | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+ | | | ° ′ | | | | F. | F. | | 250,000| 0·0258 | 59 39 | ° ′ | | | ° | ° | | 240,000| 0·0374 | 74 58 | 15 19 | 17·4 | 898 | 28·3 | 10·7 | |S 230,000| 0·0477 | 102 49 | 27 51 | 22·2 | 885 | 33·2 | 5·8 | |S 220,000| 0·0497 | 124 33 | 21 44 | 23·2 | 877 | 34·1 | 4·9 | |S 210,000| 0·0575 | 144 55 | 20 22 | 26·7 | 864 | 37·7 | 1·3 | | 200,000| 0·0569 | 168 18 | 23 23 | 26·5 | 865 | 37·4 | 1·6 | |S 190,000| 0·0532 | 190 4 | 21 46 | 24·7 | 871 | 35·7 | 3·3 | |S 180,000| 0·0476 | 209 22 | 19 18 | 22·1 | 881 | 33·1 | 5·9 | |S 170,000| 0·0437 | 228 7 | 18 45 | 20·3 | 887 | 31·3 | 7·7 | | 160,000| 0·0364 | 236 38 | 8 31 | 16·9 | 900 | 27·8 | 11·2 | | 150,000| 0·0332 | 242 56 | 6 18 | 15·4 | 905 | 26·2 | 12·8 | | 140,000| 0·0346 | 246 29 | 3 33 | 16·1 | 903 | 26·9 | 12·1 | | 130,000| 0·0384 | 259 34 | 13 5 | 17·8 | 896 | 28·8 | 10·2 | | 120,000| 0·0431 | 274 47 | 15 13 | 20·1 | 888 | 31·0 | 8·0 | | 110,000| 0·0460 | 293 48 | 19 1 | 21·4 | 883 | 32·4 | 6·6 | | 100,000| 0·0473 | 316 18 | 22 30 | 22·0 | 881 | 33·0 | 6·0 | |L 90,000| 0·0452 | 340 2 | 23 44 | 21·0 | 885 | 32·0 | 7·0 | |L 80,000| 0·0398 | 4 13 | 24 11 | 18·5 | 894 | 29·4 | 9·6 | |L 70,000| 0·0316 | 27 22 | 23 9 | 14·7 | 908 | 25·5 | 13·5 | |L 60,000| 0·0218 | 46 8 | 18 46 | | | | | | 50,000| 0·0131 | 50 14 | 4 6 | | | | | |L 40,000| 0·0109 | 28 36 | R 21 38 | | | | | |L 30,000| 0·0151 | 5 50 | R 22 46 | | | | | |L 20,000| 0·0188 | 44 0 | 38 10 | | | | | |L 10,000| 0·0187 | 78 28 | 34 28 | | | | | |A.D. 1800| 0·0168 | 99 30 | 21 2 | | | | | +---------+------------+-----------+-----------+---------+---------+-----------+-----------+
In Tables II., III., and IV., column I. represents the dates of the periods, column II. the eccentricity, column III. the longitude of the perihelion. In Table IV. the eccentricity and the longitude of the perihelion of the six periods marked with an S are copied from a letter of Mr. Stone to Sir Charles Lyell, published in the Supplement of the Phil. Mag. for June, 1865; the eight periods marked L are copied from M. Leverrier’s Table, to which reference has been made. For the correctness of everything else, both in this Table and in the other three, I alone am responsible.
Column IV. gives the number of degrees passed over by the perihelion during each 10,000 years. From this column it will be seen how irregular is the motion of the perihelion. At four different periods it had a retrograde motion for 20,000 years. Column V. shows the number of days by which the winter exceeds the summer when the winter occurs in aphelion. Column VI. shows the intensity of the sun’s heat during midwinter, when the winter occurs in aphelion, the present midwinter intensity being taken at 1,000. These six columns comprehend all the astronomical part of the Tables. Regarding the correctness of the principles upon which these columns are constructed, there is no diversity of opinion. But these columns afford no direct information as to the character of the climate, or how much the temperature is increased or diminished. To find this we pass on to columns VII. and VIII., calculated on physical principles. Now, unless the physical principles upon which these three columns are calculated be wholly erroneous, change of eccentricity must undoubtedly very seriously affect climate. Column VII. shows how many degrees Fahrenheit the temperature is lowered by a decrease in the intensity of the sun’s heat corresponding to column VI. For example, 850,000 years ago, if the winters occurred then in aphelion, the direct heat of the sun during midwinter would be only 837/1000 of what it is at present at the same season of the year, and column VII. shows that this decrease in the intensity of the sun’s heat would lower the temperature 45°·3 F.
The principle upon which this result is arrived at is this:--The temperature of space, as determined by Sir John Herschel, is −239° F. M. Pouillet, by a different method, arrived at almost the same result. If we take the midwinter temperature of Great Britain at 39°, then 239° + 39° = 278° will represent the number of degrees of rise due to the sun’s heat at midwinter; in other words, it takes a quantity of sun-heat which we have represented by 1000 to maintain the temperature of the earth’s surface in Great Britain 278° above the temperature of space. Were the sun extinguished, the temperature of our island would sink 278° below its present midwinter temperature, or to the temperature of space. But 850,000 years ago, as will be seen from Table III., if the winters occurred in aphelion, the heat of the sun at midwinter would only equal 837 instead of 1000 as at present. Consequently, if it takes 1,000 parts of heat to maintain the temperature 278° above the temperature of space, 837 parts of heat will only be able to maintain the temperature 232°·7 above the temperature of space; for 232°·7 is to 278 as 837 is to 1,000. Therefore, if the temperature was then only 232°·7 above that of space, it would be 45°·3 below what it is at present. This is what the temperature would be on the supposition, of course, that it depended wholly on the sun’s intensity and was not modified by other causes. This method has already been discussed at some length in Chapter II. But whether these values be too high or too low, one thing is certain, that a very slight increase or a very slight decrease in the quantity of heat received from the sun must affect temperature to a considerable extent. The direct heat of the moon, for example, cannot be detected by the finest instruments which we possess; yet from 238,000 observations made at Prague during 1840−66, it would seem that the temperature is sensibly affected by the mere change in the lunar perigee and inclination of the moon’s orbit.[195]
Column VIII. gives the midwinter temperature. It is found by subtracting the numbers in column VII. from 39°, the present midwinter temperature.
I have not given a Table showing the temperature of the summers at the corresponding periods. This could not well be done; for there is no relation at the periods in question between the intensity of the sun’s heat and the temperature of the summers. One is apt to suppose, without due consideration, that the summers ought to be then as much warmer than they are at present, as the winters were then colder than now. Sir Charles Lyell, in his “Principles,” has given a column of summer temperatures calculated from my table upon this principle. Astronomically the principle is correct, but physically, as was shown in Chapter IV., it is totally erroneous, and calculated to convey a wrong impression regarding the whole subject of geological climate. The summers at those periods, instead of being much warmer than they are at present, would in reality be much colder, notwithstanding the great increase in the intensity of the sun’s heat resulting from the diminished distance of the sun.
What, then, is the date of the glacial epoch? It is perfectly obvious that if the glacial epoch resulted from a high state of eccentricity, it must be referred either to the period included in Table III. or to the one in Table IV. In Table III. we have a period extending from about 980,000 to about 720,000 years ago, and in Table IV. we have a period beginning about 240,000 years ago, and extending down to about 80,000 years ago. As the former period was of greater duration than the latter, and the eccentricity also attained to a higher value, I at first felt disposed to refer the glacial epoch proper (the time of the till and boulder clay) to the former period; and the latter period, I was inclined to believe, must have corresponded to the time of local glaciers towards the close of the glacial epoch, the evidence for which (moraines) is to be found in almost every one of our Highland glens. On this point I consulted several eminent geologists, and they all agreed in referring the glacial epoch to the former period; the reason assigned being that they considered the latter period to be much too recent and of too short duration to represent that epoch.
Pondering over the subject during the early part of 1866, reasons soon suggested themselves which convinced me that the glacial epoch must be referred to the latter and not to the former period. Those reasons I shall now proceed to state at some length, since they have a direct bearing, as will be seen, on the whole question of geological time.
It is the modern and philosophic doctrine of uniformity that has chiefly led geologists to over-estimate the length of geological periods. This philosophic school teaches, and that truly, that the great changes undergone by the earth’s crust must have been produced, not by convulsions and cataclysms of nature, but by those ordinary agencies that we see at work every day around us, such as rain, snow, frost, ice, and chemical action, &c. It teaches that the valleys were not produced by violent dislocations, nor the hills by sudden upheavals, but that they were actually carved out of the solid rock by the silent and gentle agency of chemical action, frost, rain, ice, and running water. It teaches, in short, that the rocky face of our globe has been carved into hill and dale, and ultimately worn down to the sea-level, by means of these apparently trifling agents, not only once or twice, but probably dozens of times over during past ages. Now, when we reflect that with such extreme slowness do these agents perform their work, that we might watch their operations from year to year, and from century to century, if we could, without being able to perceive that they make any very sensible advance, we are necessitated to conclude that geological periods must be enormous. And the conclusion at which we thus arrive is undoubtedly correct. It is, in fact, impossible to form an adequate conception of the length of geological time. It is something too vast to be fully grasped by our minds. But here we come to the point where the fundamental mistake arises; Geologists do not err in forming too great a conception of the extent of geological periods, but in the mode in which they represent the length of these periods in numbers. When we speak of units, tens, hundreds, thousands, we can form some notion of what these quantities represent; but when we come to millions, tens of millions, hundreds of millions, thousands of millions, the mind is then totally unable to follow, and we can only use these numbers as representations of quantities that turn up in calculation. We know, from the way in which they do turn up in our process of calculation, whether they are correct representations of things in actual nature or not; but we could not, from a mere comparison of these quantities with the thing represented by them, say whether they were actually too small or too great.
At present, geological estimates of time are little else than mere conjectures. Geological science has hitherto afforded no trustworthy means of estimating the positive length of geological epochs. Geological phenomena tell us most emphatically that these periods must be long; but how long they have hitherto failed to inform us. Geological phenomena represent time to the mind under a most striking and imposing form. They present to the eye, as it were, a sensuous representation of time; the mind thus becomes deeply impressed with a sense of immense duration; and when one under these feelings is called upon to put down in figures what he believes will represent that duration, he is very apt to be deceived. If, for example, a million of years as represented by geological phenomena and a million of years as represented by figures were placed before our eyes, we should certainly feel startled. We should probably feel that a unit with six ciphers after it was really something far more formidable than we had hitherto supposed it to be. Could we stand upon the edge of a gorge a mile and a half in depth that had been cut out of the solid rock by a tiny stream, scarcely visible at the bottom of this fearful abyss, and were we informed that this little streamlet was able to wear off annually only 1/10 of an inch from its rocky bed, what would our conceptions be of the prodigious length of time that this stream must have taken to excavate the gorge? We should certainly feel startled when, on making the necessary calculations, we found that the stream had performed this enormous amount of work in something less than a million of years.
If, for example, we could possibly form some adequate conception of a period so prodigious as one hundred millions of years, we should not then feel so dissatisfied with Sir W. Thomson’s estimate that the age of the earth’s crust is not greater than that.
Here is one way of conveying to the mind some idea of what a million of years really is. Take a narrow strip of paper an inch broad, or more, and 83 feet 4 inches in length, and stretch it along the wall of a large hall, or round the walls of an apartment somewhat over 20 feet square. Recall to memory the days of your boyhood, so as to get some adequate conception of what a period of a hundred years is. Then mark off from one of the ends of the strip 1/10 of an inch. The 1/10 of the inch will then represent one hundred years, and the entire length of the strip a million of years. It is well worth making the experiment, just in order to feel the striking impression that it produces on the mind.
The latter period, which we have concluded to be that of the glacial epoch, extended, as we have seen, over a period of 160,000 years. But as the glaciation was only on one hemisphere at a time, 80,000 years or so would represent the united length of the cold periods. In order to satisfy ourselves that this period is sufficiently long to account for all the amount of denudation effected during the glacial epoch, let us make some rough estimate of the probable rate at which the surface of the country would be ground down by the ice. Suppose the ice to grind off only one-tenth of an inch annually this would give upwards of 650 feet as the quantity of rock removed during the time. But it is probable that it did not amount to one-fourth part of that quantity. Whether one-tenth of an inch per annum be an over-estimate or an under-estimate of the rate of denudation by the ice, it is perfectly evident that the period in question is sufficiently long, so far as denudation is concerned, to account for the phenomena of the glacial epoch.
But admitting that the period under consideration is sufficiently long to account for all the denudation which took place during the glacial epoch, we have yet to satisfy ourselves that it is also sufficiently remote to account for all the denudation which has taken place since the glacial epoch. Are the facts of geology consistent with the idea that the close of the glacial epoch does not date back beyond 80,000 years?
This question could be answered if we knew the present rate of subaërial denudation, for the present rate evidently does not differ greatly from that which has obtained since the close of the glacial epoch.
Chapter XX
GEOLOGICAL TIME.—METHOD OF MEASURING THE RATE OF SUBAËRIAL DENUDATION.
Rate of Subaërial Denudation a Measure of Time.—Rate determined from Sediment of the Mississippi.—Amount of Sediment carried down by the Mississippi; by the Ganges.—Professor Geikie on Modern Denudation.—Professor Geikie on the Amount of Sediment conveyed by European Rivers.—Rate at which the Surface of the Globe is being denuded.—Alfred Tylor on the Sediment of the Mississippi.—The Law which determines the Rate of Denudation.—The Globe becoming less oblate.—Carrying Power of our River Systems the true Measure of Denudation.—Marine Denudation trifling in comparison to Subaërial.—Previous Methods of measuring Geological Time.—Circumstances which show the recent Date of the Glacial Epoch.—Professor Ramsay on Geological Time.
It is almost self-evident that the rate of subaërial denudation must be equal to the rate at which the materials are carried off the land into the sea, but the rate at which the materials are carried off the land is measured by the rate at which sediment is carried down by our river systems. Consequently, in order to determine the present rate of subaërial denudation, we have only to ascertain the quantity of sediment annually carried down by the river systems.
Knowing the quantity of sediment transported by a river, say annually, and the area of its drainage, we have the means of determining the rate at which the surface of this area is being lowered by subaërial denudation. And if we know this in reference to a few of the great continental rivers draining immense areas in various latitudes, we could then ascertain with tolerable correctness the rate at which the surface of the globe is being lowered by subaërial denudation, and also the length of time which our present continents can remain above the sea-level. Explaining this to Professor Ramsay during the winter of 1865, I learned from him that accurate measurements had been made of the amount of sediment annually carried down by the Mississippi River, full particulars of which investigations were to be found in the Proceedings of the American Association for the Advancement of Science for 1848. These proceedings contain a report by Messrs. Brown and Dickeson, which unfortunately over-estimated the amount of sediment transported by the Mississippi by nearly four times what was afterwards found by Messrs. Humphreys and Abbot to be the actual amount. From this estimate, I was led to the conclusion that if the Mississippi is a fair representative of rivers in general, our existing continents would not remain longer than one million and a half years above the sea-level.[196] This was a conclusion so startling as to excite suspicion that there must have been some mistake in reference to Messrs. Brown and Dickeson’s data. It showed beyond doubt, however, that the rate of subaërial denudation, when accurately determined by this method, would be found to be enormously greater than had been supposed. Shortly afterwards, on estimating the rate from the data furnished by Humphreys and Abbot, I found the rate of denudation to be about one foot in 6,000 years. Taking the mean elevation of all the land as ascertained by Humboldt to be 1,000 feet, the whole would therefore be carried down into the ocean by our river systems in about 6,000,000 of years if no elevation of the land took place.[197] The following are the data and mode of computation by which this conclusion was arrived at. It was found by Messrs. Humphreys and Abbot that the average amount of sediment held in suspension in the waters of the Mississippi is about 1/1500 of the weight of the water, or 1/2900 by bulk. The annual discharge of the river is 19,500,000,000,000 cubic feet of water. The quantity of sediment carried down into the Gulf of Mexico amounts to 6,724,000,000 cubic feet. But besides that which is held in suspension, the river pushes down into the sea about 750,000,000 cubic feet of earthy matter, making in all a total of 7,474,000,000 cubic feet transferred from the land to the sea annually. Where does this enormous mass of material come from? Unquestionably it comes from the ground drained by the Mississippi. The area drained by the river is 1,244,000 square miles. Now 7,474,000,000 cubic feet removed off 1,224,000 square miles of surface is equal to 1/4566 of a foot off that surface per annum, or one foot in 4,566 years. The specific gravity of the sediment is taken at 1·9, that of rock is about 2·5; consequently the amount removed is equal to one foot of rock in about 6,000 years. The average height of the North American continent above the sea-level, according to Humboldt, is 748 feet; consequently, at the present rate of denudation, the whole area of drainage will be brought down to the sea-level in less than 4,500,000 years, if no elevation of the land takes place.
Referring to the above, Sir Charles Lyell makes the following appropriate remarks:—“There seems no danger of our overrating the mean rate of waste by selecting the Mississippi as our example, for that river drains a country equal to more than half the continent of Europe, extends through twenty degrees of latitude, and therefore through regions enjoying a great variety of climate, and some of its tributaries descend from mountains of great height. The Mississippi is also more likely to afford us a fair test of ordinary denudation, because, unlike the St. Lawrence and its tributaries, there are no great lakes in which the fluviatile sediment is thrown down and arrested on its way to the sea.”[198]
The rate of denudation of the area drained by the river Ganges is much greater than that of the Mississippi. The annual discharge of that river is 6,523,000,000,000 cubic feet of water. The sediment held in suspension is equal to 1/510 by weight; area of drainage 432,480 square miles. This gives one foot of rock in 2,358 years as the amount removed.
Rough estimates have been made of the amount of sediment carried down by some eight or ten European rivers; and although those estimates cannot be depended upon as being anything like perfectly accurate, still they show (what there is very little reason to doubt) that it is extremely probable that the European continent is being denuded about as rapidly as the American.
For a full account of all that is known on this subject I must refer to Professor Geikie’s valuable memoir on Modern Denudation (Transactions of Geological Society of Glasgow, vol. iii.; also Jukes and Geikie’s “Manual of Geology,” chap. xxv.) It is mainly through the instrumentality of this luminous and exhaustive memoir that the method under consideration has gained such wide acceptance amongst geologists.
Professor Geikie finds that at the present rate of erosion the following is the number of years required by the undermentioned rivers to remove one foot of rock from the general surface of their basins. Professor Geikie thus shows that the rate of denudation, as determined from the amount of sediment carried down the Mississippi, is certainly not too high.
Danube 6,846 years. Mississippi 6,000 〃 Nith 4,723 〃 Ganges 2,358 〃 Rhone 1,528 〃 Hoang Ho 1,464 〃 Po 729 〃
By means of subaërial agencies continents are being cut up into islands, the islands into smaller islands, and so on till the whole ultimately disappears.
No proper estimate has been made of the quantity of sediment carried down into the sea by our British rivers. But, from the principles just stated, we may infer that it must be as great in proportion to the area of drainage as that carried down by the Mississippi. For example, the river Tay, which drains a great portion of the central Highlands of Scotland, carries to the sea three times as much water in proportion to its area of drainage as is carried by the Mississippi. And any one who has seen this rapidly running river during a flood, red and turbid with sediment, will easily be convinced that the quantity of solid material carried down by it into the German Ocean must be very great. Mr. John Dougall has found that the waters of the Clyde during a flood hold in suspension 1/800 by bulk of sediment. The observations were made about a mile above the city of Glasgow. But even supposing the amount of sediment held in suspension by the waters of the Tay to be only one-third (which is certainly an under-estimate) of that of the Mississippi, viz. 1/4500 by weight, still this would give the rate of denudation of the central Highlands at one foot in 6,000 years, or 1,000 feet in 6 millions of years.
It is remarkable that although so many measurements have been made of the amount of fluviatile sediment being transported seawards, yet that the bearing which this has on the broad questions of geological time and the rate of subaërial denudation should have been overlooked. One reason for this, no doubt, is that the measurements were made, not with a view to determine the rate at which the river basins are being lowered, but mainly to ascertain the age of the river deltas and the rate at which these are being formed.[199]
The Law which determines the Rate at which any Country is being denuded.—By means of subaërial agencies continents are being cut up into islands, the islands into smaller islands, and so on till the whole ultimately disappears.
So long as the present order of things remains, the rate of denudation will continue while land remains above the sea-level; and we have no warrant for supposing that the rate was during past ages less than it is at the present day. It will not do to object that, as a considerable amount of the sediment carried down by rivers is boulder clay and other materials belonging to the Ice age, the total amount removed by the rivers is on that account greater than it would otherwise be. Were this objection true, it would follow that, prior to the glacial period, when it is assumed that there was no boulder clay, the face of the country must have consisted of bare rock; for in this case no soil could have accumulated from the disintegration and decomposition of the rocks, since, unless the rocks of a country disintegrate more rapidly than the river systems are able to carry the disintegrated materials to the sea, no surface soil can form on that country. The rate at which rivers carry down sediment is evidently not determined by the rate at which the rocks are disintegrated and decomposed, but by the quantity of rain falling, and the velocity with which it moves off the face of the country. Every river system possesses a definite amount of carrying-power, depending upon the slope of the ground, the quantity of rain falling per annum, the manner in which the rain falls, whether it falls gradually or in torrents, and a few other circumstances. When it so happens, as it generally does, that the amount of rock disintegrated on the face of the country is greater than the carrying-power of the river systems can remove, then a soil necessarily forms. But when the reverse is the case no soil can form on that country, and it will present nothing but barren rock. This is no doubt the reason why in places like the Island of Skye, for example, where the rocks are exceedingly hard and difficult to decompose and separate, the ground steep, and the quantity of rain falling very great, there is so much bare rock to be seen. If, prior to the glacial epoch, the rocks of the area drained by the Mississippi did not produce annually more material from their destruction under atmospheric agency than was being carried down by that river, then it follows that the country must have presented nothing but bare rock, if the amount of rain falling then was as great as at present.
But, after all, one foot removed off the general level of the country since the creation of man, according to Mosaic chronology, is certainly not a very great quantity. No person but one who had some preconceived opinions to maintain, would ever think of concluding that one foot of soil during 6,000 years was an extravagant quantity to be washed off the face of the country by rain and floods during that long period. Those who reside in the country and are eye-witnesses of the actual effects of heavy rains upon the soil, our soft country roads, ditches, brooks, and rivers, will have considerable difficulty in actually believing that only one foot has been washed away during the past 6,000 years.
Some may probably admit that a foot of soil may be washed off during a period so long as 6,000 years, and may tell us that what they deny is not that a foot of loose and soft soil, but a foot of solid rock can be washed away during that period. But a moment’s reflection must convince them that, unless the rocks of the country were disintegrating and decomposing as rapidly into soil as the rain is carrying the soil away, the surface of the country would ultimately become bare rock. It is true that the surface of our country in many places is protected by a thick covering of boulder clay; but when this has once been removed, the rocks will then disintegrate far more rapidly than they are doing at present.
But slow as is the rate at which the country is being denuded, yet when we take into consideration a period so enormous as 6 millions of years, we find that the results of denudation are really startling. One thousand feet of solid rock during that period would be removed from off the face of the country. But if the mean level of the country would be lowered 1,000 feet in 6 millions of years, how much would our valleys and glens be deepened during that period? This is a problem well worthy of the consideration of those who treat with ridicule the idea that the general features of our country have been carved out by subaërial agency.
In consequence of the retardation of the earth’s rotation, occasioned by the friction of the tidal wave, the sea-level must be slowly sinking at the equator and rising at the poles. But it is probable that the land at the equator is being lowered by denudation as rapidly as the sea-level is sinking. Nearly one mile must have been worn off the equator during the past 12 millions of years, if the rate of denudation all along the equator be equal to that of the basin of the Ganges. It therefore follows that we cannot infer from the present shape of our globe what was its form, or the rate at which it was rotating, at the time when its crust became solidified. Although it had been as oblate as the planet Jupiter, denudation must in time have given it its present form.
There is another effect which would result from the denudation of the equator and the sinking of the ocean at the equator and its rise at the poles. This, namely, that it would tend to increase the rate of rotation; or, more properly, it would tend to lessen the rate of tidal retardation.
But if the rate of denudation be at present so great, what must it have been during the glacial epoch? It must have been something enormous. At present, denudation is greatly retarded by the limited power of our river systems to remove the loose materials resulting from the destruction of the rocks. These materials accumulate and form a thick soil over the surface of the rocks, which protects them, to a great extent, from the weathering effects of atmospheric agents. So long as the amount of rock disintegrated exceeds that which is being removed by the river systems, the soil will continue to accumulate till the amount of rock destroyed per annum is brought to equal that which is being removed. It therefore follows from this principle that the CARRYING-POWER OF OUR RIVER SYSTEMS IS THE TRUE MEASURE OF DENUDATION. But during the glacial epoch the thickness of the soil would have but little effect in diminishing the waste of the rocks; for at that period the rocks were not decomposed by atmospheric agency, but were ground down by the mechanical friction of the ice. But the presence of a thick soil at this period, instead of retarding the rate of denudation, would tend to increase it tenfold, for the soil would then be used as grinding-material for the ice-sheet. In places where the ice was, say, 2,000 feet in thickness, the soil would be forced along over the rocky face of the country, exerting a pressure on the rocks equal to 50 tons on the square foot.
It is true that the rate at which many kinds of rocks decompose and disintegrate is far less than what has been concluded to be the mean rate of denudation of the whole country. This is evident from the fact which has been adduced by some writers, that inscriptions on stones which have been exposed to atmospheric agency for a period of 2,000 years or so, have not been obliterated. But in most cases epitaphs on monuments and tombstones, and inscriptions on the walls of buildings, 200 years old, can hardly be read. And this is not all: the stone on which the letters were cut has during that time rotted in probably to the depth of several inches; and during the course of a few centuries more the whole mass will crumble into dust.
The facts which we have been considering show also how trifling is the amount of denudation effected by the sea in comparison with that by subaërial agents. The entire sea-coast of the globe, according to Dr. A. Keith Johnston, is 116,531 miles. Suppose we take the average height of the coast-line at 25 feet, and take also the rate at which the sea is advancing on the land at one foot in 100 years, then this gives 15,382,500,000 cubic feet of rock as the total amount removed in 100 years by the action of the sea. The total amount of land is 57,600,000 square miles, or 1,605,750,000,000,000 square feet; and if one foot is removed off the surface in 6,000 years, then 26,763,000,000,000 cubic feet is removed by subaërial agency in 100 years, or about 1,740 times as much as that removed by the sea. Before the sea could denude the globe as rapidly as the subaërial agents, it would have to advance on the land at the rate of upwards of 17 feet annually.
It will not do, however, to measure marine denudation by the rate at which the sea is advancing on the land. There is no relation whatever between the rate at which the sea is advancing on the land and the rate at which the sea is denuding the land. For it is evident that as the subaërial agents bring the coast down to the sea-level, all that the sea has got to do is simply to advance, or at most to remove the loose materials which may lie in its path. The amount of denudation which has been effected by the sea during past geological ages, compared with what has been effected by subaërial agency, is evidently but trifling. Denudation is not the proper function of the sea. The great denuding agents are land-ice, frost, rain, running-water, chemical agency, &c. The proper work which belongs to the sea is the transporting of the loose materials carried down by the rivers, and the spreading of these out so as to form the stratified beds of future ages.
Previous Methods of measuring Geological Time unreliable.—The method which has just been detailed of estimating the rate of subaërial denudation seems to afford the only reliable means of a geological character of determining geological time in absolute measure. The methods which have hitherto been adopted not only fail to give the positive length of geological periods, but some of them are actually calculated to mislead.
The common method of calculating the length of a period from the thickness of the stratified rocks belonging to that period is one of that class. Nothing whatever can be inferred from the thickness of a deposit as to the length of time which was required to form it. The thickness of a deposit will depend upon a great many circumstances, such as whether the deposition took place near to land or far away in the deep recesses of the ocean, whether it occurred at the mouth of a great river or along the sea-shore, or at a time when the sea-bottom was rising, subsiding, or remaining stationary. Stratified formations 10,000 feet in thickness, for example, may, under some conditions, have been formed in as many years, while under other conditions it may have required as many centuries. Nothing whatever can be safely inferred as to the absolute length of a period from the thickness of the stratified formations belonging to that period. Neither will this method give us a trustworthy estimate of the relative lengths of geological periods. Suppose we find the average thickness of the Cambrian rocks to be, say, 26,000 feet, the Silurian to be 28,000 feet, the Devonian to be 6,000 feet, and the Tertiary to be 10,000 feet, it would not be safe to assume, as is sometimes done, that the relative duration of those periods must have corresponded to these numbers. Were we sure that we had got the correct average thickness of all the rocks belonging to each of those formations, we might probably be able to arrive at the relative lengths of those periods; but we can never be sure of this. Those formations all, at one time, formed sea-bottoms; and we can only measure such deposits as are now raised above the sea-level. But is not it probable that the relative positions of sea and land during the Cambrian, Silurian, Old Red Sandstone, Carboniferous, and other early periods of the earth’s history, differed more from the present than the distribution of sea and land during the Tertiary period differed from that which obtains now? May not the greater portion of the Tertiary deposits be still under the sea-bottom? And if this be the case, it may yet be found at some day in the distant future, when these deposits are elevated into dry land, that they are much thicker than we now conclude them to be. Of course, it is by no means asserted that this is so, but only that they may be thicker for anything we know to the contrary; and the possibility that they may, destroys our confidence in the accuracy of this method of determining the relative lengths of geological periods.
Neither does palæontology afford any better mode of measuring geological time. In fact, the palæontological method of estimating geological time, either absolute or relative, from the rate at which species change, appears to be even still more unsatisfactory. If we could ascertain by some means or other the time that has elapsed from some given epoch (say, for example, the glacial) till the present day, and were we sure at the same time that species have changed at a uniform rate during all past ages, then, by ascertaining the percentage of change that has taken place since the glacial epoch, we should have a means of making something like a rough estimate of the length of the various periods. But without some such period to start with, the palæontological method is useless. It will not do to take the historic period as a base-line. It is far too short to be used with safety in determining the distance of periods so remote as those which concern the geologist. But even supposing the palæontologist had a period of sufficient length measured off correctly to begin with, his results would still be unsatisfactory; for it is perfectly obvious, that unless the climatic conditions of the globe during the various periods were nearly the same, the rate at which the species change would certainly not be uniform; but such has not been the case, as an examination of the Tables of eccentricity will show. Take, for example, that long epoch of 260,000 years, beginning about 980,000 years ago and terminating about 720,000 years ago. During that long period the changes from cold to warm conditions of climate every 10,000 or 12,000 years must have been of the most extreme character. Compare that period with the period beginning, say, 80,000 years ago, and extending to nearly 150,000 years into the future, during which there will be no extreme variations of climate, and how great is the contrast! How extensive the changes in species must have been during the first period as compared with those which are likely to take place during the latter!
Besides, it must also be taken into consideration that organization was of a far more simple type in the earlier Palæozoic ages than during the Tertiary period, and would probably on this account change much more slowly in the former than in the latter.
The foregoing considerations render it highly probable, if not certain, that the rate at which the general surface of the globe is being lowered by subaërial denudation cannot be much under one foot in 6,000 years. How, if we assign the glacial epoch to that period of high eccentricity beginning 980,000 years ago, and terminating 720,000 years ago, then we must conclude that as much as 120 feet must have been denuded off the face of the country since the close of the glacial epoch. But if as much as this had been carried down by our rivers into the sea, hardly a patch of boulder clay, or any trace of the glacial epoch, should be now remaining on the land. It is therefore evident that the glacial epoch cannot be assigned to that remote period, but ought to be referred to the period terminating about 80,000 years ago. We have, in this latter case, 13 feet, equal to about 18 feet of drift, as the amount removed from the general surface of the country since the glacial epoch. This amount harmonizes very well with the direct evidence of geology on this point. Had the amount of denudation since the close of the glacial epoch been much greater than this, the drift deposits would not only have been far less complete, but the general appearance and outline of the surface of all glaciated countries would have been very different from what they really are.
Circumstances which show the Recent Date of the Glacial Epoch.—One of the circumstances to which I refer is this. When we examine the surface of any glaciated country, such as Scotland, we can easily satisfy ourselves that the upper surface of the ground differs very much from what it would have been had its external features been due to the action of rain and rivers and the ordinary agencies which have been at work since the close of the Ice period. Go where one will in the Lowlands of Scotland, and he shall hardly find a single acre whose upper surface bears the marks of being formed by the denuding agents which are presently in operation. He will observe everywhere mounds and hollows, the existence of which cannot be accounted for by the present agencies at work. In fact these agencies are slowly denuding pre-existing heights and silting up pre-existing hollows. Everywhere one comes upon patches of alluvium which upon examination prove to be simply old glacially formed hollows silted up. True, the main rivers, streams, and even brooks, occupy channels which have been formed by running water, either since or prior to the glacial epoch, but, in regard to the general surface of the country, the present agencies may be said to be just beginning to carve a new line of features out of the old glacially formed surface. But so little progress has yet been made, that the kames, gravel mounds, knolls of boulder clay, &c., still retain in most cases their original form. Now, when we reflect that more than a foot of drift is being removed from the general surface of the country every 5,000 years or so, it becomes perfectly obvious that the close of the glacial epoch must be of comparatively recent date.
There is another circumstance which shows that the glacial epoch must be referred to the latest period of great eccentricity. If we refer the glacial epoch to the penultimate period of extreme eccentricity, and place its commencement one million of years back, then we must also lengthen out to a corresponding extent the entire geological history of the globe. Sir Charles Lyell, who is inclined to assign the glacial epoch to this penultimate period, considers that when we go back as far as the Lower Miocene formations, we arrive at a period when the marine shells differed as a whole from those now existing. But only 5 per cent. of the shells existing at the commencement of the glacial epoch have since died out. Hence, assuming the rate at which the species change to be uniform, it follows that the Lower Miocene period must be twenty times as remote as the commencement of the glacial epoch. Consequently, if it be one million of years since the commencement of the glacial epoch, 20 millions of years, Sir Charles concludes, must have elapsed since the time of the Lower Miocene period, and 60 millions of years since the beginning of the Eocene period, and about 160 millions of years since the Carboniferous period, and about 240 millions of years must be the time which has elapsed since the beginning of the Cambrian period. But, on the other hand, if we refer the glacial epoch to the latest period of great eccentricity, and take 250,000 years ago as the beginning of that period, then, according to the same mode of calculation, we have 15 millions of years since the beginning of the Eocene period, and 40 millions of years since the Carboniferous period, and 60 millions of years in all since the beginning of the Cambrian period.
If the beginning of the glacial epoch be carried back a million years, then it is probable, as Sir Charles Lyell concludes, that the beginning of the Cambrian period will require to be placed 240 millions of years back. But it is very probable that the length of time embraced by the pre-Cambrian ages of geological history may be as great as that which has elapsed since the close of the Cambrian period, and, if this be so, then we shall be compelled to admit that nearly 500 millions of years have passed away since the beginning of the earth’s geological history. But we have evidence of a physical nature which proves that it is absolutely impossible that the existing order of things, as regards our globe, can date so far back as anything like 500 millions of years. The arguments to which I refer are those which have been advanced by Professor Sir William Thomson at various times. These arguments are well known, and to all who have really given due attention to them must be felt to be conclusive. It would be superfluous to state them here; I shall, however, for reasons which will presently appear, refer briefly to one of them, and that one which seems to be the most conclusive of all, viz., the argument derived from the limit to the age of the sun’s heat.
Professor Ramsay on Geological Time.—In an interesting suggestive memoir, “On Geological Ages as items of Geological Time,”[200] Professor Ramsay discusses the comparative values of certain groups of formations as representative of geological time, and arrives at the following general conclusion, viz., “That the local continental era which began with the Old Red Sandstone and closed with the New Red Marl is comparable, in point of geological time, to that occupied in the deposition of the whole of the Mesozoic, or Secondary series, later than the New Red Marl and all the Cainozoic or Tertiary formations, and indeed of all the time that has elapsed since the beginning of the deposition of the Lias down to the present day.” This conclusion is derived partly from a comparison of the physical character of the formations constituting each group, but principally from the zoological changes which took place during the time represented by them.
The earlier period represented by the Cambrian and Silurian rocks he also, from the same considerations, considers to have been very long, but he does not attempt to fix its relative length. Of the absolute length of any or all of these great eras of geological time no estimate or guess is given. He believes, however, that the whole time represented by all the fossiliferous rocks, from the earliest Cambrian to the most recent, is, geologically speaking, short compared with that which went before it. After quoting Professor Huxley’s enumeration of the many classes and orders of marine life (identical with those still existing), whose remains characterize the lowest Cambrian rocks, he says, “The inference is obvious that in this earliest known varied life we find no evidence of its having lived near the beginning of the zoological series. In a broad sense, compared with what must have gone before, both biologically and physically, all the phenomena connected with this old period seem to my mind to be quite of a recent description, and the climates of seas and lands were of the very same kind as those that the world enjoys at the present day.”... “In the words of Darwin, when discussing the imperfection of the geological record of this history, ‘we possess the last volume alone relating only to two or three countries,’ and the reason why we know so little of pre-Cambrian faunas and the physical characters of the more ancient formations as originally deposited, is that below the Cambrian strata we get at once involved in a sort of chaos of metamorphic strata.’”
It seems to me that Professor Ramsay’s results lead to the same conclusion regarding the positive length of geological periods as those derived from physical considerations. It is true that his views lead us back to an immense lapse of unknown time prior to the Cambrian period, but this practically tends to shorten geological periods. For it is evident that the geological history of our globe must be limited by the age of the sun’s heat, no matter how long or short its age may be. This being the case, the greater the length of time which must have elapsed prior to the Cambrian period, the less must be the time which has elapsed since that period. Whatever is added to the one period must be so much taken from the other. Consequently, the longer we suppose the pre-Cambrian periods to have been, the shorter must we suppose the post-Cambrian to be.
XXI. THE PROBABLE AGE AND ORIGIN OF THE SUN
Gravitation Theory.—Amount of Heat emitted by the Sun.—Meteoric Theory.—Helmholtz’s Condensation Theory.—Confusion of Ideas.—Gravitation not the chief Source of the Sun’s Heat.—Original Heat.—Source of Original Heat.—Original Heat derived from Motion in Space.—Conclusion as to Date of Glacial Epoch.—False Analogy.—Probable Date of Eocene and Miocene Periods.
Gravitation Theory of the Origin and Source of the Sun’s Heat.—There are two forms in which this theory has been presented: the first, the meteoric theory, propounded by Dr. Meyer, of Heilbronn; and the second, the contraction theory, advocated by Helmholtz.
It is found that 83·4 foot-pounds of heat per second are incident upon a square foot of the earth’s surface exposed to the perpendicular rays of the sun. The amount radiated from a square foot of the sun’s surface is to that incident on a square foot of the earth’s surface as the square of the sun’s distance to the square of his radius, or as 46,400 to 1. Consequently 3,869,000 foot-pounds of heat are radiated off every square foot of the sun’s surface per second—an amount equal to about 7,000 horse power. The total amount radiated from the whole surface of the sun per annum is 8,340 × 10^{30} foot-pounds. To maintain the present rate of radiation, it would require the combustion of about 1,500 lbs. of coal per hour on every square foot of the sun’s surface; and were the sun composed of that material, it would be all consumed in less than 5,000 years. The opinion that the sun’s heat is maintained by combustion cannot be entertained for a single moment. A pound of coal falling into the sun from an infinite distance would produce by its concussion more than 6,000 times the amount of heat that would be generated by its combustion.
It is well known that the velocity with which a body falling from an infinite distance would reach the sun would be equal to that which would be generated by a constant force equal to the weight of the body at the sun’s surface operating through a space equal to the sun’s radius. One pound would at the sun’s surface weigh about 28 pounds. Taking the sun’s radius at 441,000 miles,[201] the energy of a pound of matter falling into the sun from infinite space would equal that of a 28-pound weight descending upon the earth from an elevation of 441,000 miles, supposing the force of gravity to be as great at that elevation as it is at the earth’s surface. It would amount to upwards of 65,000,000,000 foot-pounds. A better idea of this enormous amount of energy exerted by a one-pound weight falling into the sun will be conveyed by stating that it would be sufficient to raise 1,000 tons to a height of 5½ miles. It would project the Warrior, fully equipped with guns, stores, and ammunition, over the top of Ben Nevis.
Gravitation is now generally admitted to be the only conceivable source of the sun’s heat. But if we attribute the energy of the sun to gravitation as a source, we assign it to a cause the value of which can be accurately determined. Prodigious as is the energy of a single pound of matter falling into the sun, nevertheless a range of mountains, consisting of 176 cubic miles of solid rock, falling into the sun, would maintain his heat for only a single second. A mass equal to that of the earth would maintain the heat for only 93 years, and a mass equal to that of the sun itself falling into the sun would afford but 33,000,000 years’ sun-heat.
It is quite possible, however, that a meteor may reach the sun with a velocity far greater than that which it could acquire by gravitation; for it might have been moving in a direct line towards the sun with an original velocity before coming under the sensible influence of the sun’s attraction. In this case a greater amount of heat would be generated by the meteor than would have resulted from its merely falling into the sun under the influence of gravitation. But then meteors of this sort must be of rare occurrence. The meteoric theory of the sun’s heat has now been pretty generally abandoned for the contraction theory advanced by Helmholtz.
Suppose, with Helmholtz, that the sun originally existed as a nebulous mass, filling the entire space presently occupied by the solar system and extending into space indefinitely beyond the outermost planet. The total amount of work in foot-pounds performed by gravitation in the condensation of this mass to an orb of the sun’s present size can be found by means of the following formula given by Helmholtz,[202]
3 r^{2}M^{2} Work of condensation = — × ———————————— × g 5 R_m_
M is the mass of the sun, m the mass of the earth, R the sun’s radius, and r the earth’s radius. Taking M = 4230 × 10^{27} lbs., m = 11,920 × 10^{21} lbs., R = 2,328,500,000 feet, and r = 20,889,272 feet; we have then for the total amount of work performed by gravitation in foot-pounds,
3 (20,889,272·5)^2 × (4230 × 10^{27})^2 Work = — × ————————————————————————————————————— 5 2,328,500,000 × 11,920 × 10^{21}
= 168,790 × 10^{36} foot-pounds.
The amount of heat thus produced by gravitation would suffice for nearly 20,237,500 years.
These calculations are based upon the assumption that the density of the sun is uniform throughout. But it is highly probable that the sun’s density increases towards the centre, in which case the amount of work performed by gravitation would be somewhat more than the above.
Some confusion has arisen in reference to this subject by the introduction of the question of the amount of the sun’s specific heat. If we simply consider the sun as an incandescent body in the process of cooling, the question of the amount of the sun’s specific heat is of the utmost importance; because the absolute amount of heat which the sun is capable of giving out depends wholly upon his temperature and specific heat. In this case three things only are required: (1), the sun’s mass; (2), temperature of the mass; (3), specific heat of the mass. But if we are considering what is the absolute amount of heat which could have been given out by the sun on the hypothesis that gravitation, either according to the meteoric theory suggested by Meyer or according to the contraction theory advocated by Helmholtz, is the only source of his heat, then we have nothing whatever to do with any inquiries regarding the specific heat of the sun. This is evident because the absolute amount of work which gravitation can perform in the pulling of the particles of the sun’s mass together, is wholly independent of the specific heat of those particles. Consequently, the amount of energy in the form of heat thus imparted to the particles by gravity must also be wholly independent of specific heat. That is to say, the amount of heat imparted to a particle will be the same whatever may be its specific heat.
Even supposing we limit the geological history of our globe to 100 millions of years, it is nevertheless evident that gravitation will not account for the supply of the sun’s heat during so long a period. There must be some other source of much more importance than gravitation. What other source of energy greater than that of gravitation can there be? It is singular that the opinion should have become so common even among physicists, that there is no other conceivable source than gravitation from which a greater amount of heat could have been derived.
The Origin and Chief Source of the Sun’s Heat.—According to the foregoing theories regarding the source of the sun’s heat, it is assumed that the matter composing the sun, when it existed in space as a nebulous mass, was not originally possessed of temperature, but that the temperature was given to it as the mass became condensed under the force of gravitation. It is supposed that the heat given out was simply the heat of condensation. But it is quite conceivable that the nebulous mass might have been possessed of an original store of heat previous to condensation.
It is quite possible that the very reason why it existed in such a rarefied or gaseous condition was its excessive temperature, and that condensation only began to take place when the mass began to cool down. It seems far more probable that this should have been the case than that the mass existed in so rarefied a condition without temperature. For why should the particles have existed in this separated form when devoid of the repulsive energy of heat, seeing that in virtue of gravitation they had such a tendency to approach to one another? But if the mass was originally in a heated condition, then in condensing it would have to part not only with the heat generated in condensing, but also with the heat which it originally possessed, a quantity which would no doubt much exceed that produced by condensation. To illustrate this principle, let us suppose a pound of air, for example, to be placed in a cylinder and heat applied to it. If the piston be so fixed that it cannot move, 234·5 foot-pounds of heat will raise the temperature of the air 1° C. But if the piston be allowed to rise as the heat is applied, then it will require 330·2 foot-pounds of heat to raise the temperature 1° C. It requires 95·7 foot-pounds more heat in the latter case than in the former. The same amount of energy, viz., 234·5 foot-pounds, in both cases goes to produce temperature; but in the latter case, where the piston is allowed to move, 95·7 foot-pounds of additional heat are consumed in the mechanical work of raising the piston. Suppose, now, that the air is allowed to cool under the same conditions: in the one case 234·5 foot-pounds of heat will be given out while the temperature of the air sinks 1° C.; in the other case, where the piston is allowed to descend, 330·2 foot-pounds will be given out while the temperature sinks 1° C. In the former case, the air in cooling has simply to part with the energy which it possesses in the form of temperature; but in the latter case it has, in addition to this, to part with the energy bestowed upon its molecules by the descending piston. While the temperature of the gas is sinking 1°, 95·7 foot-pounds of energy in the form of heat are being imparted to it by the descending piston; and these have to be got rid of before the temperature is lowered by 1°. Consequently 234·5 foot-pounds of the heat given out previously existed in the air under the form of temperature, and the remaining 95·7 foot-pounds given out were imparted to the air by the descending piston while the gas was losing its temperature. 234·5 foot-pounds represent the energy or heat which the air previously possessed, and 95·7 the energy or heat of condensation.
In the case of the cooling of the sun from a nebulous mass, there would of course be no external force or pressure exerted on the mass analogous to that of the piston on the air; but there would be, what is equivalent to the same, the gravitation of the particles to each other. There would be the pressure of the whole mass towards the centre of convergence. In the case of air, and all perfect gases cooling under pressure, about 234 foot-pounds of the original heat possessed by the gas are given out while 95 foot-pounds are being generated by condensation. We have, however, no reason whatever to believe that in the case of the cooling of the sun the same proportions would hold true. The proportion of original heat possessed by the mass of the sun to that produced by condensation may have been much greater than 234 to 95, or it may have been much less. In the absence of all knowledge on this point, we may in the meantime assume that to be the proportion. The total quantity of heat given out by the sun resulting from the condensation of his mass, on the supposition that the density of the sun is uniform throughout, we have seen to be equal to 20,237,500 years’ sun-heat. Then the quantity of heat given out, which previously existed in the mass as original temperature, must have been 49,850,000 years’ heat, making in all 70,087,500 years’ heat as the total amount.
The above quantity represents, of course, the total amount of heat given out by the mass since it began to condense. But the geological history of our globe must date its beginning at a period posterior to that. For at that time the mass would probably occupy a much greater amount of space than is presently possessed by the entire solar system; and consequently, before it had cooled down to within the limits of the earth’s present orbit, our earth could not have had an existence as a separate planet. Previously to that time it must have existed as a portion of the sun’s fiery mass. If we assume that it existed as a globe previously to that, and came in from space after the condensation of the sun, then it is difficult to conceive how its orbit should be so nearly circular as it is at present.
Let us assume that by the time that the mass of the sun had condensed to within the space encircled by the orbit of the planet Mercury (that is, to a sphere having, say, a radius of 18,000,000 miles) the earth’s crust began to form; and let this be the time when the geological history of our globe dates its commencement. The total amount of heat generated by the condensation of the sun’s mass from a sphere of this size to its present volume would equal 19,740,000 years’ sun-heat. The amount of original heat given out during that time would equal 48,625,000 years’ sun-heat,—thus giving a total of 68,365,000 years’ sun-heat enjoyed by our globe since that period. The total quantity may possibly, of course, be considerably more than that, owing to the fact that the sun’s density may increase greatly towards his centre. But we should require to make extravagant assumptions regarding the interior density of the sun and the proportion of original heat to that produced by condensation before we could manage to account for anything like the period that geological phenomena are supposed by some to demand.
The question now arises, by what conceivable means could the mass of the sun have become possessed of such a prodigious amount of energy in the form of heat previous to condensation? What power could have communicated to the mass 50,000,000 years’ heat before condensation began to take place?
The Sun’s Energy may have originally been derived from Motion in Space.—There is nothing at all absurd or improbable in the supposition that such an amount of energy might have been communicated to the mass. The Dynamical Theory of Heat affords an easy explanation of at least how such an amount of energy may have been communicated. Two bodies, each one-half the mass of the sun, moving directly towards each other with a velocity of 476 miles per second, would by their concussion generate in a single moment the 50,000,000 years’ heat. For two bodies of that mass moving with a velocity of 476 miles per second would possess 4149 × 10^{38} foot-pounds of energy in the form of vis viva; and this, converted into heat by the stoppage of their motion, would give an amount of heat which would cover the present rate of the sun’s radiation, for a period of 50,000,000 years.
Why may not the sun have been composed of two such bodies? And why may not the original store of heat possessed by him have all been derived from the concussion of these two bodies? Two such bodies coming into collision with that velocity would be dissipated into vapour by such an inconceivable amount of heat as would thus be generated; and when they condensed on cooling, they would form one spherical mass like the sun. It is perfectly true that two such bodies could never attain the required amount of velocity by their mutual gravitation towards each other. But there is no necessity whatever for supposing that their velocities were derived from their mutual attraction alone. They might have been approaching towards each other with the required velocity wholly independent of gravitation.
We know nothing whatever regarding the absolute motion of bodies in space. And beyond the limited sphere of our observation, we know nothing even of their relative motions. There may be bodies moving in relation to our system with inconceivable velocity. For anything that we know to the contrary, were one of these bodies to strike our earth, the shock might be sufficient to generate an amount of heat that would dissipate the earth into vapour, though the striking body might not be heavier than a cannon-ball. There is, however, nothing very extraordinary in the velocity which we have found would be required in the two supposed bodies to generate the 50,000,000 years’ heat. A comet, having an orbit extending to the path of the planet Neptune, approaching so near the sun as to almost graze his surface in passing, would have a velocity of about 390 miles per second, which is within 86 miles of the required velocity.
But in the original heating and expansion of the sun into a gaseous mass, an amount of work must have been performed against gravitation equal to that which has been performed by gravitation during his cooling and condensation, a quantity which we have found amounts to about 20,000,000 years’ heat. The total amount of energy originally communicated by the concussion must have been equal to 70,000,000 years’ sun-heat. A velocity of 563 miles per second would give this amount. It must be borne in mind, however, that the 563 miles per second is the velocity at the moment of collision; about one-half of this velocity would be derived from the mutual attraction of the two bodies in their approach to each other. Suppose each body to be equal in volume to the sun, and of course one-half the density, the amount of velocity which they would acquire by their mutual attraction would be 274 miles per second, consequently we have to assume an original or projected velocity of only 289 miles per second.
If we admit that gravitation is not sufficient to account for the amount of heat given out by the sun during the geological history of our globe, we are compelled to assume that the mass of which the sun is composed existed prior to condensation in a heated condition; and if so, we are further obliged to admit that the mass must have received its heat from some source or other. And as the dissipation of heat into space must have been going on, in all probability, as rapidly before as after condensation took place, we are further obliged to conclude that the heat must have been communicated to the mass immediately before condensation began, for the moment the mass began to lose its heat condensation would ensue. If we confine our speculations to causes and agencies known to exist, the cause which has been assigned appears to be the only conceivable one that will account for the production of such an enormous amount of heat.
The general conclusion to which we are therefore led from physical considerations regarding the age of the sun’s heat is, that the entire geological history of our globe must be comprised within less than 100 millions of years, and that consequently the commencement of the glacial epoch cannot date much farther back than 240,000 years.
The facts of geology, more especially those in connection with denudation, seem to geologists to require a period of much longer duration than 100 millions of years, and it is this which has so long prevented them accepting the conclusions of physical science in regard to the age of our globe. But the method of measuring subaërial denudation already detailed seems to me to show convincingly that the geological data, when properly interpreted, are in perfect accord with the deductions of physical science. Perhaps there are now few who have fairly considered the question who will refuse to admit that 100 millions of years are amply sufficient to comprise the whole geological history of our globe.
A false Analogy supposed to exist between Astronomy and Geology.—Perhaps one of the things which has tended to mislead on this point is a false analogy which is supposed to subsist between astronomy and geology, viz., that geology deals with unlimited time, as astronomy deals with unlimited space. A little consideration, however, will show that there is not much analogy between the two cases.
Astronomy deals with the countless worlds which lie spread out in the boundless infinity of space; but geology deals with only one world. No doubt reason and analogy both favour the idea that the age of the material universe, like its magnitude, is immeasurable; we have no reason, however, to conclude that it is eternal, any more than we have to infer that it is infinite. But when we compare the age of the material universe with its magnitude, we must not take the age of one of its members (say, our globe) and compare it with the size of the universe. Neither must we compare the age of all the presently existing systems of worlds with the magnitude of the universe; but we must compare the past history of the universe as it stretches back into the immensity of bygone time, with the presently existing universe as it stretches out on all sides into limitless space. For worlds precede worlds in time as worlds lie beyond worlds in space. Each world, each individual, each atom is evidently working out a final purpose, according to a plan prearranged and predetermined by the Divine Mind from all eternity. And each world, like each individual, when it serves the end for which it was called into existence, disappears to make room for others. This is the grand conception of the universe which naturally impresses itself on every thoughtful mind that has not got into confusion about those things called in science the Laws of Nature.[203]
But the geologist does not pass back from world to world as they stand related to each other in the order of succession in time, as the astronomer passes from world to world as they stand related to each other in the order of coexistence in space. The researches of the geologist, moreover, are not only confined to one world, but it is only a portion of the history of that one world that can come under his observation. The oldest of existing formations, so far as is yet known, the Laurentian Gneiss, is made up of the waste of previously existing rocks, and it, again, has probably been derived from the degradation of rocks belonging to some still older period. Regarding what succeeds these old Laurentian rocks geology tells us much; but of the formations that preceded, we know nothing whatever. For anything that geology shows to the contrary, the time which may have elapsed from the solidifying of the earth’s crust to the deposition of the Laurentian strata—an absolute blank—may have been as great as the time that has since intervened.
Probable Date of the Eocene and Miocene Periods.—If we take into consideration the limit which physical science assigns to the age of our globe, and the rapid rate at which, as we have seen, denudation takes place, it becomes evident that the enormous period of 3 millions of years comprehended in the foregoing tables must stretch far back into the Tertiary age. Supposing that the mean rate of denudation during that period was not greater than the present rate of denudation, still we should have no less than 500 feet of rock worn off the face of the country and carried into the sea during these 3 millions of years. This fact shows how totally different the appearance and configuration of the country in all probability was at the commencement of this period from what it is at the present day. If it be correct that the glacial epoch resulted from the causes which we have already discussed, those tables ought to aid us in our endeavour to ascertain how much of the Tertiary period may be comprehended within these 3 millions of years.
We have already seen (Chapter XVIII.) that there is evidence of a glacial condition of climate at two different periods during the Tertiary age, namely, about the middle of the Miocene and Eocene periods respectively. As has already been shown, the more severe a glacial epoch is, the more marked ought to be the character of its warm inter-glacial periods; the greater the extension of the ice during the cold periods of a glacial epoch the further should that ice disappear in arctic regions during the corresponding warm periods. Thus the severity of a glacial epoch may in this case be indirectly inferred from the character of the warm periods and the extent to which the ice may have disappeared from arctic regions. Judged by this test, we have every reason to believe that the Miocene glacial epoch was one of extreme severity.
The Eocene conglomerate, devoid of all organic remains, and containing numerous enormous ice-transported blocks, is, as we have seen, immediately associated with nummulitic strata charged with fossils characteristic of a warm climate. Referring to this Sir Charles Lyell says, “To imagine icebergs carrying such huge fragments of stone in so southern a latitude, and at a period immediately preceded and followed by the signs of a warm climate, is one of the most perplexing enigmas which the geologist has yet been called upon to solve.”[204]
It is perfectly true that, according to the generally received theories of the cause of a glacial climate the whole is a perplexing enigma, but if we adopt the Secular theory of change of climate, every difficulty disappears. According to this theory the very fact of the conglomerate being formed at a period immediately preceded and succeeded by warm conditions of climate, is of itself strong presumptive evidence of the conglomerate being a glacial formation. But this is not all, the very highness of the temperature of the preceding and succeeding periods bears testimony to the severity of the intervening glacial period. Despite the deficiency of direct evidence regarding the character of the Miocene and Eocene glacial periods, we are not warranted, for reasons which have been stated in Chapter XVII., to conclude that these periods were less severe than the one which happened in Quaternary times. Judging from indirect evidence, we have some grounds for concluding that the Miocene glacial epoch at least was even more severe and protracted than our recent glacial epoch.
By referring to Table I., or the accompanying diagram, it will be seen that prior to the period which I have assigned as that of the glacial epoch, there are two periods when the eccentricity almost attained its superior limit. The first period occurred 2,500,000 years ago, when it reached 0·0721, and the second period 850,000 years ago, when it attained a still higher value, viz., 0·0747, being within 0·0028 of the superior limit. To the first of these periods I am disposed to assign the glacial epoch of Eocene times, and to the second that of the Miocene age. With the view of determining the character of these periods Tables II. and III. have been computed. They give the eccentricity and longitude of perihelion at intervals of 10,000 years. It will be seen from Table II. that the Eocene period extends from about 2,620,000 to about 2,460,000 years ago; and from Table III. it will be gathered that the Miocene period lasted from about 980,000 to about 720,000 years ago.
In order to find whether the eccentricity attained a higher value about 850,000 years ago than 0·0747, I computed the values for one or two periods immediately before and after that period, and satisfied myself that the value stated was indeed the highest, as will be seen from the subjoined table:—
851,000 0·07454 850,000 0·074664 849,500 0·07466 849,000 0·07466
How totally different must have been the condition of the earth’s climate at that period from what it is at present! Taking the mean distance of the sun to be 91,400,000 miles, his present distance at midwinter is 89,864,480 miles; but at the period in question, when the winter solstice was in perihelion, his distance at midwinter would be no less than 98,224,289 miles. But this is not all; our winters are at present shorter than our summers by 7·8 days, but at that period they would be longer than the summers by 34·7 days.
At present the difference between the perihelion and aphelion distance of the sun amounts to only 3,069,580 miles, but at the period under consideration it would amount to no less than 13,648,579 miles!
Chapter XXII
A METHOD OF DETERMINING THE MEAN THICKNESS OF THE SEDIMENTARY ROCKS OF THE GLOBE.
Prevailing Methods defective.—Maximum Thickness of British Rocks.—Three Elements in the Question.—Professor Huxley on the Rate of Deposition.—Thickness of Sedimentary Rocks enormously over-estimated.—Observed Thickness no Measure of mean Thickness.—Deposition of Sediment principally along Sea-margin.—Mistaken Inference regarding the Absence of a Formation.—Immense Antiquity of existing Oceans.
Various attempts have been made to measure the positive length of geological periods. Some geologists have sought to determine, roughly, the age of the stratified rocks by calculations based upon their probable thickness and the rate at which they may have been deposited. This method, however, is worthless, because the rates which have been adopted are purely arbitrary. One geologist will take the rate of deposit at a foot in a hundred years, while another will assume it to be a foot in a thousand or perhaps ten thousand years; and, for any reasons that have been assigned, the one rate is just as likely to be correct as the other: for if we examine what is taking place in the ocean-bed at the present day, we shall find in some places a foot of sediment laid down in a year, while in other places a foot may not be deposited in a thousand years. The stratified rocks were evidently formed at all possible rates. When we speak of the rate of their formation, we must of course refer to the mean rate; and it is perfectly true that if we knew the thickness of these rocks and the mean rate at which they were deposited, we should have a ready means of determining their positive age. But there appears to be nearly as great uncertainty regarding the thickness of the sedimentary rocks as regarding the rate at which they were formed. No doubt we can roughly estimate their probable maximum thickness; for instance, Professor Ramsay has found from actual measurement, that the sedimentary formations of Great Britain have a maximum thickness of upwards of 72,000 feet; but all such measurements give us no idea of their mean thickness. What is the mean thickness of the sedimentary rocks of the globe? On this point geology does not afford a definite answer. Whatever the present mean thickness of the sedimentary rocks of our globe may be, it must be small in comparison to the mean thickness of all the sedimentary rocks which have been formed. This is obvious from the fact that the sedimentary rocks of one age are partly formed from the destruction of the sedimentary rocks of former ages. From the Laurentian age down to the present day, the stratified rocks have been undergoing constant denudation.
Unless we take into consideration the quantity of rock removed during past ages by denudation, we cannot—even though we knew the actual mean thickness of the existing sedimentary rocks of the globe, and the rate at which they were formed—arrive at an estimate regarding the length of time represented by these rocks. For if we are to determine the age of the stratified rocks from the rate at which they were formed, we must have, not the present quantity of sedimentary rocks, but the present plus the quantity which has been denuded during past ages. In other words, we must have the absolute quantity formed. In many places the missing beds must have been of enormous thickness. The time represented by beds which have disappeared is, doubtless, as already remarked, much greater than that represented by the beds which now remain. The greater mass of the sedimentary rocks has been formed out of previously existing sedimentary rocks, and these again out of sedimentary rocks still older. As the materials composing our stratified beds may have passed through many cycles of destruction and re-formation, the time required to have deposited at a given rate the present existing mass of sedimentary rocks may be but a fraction of the time required to have deposited at the same rate the total mass that has actually been formed. To measure the age of the sedimentary rocks by the present existing rocks, assumed to be formed at some given rate, even supposing the rate to be correct, is a method wholly fallacious.
“The aggregate of sedimentary strata in the earth’s crust,” says Sir Charles Lyell, “can never exceed in volume the amount of solid matter which has been ground down and washed away by rivers, waves, and currents. How vast, then, must be the spaces which this abstraction of matter has left vacant! How far exceeding in dimensions all the valleys, however numerous, and the hollows, however vast, which we can prove to have been cleared out by aqueous erosion!”[205]
I presume there are few geologists who would not admit that if all the rocks which have in past ages been removed by denudation were restored, the mean thickness of the sedimentary rocks of the globe would be at least equal to their present maximum thickness, which we may take at 72,000 feet.
There are three elements in the question; of which if two are known, the third is known in terms of the other two. If we have the mean thickness of all the sedimentary rocks which have been formed and the mean rate of formation, then we have the time which elapsed during the formation; or having the thickness and the time, we have the rate; or, having the rate and the time, we have the thickness.
One of these three, namely, the rate, can, however, be determined with tolerable accuracy if we are simply allowed to assume—what is very probable, as has already been shown—that the present rate at which the sedimentary deposits are being formed may be taken as the mean rate for past ages. If we know the rate at which the land is being denuded, then we know with perfect accuracy the rate at which the sedimentary deposits are being formed in the ocean. This is obvious, because all the materials denuded from the land are deposited in the sea; and what is deposited in the sea is just what comes off the land, with the exception of the small proportion of calcareous matter which may not have been derived from the land, and which in our rough estimate may be left out of account.
Now the mean rate of subaërial denudation, we have seen, is about one foot in 6,000 years. Taking the proportion of land to that of water at 576 to 1,390, then one foot taken off the land and spread over the sea-bottom would form a layer 5 inches thick. Consequently, if one foot in 6,000 years represents the mean rate at which the land is being denuded, one foot in 14,400 years represents the mean rate at which the sedimentary rocks are being formed.
Assuming, as before, that 72,000 feet would represent the mean thickness of all the sedimentary rocks which have ever been formed, this, at the rate of one foot in 14,400 years, gives 1,036,800,000 years as the age of the stratified rocks.
Professor Huxley, in his endeavour to show that 100,000,000 years is a period sufficiently long for all the demands of geologists, takes the thickness of the stratified rocks at 100,000 feet, and the rate of deposit at a foot in 1,000 years. One foot of rock per 1,000 years gives, it is true, 100,000 feet in 100,000,000 years. But what about the rocks which have disappeared? If it takes a hundred millions of years to produce a mass of rock equal to that which now exists, how many hundreds of millions of years will it require to produce a mass equal to what has actually been produced?
Professor Huxley adds, “I do not know that any one is prepared to maintain that the stratified rocks may not have been formed on the average at the rate of 1/83rd of an inch per annum.” When the rate, however, is accurately determined, it is found to be, not 1/83rd of an inch per annum, but only 1/1200th of an inch, so that the 100,000 feet of rock must have taken 1,440,000,000 years in its formation,—a conclusion which, according to the results of modern physics, is wholly inadmissible.
Either the thickness of the sedimentary rocks has been over-estimated, or the rate of their formation has been under-estimated, or both. If it be maintained that a foot in 14,400 years is too slow a rate of deposit, then it must be maintained that the land must have been denuded at a greater rate than one foot in 6,000 years. But most geologists probably felt surprised when the announcement was first made, that at this rate of denudation the whole existing land of the globe would be brought under the ocean in 6,000,000 of years.
The error, no doubt, consists in over-estimating the thickness of the sedimentary rocks. Assuming, for physical reasons already stated, that 100,000,000 years limits the age of the stratified rocks, and that the proportion of land to water and the rate of denudation have been on the average the same as at present, the mean thickness of sedimentary rocks formed in the 100,000,000 years amounts to only 7,000 feet.
But be it observed that this is the mean thickness on an area equal to that of the ocean. Over the area of the globe it amounts to only 5,000 feet; and this, let it be observed also, is the total mean thickness formed, without taking into account what has been removed by denudation. If we wish to ascertain what is actually the present mean thickness, we must deduct from this 5,000 feet an amount of rock equal to all the sedimentary rocks which have been denuded during the 100,000,000 years; for the 5,000 feet is not the present mean thickness, but the total mean thickness formed during the whole of the 100,000,000 years. If we assume, what no doubt most geologists would be willing to grant, that the quantity of sedimentary rocks now remaining is not over one-half of what has been actually deposited during the history of the globe, then the actual mean thickness of the stratified rocks of the globe is not over 2,500 feet. This startling result would almost necessitate us to suspect that the rate of subaërial denudation is probably greater than one foot in 6,000 years. But, be this as it may, we are apt, in estimating the mean thickness of the stratified rocks of the globe from their ascertained maximum thickness, to arrive at erroneous conclusions. There are considerations which show that the mean thickness of these rocks must be small in proportion to their maximum thickness. The stratified rocks are formed from the sediment carried down by rivers and streamlets and deposited in the sea. It is obvious that the greater quantity of this sediment is deposited near the mouths of rivers, and along a narrow margin extending to no great distance from the land. Did the land consist of numerous small islands equally distributed over the globe, the sediment carried off from these islands would be spread pretty equally over the sea-bottom. But the greater part of the land-surface consists of two immense continents. Consequently, the materials removed by denudation are not spread over the ocean-bottom, but on a narrow fringe surrounding those two continents. Were the materials spread over the entire ocean-bed, a foot removed off the general surface of the land would form a layer of rock only five inches thick. But in the way in which the materials are at present deposited, the foot removed from the land would form a layer of rock many feet in thickness. The greater part of the sediment is deposited within a few miles of the shore.
The entire coast-line of the globe is about 116,500 miles. I should think that the quantity of sediment deposited beyond, say, 100 miles from this coast-line is not very great. No doubt several of the large rivers carry sediment to a much greater distance from their mouths than 100 miles, and ocean currents may in some cases carry mud and other materials also to great distances. But it must be borne in mind that at many places within the 100 miles of this immense coast-line little or no sediment is deposited, so that the actual area over which the sediment carried off the land is deposited is probably not greater than the area of this belt—116,500 miles long and 100 miles broad. This area on which the sediment is deposited, on the above supposition, is therefore equal to about 11,650,000 square miles. The amount of land on the globe is about 57,600,000 square miles. Consequently, one foot of rock, denuded from the surface of the land and deposited on this belt, would make a stratum of rock 5 feet in thickness; but were the sediment spread over the entire bed of the ocean, it would form, as has already been stated, a stratum of rock of only 5 inches in thickness.
Suppose that no subsidence of the land should take place for a period of, say, 3,000,000 of years. During that period 500 feet would be removed by denudation, on an average, off the land. This would make a formation 2,500 feet thick, which some future geologist might call the Post-tertiary formation. But this, be it observed, would be only the mean thickness of the formation on this area; its maximum thickness would evidently be much greater, perhaps twice, thrice, or even four times that thickness. A geologist in the future, measuring the actual thickness of the formation, might find it in some places 10,000 feet in thickness, or perhaps far more. But had the materials been spread over the entire ocean-bed, the formation would have a mean thickness of little more than 200 feet; and spread over the entire surface of the globe, would form a stratum of scarcely 150 feet in thickness. Therefore, in estimating the mean thickness of the stratified rocks of the globe, a formation with a maximum thickness of 10,000 feet may not represent more than 150 feet. A formation with a mean thickness of 10,000 feet represents only 600 feet.
It may be objected that in taking the present rate at which the sedimentary deposits are being formed as the mean rate for all ages, we probably under-estimate the total amount of rock formed, because during the many glacial periods which must have occurred in past ages the amount of materials ground off the rocky surface of the land in a given period would be far greater than at present. But, in reply, it must be remembered that although the destruction in ice-covered regions would be greater during these periods than at present, yet the quantity of materials carried down by rivers into the sea would be less. At the present day the greater part of the materials carried down by our rivers is not what is being removed off the rocky face of the country, but the boulder clay, sand, and other materials which were ground off during the glacial epoch. It is therefore possible, on this account, that the rate of deposit may have been less during the glacial epoch than at present.
When any particular formation is wanting in a given area, the inference generally drawn is, that either the formation has been denuded off the area, or the area was a land-surface during the period when that formation was being deposited. From the foregoing it will be seen that this inference is not legitimate; for, supposing that the area had been under water, the chances that materials should have been deposited on that area are far less than are the chances that there should not. There are sixteen chances against one that no formation ever existed in the area.
If the great depressions of the Atlantic, Pacific, and Indian Oceans be, for example, as old as the beginning of the Laurentian period—and they may be so for anything which geology can show to the contrary—then under these oceans little or no stratified rocks may exist. The supposition that the great ocean basins are of immense antiquity, and that consequently only a small proportion of the sedimentary strata can possibly occupy the deeper bed of the sea, acquires still more probability when we consider the great extent and thickness of the Old Red Sandstone, the Permian, and other deposits, which, according to Professor Ramsay and others, have been accumulated in vast inland lakes.
Chapter XXIII
THE PHYSICAL CAUSE OF THE SUBMERGENCE AND EMERGENCE OF THE LAND DURING THE GLACIAL EPOCH.
Displacement of the Earth’s Centre of Gravity by Polar Ice-cap.—Simple Method of estimating Amount of Displacement.—Note by Sir W. Thomson on foregoing Method.—Difference between Continental Ice and a Glacier.—Probable Thickness of the Antarctic Ice-cap.—Probable Thickness of Greenland Ice-sheet.—The Icebergs of the Southern Ocean.—Inadequate Conceptions regarding the Magnitude of Continental Ice.
Displacement of the Earth’s Centre of Gravity by Polar Ice-cap.[206]—In order to represent the question in its most simple elementary form, I shall assume an ice-cap of a given thickness at the pole and gradually diminishing in thickness towards the equator in the simple proportion of the sines of the latitudes, where at the equator its thickness of course is zero. Let us assume, what is actually the case, that the equatorial diameter of the globe is somewhat greater than the polar, but that when the ice-cap is placed on one hemisphere the whole forms a perfect sphere.
I shall begin with a period of glaciation on the southern hemisphere. Let W N E S′ (Fig. 5) be the solid part of the earth, and c its centre of gravity. And let E S W be an ice-cap covering the southern hemisphere. Let us in the first case assume the earth to be of the same density as the cap. The earth with its cap forms now a perfect sphere with its centre of gravity at o; for W N E S is a circle, and o is its centre. Suppose now the whole to be covered with an ocean a few miles deep, the ocean will assume the spherical form, and will be of uniform depth. Let the southern winter solstice begin now to move round from the aphelion. The ice-cap will also commence gradually to diminish in thickness, and another cap will begin to make its appearance on the northern hemisphere. As the northern cap may be supposed, for simplicity of calculation, to increase at the same rate that the southern will diminish, the spherical form of the earth will always be maintained. By the time that the northern cap has reached a maximum, the southern cap will have completely disappeared. The circle W N′ E S′ will now represent the earth with its cap on the northern hemisphere, and o′ will be its centre of gravity; for o′ is the centre of the circle W N′ E S′. And as the distance between the centres o and o′ is equal to N N′, the thickness of the cap at the pole N N′ will therefore represent the extent to which the centre of gravity has been displaced. It will also represent the extent to which the ocean has risen at the north pole and sunk at the south. This is evident; for as the sphere W N′ E S′ is the same in all respects as the sphere W N E S, with the exception only that the cap is on the opposite side, the surface of the ocean at the poles will now be at the same distance from the centre o′ as it was from the centre o when the cap covered the southern hemisphere. Hence the distance between o and o′ must be equal to the extent of the submergence at the north pole and the emergence at the south. Neglect the attraction of the altering water on the water itself, which later on will come under our consideration.
We shall now consider the result when the earth is taken at its actual density, which is generally believed to be about 5·5. The density of ice being ·92, the density of the cap to that of the earth will therefore be as 1 to 6.
Let Fig. 6 represent the earth with an ice-cap on the northern hemisphere, whose thickness is, say, 6,000 feet at the pole. The centre of gravity of the earth without the cap is at c. When the cap is on, the centre of gravity is shifted to o, a point a little more than 500 feet to the north of c. Had the cap and the earth been of equal density, the centre of gravity would have been shifted to o′ the centre of the figure, a point situated, of course, 3,000 feet to the north of c. Now it is very approximately true that the ocean will tend to adjust itself as a sphere around the centre of gravity, o. Thus it would of course sink at the south pole and rise to the same extent at the north, in any opening or channel in the ice allowing the water to enter.
Let the ice-cap be now transferred over to the southern hemisphere, and the condition of things on the two hemispheres will in every particular be reversed. The centre of gravity will then lie to the south of c, or about 1,000 feet from its former position. Consequently the transference of the cap from the one hemisphere to the other will produce a total submergence of about 1,000 feet.
It is, of course, absurd to suppose that an ice-cap could ever actually reach down to the equator. It is probable that the great ice-cap of the glacial epoch nowhere reached even halfway to the equator. Our cap must therefore terminate at a moderately high latitude. Let it terminate somewhere about the latitude of the north of England, say at latitude 55°. All that we have to do now is simply to imagine our cap, up to that latitude, becoming converted into the fluid state. This would reduce the cap to less than one-half its former mass. But it would not diminish the submergence to anything like that extent. For although the cap would be reduced to less than one-half its former mass, yet its influence in displacing the centre of gravity would not be diminished to that extent. This is evident; for the cap now extending down to only latitude 55°, has its centre of gravity much farther removed from the earth’s centre of gravity than it had when it extended down to the equator. Consequently it now possesses, in proportion to its mass, a much greater power in displacing the earth’s centre of gravity.
There is another fact which must be taken into account. The common centre of gravity of the earth and cap is not exactly the point around which the ocean tends to adjust itself. It adjusts itself not in relation to the centre of gravity of the solid mass alone, but in relation to the common centre of gravity of the entire mass, solid and liquid. Now the water which is pulled over from the one hemisphere to the other by the attraction of the cap will also aid in displacing the centre of gravity. It will co-operate with the cap and carry the true centre of gravity to a point beyond that of the centre of gravity of the earth and cap, and thus increase the effect.
It is of course perfectly true that when the ice-cap does not extend down to the equator, as in the latter supposition, and is of less density than the globe, the ocean will not adjust itself uniformly around the centre of gravity; but the deviation from perfect uniformity is so trifling, as will be seen from the appended note of Sir William Thomson, that for all practical purposes it may be entirely left out of account.
In the Reader for January 13, 1866, I advanced an objection to the submergence theory on the grounds that the lowering of the ocean-level by the evaporation of the water to form the ice-cap, would exceed the submergence resulting from the displacement of the earth’s centre of gravity. But, after my letter had gone to press, I found that I had overlooked some important considerations which seem to prove that the objection had no real foundation. For during a glacial period, say on the northern hemisphere, the entire mass of ice which presently exists on the southern hemisphere would be transferred to the northern, leaving the quantity of liquid water to a great extent unchanged.
Note on the preceding by Sir William Thomson, F.R.S.
“Mr. Croll’s estimate of the influence of a cap of ice on the sea-level is very remarkable in its relation to Laplace’s celebrated analysis, as being founded on that law of thickness which leads to expressions involving only the first term of the series of ‘Laplace’s functions,’ or ‘spherical harmonics.’ The equation of the level surface, as altered by any given transference of solid matter, is expressed by equating the altered potential function to a constant. This function, when expanded in the series of spherical harmonics, has for its first term the potential due to the whole mass supposed collected at its altered centre of gravity. Hence a spherical surface round the altered centre of gravity is the first approximation in Laplace’s method of solution for the altered level surface. Mr. Croll has with admirable tact chosen, of all the arbitrary suppositions that may be made foundations for rough estimates of the change of sea-level due to variations in the polar ice-crusts, the one which reduces to zero all terms after the first in the harmonic series, and renders that first approximation (which always expresses the essence of the result) the whole solution, undisturbed by terms irrelevant to the great physical question.
“Mr. Croll, in the preceding paper, has alluded with remarkable clearness to the effect of the change in the distribution of the water in increasing, by its own attraction, the deviation of the level surface above that which is due to the given change in the distribution of solid matter. The remark he makes, that it is round the centre of gravity of the altered solid and altered liquid that the altering liquid surface adjusts itself, expresses the essence of Laplace’s celebrated demonstration of the stability of the ocean, and suggests the proper elementary solution of the problem to find the true alteration of sea-level produced by a given alteration of the solid. As an assumption leading to a simple calculation, let us suppose the solid earth to rise out of the water in a vast number of small flat-topped islands, each bounded by a perpendicular cliff, and let the proportion of water area to the whole be equal in all quarters. Let all of these islands in one hemisphere be covered with ice, of thickness according to the law assumed by Mr. Croll—that is, varying in simple proportion of the sine of the latitude. Let this ice be removed from the first hemisphere and similarly distributed over the islands of the second. By working out according to Mr. Croll’s directions, it is easily found that the change of sea-level which this will produce will consist in a sinking in the first hemisphere and rising in the second, through heights varying according to the same law (that is, simple proportionality to sines of latitudes), and amounting at each pole to
(1 - ω)it —————————, 1 - ωw
where t denotes the thickness of the ice-crust at the pole; i the ratio of the density of ice, and w that of sea-water to the earth’s mean density; and ω the ratio of the area of ocean to the whole surface.
“Thus, for instance, if we suppose ω = ⅔, and t = 6,000 feet, and take ⅙ and 1/(5½) as the densities of ice and water respectively, we find for the rise of sea-level at one pole, and depression at the other,
⅓ × ⅙ × 6000 ————————————, 2 1 1 - — × — 3 5½
or approximately 380 feet.
“I shall now proceed to consider roughly what is the probable extent of submergence which, during the glacial epoch, may have resulted from the displacement of the earth’s centre of gravity by means of the transferrence of the polar ice from the one hemisphere to the other.”
Difference between Continental-ice and a Glacier.—An ordinary glacier descends in virtue of the slope of its bed, and, as a general rule, it is on this account thin at its commencement, and thickens as it descends into the lower valleys, where the slope is less and the resistance to motion greater. But in the case of continental ice matters are entirely different. The slope of the ground exercises little or no influence on the motion of the ice. In a continent of one or two thousand miles across, the general slope of the ground may be left out of account; for any slight elevation which the centre of such a continent may have will not compensate for the resistance offered to the flow of the ice by mountain ridges, hills, and other irregularities of its surface. The ice can move off such a surface only in consequence of pressure acting from the interior. In order to produce such a pressure, there must be a piling up of the ice in the interior; or, in other words, the ice-sheet must thicken from the edge inwards to the centre. We are necessarily led to the same conclusion, though we should not admit that the ice moves in consequence of pressure from behind, but should hold, on the contrary, that each particle of ice moves by gravity in virtue of its own weight; for in order to have such a motion there must be a slope, and as the slope is not on the ground, it must be on the ice itself: consequently we must conclude that the upper surface of the ice slopes upwards from the edge to the interior. What, then, is the least slope at which the ice will descend? Mr. Hopkins found that ice barely moves on a slope of one degree. We have therefore some data for arriving at least at a rough estimate of the probable thickness of an ice-sheet covering a continent, such, for example, as Greenland or the Antarctic Continent.
Probable Thickness of the Antarctic Ice-cap.—The antarctic continent is generally believed to extend, on an average, from the South Pole down to about, at least, lat. 70°. In round numbers, we may take the diameter of this continent at 2,800 miles. The distance from the edge of this ice-cap to its centre, the South Pole, will, therefore, be 1,400 miles. The whole of this continent, like Greenland, is undoubtedly covered with one continuous sheet of ice gradually thickening inwards from its edge to its centre. A slope of one degree continued for 1,400 miles will give twenty-four miles as the thickness of the ice at the pole. But suppose the slope of the upper surface of the cap to be only one-half this amount, viz., a half degree,—and we have no evidence that a slope so small would be sufficient to discharge the ice,—still we have twelve miles as the thickness of the cap at the pole. To those who have not been accustomed to reflect on the physical conditions of the problem, this estimate may doubtless be regarded as somewhat extravagant; but a slight consideration will show that it would be even more extravagant to assume that a slope of less than half a degree would be sufficient to produce the necessary outflow of the ice. In estimating the thickness of a sheet of continental ice of one or two thousand miles across, our imagination is apt to deceive us. We can easily form a pretty accurate sensuous representation of the thickness of the sheet; but we can form no adequate representation of its superficial area. We can represent to the mind with tolerable accuracy a thickness of a few miles, but we cannot do this in reference to the area of a surface 2,800 miles across. Consequently, in judging what proportion the thickness of the sheet should bear to its superficial area, we are apt to fall into the error of under-estimating the thickness. We have a striking example of this in regard to the ocean. The thing which impresses us most forcibly in regard to the ocean is its profound depth. A mean depth of, say, three miles produces a striking impression; but if we could represent to the mind the vast area of the ocean as correctly as we can do its depth, shallowness rather than depth would be the impression produced. A sheet of water 100 yards in diameter, and only one inch deep, would not be called a deep but a very shallow pool or thin layer of water. But such a layer would be a correct representation of the ocean in miniature. Were we in like manner to represent to the eye in miniature the antarctic ice-cap, we would call it a thin crust of ice. Taking the mean thickness of the ice at four miles, the antarctic ice-sheet would be represented by a carpet covering the floor of an ordinary-sized dining-room. Were those who consider the above estimate of the thickness of the antarctic ice-cap as extravagantly great called upon to sketch on paper a section of what they should deem a cap of moderate thickness, ninety-nine out of every hundred would draw one of much greater thickness than twelve miles at the centre.
The diagram on following page (Fig. 7) represents a section across the cap drawn to a natural scale; the upper surface of the sheet having a slope of half a degree. No one on looking at the section would pronounce it to be too thick at the centre, unless he were previously made aware that it represented a thickness of twelve miles at that place. It may be here mentioned that had the section been drawn upon a much larger scale—had it, for instance, been made seven feet long, instead of seven inches—it would have shown to the eye in a more striking manner the thinness of the cap.
But to avoid all objections on the score of over-estimating the thickness of the cap, I shall assume the angle of the upper surface to be only a quarter of a degree, and the thickness of the sheet one-half what it is represented in the section. The thickness at the pole will then be only six miles instead of twelve, and the mean thickness of the cap two instead of four miles.
Is there any well-grounded reason for concluding the above to be an over-estimate of the actual thickness of the antarctic ice? It is not so much in consequence of any à priori reason that can be urged against the probability of such a thickness of ice, but rather because it so far transcends our previous experience that we are reluctant to admit such an estimate. If we never had any experience of ice thicker than what is found in England, we should feel startled on learning for the first time that in the valleys of Switzerland the ice lay from 200 to 300 feet in depth. Again, if we had never heard of glaciers thicker than those of Switzerland, we could hardly credit the statement that in Greenland they are actually from 2,000 to 3,000 feet thick. We, in this country, have long been familiar with Greenland; but till very lately no one ever entertained the idea that that continent was buried under one continuous mass of ice, with scarcely a mountain top rising above the icy mantle. And had it not been that the geological phenomena of the glacial epoch have for so many years accustomed our minds to such an extraordinary condition of things, Dr. Rink’s description of the Greenland ice would probably have been regarded as the extravagant picture of a wild imagination.
Let us now consider whether or not the facts of observation and experience, so far as they go, bear out the conclusions to which physical considerations lead us in reference to the magnitude of continental ice; and more especially as regards the ice of the antarctic regions.
First. In so far as the antarctic ice-sheet is concerned, observation and experience to a great extent may be said to be a perfect blank. One or two voyagers have seen the outer edge of the sheet at a few places, and this is all. In fact, we judge of the present condition of the interior of the antarctic continent in a great measure from what we know of Greenland. But again, our experience of Greenland ice is almost wholly confined to the outskirts.
Few have penetrated into the interior, and, with the exception of Dr. Hayes and Professor Nordenskjöld, none, as far as I know, have passed to any considerable distance over the inland ice. Dr. Robert Brown in his interesting memoir on “Das Innere von Grönland,”[207] gives an account of an excursion made in 1747 by a Danish officer of the name of Dalager, from Fredrikshaab, near the southern extremity of the continent, into the interior. After a journey of a day or two, he reached an eminence from which he saw the inland ice stretching in an unbroken mass as far as the eye could reach, but was unable to proceed further. Dr. Brown gives an account also of an excursion made in the beginning of March, 1830, by O. B. Kielsen, a Danish whale-fisher, from Holsteinborg (lat. 67° N.). After a most fatiguing journey of several days, he reached a high point from which he could see the ice of the interior. Next morning he got up early, and towards midday reached an extensive plain. From this the land sank inwards, and Kielsen now saw fully in view before him the enormous ice-sheet of the interior. He drove rapidly over all the little hills, lakes, and streams, till he reached a pretty large lake at the edge of the ice-sheet. This was the end of his journey, for after vainly attempting to climb up on the ice-sheet, he was compelled to retrace his steps, and had a somewhat difficult return. When he arrived at the fiord, he found the ice broken up, so that he had to go round by the land way, by which he reached the depôt on the 9th of March. The distance which he traversed in a straight line from Holsteinborg into the interior measured eighty English miles.
Dr. Hayes’s excursion was made, however, not upon the real inland ice, but upon a smaller ice-field connected with it; while Professor Nordenskjöld’s excursion was made at a place too far south to afford an accurate idea of the actual condition of the interior of North Greenland, even though he had penetrated much farther than he actually did. However, the state of things as recorded by Hayes and by Nordenskjöld affords us a glimpse into the condition of things in the interior of the continent. They both found by observation, what follows as a necessary result from physical considerations, that the upper surface of the ice plain, under which hills and valleys are buried, gradually slopes upwards towards the interior of the continent. Professor Nordenskjöld states that when at the extreme point at which he reached, thirty geographical miles from the coast, he had attained an elevation of 2,200 feet, and that the inland ice continued constantly to rise towards the interior, so that the horizon towards the east, north, and south, was terminated by an ice-border almost as smooth as that of the ocean.”[208]
Dr. Hayes and his party penetrated inwards to the distance of about seventy miles. On the first day they reached the foot of the great Mer de Glace; the second day’s journey carried them to the upper surface of the ice-sheet. On the third day they travelled 30 miles, and the ascent, which had been about 6°, diminished gradually to about 2°. They advanced on the fourth day about 25 miles; the temperature being 30° below zero (Fah.). “Our station at the camp,” he says, “was sublime as it was dangerous. We had attained an altitude of 5,000 feet above the sea-level, and were 70 miles from the coast, in the midst of a vast frozen Sahara immeasurable to the human eye. There was neither hill, mountain, nor gorge, anywhere in view. We had completely sunk the strip of land between the Mer de Glace and the sea, and no object met the eye but our feeble tent, which bent to the storm. Fitful clouds swept over the face of the full-orbed moon, which, descending towards the horizon, glimmered through the drifting snow that scudded over the icy plain—to the eye in undulating lines of downy softness, to the flesh in showers of piercing darts.”[209]
Dr. Rink, referring to the inland ice, says that the elevation or height above the sea of this icy plain at its junction with the outskirts of the country, and where it begins to lower itself through the valleys to the firths, is, in the ramifications of the Bay of Omenak, found to be 2,000 feet, from which level it gradually rises towards the interior.[210]
Dr. Robert Brown, who, along with Mr. Whymper in 1867, attempted a journey to some distance over the inland ice, is of opinion that Greenland is not traversed by any ranges of mountains or high land, but that the entire continent, 1,200 miles in length and 400 miles in breadth, is covered with one continuous unbroken field of ice, the upper surface of which, he says, rises by a gentle slope towards the interior.[211]
Suppose now the point reached by Hayes to be within 200 miles of the centre of dispersion of the ice, and the mean slope from that point to the centre, as in the case of the antarctic cap, to be only half a degree; this would give 10,000 feet as the elevation of the centre above the point reached. But the point reached was 5,000 feet above sea-level, consequently the surface of the ice at the centre of dispersion would be 15,000 feet above sea-level, which is about one-fourth what I have concluded to be the elevation of the surface of the antarctic ice-cap at its centre. And supposing we assume the general surface of the ground to have in the central region an elevation as great as 5,000 feet, which is not at all probable, still this would give 10,000 feet for the thickness of the ice at the centre of the Greenland continent. But if we admit this conclusion in reference to the thickness of the Greenland ice, we must admit that the antarctic ice is far thicker, because the thickness, other things being equal, will depend upon the size, or, more properly, upon the diameter of the continent; for the larger the surface the greater is the thickness of ice required to produce the pressure requisite to make the rate of discharge of the ice equal to the rate of increase. Now the area of the antarctic continent must be at least a dozen of times greater than that of Greenland.
Second. That the antarctic ice must be far thicker than the arctic is further evident from the dimensions of the icebergs which have been met with in the Southern Ocean. No icebergs over three hundred feet in height have been found in the arctic regions, whereas in the antarctic regions, as we shall see, icebergs of twice and even thrice that height have been reported.
Third. We have no reason to believe that the thickness of the ice at present covering the antarctic continent is less than that which covered a continent of a similar area in temperate regions during the glacial epoch. Take, for example, the North American continent, or, more properly, that portion of it covered by ice during the glacial epoch. Professor Dana has proved that during that period the thickness of the ice on the American continent must in many places have been considerably over a mile. He has shown that over the northern border of New England the ice had a mean thickness of 6,500 feet, while its mean thickness over the Canada watershed, between St. Lawrence and Hudson’s Bay, was not less than 12,000 feet, or upwards of two miles and a quarter (see American Journal of Science and Art for March, 1873).
Fourth. Some may object to the foregoing estimate of the amount of ice on the antarctic continent, on the grounds that the quantity of snowfall in that region cannot be much. But it must be borne in mind that, no matter however small the annual amount of snowfall may be, if more falls than is melted, the ice must continue to accumulate year by year till its thickness in the centre of the continent be sufficiently great to produce motion. The opinion that the snowfall of the antarctic regions is not great does not, however, appear to be borne out by the observation and experience of those who have visited those regions. Captain Wilkes, of the American Exploring Expedition, estimated it at 30 feet per annum; and Sir James Ross says, that during a whole month they had only three days free from snow. The fact that perpetual snow is found at the sea-level at lat. 64° S. proves that the snowfall must be great. But there is another circumstance which must be taken into account, viz., that the currents carrying moisture move in from all directions towards the pole, consequently the area on which they deposit their snow becomes less and less as the pole is reached, and this must, to a corresponding extent, increase the quantity of snow falling on a given area. Let us assume, for example, that the clouds in passing from lat. 60° to lat. 80° deposit moisture sufficient to produce, say, 30 feet of snow per annum, and that by the time they reach lat. 80° they are in possession of only one-tenth part of their original store of moisture. As the area between lat. 80° and the pole is but one-eighth of that between lat. 60° and 80°, this would, notwithstanding, give 24 feet as the annual amount of snowfall between lat. 80° and the pole.[212]
Fifth. The enormous size and thickness of the icebergs which have been met with in the Southern Ocean testify to the thickness of the antarctic ice-cap.
We know from the size of some of the icebergs which have been met with in the southern hemisphere that the ice at the edge of the cap where the bergs break off must in some cases be considerably over a mile in thickness, for icebergs of more than a mile in thickness have been found in the southern hemisphere. The following are the dimensions of a few of these enormous bergs taken from the Twelfth Number of the Meteorological Papers published by the Board of Trade, and from the excellent paper of Mr. Towson on the Icebergs of the Southern Ocean, published also by the Board of Trade.[213] With one or two exceptions, the heights of the bergs were accurately determined by angular measurement:—
Sept. 10th, 1856.—The Lightning, when in lat. 55° 33′ S., long. 140° W., met with an iceberg 420 feet high.
Nov., 1839.—In lat. 41° S., long. 87° 30′ E., numerous icebergs 400 feet high were met with.
Sept., 1840.—In lat. 37° S., long. 15° E., an iceberg 1,000 feet long and 400 feet high was met with.
Feb., 1860.—Captain Clark, of the Lightning, when in lat. 55° 20′ S., long. 122° 45′ W., found an iceberg 500 feet high and 3 miles long.
Dec. 1st, 1859.—An iceberg, 580 feet high, and from two and a half to three miles long, was seen by Captain Smithers, of the Edmond, in lat. 50° 52′ S., long. 43° 58′ W. So strongly did this iceberg resemble land, that Captain Smithers believed it to be an island, and reported it as such, but there is little or no doubt that it was in reality an iceberg. There were pieces of drift-ice under its lee.
Nov., 1856.—Three large icebergs, 500 feet high, were found in lat. 41° 0′ S., long. 42° 0′ E.
Jan., 1861.—Five icebergs, one 500 feet high, were met with in lat. 55° 46′ S., long. 155° 56′ W.
Jan., 1861.—In lat. 56° 10′ S., long. 160° 0′ W., an iceberg 500 feet high and half a mile long was found.
Jan., 1867.—The barque Scout, from the West Coast of America, on her way to Liverpool, passed some icebergs 600 feet in height, and of great length.
April, 1864.—The Royal Standard came in collision with an iceberg 600 feet in height.
Dec., 1856.—Four large icebergs, one of them 700 feet high, and another 500 feet, were met with in lat. 50° 14′ S., long. 42° 54′ E.
Dec. 25th, 1861.—The Queen of Nations fell in with an iceberg in lat. 53° 45′ S., long. 170° 0′ W., 720 feet high.
Dec., 1856.—Captain P. Wakem, ship Ellen Radford, found, in lat. 52° 31′ S., long. 43° 43′ W., two large icebergs, one at least 800 feet high.
Mr. Towson states that one of our most celebrated and talented naval surveyors informed him that he had seen icebergs in the southern regions 800 feet high.
March 23rd, 1855.—The Agneta passed an iceberg in lat. 53° 14′ S., long. 14° 41′ E., 960 feet in height.
Aug. 16th, 1840.—The Dutch ship, General Baron von Geen, passed an iceberg 1,000 feet high in lat. 37° 32′ S., long. 14° 10′ E.
May 15th, 1859.—The Roseworth found in lat. 53° 40′ S., long. 123° 17′ W., an iceberg as large as “Tristan d’Acunha.”
In the regions where most of these icebergs were met with, the mean density of the sea is about 1·0256. The density of ice is ·92. The density of icebergs to that of the sea is therefore as 1 to 1·115; consequently every foot of ice above water indicates 8·7 feet below water. It therefore follows that those icebergs 400 feet high had 3,480 feet under water,—3,880 feet would consequently be the total thickness of the ice. The icebergs which were 500 feet high would be 4,850 feet thick, those 600 feet high would have a total thickness of 5,820 feet, and those 700 feet high would be no less than 6,790 feet thick, which is more than a mile and a quarter. The iceberg 960 feet high, sighted by the Agneta, would be actually 9,312 feet thick, which is upwards of a mile and three-quarters.
Although the mass of an iceberg below water compared to that above may be taken to be about 8·7 to 1, yet it would not be always safe to conclude that the thickness of the ice below water bears the same proportion to its height above. If the berg, for example, be much broader at its base than at its top, the thickness of the ice below water would bear a less proportion to the height above water than as 8·7 to 1. But a berg such as that recorded by Captain Clark, 500 feet high and three miles long, must have had only 1/8·7 of its total thickness above water. The same remark applies also to the one seen by Captain Smithers, which was 580 feet high, and so large that it was taken for an island. This berg must have been 5,628 feet in thickness. The enormous berg which came in collision with the Royal Standard must have been 5,820 feet thick. It is not stated what length the icebergs 730, 960, and 1,000 feet high respectively were; but supposing that we make considerable allowance for the possibility that the proportionate thickness of ice below water to that above may have been less than as 8·7 to 1, still we can hardly avoid the conclusion that the icebergs were considerably above a mile in thickness. But if there are icebergs above a mile in thickness, then there must be land-ice somewhere on the southern hemisphere of that thickness. In short, the great antarctic ice-cap must in some places be over a mile in thickness at its edge.
Inadequate Conceptions regarding the Magnitude of Continental Ice.—Few things have tended more to mislead geologists in the interpretation of glacial phenomena than inadequate conceptions regarding the magnitude of continental ice. Without the conception of continental ice the known facts connected with glaciation would be perfectly inexplicable. It was only when it was found that the accumulated facts refused to be explained by any other conception, that belief in the very existence of such a thing as continental ice became common. But although most geologists now admit the existence of continental ice, yet, nevertheless, adequate conceptions of its real magnitude are by no means so common. Year by year, as the outstanding facts connected with glaciation accumulate, we are compelled to extend our conceptions of the magnitude of land-ice. Take the following as an example. It was found that the transport of the Wastdale Crag blocks, the direction of the striæ on the islands of the Baltic, on Caithness and on the Orkney, Shetland, and Faroe, islands, the boulder clay with broken shells in Caithness, Holderness, and other places, were inexplicable on the theory of land-ice. But it was so only in consequence of the inadequacy of our conceptions of the magnitude of the ice; for a slight extension of our ideas of its thickness has explained not only these phenomena,[214] but others of an equally remarkable character, such as the striation of the Long Island and the submerged rock-basins around our coasts described by Mr. James Geikie. In like manner, if we admit the theory of the glacial epoch propounded in former chapters, all that is really necessary to account for the submergence of the land is a slight extension of our hitherto preconceived estimate of the thickness of the ice on the antarctic continent. If we simply admit a conclusion to which all physical considerations, as we have seen, necessarily lead us, viz., that the antarctic continent is covered with a mantle of ice at least two miles in thickness, we have then a complete explanation of the cause of the submergence of the land during the glacial epoch.
Although of no great importance to the question under consideration, it may be remarked that, except during the severest part of the glacial epoch, we have no reason to believe that the total quantity of ice on the globe was much greater than at present, only it would then be all on one hemisphere. Remove two miles of ice from the antarctic continent, and place it on the northern hemisphere, and this, along with the ice that now exists on this hemisphere, would equal, in all probability, the quantity existing on our hemisphere during the glacial epoch; at least, before it reached its maximum severity.
Chapter XXIV
THE PHYSICAL CAUSE OF THE SUBMERGENCE AND EMERGENCE OF THE LAND DURING THE GLACIAL EPOCH.—Continued.
Extent of Submergence from Displacement of Earth’s Centre of Gravity.—Circumstances which show that the Glacial Submergence resulted from Displacement of the Earth’s Centre of Gravity.—Agreement between Theory and observed Facts.—Sir Charles Lyell on submerged Areas during Tertiary Period.—Oscillations of Sea-level in Relation to Distribution.—Extent of Submergence on the Hypothesis that the Earth is fluid in the Interior.
Extent of Submergence from Displacement of Earth’s Centre of Gravity.—How much, then, would the transference of the two miles of ice from the southern to the northern hemisphere raise the level of the ocean on the latter hemisphere? This mass, be it observed, is equal to only one-half that represented in our section. A considerable amount of discussion has arisen in regard to the method of determining this point. According to the method already detailed, which supposes the rise at the pole to be equal to the extent of the displacement of the earth’s centre of gravity, the rise at the North Pole would be about 380 feet, taking into account the effect produced by the displaced water; and the rise in the latitude of Edinburgh would be 312 feet. The fall of level on the southern hemisphere would, of course, be equal to the rise of level on the northern. According to the method advanced by Mr. D. D. Heath,[215] the rise of level at the North Pole would be about 650 feet. Archdeacon Pratt’s method[216] makes the rise still greater; while according to Rev. O. Fisher’s method[217] the rise would be no less than 2,000 feet. There is, however, another circumstance which must be taken into account, which will give an additional rise of upwards of one hundred feet.
The greatest extent of the displacement of the earth’s centre of gravity, and consequently the greatest rise of the ocean resulting from that displacement, would of course occur at the time of maximum glaciation, when the ice was all on one hemisphere. But owing to the following circumstance, a still greater rise than that resulting from the displacement of the earth’s centre of gravity alone might take place at some considerable time, either before or after the period of maximum glaciation.
It is not at all probable that the ice would melt on the warm hemisphere at exactly the same rate as it would form on the cold hemisphere. It is probable that the ice would melt more rapidly on the warm hemisphere than it would form on the cold. Suppose that during the glacial epoch, at a time when the cold was gradually increasing on the northern and the warmth on the southern hemisphere, the ice should melt more rapidly off the antarctic continent than it was being formed on the arctic and subarctic regions; suppose also that, by the time a quantity of ice, equal to one-half what exists at present on the antarctic continent, had accumulated on the northern hemisphere, the whole of the antarctic ice had been melted away, the sea would then be fuller than at present by the amount of water resulting from the one mile of melted ice. The height to which this would raise the general level of the sea would be as follows:—
The antarctic ice-cap is equal in area to 1/23·46 of that covered by the ocean. The density of ice to that of water being taken at ·92 to 1, it follows that 25 feet 6 inches of ice melted off the cap would raise the general level of the ocean one foot, and the one mile of ice melted off would raise the level 200 feet. This 200 feet of rise resulting from the melted ice we must add to the rise resulting from the displacement of the earth’s centre of gravity. The removal of the two miles of ice from the antarctic continent would displace the centre of gravity 190 feet, and the formation of a mass of ice equal to the one-half of this on the arctic regions would carry the centre of gravity 95 feet farther; giving in all a total displacement of 285 feet, thus producing a rise of sea-level at the North Pole of 285 feet, and in the latitude of Edinburgh of 234 feet. Add to this the rise of 200 feet resulting from the melted ice, and we have then 485 feet of submergence at the pole, and 434 feet in the latitude of Edinburgh. A rise to a similar extent might probably take place after the period of maximum glaciation, when the ice would be melting on the northern hemisphere more rapidly than it would be forming on the southern.
If we assume the antarctic ice-cap to be as thick as is represented in the diagram, the extent of the submergence would of course be double the above, and we might have in this case a rise of sea-level in the latitude of Edinburgh to the extent of from 800 to 1,000 feet. But be this as it may, it is evident that the quantity of ice on the antarctic continent is perfectly sufficient to account for the submergence of the glacial epoch, for we have little evidence to conclude that the general submergence much exceeded 400 or 500 feet.[218] We have evidence in England and other places of submergence to the extent of from 1,000 to 2,000 feet, but these may be quite local, resulting from subsidence of the land in those particular areas. Elevations and depressions of the land have taken place in all ages, and no doubt during the glacial epoch also.
Circumstances which show that the Glacial Submergence resulted from Displacement of the Earth’s Centre of Gravity.—In favour of this view of the cause of the submergence of the glacial epoch, it is a circumstance of some significance, that in every part of the globe where glaciation has been found evidence of the submergence of the land has also been found along with it. The invariable occurrence of submergence along with glaciation points to some physical connection between the two. It would seem to imply, either that the two were the direct effects of a common cause, or that the one was the cause of the other; that is, the submergence the cause of the glaciation, or the glaciation the cause of the submergence. There is, I presume, no known cause to which the two can be directly related as effects. Nor do I think that there is any one who would suppose that the submergence of the land could have been the cause of its glaciation, even although he attributed all glacial effects to floating ice. The submergence of our country would, of course, have allowed floating ice to pass over it had there been any to pass over; but submergence would not have produced the ice, neither would it have brought the ice from the arctic regions where it already existed. But although submergence could not have been the cause of the glacial epoch, yet we can, as we have just seen, easily understand how the ice of the glacial epoch could have been the cause of the submergence. If the glacial epoch was brought about by an increase in the eccentricity of the earth’s orbit, then a submergence of the land as the ice accumulated was a physical necessity.
There is another circumstance connected with glacial submergence which it is difficult to reconcile with the idea that it resulted from a subsidence of the land. It is well known that during the glacial epoch the land was not once under water only, but several times; and, besides, there were not merely several periods when the land stood at a lower level in relation to the sea than at present, but there were also several periods when it stood at a much higher level than now. And this holds true, not merely of our own country, but of every country on the northern hemisphere where glaciation has yet been found. All this follows as a necessary consequence from the theory that the oscillations of sea-level resulted from the transference of the ice from the one hemisphere to the other; but it is wholly inconsistent with the idea that they resulted from upheavals and subsidence of the land during a very recent period.
But this is not all, there is more still to be accounted for. It has been the prevailing opinion that at the time when the land was covered with ice, it stood at a much greater elevation than at present. It is, however, not maintained that the facts of geology establish such a conclusion. The greater elevation of the land is simply assumed as an hypothesis to account for the cold.[219] The facts of geology, however, are fast establishing the opposite conclusion, viz., that when the country was covered with ice, the land stood in relation to the sea at a lower level than at present, and that the continental periods or times when the land stood in relation to the sea at a higher level than now were the warm inter-glacial periods, when the country was free of snow and ice, and a mild and equable condition of climate prevailed. This is the conclusion towards which we are being led by the more recent revelations of surface geology, and also by certain facts connected with the geographical distribution of plants and animals during the glacial epoch.
The simple occurrence of a rise and fall of the land in relation to the sea-level in one or in two countries during the glacial epoch, would not necessarily imply any physical connection. The coincidence of these movements with the glaciation of the land might have been purely accidental; but when we find that a succession of such movements occurred, not merely in one or in two countries, but in every glaciated country where proper observations have been made, we are forced to the conclusion that the connection between the two is not accidental, but the result of some fixed cause.
If we admit that an increase in the eccentricity of the earth’s orbit was the cause of the glacial epoch, then we must admit that all those results followed as necessary consequences. For if the glacial epoch lasted for upwards of one hundred thousand years or so, there would be a succession of cold and warm periods, and consequently a succession of elevations and depressions of sea-level. And the elevations of the sea-level would take place during the cold periods, and the depressions during the warm periods.
But the agreement between theory and observed facts does not terminate here. It follows from theory that the greatest oscillations of sea-level would take place during the severest part of the glacial epoch, when the eccentricity of the earth’s orbit would be at its highest value, and that the oscillations would gradually diminish in extent as the eccentricity diminished and the climate gradually became less severe. Now it is well known that this is actually what took place; the great submergence, as well as the great elevation or continental period, occurred during the earlier or more severe part of the glacial epoch, and as the climate grew less severe these changes became of less extent, till we find them terminating in our submerged forests and 25-foot raised beach.
It follows, therefore, according to the theory advanced, that the mere fact of an area having been under sea does not imply that there has been any subsidence or elevation of the land, and that consequently the inference which has been drawn from these submerged areas as to changes in physical geography may be in many cases not well founded.
Sir Charles Lyell, in his “Principles,” publishes a map showing the extent of surface in Europe which has been covered by the sea since the earlier part of the Tertiary period. This map is intended to show the extraordinary amount of subsidence and elevation of the land which has taken place during that period. It is necessary for Sir Charles’s theory of the cause of the glacial epoch that changes in the physical geography of the globe to an enormous extent should have taken place during a very recent period, in order to account for the great change of climate which occurred at that epoch. But if the foregoing results be anything like correct, it does not necessarily follow that there must have been great changes in the physical geography of Europe, simply because the sea covered those areas marked in the map, for this may have been produced by oscillations of sea-level, and not by changes in the land. In fact, the areas marked in Sir Charles’s map as having been covered by the sea, are just those which would be covered were the sea-level raised a few hundred feet. No doubt there were elevations and subsidences in many of the areas marked in the map during the Tertiary period, and to this cause a considerable amount of the submergence might be due; but I have little doubt that by far the greater part must be attributed to oscillations of sea-level. It is no objection that the greater part of the shells and other organic remains found in the marine deposits of those areas are not indicative of a cold or glacial condition of climate, for, as we have seen, the greatest submergence would probably have taken place either before the more severe cold had set in or after it had to a great extent passed away. That the submergence of those areas probably resulted from elevations of sea-level rather than depressions of the land, is further evident from the following considerations. If we suppose that the climate of the glacial epoch was brought about mainly by changes in the physical geography of the globe, we must assume that these great changes took place, geologically speaking, at a very recent date. Then when we ask what ground is there for assuming that any such change in the relations of sea and land as is required actually took place, the submergence of those areas is adduced as the proof. Did it follow as a physical necessity that all submergence must be the result of subsidence of the land, and not of elevations of the sea, there would be some force in the reasons adduced. But such a conclusion by no means follows, and, à priori, it is just as likely that the appearance of the ice was the cause of the submergence as that the submergence was the cause of the appearance of the ice. Again, a subsidence of the land to the extent required would to a great extent have altered the configuration of the country, and the main river systems of Europe; but there is no evidence that any such change has taken place. All the main valleys are well known to have existed prior to the glacial epoch, and our rivers to have occupied the same channels then as they do now. In the case of some of the smaller streams, it is true, a slight deviation has resulted at some points from the filling up of their channels with drift during the glacial epoch; but as a general rule all the principal valleys and river systems are older than the glacial epoch. This, of course, could not be the case if a subsidence of the land sufficiently great to account for the submergence of the areas in question, or changes in the physical geography of Europe necessary to produce a glacial epoch, had actually taken place. The total absence of any geological evidence for the existence of any change which could explain either the submergence of the areas in question or the climate of the glacial epoch, is strong evidence that the submergence of the glacial epoch, as well as of the areas in question, was the result of a simple oscillation of sea-level resulting from the displacement of the earth’s centre of gravity by the transferrence of the ice-cap from the southern to the northern hemisphere.
Oscillations of Sea-level in relation to Distribution.—The oscillations of sea-level resulting from the displacement of the earth’s centre of gravity help to throw new light on some obscure points connected with the subject of the geographical distribution of plants and animals. At the time when the ice was on the southern hemisphere during the glacial epoch, and the northern hemisphere was enjoying a warm and equable climate, the sea-level would be several hundred feet lower than at present, the North Sea would probably be dry land, and Great Britain and Ireland joined to the continent, thus opening up a pathway from the continent to our island. As has been shown in former chapters, during the inter-glacial periods the climate would be much warmer and more equable than now, so that animals from the south, such as the hippopotamus, hyæna, lion, Elephas antiquus and Rhinoceros megarhinus, would migrate into this country, where at present they could not live in consequence of the cold. We have therefore an explanation, as was suggested on a former occasion,[220] of the fact that the bones of these animals are found mingled in the same grave with those of the musk-ox, mammoth, reindeer, and other animals which lived in this country during the cold periods of the glacial epoch; the animals from the north would cross over into this country upon the frozen sea during the cold periods, while those from the south would find the English Channel dry land during the warm periods.
The same reasoning will hold equally true in reference to the old and new world. The depth of Behring Straits is under 30 fathoms; consequently a lowering of the sea-level of less than 200 feet would connect Asia with America, and thus allow plants and animals, as Mr. Darwin believes, to pass from the one continent to the other.[221] During this period, when Behring Straits would be dry land, Greenland would be comparatively free from ice, and the arctic regions enjoying a comparatively mild climate. In this case plants and animals belonging to temperate regions could avail themselves of this passage, and thus we can explain how plants belonging to temperate regions may have, during the Miocene period, passed from the old to the new continent, and vice versâ.
As has already been noticed, during the time of the greatest extension of the ice, the quantity of ice on the southern hemisphere might be considerably greater than what exists on the entire globe at present. In that case there might, in addition to the lowering of the sea-level resulting from the displacement of the earth’s centre of gravity, be a considerable lowering resulting from the draining of the ocean to form the additional ice. This decrease and increase in the total quantity of ice which we have considered would affect the level of the ocean as much at the equator as at the poles; consequently during the glacial epoch there might have been at the equator elevations and depressions of sea-level to the extent of a few hundred feet.
Extent of Submergence on the Hypothesis that the Earth is fluid in the Interior.—But we have been proceeding upon the supposition that the earth is solid to its centre. If we assume, however, what is the general opinion among geologists, that it consists of a fluid interior surrounded by a thick and rigid crust or shell, then the extent of the submergence resulting from the displacement of the centre of gravity for a given thickness of ice must be much greater than I have estimated it to be. This is evident, because, if the interior of the globe be in a fluid state, it, in all probability, consists of materials differing in density. The densest materials will be at the centre, and the least dense at the outside or surface. Now the transferrence of an ice-cap from the one pole to the other will not merely displace the ocean—the fluid mass on the outside of the shell—but it will also displace the heavier fluid materials in the interior of the shell. In other words, the heavier materials will be attracted by the ice-cap more forcibly than the lighter, consequently they will approach towards the cap to a certain extent, sinking, as it were, into the lighter materials, and displacing them towards the opposite pole. This displacement will of course tend to shift the earth’s centre of gravity in the direction of the ice-cap, because the heavier materials are shifted in this direction, and the lighter materials in the opposite direction. This process will perhaps be better understood from the following figures.
In Fig. 8, where there is no ice-cap, the centre of gravity of the earth coincides with the centre of the concentric layers of the fluid interior. In Fig. 9, where there is an ice-cap placed on one pole, the concentric layer F^1 being denser than layer F, is attracted towards the cap more forcibly than F, and consequently sinks to a certain depth in F. Again, F^2 being denser than F^1, it also sinks to a certain extent in F^1. And again F^3, the mass at the centre, being denser than F^2, it also sinks in F^2. All this being combined with the effects of the ice-cap, and the displaced ocean outside the shell, the centre of gravity of the entire globe will no longer be at C, but at C^1, a considerable distance nearer to the side of the shell on which the cap rests than C, and also a considerable distance nearer than it would have been had the interior of the globe been solid. There are here three causes tending to shift the centre of gravity, (1) the ice-cap, (2) the displaced ocean, and (3) the displaced materials in the interior. Two of the three causes mutually react on each other in such a way as to increase each other’s effect. Thus the more the ocean is drawn in the direction of the ice-cap, the more effect it has in drawing the heavier materials in the interior in the same direction; and in turn the more the heavier materials in the interior are drawn towards the cap, the greater is the displacement of the earth’s centre of gravity, and of course, as a consequence, the greater is the displacement of the ocean. It may be observed also that, other things being equal, the thinner the solid crust or shell is, and the greater the difference in the density of the fluid materials in the interior, the greater will be the extent of the displacement of the ocean, because the greater will be the displacement of the centre of gravity.
It follows that if we knew (1) the extent of the general submergence of the glacial epoch, and (2) the present amount of ice on the southern hemisphere, we could determine whether or not the earth is fluid in the interior.
Chapter XXV
THE INFLUENCE OF THE OBLIQUITY OF THE ECLIPTIC ON CLIMATE AND ON THE LEVEL OF THE SEA.
The direct Effect of Change of Obliquity on Climate.—Mr. Stockwell on the maximum Change of Obliquity.—How Obliquity affects the Distribution of Heat over the Globe.—Increase of Obliquity diminishes the Heat at the Equator and increases that at the Poles.—Influence of Change of Obliquity on the Level of the Sea.—When the Obliquity was last at its superior Limit.—Probable Date of the 25-foot raised Beach.—Probable Extent of Rise of Sea-level resulting from Increase of Obliquity.—Lieutenant-Colonel Drayson’s and Mr. Belt’s Theories.—Sir Charles Lyell on Influence of Obliquity.
The direct Effect of Change in the Obliquity of the Ecliptic on Climate.—There is still another cause which, I feel convinced, must to a very considerable extent have affected climate during past geological ages. I refer to the change in the obliquity of the ecliptic. This cause has long engaged the attention of geologists and physicists, and the conclusion generally come to is that no great effect can be attributed to it. After giving special attention to the matter, I have been led to the very opposite conclusion. It is quite true, as has been urged, that the changes in the obliquity of the ecliptic cannot sensibly affect the climate of temperate regions; but it will produce a slight change on the climate of tropical latitudes, and a very considerable effect on that of the polar regions, especially at the poles themselves. We shall now consider the matter briefly.
It was found by Laplace that the obliquity of the ecliptic will oscillate to the extent of 1° 22′ 34″ on each side of 23° 28′, the obliquity in the year 1801.[222] This point has lately been examined by Mr. Stockwell, and the results at which he has arrived are almost identical with those of Laplace. “The mean value of the obliquity,” he says, “of both the apparent and fixed ecliptics to the equator is 23° 17′ 17″. The limits of the obliquity of the apparent ecliptic to the equator are 24° 35′ 58″ and 21° 58′ 36″; whence it follows that the greatest and least declinations of the sun at the solstices can never differ from each other to any greater extent than 2° 37′ 22″.”[223]
This change will but slightly affect the climate of the temperate regions, but it will exercise a very considerable influence on the climate of the polar regions. According to Mr. Meech,[224] if 365·24 thermal days represent the present total annual quantity of heat received at the equator from the sun, 151·59 thermal days will represent the quantity received at the poles. Adopting his method of calculation, it turns out that when the obliquity of the ecliptic is at the maximum assigned by Laplace the quantity received at the equator would be 363·51 thermal days, and at the poles 160·04 thermal days. The equator would therefore receive 1·73 thermal days less heat, and the poles 8·45 thermal days more heat than at present.
ANNUAL AMOUNT OF SUN’S HEAT.
+-------------------+-------------+-----------+ | Amount in 1801. | Amount at | | | Obliquity 23° 28′.| maximum, |Difference.| | | 24° 50′ 34“.| | +---------+---------+-------------+-----------+ |Latitude.| Thermal | Thermal | Thermal | | | days. | days. | days. | | 0 | 365·24 | 363·51 | −1·73 | | 40 | 288·55 | 288·32 | −0·23 | | 70 | 173·04 | 179·14 | +6·10 | | 80 | 156·63 | 164·63 | +8·00 | | 90 | 151·59 | 160·04 | +8·45 | +---------+---------+-------------+-----------+
When the obliquity was at a maximum, the poles would therefore be receiving 19 rays for every 18 they are receiving at present. The poles would then be receiving nearly as much heat as latitude 76° is receiving at present.
The increase of obliquity would not sensibly affect the polar winter. It is true that it would slightly increase the breadth of the frigid zone, but the length of the winter at the poles would remain unaffected. After the sun disappears below the horizon his rays are completely cut off, so that a further descent of 1° 22′ 34″ would make no material difference in the climate. In the temperate regions, the sun’s altitude at the winter solstice would be 1° 22′ 34″ less than at present. This would slightly increase the cold of winter in those regions. But the increase in the amount of heat received by the polar regions would materially affect the condition of the polar summer. What, then, is the rise of temperature at the poles which would result from the increase of 8·45 thermal days in the total amount received from the sun?
An increase of 8·45 thermal days, or 1/18th of the total quantity received from the sun, according to the mode of calculation adopted in Chap. II. would produce, all other things being equal, a rise in the mean annual temperature equal to 14° or 15°.
According to Professor Dove[225] there is a difference of 7°·6 between the mean annual temperature of latitude 76° and the pole; the temperature of the former being 9°·8, and that of the latter 2°·2. Since it follows that when the obliquity of the ecliptic is at a maximum the poles would receive about as much heat per annum as latitude 76° receives at present, it may be supposed that the temperature of the poles at that period ought to be no higher than that of latitude 76° at the present time. A little consideration will, however, show that this by no means follows. Professor Dove’s Tables represent correctly the mean annual temperature corresponding to every tenth degree of latitude from the equator to the pole. But it must be observed that the rate at which the temperature diminishes from the equator to the pole is not proportionate to the decrease in the total quantity of heat received from the sun as we pass from the equator to the pole. Were the mean annual temperature of the various latitudes proportionate to the amount of direct heat received, the equator would be much warmer than it actually is at present, and the poles much colder. The reason of this, as has been shown in Chapter II., is perfectly obvious. There is a constant transferrence of heat from the equator to the poles, and of cold from the poles to the equator. The warm water of the equator is constantly flowing towards the poles, and the cold water at the poles is constantly flowing to the equator. The same is the case in regard to the aërial currents. Consequently a great portion of the direct heat of the sun goes, not to raise the temperature of the equator, but to heat the poles. And, on the other hand, the cold materials at the poles are transferred to the equator, and thus lower the temperature of that part of the globe to a great extent. The present difference of temperature between lat. 76° and the pole, determined according to the rate at which the temperature is found to diminish between the equator and the pole, amounts to only about 7° or 8°. But were there no mutual transferrence of warm and cold materials between the equatorial and polar regions, and were the temperature of each latitude to depend solely upon the direct rays of the sun, the difference would far exceed that amount.
Now, when the obliquity of the ecliptic was at its superior limit, and the poles receiving about 1/18th more direct heat from the sun than at present, the increase of temperature due to this increase of heat would be far more than 7° or 8. It would probably be nearly double that amount.
“We may, therefore, conclude that when the obliquity of the ecliptic was at a maximum, and the poles were receiving 1/18th more heat than at present, the temperature of the poles ought to have been about 14° or 15° warmer than at the present day, provided, of course, that this extra heat was employed wholly in raising the temperature. Were the polar regions free from snow and ice, the greater portion of the extra heat would go to raise the temperature. But as those regions are covered with snow and ice, the extra heat would have no effect in raising the temperature, but would simply melt the snow and ice. The ice-covered surface upon which the rays fell could never rise above 32°. At the period under consideration, the total annual quantity of ice melted at the poles would be 1/18th more than at present.
The general effect which the change in the obliquity of the ecliptic would have upon the climate of the polar regions when combined with the effects resulting from the eccentricity of the earth’s orbit, would be this:—When the eccentricity was at a very high value, the hemisphere whose winter occurred in the aphelion (for physical reasons, which have already been discussed)[226] would be under a condition of glaciation, while the other hemisphere, having its winter in perihelion, would be enjoying a warm and equable climate. When the obliquity of the ecliptic was at a maximum, and 1/18th more heat falling at the poles than at present, the effect would be to modify to a great extent the rigour of the glaciation in the polar zone of the hemisphere under a glacial condition, and, on the other hand, to produce a more rapid melting of the ice on the other hemisphere enjoying the equable climate. The effects of eccentricity and obliquity thus combined would probably completely remove the polar ice-cap from off the latter hemisphere, and forest trees might then grow at the pole. Again, when the obliquity was at its minimum condition and less heat reaching the poles than at present, the glaciation of the former hemisphere would be increased and the warmth of the latter diminished.
The Influence of Change in the Obliquity of the Ecliptic on the Level of the Sea.—One very remarkable effect which seems to result indirectly from a variation of the obliquity under certain conditions, is an influence on the level of the sea. As this probably may have had something to do with those recent changes of sea-level with which the history of the submarine forests and raised beaches have made us all so familiar, it may be of interest to enter at some length into this part of this subject.
It appears almost certain that at the time when the northern winter solstice was in the aphelion last, a rise of the sea on the northern hemisphere to a considerable number of feet must have taken place from the combined effect of eccentricity and obliquity. About 11,700 years ago, the northern winter solstice was in the aphelion. The eccentricity at that time was ·0187, being somewhat greater than it is now; but the winters occurring in aphelion instead of, as now, in perihelion, they would on that account be probably 10° or 15° colder than they are at the present day. It is probable, also, for reasons stated in a previous chapter, that the Gulf-stream at that time would be considerably less than now. This would tend to lower the temperature to a still greater extent. As snow instead of rain must have fallen during winter to a greater extent than at present, this no doubt must have produced a slight increase in the quantity of ice on the northern hemisphere had no other cause come into operation. But the condition of things, we have every reason to believe, must have been affected by the greater obliquity of the ecliptic at that period. We have no formula, except, perhaps, that given by Mr. Stockwell, from which to determine with perfect accuracy the extent of the obliquity at a period so remote as the one under consideration. If we adopt the formula given by Struve and Peters, which agrees pretty nearly with that obtained from Mr. Stockwell’s formula, we have the obliquity at a maximum about the time that the solstice-point was in the aphelion. The formula given by Leverrier places the maximum somewhat later. At all events, we cannot be far from the truth in assuming that at the time the northern winter solstice was in the aphelion, the obliquity of the ecliptic would be about a maximum, and that since then it has been gradually diminishing. It is evident, then, that the annual amount of heat received by the arctic regions, and especially about the pole, would be considerably greater than at present. And as the heat received on those regions is chiefly employed in melting the ice, it is probable that the extra amount of ice which would then be melted in the arctic regions would prevent that slight increase of ice which would otherwise have resulted in consequence of the winter occurring in the aphelion. The winters at that period would be colder than they are at present, but the total quantity of ice on the northern hemisphere would not probably be greater.
Let us now turn to the southern hemisphere. As the southern winter would then occur in the perihelion, this would tend to produce a slight decrease in the quantity of ice on the southern hemisphere. But on this hemisphere the effects of eccentricity would not, as on the northern hemisphere, be compensated by those of obliquity; for both causes would here tend to produce the same effect; namely, a melting of the ice in the antarctic regions.
It is probable that at this time the quantity of warm water flowing from the equatorial regions into the Southern Ocean would be much greater than at present. This would tend to raise the temperature of the air of the antarctic regions, and thus assist in melting the ice. These causes, combined with the great increase of heat resulting from the change of obliquity, would tend to diminish to a considerable extent the quantity of ice on the southern hemisphere. I think we may assume that the slight increase of eccentricity at that period, the occurrence of the southern winter in perihelion, and the extra quantity of warm water flowing from the equatorial to the antarctic regions, would produce an effect on the south polar ice-cap equal to that produced by the increase in the obliquity of the ecliptic. It would, therefore, follow that for every eighteen pounds of ice melted annually at present at the south pole twenty pounds would then be melted.
Let us now consider the effect that this condition of things would have upon the level of the sea. It would evidently tend to produce an elevation of the sea-level on the northern hemisphere in two ways. 1st. The addition to the sea occasioned by the melting of the ice from off the antarctic land would tend to raise the general level of the sea. 2ndly. The removal of the ice would also tend to shift the earth’s centre of gravity to the north of its present position—and as the sea must shift along with the centre, a rise of the sea on the northern hemisphere would necessarily take place.
The question naturally suggests itself, might not the last rise of the sea, relative to the land, have resulted from this cause? We know that during the period of the 25-foot beach, the time when the estuarine mud, which now forms the rich soil of the Carses of the Forth and Tay, was deposited, the sea, in relation to the land, stood at least 20 or 30 feet higher than at present. But immediately prior to this period, we have the age of the submarine forests and peat-beds, when the sea relative to the land stood lower than it does now. We know also that these changes of level were not mere local affairs. There seems every reason to believe that our Carse clay, as Mr. Fisher states, is the equivalent of the marine mud, with Scrobicularia, which covers the submarine forests of England.[227] And on the other hand, those submarine forests are not confined to one locality. “They may be traced,” says Mr. Jamieson, “round the whole of Britain and Ireland, from Orkney to Cornwall, from Mayo to the shores of Fife, and even, it would seem, along a great part of the western sea-board of Europe, as if they bore witness to a period of widespread elevation, when Ireland and Britain, with all its numerous islands, formed one mass of dry land, united to the continent, and stretching out into the Atlantic.”[228] “These submarine forests”“ remarks De la Beche, also, “are to be found under the same general condition from the shores of Scandinavia to those of Spain and Portugal, and around the British islands.”[229] Those buried forests are not confined to Europe, but are found in the valley of the Mississippi and in Nova Scotia, and other parts of North America. And again, the strata which underlie those forests and peat-beds bear witness to the fact of a previous elevation of the sea-level. In short, we have evidence of a number of oscillations of sea-level during post-tertiary times.[230]
Had there been only one rise of the land relative to the sea-level, or one depression, it might quite reasonably, as already remarked, have been attributed to an upheaval or a sinking of the ground, occasioned by some volcanic, chemical, or other agency. But certainly those repeated oscillations of sea-level, extending as they do over so wide an area, look more like a rising and sinking of the sea than of the land. But, be this as it may, since it is now established, I presume, beyond controversy, that the old notion that the general level of the sea remains permanent, and that the changes must be all attributed to the land is wholly incorrect, and that the sea, as well as the land, is subject to changes of level, it is certainly quite legitimate to consider whether the last elevation of the sea-level relatively to the land may not have resulted from the rising of the sea rather than from the sinking of the land, in short, whether it may not be attributed to the cause we are now considering. The fact that those raised beaches and terraces are found at so many different heights, and also so discontinuously along our coasts, might be urged as an objection to the opinion that they were due to changes in the level of the sea itself. Space will not permit me to enter upon the discussion of this point at present; but it may be stated that this objection is more apparent than real. It by no means follows that beaches of the same age must be at the same level. This has been shown very clearly by Mr. W. Pengelly in a paper on “Raised Beaches,” read before the British Association at Nottingham, 1866.
We have, as I think, evidence amounting to almost absolute certainty that 11,700 years ago the general sea-level on the northern hemisphere must have been higher than at present. And in order to determine the question of the 25-foot beach, we have merely to consider whether a rise to something like this extent probably took place at the period in question. We have at present no means of determining the exact extent of the rise which must have taken place at that period, for we cannot tell what quantity of ice was then melted off the antarctic regions. But we have the means of making a very rough estimate, which, at least, may enable us to determine whether a rise of some 20 or 30 feet may not possibly have taken place.
If we assume that the southern ice-cap extends on an average down to lat. 70°, we shall have an area equal to 1/33·163 of the entire surface of the globe. The proportion of land to that of water, taking into account the antarctic continent, is as 526 to 1272. The southern ice-cap will therefore be equal to 1/23·46 of the area covered by water. The density of ice to that of water being taken at ·92 to 1, it follows that 25 feet 6 inches of ice melted from off the face of the antarctic continent would raise the level of the ocean one foot. If 470 feet were melted off—and this is by no means an extravagant supposition, when we reflect that for every 18 pounds of ice presently melted an additional pound or two pounds, or perhaps more, would then be melted, and that for many ages in succession—the water thus produced from the melted ice would raise the level of the sea 18 feet 5 inches. The removal of the 470 feet of solid ice— which must be but a very small fraction of the total quantity of ice lying upon the antarctic continent—would shift the earth’s centre of gravity about 7 feet to the north of its present position. The shifting of the centre of gravity would cause the sea to sink on the southern hemisphere and rise on the northern. And the quantity of water thus transferred from the southern hemisphere to the northern would carry the centre of gravity about one foot further, and thus give a total displacement of the centre to the extent of about 8 feet. The sea would therefore rise about 8 feet at the North Pole, and in the latitude of Edinburgh about 6 feet 7 inches. This, added to the rise of 18 feet 5 inches, occasioned by the melting of the ice, would give 25 feet as the total rise in the latitude of Scotland 11,700 years ago.
Each square foot of surface at the poles 11,700 years ago would be receiving 18,223,100 foot-pounds more of heat annually than at present. If we deduct 22 per cent. as the amount absorbed in passing through the atmosphere, we have 14,214,000 foot-pounds. This would be sufficient to melt 2·26 feet of ice. But if 50, instead of 22, per cent. were cut off, 1·45 cubic feet would be melted. In this case the 470 feet of ice would be melted, independently of the effects of eccentricity, in about 320 years. And supposing that only one-fourth part of the extra heat reached the ground, 470 feet of ice would be removed in about 640 years.
As to the exact time that the obliquity was at a maximum, previous to that of 11,700 years ago, our uncertainty is still greater. If we are permitted to assume that the ecliptic passes from its maximum to its minimum state and back to its maximum again with anything like uniformity, at the rate assigned by Leverrier and others, the obliquity would not be far from a maximum about 60,000 years ago. Taking the rate of precession at 50″·21129, and assuming it to be uniform—which it probably is not—the winter solstice would be in the aphelion about 61,300 years ago.[231] In short, it seems not at all improbable that at the time the solstice-point was in the aphelion, the obliquity of the ecliptic would not be far from its maximum state. But at that time the value of the eccentricity was 0·023, instead of 0·0187, its value at the last period. Consequently the rise of the sea would probably be somewhat greater than it was 11,700 years ago. Might not this be the period of the 40-foot beach? In this case 11,000 or 12,000 years would be the age of the 25-foot beach, and 60,000 years the age of the 40-foot beach.
About 22,000 years ago, the winter solstice was in the perihelion, and as the eccentricity was then somewhat greater than it is at present, the winters would be a little warmer and the climate more equable than it is at the present day. This perhaps might be the period of the submarine forests and lower peat-beds which underlie the Carse clays, Scrobicularia mud, and other deposits belonging to the age of the 25-foot beach. At any rate, it is perfectly certain that a condition of climate at this period prevailed exceedingly favourable to the growth of peat. It follows also that at this time, owing to a greater accumulation of ice on the southern hemisphere, the sea-level would be a few feet lower than at present, and that forests and peat may have then grown on places which are now under the sea-level.
For a few thousand years before and after 11,700 years ago, when the winter solstice was evidently not far from the aphelion, and the sea standing considerably above its present level, would probably, as we have already stated, be the time when the Carse clays and other recent deposits lying above the present level of the river were formed. And it is also a singular fact that the condition of things at that period must have been exceedingly favourable to the formation of such estuarine deposits; for at that time the winter temperature of our island, as has been already shown, would be considerably lower than at present, and, consequently, during that season, snow, to a much larger extent than now, would fall instead of rain. The melting of the winter’s accumulation of snow on the approach of summer would necessarily produce great floods, similar to what occur in the northern parts of Asia and America at the present day from this very same cause. The loose upper soil would be carried down by those floods and deposited in the estuaries of our rivers.
The foregoing is a rough and imperfect sketch of the history of the climate and the physical conditions of our globe for the past 60,000 years, in so far as physical and cosmical considerations seem to afford us information on the subject, and its striking agreement with that derived from geological sources is an additional evidence in favour of the opinion that geological and cosmical phenomena are physically related by a bond of causation.
Lieutenant-Colonel Drayson’s Theory of the Cause of the Glacial Epoch.—In a paper read before the Geological Society by Lieutenant-Colonel Drayson, R.A., on the 22nd February, 1871,[232] that author states, that after calculating from the recorded positions of the pole of the heavens during the last 2,000 years, he finds the pole of the ecliptic is not the centre of the circle traced by the pole of the heavens. The pole of the heavens, he considers, describes a circle round a point 6° distant from the pole of the ecliptic and 29° 25′ 47″ from the pole of the heavens, and that about 13,700 years b.c. the angular distance of the two poles was 35° 25′ 47″. This would bring the Arctic Circle down to latitude 54° 34′ 13″ N. I fear that this is a conclusion that will not be generally accepted by those familiar with celestial mechanics. But, be this as it may, my present object is not to discuss the astronomical part of Colonel Drayson’s theory, but to consider whether the conclusions which he deduces from his theory in regard to the cause of the glacial epoch be legitimate or not. Assuming for argument’s sake that the obliquity of the ecliptic can possibly reach to 35° or 36°, so as to bring the Arctic Circle down to the centre of England, would this account for the glacial epoch? Colonel Drayson concludes that the shifting of the Arctic Circle down to the latitude of England would induce here a condition of climate similar to that which obtains in arctic regions. This seems to be the radical error of the theory. It is perfectly true that were the Arctic Circle brought down to latitude 54° 35′ part of our island would be in the arctic regions, but it does not on that account follow that our island would be subjected to an arctic climate.
The polar regions owe their cold not to the obliquity of the ecliptic, but to their distance from the equator. Indeed were it not for obliquity those regions would be much colder than they really are, and an increase of obliquity, instead of increasing their cold, would really make them warmer. The general effect of obliquity, as we have seen, is to diminish the amount of heat received in equatorial and tropical regions, and to increase it in the polar and temperate regions. The greater the obliquity, and, consequently, the farther the sun recedes from the equator, the smaller is the quantity of heat received by equatorial regions, and the greater the amount bestowed on polar and temperate regions. If, for example, we represent the present amount of heat received from the sun at the equator on a given surface at 100 parts, 42·47 parts will then represent the amount received at the poles on the same given surface. But were the obliquity increased to 35° the amount received at the equator would be reduced to 94·93 parts, and that at the poles increased to 59·81; being an increase at the poles of nearly one half. At latitude 60° the present quantity is equal to 57 parts; but about 63 parts would be received were the obliquity increased to 35°. It therefore follows that although the Arctic Circle were brought down to the latitude of London so that the British islands would become a part of the arctic regions, the mean temperature of these islands would not be lowered, but the reverse. The winters would no doubt be colder than they are at present, but the cold of winter would be far more than compensated for by the heat of summer. It is not a fair representation of the state of things, merely to say that an increase of obliquity tends to make the winters colder and the summers hotter, for it affects the summer heat far more than it does the winter cold. And the greater the obliquity the more does the increase of heat during summer exceed the decrease during winter. This is obvious because the greater the obliquity the greater the total annual amount of heat received.
If an increase of obliquity tended to produce an increase of ice in temperate and polar regions, and thus to lead to a glacial epoch, then the greater the obliquity the greater would be the tendency to produce such an effect. Conceive, then, the obliquity to go on increasing until it ultimately reached its absolute limit, 90°, and the earth’s axis to coincide with the plane of the ecliptic. The Arctic Circle would then extend to the equator. Would this produce a glacial epoch? Certainly not. A square foot of surface at the poles would then be receiving as much heat per annum as a square foot at the equator at present, supposing the sun remained on the equator during the entire year. Less heat, however, would be reaching the equatorial regions than now. At present, as we have just seen, the annual quantity of heat received at either pole is to that received at the equator as 42·47 to 100; but at the period under consideration the poles would be actually obtaining one-half more heat than the equator. The amount received per square foot at the poles, to that received per square foot at the equator, would be in the ratio of half the circumference of a circle to its diameter, or as 1·5708 to 1. But merely to say that the poles would be receiving more heat per annum than the equator is at present, does not convey a correct idea of the excessive heat which the poles would then have to endure; for it must be borne in mind that the heat reaching the equator is spread over the whole year, whereas the poles would get their total amount during the six months of their summer. Consequently, for six months in the year the poles would be obtaining far more than double the quantity of heat received at present by the equator during the same length of time, and more than three times the quantity then received by the equator. The amount reaching the pole during the six months to that reaching the equator would be as 3·1416 to 1.
At the equator twelve hours’ darkness alternates with twelve hours’ sunshine, and this prevents the temperature from rising excessively high; but at the poles it would be continuous sunshine for six months without the ground having an opportunity of cooling for a single hour. At the summer solstice, when the sun would be in the zenith of the pole, the amount of heat received there every twenty-four hours would actually be nearly three-and-a-quarter times greater than that presently received at the equator. Now what holds true with regard to the poles would hold equally true, though to a lesser extent, of polar and temperate regions. We can form but a very inadequate idea of the condition of things which would result from such an enormous increase of heat. Nothing living on the face of the globe could exist in polar regions under so fearful a temperature as would then prevail during summer months. How absurd would it be to suppose that this condition of things would tend to produce a glacial epoch! Not only would every particle of ice in polar regions be dissipated, but the very seas around the pole would be, for several months in the year, at the boiling point.
If it could be shown from physical principles—which, to say the least, is highly improbable—that the obliquity of the ecliptic could ever have been as great as 35°, it would to a very considerable extent account for the comparative absence of ice in Greenland and other regions in high latitudes, such as we know was the case during the Carboniferous, Miocene, and other periods. But although a great increase of obliquity might cause a melting of the ice, yet it could not produce that mild condition of climate which we know prevailed in high latitudes during those periods; while no increase of obliquity, however great, could in any way tend to produce a glacial epoch.
Colonel Drayson, however, seems to admit that this great increase of obliquity would make our summers much warmer than they are at present. How, then, according to his theory, is the glacial epoch accounted for? The following is the author’s explanation as stated in his own words:—
“At the date 13,700 B.C. the same conditions appear to have prevailed down to about 54° of latitude during winter as regards the sun being only a few degrees above the horizon. We are, then, warranted in concluding that the same climate prevailed down to 54° of latitude as now exists in winter down to 67° of latitude.
“Thus in the greater part of England and Wales, and in the whole of Scotland, icebergs of large size would be formed each winter; every river and stream would be frozen and blocked with ice, the whole country would be covered with a mantle of snow and ice, and those creatures which could neither migrate nor endure the cold of an arctic climate would be exterminated.”—“The Last Glacial Epoch,” p. 146.
“At the summer solstice the midday altitude of the sun for the latitude 54° would be about 71½°, an altitude equal to that which the sun now attains in the south of Italy, the south of Spain, and in all localities having a latitude of about 40°.”
“There would, however, be this singular difference from present conditions, that in latitude 54° the sun at the period of the summer solstice would remain the whole twenty-four hours above the horizon; a fact which would give extreme heat to those very regions which, six months previously, had been subjected to an arctic cold. Not only would this greatly increased heat prevail in the latitude of 54°, but the sun’s altitude would be 12° greater at midday in midsummer, and also 12° greater at midnight in high northern latitudes, than it ever attains now; consequently the heat would be far greater than at present, and high northern regions, even around the pole itself, would be subjected to a heat during summer far greater than any which now ever exists in those localities. The natural consequence would be, that the icebergs and ice which had during the severe winter accumulated in high latitudes would be rapidly thawed by this heat” (p. 148).
“Each winter the whole northern and southern hemispheres would be one mass of ice; each summer nearly the whole of the ice of each hemisphere would be melted and dispersed” (p. 150).
According to this theory, not only is the whole country covered each winter with a continuous mass of ice, but large icebergs are formed during that short season, and when the summer heat sets in all is melted away. Here we have a misapprehension not only as to the actual condition of things during the glacial epoch, but even as to the way in which icebergs and land-ice are formed. Icebergs are formed from land-ice, but land-ice is not formed during a single winter, much less a mass of sufficient thickness to produce icebergs. Land-ice of this thickness requires the accumulated snows of centuries for its production. All that we could really have, according to this theory, would be a thick covering of snow during winter, which would entirely disappear during summer, so that there could be no land-ice.
Mr. Thomas Belt’s Theory.—The theory that the glacial epoch resulted from a great increase in the obliquity of the ecliptic has recently been advocated by Mr. Thomas Belt.[233] His conceptions on the subject, however, appear to me to be even more irreconcilable with physics than those we have been considering. Lieutenant-Colonel Drayson admits that the increase of heat to polar regions resulting from the great increase of obliquity would dissipate the ice there, but Mr. Belt does not even admit that an increase of obliquity would bring with it an increase of heat, far less that it would melt the polar ice. On the contrary, he maintains that the tendency of obliquity is to increase the rigour of polar climate, and that this is the reason “that now around the poles some lands are being glaciated, for excepting for that obliquity snow and ice would not accumulate, excepting on mountain chains.” “Thus,” he says, “there exist glacial conditions at present around the poles, due primarily to the obliquity of the ecliptic.” And he also maintains that if there were no obliquity and the earth’s axis were perpendicular to the plane of its orbit, an eternal “spring would reign around the arctic circle,” and that “under such circumstances the piling up of snow, or even its production at the sea-level, would be impossible, excepting perhaps in the immediate neighbourhood of the poles, where the rays of the sun would have but little heating power from its small altitude.”
Mr. Belt has apparently been led to these strange conclusions by the following singular misapprehension of the effects of obliquity on the distribution of the sun’s heat over the globe. “The obliquity of the ecliptic,” he remarks, “does not affect the mean amount of heat received at any one point from the sun, but it causes the heat and the cold to predominate at different seasons of the year.”
It is not necessary to dwell further on the absurdity of the supposition that an increase of obliquity can possibly account for the glacial epoch, but we may in a few words consider whether a decrease of obliquity would mitigate the climate and remove the snow from polar regions. Supposing obliquity to disappear and the earth’s axis to become perpendicular to the plane of its orbit, it is perfectly true that day and night would be equal all over the globe, but then the quantity of heat received by the polar regions would be far less than at present. It is well known that at present at the equinoxes, when day and night are equal, snow and not rain prevails in the arctic regions, and can we suppose it could be otherwise in the case under consideration? How, we may well ask, could these regions, deprived of their summer, get rid of their snow and ice?
But even supposing it could be shown that a change in the obliquity of the ecliptic to the extent assumed by Mr. Belt and Lieutenant-Colonel Drayson would produce a glacial epoch, still the assumption of such a change is one which physical astronomy will not permit. Mr. Belt does not appear to dispute the accuracy of the methods by which it is proved that the variations of obliquity are confined within narrow limits; but he maintains that physical astronomers, in making their calculations have left out of account some circumstances which materially affect the problem. These, according to Mr. Belt, are the following:—(1) Upheavals and subsidences of the land which may have taken place in past ages. (2) The unequal distribution of sea and land on the globe. (3) The fact that the equatorial protuberance is not a regular one, “but approaches in a general outline to an ellipse, of which the greater diameter is two miles longer than the other.” (4) The heaping up of ice around the poles during the glacial period.
We may briefly consider whether any or all of these can sensibly affect the question at issue. In reference to the last-mentioned element, it is no doubt true that if an immense quantity of water were removed from the ocean and placed around the poles in the form of ice it would affect the obliquity of the ecliptic; but this is an element of change which is not available to Mr. Belt, because according to his theory the piling up of the ice is an effect which results from the change of obliquity.
In reference to the difference of two miles in the equatorial diameters of the earth, the fact must be borne in mind that the longer diameter passes through nearly the centre of the great depression of the Pacific Ocean,[234] whereas the shorter diameter passes through the opposite continents of Asia and America. Now, when we take into consideration the fact that these continents are not only two-and-a-half times denser than the ocean, but have a mean elevation of about 1,000 feet above the sea-level, it becomes perfectly obvious that the earth’s mass must be pretty evenly distributed around its axis of rotation, and that therefore the difference in the equatorial diameters can exercise no appreciable effect on the change of obliquity. It follows also that the present arrangement of sea and land is the best that could be chosen to prevent disturbance of motion.
That there ever were upheavals and depressions of the land of so enormous a magnitude as to lead to a change of obliquity to the extent assumed by Lieutenant-Colonel Drayson and Mr. Belt is what, I presume, few geologists would be willing to admit. Suppose the great table-land of Thibet, with the Himalaya Mountains, were to sink under the sea, it would hardly produce any sensible effect on the obliquity of the ecliptic. Nay more; supposing that all the land in the globe were sunk under the sea-level, or the ocean beds converted into dry land, still this would not materially affect obliquity. The reason is very obvious. The equatorial bulge is so immense that those upheavals and depressions would not to any great extent alter the oblate form of the earth. The only cause which could produce any sensible effect on obliquity, as has already been noticed, would be the removal of the water of the ocean and the piling of it up in the form of ice around the poles; but this is a cause which is not available to Mr. Belt.
Sir Charles Lyell’s Theory.—I am also unable to agree with Sir Charles Lyell’s conclusions in reference to the influence of the obliquity of the ecliptic on climate. Sir Charles says, “It may be remarked that if the obliquity of the ecliptic could ever be diminished to the extent of four degrees below its present inclination, such a deviation would be of geological interest, in so far as it would cause the sun’s light to be disseminated over a broader zone inside of the arctic and antarctic circles. Indeed, if the date of its occurrence in past time could be ascertained, this greater spread of the solar rays, implying a shortening of the polar night, might help in some slight degree to account for a vegetation such as now characterizes lower latitudes, having had in the Miocene and Carboniferous periods a much wider range towards the pole.”[235]
The effects, as we have seen, would be directly the reverse of what is here stated, viz., the more the obliquity was diminished the less would the sun’s rays spread over the arctic and antarctic regions, and conversely the more the obliquity was increased the greater would be the amount of heat spread over polar latitudes. The farther the sun recedes from the equator, the greater becomes the amount of heat diffused over the polar regions; and if the obliquity could possibly attain its absolute limit (90°), it is obvious that the poles would then be receiving more heat than the equator is now.