Physics of the earth's crust

Preface

For many years past I have been convinced that various questions of Physical Geology might be answered negatively, if not positively, by applying to them simple mathematical reasoning, and quantitative treatment. My own views have, in some respects, been greatly altered by the application of this method ; and I confess that the present work contains within itself evidence of the circumstance ; for not only will it be found that the views now put forward differ in some respects from those which I have previously published in contributions to scientific periodicals ; but the effect of the progressive application of the quantitative method may be traced in the book itself; and the development of ideas, proposed in the earlier chapters, will sometimes be found to have taken an unexpected turn later on. This remark applies especially to certain hypotheses, which at first presented themselves in a favourable light, to account for compression and for the formation of ocean basins.

It is extremely probable that, if these investigations are carried further, some of the theories now offered as fairly established, may turn out to be untenable. With a growing science like Geology this is unavoidable. On a review of what I have written, I feel how many difficulties have been left unsolved, and some which have occurred to me not even mentioned. Nevertheless I hope that this attempt will not be without a certain value in advancing the study of the Physics of the Earth's Crust.

vi

PREFACE,

The mathematical reader will perhaps be surprised by the rough and ready mode of treatment adopted in some instances. But when it is recollected that, for the most part, we can assign only very hypothetical values for our symbols, it would be affectation to seek close results, which would after all have no greater value than those which claim to be only distant approximations.

The course of the argument and the general conclusions, will be found repeated in the Summary at Chapter XXII. But it is hoped that a perusal of this may not be substituted for reading the book. It is believed that the reasoning of the several chapters will be found intelligible, even without wading through the calculations.

My thanks are due to the Councils of the Geological Society of London, and of the Philosophical Society of Cambridge, for permission to make free use of papers contributed by me to their publications. I have similar acknowledgments to make to the Proprietors of the Philosophical Magazine, the Geological Magazine, and the Quarterly Journal of Science. My kind friends, H. W. BmsTOW, Esq., F.R.S., Senior Director of the Geological Survey, and A. F. Griffith, Esq., B.A., of Lincoln's Inn, Scholar of Christ's College, Cambridge, have rendered me most valuable help in revising the proofs while they were passing through the press.

OSMOND FISHER.

Harlton Rectory,

Chapter I. On Undergeound Temperatuee

The rise of tcmjperature on descending into the earth — The causes ivhich have been assigned for it — Attempts to determine the law of increase by observation — Their results — Deep bore-hole at Sperenberg and methods of observation used there — General effects of convection currents in a bore-hole — Tabulated observations at Sperenberg — Anomalous result supposed to be deducible therefrom — Anomaly explained — General laio of average rise of temperature not impaired thereby — Hot springs and volcanos prove that the rise of temperature continues, but do not inform us whether the law near the surface obtains unaltered for all deptJis ........... 1

CHAPTER 11.

CONDITION OF INTERIOR.

Little known about the condition of the interior of the earth — Results of the mathematical Theory of the Earth" point to a former condition of fluidity — Determination of the mean and surface densities — The question proposed whether the fluid condition still partially exists more or less — Connection betiveen this question and that of the law of internal temperature — Tivo modes of attacking the question, (1) Precession, (2) the tides — Opinions of Sir Wm. Thomson, Hopkins, Delaunay, and others — Possibility of a cooled crust resting on an internal fluid layer 18

Chapter III. Inteenal Densities And Pressures

Speculations concerning the materials in successive couches — Waltershausen^s theory — His law of density open to correction — His tables of densities and pressures — Fluid pressures within the earth calculated from Laplace^s law of density — Fluid pressure at the centre 28 viii

CONTENTS.

Chapter IV. Lateeal Pbessuke, Its Amount

Generally received vieivs regarding the contortion of rocks by lateral pressure — Calculation of the possible amount of such pressure at the surface — Attempt to estimate the same loithin the earth — Mountain chains elevated by lateral pressure — The Himalayas 34

Chapter V. Elevations And Depeessions

Distinction betioeen compression and contraction — Definition of datum levels — General geometrical relation between the compression of a portion of the earth^s crust and the elevations and depressions referred to the upper datum level resulting therefrom — The same extended to the ivhole surface of the globe — Modification of this relation if the globe is supposed to be ivholly solid — Average height of all the elevations above the dat^im level upon the supposition of solidity, expressed in terms of depth of sea and height of land, and of areas of the same — This average height of actual elevations estimated in feet 45

Chapter VI. Elevations On The Hypothesis Of Solidity

Any physical hypothesis regarding the condition of the interior of the earth may be tested by comparing the average height of the elevations it would produce with that which exists in nature — Sir Wm. Thomson regards the earth as a solid cooling by conduction — Some of the results of his paper *' On the Secular Cooling of the Earth^^ — His mathematical formula for expressing the law of temperature in descending — Calculation in general symbols of the average height of the elevations which would be produced upon the supposition of the earth cooling as a solid — Numerical result obtained icith a value of the coefficient of contraction deduced from MalleVs experiments and Sir Wm. Thomson's estimates of the melting temperature and conductivity — The same with Mr MalleVs estimate of the melting temperature of slag — The corresponding age of the earth — Amoun t of radial contraction 57

Chapter VII. Hypothesis Of Solidity Fails

Summary of results of Chap. VI. — Grounds on lohich Physicists have restricted geological time within certain limits — Discrepancy between height of the actual average elevations and of those which xoould be produced upon a cooling solid globe — Necessary alternative suppositions — Captain Dutton's

CONTENTS.

ix argument — Ocean hasi7ts — Opinions about them of Pratt, Mallet, Hopkins, LeConte — Radial contraction cannot explain them — Still less oscillations of surface — Examples of oscillation — N. Wales, Appallachians, New Zealand, India, Colorado Plateau — Gwyn Jeffreys on changes of level — Bahbage — The distribution of elevations in ranges requires a fluid substratum — This supposition explains other surface movements — The pressures under which any part of the crust is in equilibrium — The so-called contr actional hypothesis'*^ not to be abandoned — Captain Button's objections to it considered . . 73

Chapter VIII. Fluid Substkatum

The extravasation of water-substance from beneath the crust suggested as a cause of contraction of volume — Igneo-aqueous fusion — Dissolving power of luater lohen above the critical temperature — Scrope — LeConte — Escape of steam from volcanic vents — Opinion that sea-ivater gains access to volcanic foci — Objections to this hypothesis — Experiment of Daubree not in point — Views on cosmogony — Dr Sterry Hunt's theory — Objections to it — Fails to account for the facts — A suggestion to explain the presence of ivater-substance below the cooled crust 87

CHAPTER IX. CKUST TilOT FLEXIBLE

The ''datum leveV equation has served an important purpose— Supposition of a flexible crust — Mode of determining the general character of the undulations ivhich a thin flexible crust would assume ivhen resting upon a liquid — Mathematical investigation of the problem — Certain negative conclusions therefrom regarding the earth's crust — Alternative assumption to which ive are 99

Chapter X. Disturbed Tract

Conditions of equilibrium of a disturbed portion of the earth's crust— Probable result of compression— Part of the crust sheared upwards and part downwards— These separated by a ''neutral zone"— Calculation of its position— Confused contortions in highly metamorphosed rocks explained— Depth of neutral zone —Probable thickness of crust— Prof . A. Favre's experiments on contortions- Inverted flexures— Formation of a mountain chain and its elevation above the ocean— Subsequent efects of denudation and accumulation of additional sediment— Consequent tilting of tract— Also general elevation from the same cause— Why areas of deposition are sinking areas— Degree of tilting depends upon width of tract and the existence of a mountain chain . . .114

X CONTENTS.

Chapter XI. The Revelations Of The Plumb-line

Mountains the '^bacJchones^^ of continents — They have "roots'^ — These are revealed by the plumb-line — Pratt's calculation of the attraction of the Himalayas — The actual attraction less than that calculated — His attempted explanation of the discrepancy — Sir G. B. Airy's explanation more satisfactory — Pratfs reply shoion to be inconclusive — The result confirms the reasoning of the preceding chapter — The plumb-line reveals a greater density beneath oceans 142

Chapter XII. The Revelations Of The Thermometer

Recapitulation of results of previous chapter — Roots of mountains should be revealed by phenomena of underground temperature — Conditions upon which the mean rate of increase of temperature will depend — Rate greater in plains and less in mountains — Dr Stapff — His observations on temperature of rocks in St Gothard tunnel — His explanation of the smallness of the rate — Why not satisfactory — Effect of convexity of mountain upon the rate — The rate may he considered uniform above — The conclusion from the premises is that the mountain has roots — The rate may be regarded as nearly uniform throughout — General method of determining the thickness of the crust at the sea-level, and the melting temperature, from the rates beneath the mountain and the usual rate — Application to St Gothard — Thickness of crust at sea-level and melting temperature deduced numerically from the data — The like for Mont Cenis — Results confirmatory of previous conclusions — Considerations about the oceanic areas — How the icater is retained there — The thickness of the sub-oceanic crust and its density ........ 151

Chapter XIII. Amount Of Compression

Our ideas respecting the sub-oceanic crust necessarily speculative — Compression possibly confined to continental areas — Compression might arise from extravasation of matter from beneath the crust, or from expansion of the crust — Amount of compression needs to be estimated afresh — Datum-level equation transformed to mean level — Formula to express compression in terms of inequalities — Estimate of inequalities from Atlas — (1) Contraction on supposition that Oceans are due to compression, (2) that they are due to denser crust .... ......... 168

CONTENTS.

xi

Chapter XIV. Exteavasation Of Water Will Not Account For Compression

Hypothesis that oceans consist of water that has been extravasated— Density of the water before extravasation — Volume of interior which tvould need to have contributed it — Hypothesis shoivn to be inadequate to produce the entire compression — Disturbance of crust by change of ellipticity of spheroid — Inequalities do not appear connected with such a cause .... 180

Chapter XV. Compression And Volcanic Action

Compression not being sufficiently accounted for by contraction of the globe, alternative hypothesis that the cause of it is situated within the crust — Attraction of thickened crust not operative — Intrusive dykes may afford a key to the problem — may be widened by fluid pressure — Excess of horizontal over vertical pressure so caused — Their connection with volcanic vents — Hypothesis concerning the constitution of the magma — mode of its elevation in a fissure — Pressure on the sides of the fissure — Comparison of the work of compression icith that done against gravity — Mineral veins — Prof. Judd and Baron Richthofen on the relation of volcanic energy to continental inovements — Possible additional compression upon solidification of dykes — Analogies of earth's crust and ice — Prof. NordenskioWs theory of compression — Analogy of ice disturbed by skaters and earth''s crust by sedimentation — Corrugation attributed to cracks opening from below, and a continental phenomenon — Vieios of American Geologists as set forth by Dr Sterry Hunt — Their observed facts agree with the present theory — Effect of increased thickness of crust on compressing force — Whence the energy invoiced — Circulation of rock — Suggestion to explain diminished density of continental areas — ^'•Red clay" of profound ocean 185

Chapter XVI. On Faulting

Faulting due to contraction — " Hade to the downthrow^'' — Faults may die out in the depths — The fissure which gives rise to the fault — Fissure will have the same hade as the fault—Course of fault in a straight line — Fissures which cause faults commence at the surface — Faults of Utah described by Captain Dutton — Faulting superimposed on corrugation — Extent of throw of great faults — Faults loill not usually admit the fluid magma — If they do so may give rise to fissure eruptions of igneous roch — Application of datum-level equation to faulting — Faulting must depress the tract affected — General theoretical conclusion respecting the connection of faulting and corrugation 208 xii

CONTENTS.

CHAPTER XYII.

GEOLOGICAL MOVEMENTS EXPLAINED.

BecapHulation of the four suggested causes of compression — TJiree of them negatived — The fourth possibly the true one — The fact of compression certain, and the duplex character of the corrugations most probable — The consequences of denudation folloived out — Elevation its correlative — Fresh-ivater strata covered by marine — Movements most energetic near, but not confined to, continents — Degradation of mountains a laio of nature — Enormous thickness of certain strata accounted for — Raised sea beaches — Tioo classes of elevatory movements — Drainage across dip — Theories of compression compared . 217

CHAPTER XYIII.

ME MALLET'S THEOKY OF VOLCANIC ENEEGY.

Early opinions regarding the s€at of volcanic energy — Hopkins^ lava lakes — Mallefs theory — Opposed to the results of the present work — His mode of estimating the temperature derivable frorii crushing rock — His results published in the '■'■Phil. Trans. ^' — differ from those given in an earlier publication— Latent heat of fusion — Localization of heat from crushing not possible — More favourable hypothesis suggested and considered — A pressure, the greatest obtainable on the hypothesis, incapable of caxising volcanic phenomena 226

CHAPTER XIX.

THE VOLCANO IN EEUPTION.

Theories of volcanic eruption — Scrope, Diitton, Mallet — Local and temporary increase of temperature not probable — Bichthofen^s theory unsatisfactory — Explanation of phenomena on hypothe&is of fluid substratum in igneo-aqueous fusion — Amount of water-substance beneath vent probably variable — Mechanics of an eruption — Estimate of amount of ivater-substance in magma — Eruption, hoiv brought to an end — Evisceration of cone — State of intermediate activity — StromboU— Umympathctic craters — Richthofen's difficulties met — Benewal of activity— Comparison u-ith Geyser 240

CONTENTS.

xiii

CHAPTER XX.

SEQUENCE OF VOLCANIC EOCKS.

Flow of matter melted off roots of mountains — Force causing it considerable — Formation of lavas— These will differ in different areas and at different times — Laio of Bunsen — RicJitJiofen's Natural System of Volcanic EocJcs'^ — Hoiv explained by him — Difficulty arising — Captain Button's explanation — Prof. Judd on Bichthofen's System — Melting of roots of the inountains affords an explanation of the seq\ience — And of the variation of volcanic products in adjacent regions ......... 249

CHAPTER XXI.

GEOGEAPHICMi DISTBIBUTION OF VOLCANOS.

The Linear arrangement of Volcanos accords with the doctrine of a thin crust and fluid substratum — Volcanic bands related to the boundaries of continents — Distinction between coastline and oceanic volcanos — Darwin on coral islands — Platforms on lohich oceanic islands stand — their possible origin — Great volcanic band of the Pacific coast — Sinking and rising areas adjoining it — It follows nearly a great circle of the sphere — and divides the land from the water-hemisphere — Is not equally active at every part — Suggested cause of local activity — Other possible causes of the same — Unknown cosmical causes have operated — Conclusion 259

CHAPTER XXII.

SUMMARY.

[The Roman numerals refer to the Chapters.]

I. On underground temperature — II. Condition of interior — III. Internal densities and pressures — IV. Lateral pressure, its amount — V. Elevations and depressions — VI. Elevations on the hypothesis of solidity — VII. Hypothesis of solidity fails — VIII. Fluid substratum — IX. Crust not flexible — X. Disturbed tract — XI. The revelations of the plumbline — XII. The revelations of the thermometer — XIII. Amount of compression — XIV. Extravasation of water will not account for compression — XV. Compression and volcanic action — XVI. On Faulting — XVII. Geological movements explained — XVIII. Mr MalleVs theory of volcanic energy — XIX. The volcano in eruption — XX. Sequence of volcanic rocks — XXI. Geographical distribution of volcanos . 267 xiv

CONTENTS,

Appendix

Mr G. H. Danvin^^On the stresses caused by continents and mountains'' — his argumerit for solidity met by Sir G. B. Airy's explanation— M , Roche " On the constitution of the interior of the earth"" — his theory, though in accordance with Geology, requires fuller statement than is yet published . . 291

ERRATA.

„ 75, ,, 14, /or "one" r<?acZ "one or both".

„ 180, ,, 6, /or "obtaining" reatZ "obtained".

„ 219, ,, 2, of note, for "crust of" read "crest of".

244, ,, 5, /or "lava" r^fliZ "magma".

„ 273, ,, 17 (in some copies) /or "mean" read "datum".

,, 278, ,, 3 from bottom, for "not so deep as " read "deeper than".

Chapter I. On Underground Temperature

The rise of temperature on descending into the earth — The causes which have been assigned for it — Attempts to determine the law of increase by observation— Their results — Deep bore-hole at Sperenberg and methods of observation used there — General effects of convection currents in a bore-hole — Tabulated observations at Sperenberg — Anomalous result supposed to be dediicible therefrom — Anomaly explained — General law of average rise of temperature not impaired thereby — Hot springs and volcanos prove that the rise of temperature continues, but do not inform us v)hether the law near the surface obtains unaltered for all depths.

There is no fact more firmly established in terrestrial physics than that the temperature of the rocks of the earth's surface increases with increasing depth. Observations upon this subject have been made in all parts of the world, and the same result has been everywhere arrived at. Even in the frozen soil of Yakoutzk, in Siberia, this increase of temperature is found to prevail, although the ground is congealed to the whole depth penetrated \ In all mining operations this gradual increase of temperature becomes a very serious consideration, rendering human labour at great depths a very severe trial to the constitution of the workman. And

1 The increase of temperature at Yakoutzk, although the soil is frozen even beyond the depth reached, proves that this freezing is owing to the present low mean temperature of the locality, and that it is not a residual effect of a former glacial and still colder period ; for if that were so the strata would be now warmer above than below, whereas the reverse is in fact the case.

The average temperature for the year is -8 6, R. or 12-7, F. Prof. Milne, in " Geol. Mag." N. S. Vol. iv. p. 518.

F 1 indeed it is this circumstance, more than any other, which fixes a practical limit to the depth at which mining operations are possible. It is not the raising the minerals from profound depths, for the resources of modern engineering are quite competent to overcome any difficulty on that score ; it is not keeping the mines clear of water, for they are less troubled with its influx at great than at moderate depths ; but it is the impossibility of furnishing the men w^ith an atmosphere to breathe in below the temperature of the blood. For when the air has to be conveyed to long distances it acquires the temperature of the rocks, and no means have been yet suggested which could furnish it at the atmospheric temperature unaffected— or but slightly so — by its long journey through the subterranean passages.

This increase of temperature, though universal, is not everywhere the same. The average is about 1 degree Fahr. for between 50 and 60 feet of descent. Such is the result of very numerous observations. Some of these have been made by drilling holes in the rock in deep mines; others by lowering thermometers in Artesian bore-holes. A Committee was appointed by the British Association to report upon the subject, and their reports extend from the year 1869. Much information upon the matter may also be gathered from the Reports of the Parliamentary Commission upon the Coal Supply.

Unquestioned as is the fact, nevertheless the cause of this increase of heat has formed the ground for much speculation. The most obvious explanation of it is offered by the phenomena of hot springs and volcanos. These show us that, in some places at any rate, much higher temperatures exist at great depths than have ever been reached by artificial perforations. But these phenomena might be said to be local, while the general slow increase of temperature we have been describing exists more or less at every place. Are these phenomena directly connected ? Are they indirectly connected ? Or, are they altogether unconnected? Various answers have been returned to these questions.

Among " practical men " engaged in mining operations an opinion seems to have prevailed that the increase of temperature

CH. I.] ON UNDERGROUND TEMPERATURE.

in deep mines is due to the pressure of the overlying strata or ''cover." We may unhesitatingly dismiss this hypothesis. Pressure by itself cannot develop heat. Where motion is destroyed as motion, there it is that it is converted into heat. Thus the motion which is destroyed when a hammer strikes upon an anvil will develop heat that can explode fulminating powder, or heat a nail red-hot. So, also, the bearings of a wheel become heated by friction, which gradually destroys its motion. But though mountains rise on mountains, there will be no heat produced unless motion of some kind is destroyed. In deep coal-mines an effect called "creep" is caused by the enormous pressure upon the sides of a passage, or upon the pillars left to support the roof, causing the floor of the excavation to swell up. In this case there is immense friction between the particles of the rock, were it not for which the passage would become instantaneously closed. It has been remarked that considerable heat sometimes accompanies this creep, in which, be it observed, we have not pressure alone, but motion destroyed by friction and converted into heat.

Sir Humphry Davy ascribed the volcanic fires to the oxidation of earthy and metallic bases, supposed by him to exist low down in the interior of the earth. Since water is everywhere present in the crust, if it be dissipated by the abstraction of its oxygen when it encounters the bases, and by the blowing-ofF from volcanic vents of the equivalent hydrogen, then its place must be continuously supplied by the percolation downwards of fresh accessions ; and thus a generally diffused increase of temperature was supposed to arise, and to manifest itself by its escape towards the surface.

A very fascinating theory, which has met with support among many scientific men, has of late years been promulgated by Mr Mallet, who considers the heat of volcanic action to be derived from the transformed work of crushing the rocks of the earth's crust, owing to the contraction of its interior through long- sustained cooling. The cause of evolution of the volcanic heat under this theory is of the same kind as that alluded to above, in the case of creeps ; while the ubiquitous increase of temperature in descending into the earth is looked

1-^2

ON UNDERGROUND TEMPERATURE. [ch. i.

upon as chiefly a manifestation of the generally diffused heat of the interior, by the escape of which the contraction in volume is produced. Volcanic action, Mr Mallet tells us, is caused by this contraction manifesting itself locally and paroxysmally.

In order to decide what theory best accounts for the phenomena, it is obvious that the first step is to make sure of the facts themselves. In other words — -What is the law resulatinof this increase of heat? At what rate does the temperature augment ? This might be supposed to be a point easily settled. It might be supposed that nothing would be easier than to insert thermometers into the rock at different depths in a mine, and to read off their indications ; or to lower them into a borehole for the same purpose. But there are many difficulties to be overcome, and a host of disturbing causes present. The rock, or the face of the coal in a mine, is affected by the temperature of the air. The air is warmed by the presence of men and horses ; it is cooled by the ventilation carefully kept up. Hence the surface of the working is not at the true temperature of the rock. The result of careful experiments made by Sir G. Elliot showed that when thermometers were inserted in the coal in a long-wall working, at distances of 3, 6, and 12 feet from the face, no alteration could be detected in the indications given beyond 3 feet from the face of the coal ; and his observations were accordingly taken at 4 feet. It is evident, as will be seen by what will be said hereafter, that the necessary distance must be governed by the difference between the temperature of the ventilating air and of the seam, and that the greater this difference the farther it would be necessary to bore into the coal to obtain an estimate of its true temperature. If it be attempted to ascertain the law of increase by means of an Artesian bore-hole, there are here also disturbing causes present. The action of the tool warms the rock by mechanical means, the friction or pounding action developing considerable heat. Hence while the work is in progress no reliable observations can be taken, except during intervals of suspension, and then it appears— as will be seen further on — that the interval needs to consist of weeks rather than of days. When the work is completed, and the bore stands nearly full of water, it is the temcii. I.] OiV UNDERGROUND TEMPERATURE.

perature of the water wliich is obtaiDed on lowering a thermometer into it, and we cannot be sure that that coincides with the temperature of the rock. In fact many reasons may be assigned why it should not do so. Springs may enter on one side and flow out at the other; or they may rise from lower levels and flow away at higher. The very act of lowering the thermometer tends to mix up the differently heated layers of water, and to confuse the result.

A single instance will suffice to illustrate the irregularity of increase referred to. At Rose Bridge Colliery the temperatures were taken by drilling a hole a yard deep at the bottom of the shaft during the process of sinking. If the mean temperature of the surface there be taken at 50° F., the mean rate of increase for the whole depth was 1 degree for 55 feet. But at the successive depths of 605, 630, 663, 671, 679, 734, 745, 761, 775, 783, 800, 806, 815 yards respectively the rate appears to have been 1 degree for 70, 25, 49, 24, 24, 110, 66, 32, 42, 48, 51, 36, 54 feet.

Within the last few years a very deep boring has been carried down at Sperenberg, near Berlin. This has reached the extraordinary depth of 4052 Rhenish feet, or 4172 British feet. A most surprising geological fact about this boring is that, with the exception of the first 283 feet, which were carried through gypsum with some anhydrite, the remainder passed entirely through rock salt. This seemed to offer an exceptionally good opportunity for observing temperatures in a homogeneous rock, which might be expected to be comparatively free from the sources of error arisino^ from variable heat-conductinof power in the layers successively penetrated \ The observations

^ If be the flow of heat from below, k the conductivity of the rock, v the temperature, and x the depth, then

ax

Now the flow of heat at depths beyond the reach of the influence of the

seasons will be the same for moderate depths, or F is constant, and — aives the

dx

increase per foot of descent.

dv F

Hence = - shows that the increase of temperature per foot is inversely

proportional to the conductivity of the rock, so that where the rock conducts heat badly the increase will be more rapid, and vice versa.

ON UNDERGROUND TEMPERATURE, [ch. i.

in the bore were taken with much precaution, under the direction of Herr Eduard Dunker, Inspector of Mines. A resume of his paper upon them will be found in "Nature," Vol. XV. p. 240, 1877, as contained in the Ninth Report of the British Association Committee on Underground Temperature." In Vol. xil. p. 545 of the same publication (1875) there had previously appeared a notice of a contribution by Prof. Mohr, of Bonn, to the "Neues Jahrbuch fiir Mineralogie" (1875), in which that gentleman had commented upon the law of increase which he supposed to be deducible from the observations made in this bore-hole. The result at which he arrived was remarkable enough, and, if it could not have been explained away, would have justified the conclusion which he drew from it, wliich was that the source of heat within the crust of the earth was situated within the crust itself, for that after a certain depth was reached — which he put at 5170 feet — the increase would be nil. However, in the Report of the British Association just published, it is explained how this result had been arrived at, and it is distinctly shown that Prof. Mohr's conclusion was in reality not based upon the original observations themselves, but that it arose from the form of an empirical mathematical formula, representing a parabola, which Dunker had assumed to express the law. In fact it had been implicitly assumed that the increase would come to an end, and all that Mohr did was to find out at what depth it would do so, supposing that assumption true.