The ninth Bridgewater treatise. A fragment

Front matter

o

A FRAGMENT.

LONDON :

Appendix

Note A. On the great Law which regulates Matter . 163

B. On the Calculating Engine 170

C. Extract from the Theory of Probabilities

of La Place 173

D. Note to Chap. VIII. on Miracles ... 175

E. Note to Chap. X. on Hume's Argument

F. On the Consequences of Central Heat . . 182

G. On the Action of Existing Causes in pro-

ducing Elevations and Subsidences in Portions of the Earth's Surface . . . 187

H. Tables showing the Expansion of Beds of

Granite variously heated 198

I. Extracts from Letters of Sir John Herschel 202 b 2

LV

CONTENTS.

Page

K. Or. the Elevation of Beaches by Tides . . 218

L. On Ripple Mark 222

M. On the Age of Strata, as inferred from the

Rings of Trees embedded in them . . 226

N. On a Method of multiplying Illustrations

from Wood- Cuts 235

PREFACE.

The volume here presented to the public does not form a part of that series of works composed at the desire of the trustees who directed the application of the bequest of £8000, by the late Earl of Bridge water, for the purpose of advancing arguments in favour of Natural Religion.

Vi PREFACE.

I have, however, thought, that in furthering the intentions of the testator, by publishing some reflections on that subject, I might be permitted to connect with them a title which has now become familiarly associated, in the public mind, with the evidences in favour of Natural Religion.

The Bridgewater Treatises were restricted by the founder to the subject of Natural Religion ; and I had intended not to have deviated from their example. In the single instance in which the question of miracles has been discussed, I 'was led so irresistibly, by the very nature of the illustrations employed in the former argument, to the view there proposed, that I trust to being excused for having ventured one step beyond the strict limits of that argument, by entering on the first connecting link between natural religion and revelation.

The same argument will produce very various

PREFACE. Vii

degrees of conviction on different minds ; and much of this difference will depend on the extent of previous information, and on the strength of the reasoning faculty in those to whom the argument is addressed. To the great variety, therefore, of the illustrations which have been adduced in proof of design and of benevolence in the works of the Creator, there can be no objection. In truth, to the cultivated eye of science 3 the origin and consequences of the mightiest hurricane, as well as those of the smallest leaf it scatters in its course, equally lead to the inference of a designing power, the more irresistibly the more extensive the knowledge which is brought to bear on those phenomena.

One of the chief defects of the Treatises above referred to appears to me to arise from their not pursuing the argument to a sufficient extent. When a multitude of apparently unconnected facts is traced up to some

Viii PREFACE.

common principle, we feel spontaneously an admiration for him who has explained to us the connexion ; and if, advancing another stage in the investigation, he prove that other facts, apparently at variance with that principle, are not merely no exceptions, but are themselves inevitable consequences of its application, our admiration of the principle, and our respect for its discoverer, are still further enhanced.

But if this respect and admiration are yielded to the mere interpreter of Nature's laws, how much more exalted must those sentiments become when applied to the Being who called such principles into living existence by creating matter subservient to their dominion — whose mind, intimately cognizant of the remotest consequences of the present as well as of all other laws, decreed existence to that one alone, which should comprehend within its grasp the completion of its destiny —

PREFACE. ix

which should require no future intervention to meet events unanticipated by its author, in whose omniscient mind we can conceive no infirmity of purpose — no change of intention !

The object of these pages, as of the Bridgewater Treatises, is to show that the power and knowledge of the great Creator of matter and of mind are unlimited. Deeply engaged in those other pursuits from which my chief arguments are drawn, I regret the impossibility of bestowing on their full development that time and attention which the difficulty and importance of the subject equally deserve ; and in committing these fragments to the press, perhaps in too condensed a form, I wish them to be considered merely as suggestions intended to direct the reader's attention to lines of argument which appear to me new, and to views of nature which appear more magnificent, than those with which I was previously acquainted.

X PREFACE.

Probably I should not have been induced to place my reflections on the subject before the public, had I not, in common with other cultivators of the more abstract branches of mathematical science, felt that a prejudice, which I had believed to have been long eradicated from every cultivated mind, had lately received support, at least to a certain extent, from a chapter in the first* of the Bridgewater Treatises ; and in a still greater degree, from a work of a far different order — one, however, which derived its only claim to notice from the circumstance of its appearing under the sanction of the University of Oxford.

The prejudice to which I allude is, that the pursuits of science are unfavourable to religion.

There are two classes of men most deeply impressed with the conviction of the very

* It was the first in the order of publication.

PREFACE. Xi

limited extent of human knowledge — those whose contracted information renders them eminent examples of the fact, and those whose wide grasp of many of its profoundest branches has taught them, by lengthened experience, that each accession to their stock but enables them to view a larger portion of its illimitable field. Those who belong to the first of these classes must acquire the alphabet of science, in order to understand knowledge, and the elements of modesty, to use it with dignity. When they have thus graduated in the i( infant school" of philosophy, they may perhaps understand the argument, and perchance be worthy of a reply, — but not till then.

In that chapter of the first Bridgewater Treatise to which I have referred, the charge seems not even to be limited to those who pursue that branch of science which is conversant with the properties of pure number, and with abstractions of a like nature, but xii

PREFACE.

applies to all who cultivate deductive processes of reasoning.

It is maintained by the author, that long application to such inquiries disqualifies the mind from duly appreciating the force of that kind of evidence which alone can be adduced in favour of Natural Theology.

" We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe ; we have no reason whatever to expect from their speculations any help, when we ascend to the first cause and supreme ruler of the universe. But we might perhaps go farther, and assert that they are in some respects less likely than men employed in other pursuits, to make any clear advance towards such a subject of speculation." — Bridgewater Treatise, by ^cRev. Wm. Whewell, p. 334.

Admitting, for the sake of argument, that there have been individuals, possessed of high intellectual powers, successfully devoted to those subjects, who have arrived by reasoning at conclusions respecting the First Cause,

PREFACE. Xiii

totally opposite to those entertained by Mr. Whewell and myself, I should still be very reluctant to endeavour to invalidate the influence of their conclusions, by any inquiry either into their intellectual or their moral character. Reasoning is to be combated and refuted by reasoning alone. Any endeavour to raise a prejudice, or throw the shadow of an imputation, either implies the existence of some latent misgiving in the minds of those who employ such weapons, or is a tacit admission that the question is beyond the grasp of one at least of the debaters.

Who that has studied their works ever dreamed of inquiring into the moral or intellectual character of Euclid or Archimedes, for the purpose of confirming or invalidating his belief in their conclusions ? Who that possesses confidence in his own reason, justified by a laborious cultivation and successful exercise of that faculty, fails to anatomize and

XIV PREFACE.

refute the arguments, rather than analyze the mental or moral habits of those from whom he differs ?

The only case in which such extraneous matters can be fairly called in, is when facts are stated resting on testimony. Then it is not only just, but it is necessary for the sake of truth, to inquire into the habits of mind of him by whom they are adduced ; — whether he possesses sufficient talent and precision to enable him to state precisely what his senses convey to him, and nothing more; or, if he receive information from others, whether he is credulous or cautious. In both cases, it is necessary to inquire into moral feelings, in order to be assured that there is no wilful mis-statement in the groundwork of his reasoning. And even when this is well established, it is still necessary to inquire whether he had any personal, professional, or pecuniary interest

PREFACE. XV

which may insensibly have influenced his mind in one direction.

Such I conceive to be the sound distinction between those branches of knowledge resting on facts open to the observation of all, supported by reasoning addressed to the understandings of all, — and those other branches in which reasoning is mixed up with testimony. In the former, the argument is every thing — the character nothing: in the latter, the character must be sifted as well as the arguments.

Feeling convinced that the truths of Natural Religion rest on foundations far stronger than those of any human testimony ; that they are impressed in indelible characters, by almighty power, on every fragment of the material world, I cannot but regret that reflections should have been made, in connexion with this subject, calculated to throw the least

Xvi PREFACE.

shadow of doubt on evidence otherwise irresistible.

As, however, these views of the nature of the question may not bring that conviction to other minds, which they do to my own, and as one of the disturbing forces which act on our minds has been strongly put forward, it is but justice* to state the whole of them. It requires but little insight into man's heart to perceive that profession and professional advancement — that power and wealth — have a far more frequent and more effective influence on his judgment than any mental habits he may be supposed to have cultivated.

It may be right then to state, that the author of these pages has always been an ardent but not an exclusive cultivator of some of the more abstract branches of mathematical science. In pursuing one of those inquiries,

PREFACE. XVU

amongst the most recondite and apparently the most removed from any practical application, he was struck with the bearing of some of the results which presented themselves, on the question of Natural Religion ; and these he has endeavoured to place before the reader, in the following pages.

The author belongs to no profession in which he can hope for advancement, if he successfully advocate one side of the question, or in which his prospects can be injured by candidly stating any arguments on the other. He has not been invited by men high in the State, and deservedly respected, to support that great basis which precedes all revelation, and on which it must all rest. Nor has any sum of money been assigned to him, that, whatever the mercantile success or failure of the present volume may be, he shall, on its publication, reap a large pecuniary reward.

c

PREFACE.

Having chosen a career to which the institutions of the country hold out none of those great prizes that stimulate professional exertions, and which constrain men to yield a certain degree of deference to the opinions, sound or unsound, of their countrymen, he has, on the one hand, nothing to hope from their approbation, and, on the other, is equally exempt from any fear of their censure ; and, had his conviction been as strongly opposed to the doctrines this Fragment advocates, as it is in their favour, he would, had a fit occasion presented itself, fearlessly have laid before the world the arguments which had forced his mind to that conviction.

In conclusion, I have to express to my fellow-labourers in the cause, my hope that they will put no unkind interpretation on these remarks, which, founded on principles of human nature, are necessarily of general application ; that they will see that motives alien, in my

PREFACE. Xix

own opinion, to the subject, having been once introduced, candour to those who differ from us, as well as a deference to truth itself, compelled me to state them fully.

CHARLES BABBAGE.

The following account of the origin of the Bridgewater Treatises, is extracted from one of these works : —

" The Right Honourable and Reverend Francis Henry, Earl of Bridgewater, died in the month of February, 1829; and, by his last will and testament, bearing date the 25 th of February, 1825, he direcled certain Trustees therein named, to invest in the public funds the sum of eight thousand pounds sterling ; this sum, with the accruing dividends thereon, to be held at the disposal of the President, for the time being, of the Royal Society of London, to be paid to the person or persons nominated by him. The testator further directed, that the person or persons selected by the said President should be appointed to write, print, and publish, one thousand copies of a work " On the Power, Wisdom, and Goodness of God, as manifested in the Creation ;" illustrating such work by all reasonable arguments, as, for instance, the variety and formation of God's creatures in the animal, vegetable, and mineral kingdoms; the effect of digestion, and thereby of conversion; the construction of the hand of man, and an infinite variety of other arguments : as also by discoveries, ancient and modern, in arts, sciences, and the whole extent of literature. He desired, moreover, that the profits arising from the sale of the works so published should be paid to the authors of the works.

The late President of the Royal Society, Davies Gilbert, Esq., requested the assistance of his Grace the Archbishop of Canterbury, and of the Bishop of London, in determining upon the best mode of carrying into effect the intentions of the testator. Acting with their advice, and with the concurrence of a nobleman immediately connected with the deceased, Mr. Davies Gilbert appointed eight gentlemen to write separate Treatises on the different branches of the subject."

xxii

Of the eight gentlemen so appointed, four were of the clerical, and four of the medical, profession. Their names, and the subjects assigned to them, are as follows: —

1. The Rev. Thomas Chalmers, D.D., Professor of Divinity in

the University of Edinburgh — " On the Adaptation of External Nature to the Moral and Intellectual Constitution of Man."

2. The Rev. Wm. Buckland, D.D., F.R.S., Canon of Christ

Church, and Professor of Geology in the University of Oxford — "On Geology and Mineralogy."

3. The Rev. Wm. Whewell, M.A., F.R.S., Fellow of Trinity

4. The Rev. Wm. Kirby, M.A., F.R.S.— " On the History,

Habits, and Instincts of Animals."

5. John Kidd, M.D., F.R.S., Regius Professor of Medicine in

the University of Oxford — " On the Adaptation of External Nature to the Physical Condition of Man."

6. Sir Charles Bell, K.H., F.R.S.— " The Hand : its Me-

7. Peter Mark Roget, M.D., Fellow of, and Secretary to, the

Royal Society — "On Animal and Vegetable Physiology."

8. Wm. Prout, M.D., F.R.S.— " On Chemistry, Meteorology,

and the Function of Digestion."

Chap. I. Nature Of The Argument

The notions we acquire of contrivance and design arise from comparing our observations on the works of other beings with the intentions of which we are conscious in our own undertakings. We take the highest and best of human faculties, and, exalting them in our imagination to an unlimited extent, endeavour to attain an imperfect conception of that Infinite Power which created every thing around us. In pursuing this course, it is evident that we are liable to impress upon the

24 INTRODUCTION.

notion of Deity thus shadowed out, manytraces of those imperfections in our own limited faculties which are best known to those who have most deeply cultivated them. It is also evident that all those discoveries which arm human reason with new power, and all additions to our acquaintance with the material world, must from time to time render a revision of that notion necessary. The present seems to be a fit occasion for such a revision.

Many excellent and religious persons not deeply versed in what they mistakenly call " human knowledge" but which is in truth the interpretation of those laws that God himself has impressed on his creation, have endeavoured to discover proofs of design in a multitude of apparent adaptations of means to ends, and have represented the Deity as perpetually interfering, to alter for a time the laws he had previously ordained; thus by implication denying to him the possession

Introduction

of that foresight which is the highest attribute of omnipotence. Minds of this order, insensible of the existence of that combining and generalising faculty which gives to human intellect its greatest development, and tied down by the trammels of their own peculiar pursuits, have in their mistaken zeal not perceived their own unfitness for the mighty task, and have ventured to represent the Creator of the universe as fettered by the same infirmities as those by which their own limited faculties are subjugated. To causes of this kind must in some measure be attributed an opinion which has been industriously spread, that minds highly imbued with mathematical knowledge are disqualified, by the possession of that knowledge, and by the habits of mind produced during its acquisition, from rightly appreciating the works of the Creator.

At periods and in countries in which the knowledge of the priests exceeded that of the people, science has always been held up by the

INTRODUCTION.

former class as an object of regard, and its crafty possessors have too frequently defiled its purity by employing their knowledge for the delusion of the people. On the other hand, at times and in countries in which the knowledge of the people has advanced beyond that of the priesthood, the ministers of the temple have too often been afraid of the advance of knowledge, and have threatened with the displeasure of the Almighty those engaged in employing the faculties he has bestowed on the study of the works he has created. At the present period, when knowledge is so universally spread that neither class is far in advance of the other, — when every subject is submitted to unbounded discussion, — when it is at length fully acknowledged that truth alone can stand unshaken by perennial attacks, and that error, though for centuries triumphant, must fall at last, and leave behind no ashes from which it may revive, the authority of names has but little weight : facts and arguments are the basis of

INTRODUCTION.

creeds, and convictions so arrived at are the more deeply seated, and the more enduring, because they are not the wild fancies of passion or of impulse, but the deliberate results of reason and reflection.

It is a condition of our race that we must ever wade through error in our advance towards truth ; and it may even be said that in many cases we exhaust almost every variety of error before we attain the desired goal. But truths, once reached by such a course, are always most highly valued ; and when, in addition to this, they have been exposed to every variety of attack which splendid talents quickened into energy by the keen perception of personal interests can suggest, — when they have revived undying from unmerited neglect ; when the anathema of spiritual, and the arm of secular power have been found as impotent in suppressing, as their arguments were in refuting them, then they are indeed irresistible. Thus tried and thus triumphant in

INTRODUCTION.

the fiercest warfare of intellectual strife, even the temporary interests and furious passions which urged on the contest, have contributed in no small measure to establish their value, and thus to render these truths the permanent heritage of our race.

Viewed in this light, the propagation of an error, although it may be unfavourable or fatal to the temporary interest of an individual, can never be long injurious to the cause of truth. It may, at a particular time, retard its progress for a while, but it repays the transitory injury by a benefit as permanent as the duration of the truth to which it was opposed. This reasoning is offered for the purpose of proving that the toleration of the fullest discussion is most advantageous to truth. It is not offered as the advocate of or the apology for error ; and whilst it is admitted that every person who wilfully puts forward as valid an argument the soundness of w T hich he doubts, incurs a deep responsibility, it is also some

INTRODUCTION.

satisfaction to reflect that the delay thus occasioned to the great cause can be but small, and that those who in sincerity of heart maintain arguments which a more advanced state of knowledge shall prove to be erroneous, may yet ultimately contribute, by that very publication, to its speedier establishment.

*

Chap. II

ARGUMENT IN FAVOUR OF DESIGN FROM THE CHANGING OF LAWS IN NATURAL EVENTS.

The estimate we form of the intellectual capacity of our race, is founded on an examination of those productions which have resulted from the loftiest flights of individual genius, or from the accumulated labours of generations of men, by whose long-continued exertions a body of science has been raised up, surpassing in its extent the creative powers of any individual, and demanding for its development a length of time, to which no single life extends.

ARGUMENT IN FAVOUR OF DESIGN. 31

The estimate we form of the Creator of the visible world rests ultimately on the same foundation. Conscious that we each of us employ, in our own productions, means intended to accomplish the objects at which we aim, and tracing throughout the actions and inventions of our fellow- creatures the same intention, — judging also, of their capacity by the fit selection they make of the means by which they work, we are irresistibly led, when we contemplate the natural world, to attempt to trace each existing fact presented to our senses to some precontrived arrangement, itself perhaps the consequence of a yet more general law; and where the most powerful aids by which we can assist our limited faculties fail in enabling us to detect such connexions, we still, and not the less, believe that a more extended inquiry, or higher powers, would enable us to discover them.

The larger the number of consequences resulting from any law, and the more they are foreseen, the greater the knowledge and intelligence we ascribe to the being by which it was ordained. In the earlier stages of our knowledge, we behold a multitude of distinct laws, all harmonizing to produce results which we deem beneficial to our own species : as science advances/ many of these minor laws merge into some more general principles ; and with its higher progress these secondary principles appear, in their turn, the mere consequences of some still more general law. Such has been the case in two of the most curious and most elaborately cultivated branches of human knowledge, the sciences of astronomy and optics* All analogy leads us to infer, and new discoveries continually direct our expectation to the idea, that the most extensive laws to which we have hitherto attained, converge to some few simple and general principles, by which the whole of the material universe is sustained, and from which its infinitely varied phenomena emerge as the necessary consequences.*

* See Note A in the Appendix.

FAVOUR OF DESIGN.

To illustrate the distinction between a system to which the restoring hand of its contriver is applied, either frequently or at distant intervals, and one which had received at its first formation the impress of the will of its author, foreseeing the varied but yet necessary laws of its action, throughout the whole extent of its existence, we must have recourse to some machine, the produce of human skill. But far as all such engines must ever be placed at an immeasurable interval below the simplest of Nature's works, yet, from the vastness of those cycles which even human contrivance in some cases unfolds to our view, we may perhaps be enabled to form a faint estimate of the magnitude of that lowest step in the chain of reasoning, which leads us up to Nature's God.

The illustration which I shall here employ will be derived from the results afforded by the Calculating Engine ;* and this I am the

* The reader will find a short account of this engine in the Appendix, Note B.

D more disposed to use, because my own views respecting the extent of the laws of Nature were greatly enlarged by considering it, and also because it incidentally presents matter for reflection on the subject of inductive reasoning. Nor will any difficulty arise from the complexity of that engine ; no knowledge of its mechanism, nor any acquaintance with mathematical science, being necessary for comprehending the illustration, it being sufficient merely to conceive that computations of great complexity can be effected by mechanical means.

Let the reader imagine that such an engine has been adjusted; and that it is moved by a weight ; and that he sits down before it, and observes a wheel, which revolves through a small angle round its axis, at short intervals, presenting to his eye, successively, a series of numbers engraved on its divided circumference.

FAVOUR OF DESIGN.

Let the figures thus seen be the series 1, 2, 3, 4, 5, &c, of natural numbers, each of which exceeds its immediate antecedent by unity.

Now, reader, let me ask how long you will have counted before you are firmly convinced that the engine has been so adjusted that it will continue whilst its motion is maintained, to produce the same series of natural numbers ? Some minds are so constituted, that after passing the first hundred terms, they will be satisfied that they are acquainted with the law. After seeing five hundred terms, few will doubt ; and after the fifty-thousandth term the propensity to believe that the succeeding term will be fifty thousand and one, will be almost irresistible. That term will be fifty thousand and one ; and the same regular succession will continue ; the five-millionth and the fifty-millionth term will still appear in their expected order ; and one unbroken chain of natural numbers will pass before your eyes, from one up to one hundred million.

d 2

True to the vast induction which has been made, the next succeeding term will be one hundred million and one ; but the next number presented by the rim of the wheel, instead of being one hundred million and two, is one hundred million ten thousand and two. The whole series from the commencement being thus : —

2 3 4 5

100,010,002 the law changes

100,030,003

100,060,004

100,100,005

100,150,006

100,210,007

100,280,008

FAVOUR OF DESIGN.

The law which seemed at first to govern this series fails at the hundred million and second terra. This term is larger than we expected, by 10,000. The next term is larger than was anticipated, by 30,000, and the excess of each term above what we had expected forms the following table : —

10,000

30,000

being, in fact, the series of triangular numbers* each multiplied by 10,000.

* The numbers 1, 3, 6, 10, 15, 21, 28, &c. are formed by adding the successive terms of the series of natural numbers thus ;

They are called triangular numbers, because a number of points corresponding to any term can always be placed in the form of a triangle, for instance : —

1 3

6 10

If we now continue to observe the numbers presented by the wheel, we shall find, that for a hundred, or even for a thousand terms, they continue to follow the new law relating to the triangular numbers ; but after watching them for 2761 terms, we find that this law fails in the case of the 2762d term.

If we continue to observe, we shall discover another law then coming into action, which also is dependent, but in a different manner, on triangular numbers. This will continue through about 1430 terms, when a new law is again introduced, which extends over about 950 terms ; and this too, like all its predecessors, fails, and gives place to other laws, which appear at different intervals.

Now it must be remarked, that the law that each number presented by the Engine is greater by unity than the preceding number, which law the observer had deduced from an induction of a hundred million instances, was

FAVOUR OF DESIGN.

not the true law that regulated its action ; and that the occurrence of the number 100,010,002 at the 100,000, 002d term, was as necessary a consequence of the original adjustment, and might have been as fully foreknown at the commencement, as was the regular succession of any one of the intermediate numbers to its immediate antecedent. The same remark applies to the next apparent deviation from the new law, which was founded on an induction of 2761 terms, and also to the succeeding law ; with this limitation only — that whilst their consecutive introduction at various definite intervals is a necessary consequence of the mechanical structure of the engine, our knowledge of analysis does not enable us to predict the periods themselves at which the more distant laws will be introduced.