The Ninth Bridgewater Treatise, 1837.

Charles Babbage

Charles Babbage, The Ninth Bridgewater Treatise, 2nd edn London, 1838.

1. Original page numbers are included in square brackets.
2. Digitized by John van Wyhe, Ph.D., Cambridge University.

Front matter, Chapters 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, appendix

APPENDIX.

NOTE A. page 32.

ON THE GREAT LAW WHICH REGULATES MATTER. ever since the period when Newton established the great law of gravity, philosophers have occasionally speculated on the existence of some more comprehensive law, of which gravity itself is a consequence. Although some have considered it vain to search for a more general law, the great philosopher himself left encouragement to future inquirers ; and the time, perhaps, has even now arrived, when such a discovery may be near its maturity. It would occupy too much space to introduce many illustrations of this opinion ; there is, however, one which deserves attention, because it is not merely a happy conjecture, but the hypothesis on which it rests has been carried out by its author, through the aid of profound mathematical reasoning, to many of its remote consequences.

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M. Mosotti* has shown, that by supposing matter to consist of two sorts of particles, each of which repels similar particles, directly as the mass, and inversely as the squares of their distances, whilst each attracts those of the other kind, also according to the same law,— then the resulting attractions explain all the phenomena of electricity, while there remains a residual force, acting at all sensible distances,, according to the law of gravity. Many of the discoveries of the present day point towards some more general law ; and many philosophers of the present time anticipate its near approach. Under these circumstances, it may be interesting as well as useful briefly to state the principles which such a law must comprehend ; and to indicate, however imperfectly, the path to be pursued in the research. If matter be supposed to consist of two sorts of particles, or rather, perhaps, of two sorts of centres of force, of different orders of density ; and if the particles of each order repel their own particles, according to a given law, but attract particles of the other kind, according to another law,—then, if we conceive only one particle of the denser kind to exist, and an infinite

* Professor of Physics at the University of the Ionian Islands.— The paper of M. Mosotti has been translated, and published by Mr. R. Taylor, in the third number of the Scientific Memoirs; a work which it is proposed shall contain translations of all the most important original papers printed in foreign countries.

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number of the other kind, that single particle will become the centre of a system, surrounded by all the others, which will form around it an atmosphere denser near the central body. If we conceive a stream of particles, similar to those forming the atmosphere, to impinge upon it, so as just to overcome its resistance, they will, whilst continually producing undulations throughout its whole extent, gradually increase its magnitude, until it attains such a size, that the repulsion of the particles at the outer surface of this enlarged atmosphere is just balanced by the attraction of the central particle. If the stream continue after this point is reached, the whole outer layer will be pressed a little beyond the limit of attraction, and will fly off at right angles to the surface, which might then be said to radiate. If the whole of the space in which such a central particle with its atmosphere is placed, is itself full of atmospheric particles, then their density will increase in approaching the central body ; and if a stream of such particles were directed towards the centre, they might produce throughout the atmosphere vibrations, which would be transmitted from it in all directions. If two such central particles, with their atmospheres, exist at a distance from each other, they will be drawn together by a force depending on the difference between

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the mutual repulsion of their atmospheres and central bodies respectively for each other, and the attraction of each central particle for its neighbour's atmosphere : and in order to coincide with the existing law of nature, this force must be directly as the mass, and inversely as the square, of the distance. The other conditions which such a law must satisfy, are— 1. That the juxtaposition of such atoms must, in some circumstances, form a solid body :— 2. In other circumstances, a fluid. 3. That again, in still other circumstances, its particles shall repel each other, or the body become gaseous. 4. In the first state the body must possess cohesion, tenacity, malleability, elasticity ; the measure and extent of each of which must result generally from the original law, and in each particular case from the constants belonging to the substance itself. 5. In the second state, it must possess capillarity, susceptibility of being compressed without becoming solid, as also elasticity. But besides these, the central atoms must admit of a more intimate approach, so that their atmospheres may

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unite and form one atmosphere. This might constitute chemical union. Binary compounds might then (supposing the distance between the two central particles to be very small, compared with the diameters of the atmospheres) have atmospheres not quite spherical, and attracting differently in different directions; thus possessing polarity. Combinations of three or more atoms, as the central body of one atmosphere, might give great varieties of attractive forces. Each different combination would give a different atmosphere ; and the equation of its surface might, perhaps, become the mathematical expression of the substance it constituted. Thus, all the phenomena produced by bodies, acting chemically on each other, might be deduced from the comparison of the characteristic surfaces of the atmospheres of their atoms. Another result, also, might ensue. Two or more central atoms uniting, might either not be able to retain the same amount of atmosphere, or they might possibly be able to retain a larger quantity. If the particles of such atmospheres constituted heat, it would in the former case be given out, and in the latter absorbed by chemical union. Hence the whole of chemistry, and with it crystallography, would become a branch of mathematical analysis, which, like astronomy, taking its constants from observation, would enable us to predict the character of any new compound, and possibly indicate the source from which its formation might be anticipated.

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For the sake of simplicity, two species of particles only have been mentioned above ; but it seems more probable, that matter consists of at least three kinds. Suppose each of the three kinds to repel its own particles; and the central atom, whilst it repels similar particles, to attract those of the two other kinds ; and moreover, that the latter are either repulsive, or indifferent to each other. We might then conceive matter to be made up of particles, each having a central point, with an atmosphere surrounding it, and this atmosphere again inclosed within another and larger one. Under such circumstances, the outer atmosphere might give rise to heat and light, to solidity and fluidity, and the gaseous condition ; to capillarity, to elasticity, tenacity, and malleability. The more intimate union of the central atoms, by which two or more become enclosed in one common atmosphere of the second kind, might represent chemical combinations, and perhaps that atmosphere itself be electricity. Possibly, also, this intermediate atmosphere, acted on by the pressure of the external one, and by the attraction of the central atom, might take the liquid form. These binary or multiple-combinations of the original atoms, and their smaller atmospheres, would still be enclosed in an atmosphere of the outer kind, which might be nearly spherical. The joint action of the three might, at sensible distances, produce gravity.

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The reader should, however, bear in mind, that these hints are thrown out only as objects of reflection and inquiry ; and that nothing but a profound mathematical investigation can establish them, or even give to them that temporary value which arises from any hypothesis, representing a large collection of facts.

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NOTE B. page 33.

ON THE CALCULATING ENGINE.

THE nature of the arguments advanced in this volume having obliged me to refer, more frequently than I should have chosen, to the Calculating Engine, it becomes necessary to give the reader some brief account of its progress and present state.

About the year 1821, I undertook to superintend, for the Government, the construction of an engine for calculating and printing mathematical and astronomical tables. Early in the year 1833, a small portion of the machine was put together, and was found to perform its work with all the precision which had been anticipated. At that period circumstances, which I could not control, caused what I then considered a temporary suspension of its progress ; and the Government, on whose

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decision the continuance or discontinuance of the work depended, have not yet communicated to me their wishes on the question. The first illustration (p. 33 to 43) I have employed is derived from the calculations made by this engine.

About October, 1834, I commenced the design of another, and far more powerful engine. Many of the contrivances necessary for its performance have since been discussed and drawn according to various principles ; and all of them have been invented in more than one form. I consider them, even in their present state, as susceptible of practical execution ; but time, thought, and expense, will probably improve them. As the remaining illustrations are all drawn from the powers of this new engine, it may be right to state, that it will calculate the numerical value of any algebraical function—that, at any period previously fixed upon, or contingent on certain events, it will cease to tabulate that algebraic function, and commence the calculation of a different one, and that these changes may be repeated to any extent.

The former engine could employ about 120 figures in its calculations ; the present machine is intended to compute with about 4,000.

Here I should willingly have left the subject ; but the public having erroneously imagined, that the sums

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of money paid to the workmen for the construction of the engine, were the remuneration of my own services, for inventing and directing its progress; and a Committee of the House of Commons having incidentally led the public to believe that a sum of money was voted to me for that purpose,— I think it right to give to that report the most direct and unequivocal contradiction.

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NOTE C. page 111.

EXTRACT FROM THE THEORY OF PROBABILITIES OF LAPLACE.

"Nous devons donc envisager l'état présent de l'univers, comme l'effet de son état antérieur, et comme la cause de celui qui va suivre. " Une intelligence qui pour un instant donnée, connaîtrait toutes les forces dont la nature est animée, et la situation respective des êtres qui la composent, si d'ailleurs elle était assez vaste pour soumettre ces données à l'analyse, embrasserait, dans la même formule, les mouvemens des plus grands corps de l'univers et ceux du plus léger atome : rien ne serait incertain pour elle, et l'avenir, comme le passé, serait présent a ses yeux. L'esprit humain offre, dans la perfection qu'il a su donner à l'astronomie, une faible esquisse de cette intelli-

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gence. Ses découvertes en mécanique et en géométrie, jointes à celle de la pesanteur universelle, l'ont mis à portée de comprendre dans les mêmes expressions analytiques, les états passés et futurs du système du monde.

" En appliquant le même méthode à quelques autres objets de ses connaissances, il est parvenu à ramener à des lois générales, les phénomènes observés, et à prévoir ceux que des circonstances données doivent faire éclore. Tous ses efforts dans la recherche de la vérité, tendent à le rapprocher sans cesse à l'intelligence que nous venons de concevoir, mais dont il restera toujours infiniment éloigné. Cette tendance propre à l'espèce humaine, est ce qui la rend supérieure aux animaux ; et ses progrès en ce genre, distinguent les nations et les siècles, et fondent leur véritable gloire."— Laplace, Théorie Analytique des Probabilités.

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NOTE D. page 92.

NOTE TO CHAP. VIII. ON MIRACLES.

the view taken of miracles in Chapter VIII. is the same as that contained in the work of Butler, on the Analogy of Religion to the Constitution and Course of Nature. Inquiries connected with the Calculating Engine, impressed it very forcibly on my own mind, and I have drawn the illustrations chiefly from that subject. 1 cannot, however, forbear referring the reader to the opinion of Sir J. Herschel, expressed at the beginning of his letter to Mr. Lyell, (see Note I. p. 225,) because it confirms me in the belief, that the more profoundly we inquire into the mechanism of nature, the more certainly we arrive at that conclusion.

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NOTE E. page 181.

NOTE TO CHAPTER X. ON HUME’S ARGUMENT AGAINST MIRACLES.

the reader will observe, that throughout the chapter to which this note refers, as well as in the note itself, the argument of Hume is taken strictly according to his own interpretation of the terms he uses, and the calculations are founded on them ; so that it is from the very argument itself, when fairly pursued to its full extent, that the refutation results.

Both our belief in the truth of human testimony, and our belief in the permanence of the laws of nature, are, according to Hume, founded on experience ; we may, therefore, in the complete ignorance in which he assumes we are, with respect to the causes of either, treat the question as one of the probability of an event deduced solely from observations of the past.

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The argument of Hume asserts, that one improbability, namely, that of the falsehood of the testimony in favour of a miracle, must always be greater than another improbability, namely, that of the occurrence of the miracle itself; and also, that, from the very nature of human experience, this preponderance can never take place. Now the only possible mode of disproving the assertion, that one thing cannot, under any circumstances, be greater than another, is to measure, under all circumstances, the numerical value of the two things so compared, and the truth or falsehood of the assertion will then appear. The doctrine of chances, which has been much improved since the time of Hume, now enables us to apply precise measures to this argument; and it is the object of this Note to state the outlines of the calculation, and the results to which it leads. Previously to this, however, it may not be amiss to offer a few remarks on the principles about to be employed. In the great work of Laplace, " Théorie Analytique des Probabilités," those principles are established, and they are not merely undisputed, but are admitted by other writers of the highest authority on this subject. They form a part of the received knowledge of the present day, and, as such, they are employed in the present work, in which I propose to use, not to

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discuss them. I state this, because it has occasionally been asserted by persons unacquainted with the doctrine of chances, that the argument respecting the probability or improbability of miracles does not admit of the application of numbers. The received foundations of science are not to be put aside by such opinions, however highly skilled their authors may be in other branches of knowledge, and however powerful the intellect by which they may have attained those acquirements. The conclusions arrived at by the application of pure analysis must ever rest on the truth of the principles assumed at the commencement of the inquiry ; and although a knowledge of mathematics may not appear necessary for forming a right judgment of the accuracy of those principles, yet it is observed, that a clear apprehension of them is not often found in the minds of those who are unacquainted with that science. When, however, the grounds on which the principles employed in the doctrine of chances are called in question by competent authority, it will be time enough to examine the question ; and none will more eagerly enter upon that examination than those best versed in it, for none are so well aware of the extreme difficulty and delicacy of the subject. As confusion sometimes arises from the difference in the meaning of the words probable and improbable in popular language and in mathematical inquiries,

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it may be convenient to point it out ; and to state, that in this Note it is used in the mathematical sense, unless the reader's attention is directly called to a question relating to its popular sense.

In common language, an event is said to be probable when it is more likely to happen than to fail: it is said to be improbable when it is more likely to fail than to happen.

Now, an event whose probability is, in mathematical language , will be called probable or improbable, in

ordinary language, according as p is less or greater than 2.

If, in mathematical language, expresses the probability of an event happening, expresses the

probability of its failing, or the improbability of its happening.

It has been stated in the text, that two views may be taken of those extraordinary deviations from the usual course of nature, called miracles. According to the first of these, we have to calculate the probability that a white ball has been drawn from an urn (containing only white and black balls, out of which m balls have been drawn all black), as deduced from

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the testimony of witnesses whose probability of speaking truth is known :—or, of the analogous case ; it having been observed that m persons have died without any restoration to life, what is the probability that such a resurrection has happened, it having been asserted by n independent witnesses, the probability of each of whose speaking false is - ? The probability of the death without resurrection of the , and the improbability of such an occurrence, independently of testimony, is ; which is therefore the probability of a contrary occurrence, or that of a person being raised from the dead. Now only two hypotheses can be formed, collusion being, by hypothesis, out of the question: either the event did happen, and the witnesses agree in speaking the truth, the probability of their concurrence being

 , and ofthat of the hypothesis being ;

or the event did not happen, and the witnesses agree in a falsehood, the probability of their concurrence being , and that of the hypothesis The probability of the witnesses speaking truth, and the event occurring, is therefore,

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and the probability of their falsehood is,

If we interpret Hume's assertion, " that the falsehood of the witnesses must be more improbable than the occurrence of the miracle," according to the mathematical meaning of the word improbable, then we must

have,

or,

hence,

from which we find,

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are persons whose statements are more frequently correct than incorrect, and who give their testimony in favour of it without collusion,) a certain number n can always be found ; so that it shall be a greater improbability that their unanimous statement shall be a falsehood, than that the miracle shall have occurred. Let us now suppose each witness to state one falsehood for every ten truths, or p = 11, and m = 1000,000,000,000;

or twenty-five such witnesses are sufficient. If the witnesses only state one falsehood for every hundred truths, then thirteen such witnesses are sufficient. Another view of the question might be taken ; and it might be asserted that, in order to believe in the miracle, the probability of its truth must be greater than the probability of its falsehood ; in this case the expression (A) must be greater than (B) ; or,

In this case also, under the same circumstances, the condition can always be fulfilled of finding a sufficient

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number of witnesses to render the miracle probable, or even to give to it any required degree of probability.

According to the second view stated in the text, a miracle may be assimilated to the drawing of a given number i out of an urn, containing all numbers from one to m. In this case the probability of the occurrence of the event is, and the probability of the concurrence of n witnesses in falsehood is Hence the probability that the particular number i was drawn, as deduced from the testimony of n witnesses, each of whose probability of falsehood is , is expressed by,

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and the probability of the number i not having been drawn, or of their falsehood, is

Hence the improbability of the testimony must, according to Hume, be greater than that of the occurrence of the event ; or,-

If it is only required that the probability of the occurrence of the miracle shall be greater than its

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improbability, then we must make (C) greater than (D); or,

Hence in this view, also, a sufficient number of witnesses of given veracity may always be found to render the improbability of their concurrent independent testimony being false, greater than the improbability of the occurrence of the miracle. There is, however, one other view, which it seems probable would have been that taken by Hume himself, had he applied numbers to his own argument. Considering the probability of the coincidence in falsehood of « persons each having the probability

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in favour of his truth, which is —_u, that probability ought to be less than that of the occurrence of the miracle; or,

This view of the question refers to the probability of the concurrence of the witnesses before they have given their testimony. The other four cases relate to the probability of the miracle having happened, as deduced from the fact of the testimony having been given. The last seems to have been that which Hume would have himself arrived at; the others represent the true methods of estimating the probabilities of the various cases: and the important conclusion follows, that, whichever be the interpretation given to the argument of Hume, if independent witnesses can be found, who speak truth more frequently than falsehood, it is always possible to assign a number of independent witnesses, the improbability of the falsehood of whose concurring testimony shall be greater than that of the improbability of the miracle itself.

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It is to be observed, that the whole of this argument applies to independent witnesses. The possibility of the collusion, and the degree of credit to be assigned to witnesses under any given circumstances, depend on facts which have not yet been sufficiently collected to become the subject of mathematical inquiry. Some of those considerations which bear on this part of the subject, the reader will find treated of in the work of Dr. Conyers Middleton, entitled " A Free Inquiry into the Miraculous Powers which are supposed to have subsisted in the Christian Church, from the earliest Ages through several successive Centuries." London, 1749.

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NOTE F.

ON THE CONSEQUENCES OF CENTRAL HEAT.

the increase of temperature observed as we descend below the earth's surface, as well as other phenomena, have led to a very general opinion, that great heat exists in the interior of the earth, and that the body of our planet, having been at one time intensely heated, has cooled down to its present temperature. With the view of pointing out courses of inquiry, by which these opinions may ultimately be tested by observation, it may be expedient to take a cursory view of some of the consequences of such an hypothesis.

And first, let us imagine the exterior of our globe to have once been in a state of intense heat. No fluid such as water could then have existed on the surface : it would instantly have been converted into vapour ; and

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notwithstanding the increased weight of atmosphere thus produced and pressing on the surface of the globe, sufficient heat would reduce all fluids to the gaseous state. Let us, however, inquire as to the possible extent of such an atmosphere. In the first place, it could not extend beyond that point at which the moon's attraction is equal to that of the earth. In the next place, much more contracted limits would be prescribed by the effect of centrifugal force, and of the cooling of the vapour by expansion, and by its distance from the source of radiant heat, which had caused its evaporation. It would be interesting to inquire, what would be the nature of the surface of the atmosphere under such circumstances. At the distance at which the centrifugal force is equal to that of gravity, it might happen that the temperature was scarcely sufficient to maintain the water in a gaseous state. Should this have been the case, a belt of perpetual clouds might have been formed, resembling those of Jupiter. If, at this limit, a still lower degree of temperature prevailed, instead of a belt of clouds, a ring of ice might be formed. This ring of ice, being exposed to different effects of radiation from variations in the radiating power of various parts of the earth's surface, might, by the superior heat at some parts, become diminished, whilst

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the condensation of the vapour might augment parts less exposed, and situated nearer to the body of the planet: and these conditions might continue, until at last the ring itself was melted or partially melted through at one or more points, and the whole might break up, and the fragments moving in a resisting medium, would ultimately fall down on the surface of the planet. The tearing up of that surface from such an event, would be augmented by the sudden conversion of the solid ice into steam ; and after a time, the fragments of the ring would be absorbed again into the atmosphere of the planet. Let us now suppose, owing to the gradual cooling down of the whole globe, the limit of condensation oi steam into water, to occur at a nearer point than that at which the centrifugal force equals that of gravity. As soon as the steam is condensed into water, it will descend towards the surface of the earth ; but that surface being still very hot, will, by its radiation, again convert the descending shower into steam ; and this will happen at different heights above the surface, according to the radiating power of the part below. We may, therefore, conceive a shell surrounding the earth, the outer surface of which has just been condensed into water, and the inner consists of vapour, just re-converted into that state by the earth's radiation. These surfaces will attain different heights in different places. Between these two surfaces there will exist a perpetual

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rain, descending from the upper as a gentle shower, becoming gradually a violent torrent, and then as it falls re-absorbed into another gentle shower, which is entirely converted into vapour in approaching the heated surface. Such being the state of things, let us imagine the globe to cool down uniformly. The lower surface of the descending rain, which is placed at irregular heights, will at length be brought down to the earth's surface in one or more points. The effect of this, which will in the first instance be a gentle shower, would be to cool that portion of the surface on which it falls, and hence to diminish its radiating power. This change, in its turn, will lower the under surface of the watery shell, so that a more violent rain, and ultimately an impetuous torrent will continue, perhaps, for thousands of years, its unremitted vertical action on the surface exposed to its force. The excavation of the largest valleys, or even of ocean beds, is not too much to expect from such forces. But let us take another view of the consequences of such an original state of incandescence. The whole of the fluids now on the surface of the earth must then have been suspended in its atmosphere. But the extent of that atmosphere is itself limited by various causes : the attraction of other bodies, the effects of centrifugal force, the decrease of temperature, and the

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distances at which the particles of gaseous bodies cease to repel each other, all have their influence in determining its form and magnitude. Let us suppose that we possessed data from which the approximate amount of vapour contained in the entire atmosphere were known, and consequently the whole quantity of water in it ; then, since we know the area of the present seas, we might easily ascertain their average depth. If the result of such a computation should give a mean depth much less than that which we know the ocean to possess,—as, for instance, only a hundred feet,—then we might conclude, either that the surface of the earth had never been in such a state of incandescence as has been supposed, or if it had, that a new source of aqueous vapour had been supplied to it, subsequently to its cooling down.

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NOTE G. on the action of existing causes in producing elevations and subsidences in portions of the earth's surface.

the following explanation of the origin of many of the changes at present going on on the earth's surface, was suggested in endeavouring to account for the very singular phenomena presented by the temple of Jupiter Serapis, at Puzzuoli, near Naples. The facts relating to that temple were observed by me in 1828, and the theory occurred soon after my return to England ; but though occasionally mentioned to geological friends, it was not printed until it appeared in the abstract of my paper on the Temple of Serapis, presented to the Geological Society of London, in March 1854. The following positions are taken as the basis of the reasoning on this subject :—

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1. That, as we descend below the surface of the earth, the temperature increases. 2. That solid rocks expand by being heated ; but that clay, and some other substances, contract under the same circumstances. 3. That different rocks and strata conduct heat differently. 4. That the earth radiates heat differently, at different parts of its surface, according as it is covered with forests, with mountains, with deserts, or with water. 5. That existing atmospheric agents, and other causes, are constantly changing the condition of the surface of the globe. f he only one of these propositions on which, in the present state of knowledge, the slightest question can be raised, is the first. But the observations on which it depends have latterly become so numerous, that the general fact of an increase of temperature, in descending through the crust of the earth, can scarcely be questioned ; although the exact law of this increase, and the extent to which it penetrates, are yet undecided. An increase of 1° Fahrenheit's thermometer, for every 50 or 60 feet we penetrate below the earth's surface,

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seems nearly the average result of observations. If the rate continue, it is obvious that, at a small distance below the surface, we shall arrive at a heat which will keep all the substances with which we are acquainted in a state of fusion. Without, however, assuming the fluidity of the central nucleus,—a question yet unsettled, and which rests on very inferior evidence* to that by which the principles here employed are supported,—we may yet arrive at important conclusions ; and these may be applied to the case of central fluidity, according to the opinions of the inquirer. If we consider the temperature of any point :—for example, G, situated two miles below the surface of an elevated table land, A, in the annexed wood-cut ; and if we imagine a surface passing through all the points of equal temperature within the globe ; then, as this surface passes under the adjacent ocean, which we may suppose, on an average, to be two miles deep, it is evident that the surface of equal heat will descend towards the earth's centre ; because, if it did not, we should have great heat nearly in contact with the bottom of the sea. In the first figure, B is the surface of the ocean. A D, the surface of the land, and of the bed of the ocean. The broken line, G F, is the isothermal line. Let us now

* The reader will find this question fully discussed in the 17th chapter of Lyell's Geology ; On the Causes of Earthquakes and Volcanoes.

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suppose, by the continual wearing down of the continents and islands adjoining this ocean, that it becomes yearly filled up. The broken line C, in the second figure of the wood-cut, indicates the new bottom. The former bottom of the ocean being now covered with a bad conductor of heat, instead of with a fluid which rapidly conveyed it away, the surface of uniform temperature will rise, slowly but considerably, as is shown at G E, in the third figure. In the fourth figure, the first bed of the ocean, A D, and its isothermal line, G F, as well as the new bed, A C, of the ocean, and its corresponding isothermal line, G E, are all shown at one view. The newly formed strata will be consolidated by the application of heat; they may, perhaps, contract in bulk, and thus give space for new deposits, which will, in their turn, become similarly consolidated. But the surface of uniform temperature below the bed of the ocean cannot rise towards the earth's surface, without an increase in the temperature of all the beds of various rock on which it rests ; and this increase must take place for a considerable depth. The consequence must be a gradual rise of the ancient bed of the ocean, and of all the deposits newly formed upon it. The shallowness of this altered ocean will, by exposing it to greater evaporation from the effect of the sun's heat, give increased force to the atmospheric causes still operating upon

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the inequalities of the solid surface, and tend more rapidly to fill up the depressions. Possibly the conducting power of the heated rocks may be so slow, that its total effect may not be produced for centuries after the sea has given place to dry land ; and we can conceive, that in such circumstances,— the force of the sun's rays from without, and the increasing heat from below, so consolidating the surface, that the land may again descend below the level of adjacent seas, even though its first bottom is still subject to the elevatory process. Thus, a series of shallow seas or large lakes might be formed ; and these processes might even be repeated several times, before the full effect of the expansion from below had permanently raised the whole newly-formed land above . the influence of the adjacent seas. If the sea were originally much deeper, or, if in particular parts it were much deeper, as, for instance, ten or twenty miles, then a portion of the solid matter beneath its surface might, after the lapse of many ages, acquire a red, or even a melting heat, and the conversion into gases of some of the substances thus operated on, might give rise to earthquakes, or to subterraneous volcanoes. On the other hand, as the high land gradually wears away, by the removal of a portion of its thickness, and

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as the cooling down of its surface takes place, its contraction might give rise to enormous rents. If these cracks penetrate to any great reservoirs of melted matter, such as appear to subsist beneath volcanoes, then they will be compressed by the contraction, and the melted matter will rise and fill the cracks, which, when cooled down, will become dykes. If these rents do not reach the internal reservoir of melted matter, and if there exist in the neighbourhood any volcanic vents connected with it, the contraction of the upper strata may give rise to volcanic eruptions, through those vents, which might be driven by such a force to almost any height. These eruptions may themselves diminish the heat of the beds immediately above the melting cauldron from which they arise; for the conversion of some of the fluid substances into gases, on the removal of the enormous pressure, will rapidly abstract heat from the melted mass. As the removal of the upper surface of the high land will diminish its resistance to fracture, so the altered pressure arising from the removal of that weight, and its transfer to the bottom of the ocean, may determine the exit of the melted matter. Other consequences 'might arise from the different fusibility of the various strata deposited in the bed of the ocean. Let us imagine, in the annexed wood cut,

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the two beds, A and B, to melt at a much lower temperature than those between which they intervene. It might happen, by the gradual rising of the isothermal surfaces, that one or both of those strata should be

melted ; and thus, supposing all the beds originally to have contained marine remains, we might, at a distant period, discover two interposed beds, without any trace of such remains, but presenting all the appearances of former fusion, resting on, separated by, and existing under, other beds of demonstrably marine foimation. If, during that former state of fusion, rents should have been formed through several of the strata, injection of the liquid matter might proceed from these melted beds, both upwards and downwards. If, on the contrary, older dykes had penetrated all the strata, it is possible to suppose such a degree of fusibility in the older dyke, or such chemical relation to the melted bed, that the portions of the dyke passing through that bed shall be obliterated, whilst those which traverse

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the less fusible beds, protected from r.uch action, shall remain unaltered, as in the annexed cut.

Another consequence of this constant change in the position of the isothermal surfaces must be the development of thermo-electricity, which, acting on an immense scale, may determine the melting of some beds, or the combination of the melted masses of others, or cause the segregation of veins and crystals, in heated, though not fluid, portions of the strata exposed to its influence. Nor may the dykes themselves be without their use, either in keeping up the communication for the passage of electricity, if they are good conductors, —or in separating the groups of strata which produce it, if they are bad conductors. For the elucidation of this subject, it appears very important that experiment should be made on the effects of long-continued artificial heat in altering and obliterating the traces of organic remains existing in known rocks. It seems probable that by a well-planned series of such experiments, we might be enabled to

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trace the gradually disappearing structure of animal remains existing in rocks subjected to fire, into marks which, without such aid, seem utterly distinct from that origin ; and that we might thus establish new alphabets with which to attempt the deciphering of some of the older rocks.* It appears, therefore, that from changes continually going on, by the destruction of forests, the filling up of seas, the wearing down of elevated lands,—the heat radiated from the earth's surface varies considerably at different periods. Inconsequence of this variation, and also in consequence of the covering up of the bottoms of seas, by the detritus of the land, the surfaces of equal temperature within the earth are continually changing their form, and exposing thick beds near the exterior to alterations of temperature. The expansion and contraction of these strata may form rents and veins, produce earthquakes, determine volcanic eruptions, elevate continents, and possibly raise mountain chains. The further consequences resulting from the working out of this theory would fill a volume, rather than a note.

* Some experiments, with this object in view, were undertaken at the recommendation of the British Association, (See Third Report, p. 479, and Fourth Report, p. 576.) and portions of rock, containing organic remains, have already (1838) been exposed, for above five years, to the heat of the hearth of a blast furnace, at the Elsecar iron works in Yorkshire, through the permission of Earl Fitzwilliam, and at the Low Moor works, by that of the proprietors.

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It may, however, be remarked, that whilst the principles on which it is founded are really existing causes, yet that the sufficiency of the theory for explaining all the phenomena cannot be admitted until it shall have been shown, that their power is fully adequate to produce all the observed effects.

NOTE H.

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TABLE

Showing the Expansion of Beds of Granite variously heated, from One Degree to One Hundred Degrees Fahrenheit, and from One to Five Hundred Miles thick.

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TABLE

Showing the Expansion of Beds of Granite variously heated, from Two Hundred Degrees to Three Thousand Degrees Fahrenheit, and from One to Five Hundred Miles thick.

APPENDIX.

The table was calculated from experiments made under the direction of Colonel Totten, by Mr. H. C. Bartlett, of the United States Engineers; an account of which is given in the American Journal of Science, Vol. XXII. p. 136. From the result of these experiments it was found that, for every degree of Fahrenheit,

Granite expands ............. .000004825 Marble.................. .000005668 Sandstone ................ .000009532

The tables were computed by the Calculating Engine, from the first line, which was deduced from the experiment. It will be observed that the numbers given are always true to the last figure, a compensation which the Engine itself made. In order to find the expansion for marble, increase the numbers by one-sixth. To find the expansion for sandstone, double the numbers found in the table. Other experiments have since been made by Mr. Adie, of which an account is given in the thirteenth volume of the Transactions of the Royal Society of Edinburgh : from these I have selected the following list of expansions :—

Roman Cement expands ......... .00000750 Sicilian White Marble .......... .00000613 Carrara Marble .............. .00000363

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Sandstone, from Craigleith quarry .... .00000652 Slate, from Penrhyn, Wales ....... .00000576 Peterhead Red Granite .......... .00000498 Arbroath Pavement............ .00000499 Caithness Pavement. ........... .00000497 Greenstone, from Ratho ......... .00000449 Aberdeen Grey Granite ......... .00000438 Best Stock Brick ............. .00000306 Fire Brick ................. .00000274 Black Marble, Galway .......... .00000247

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NOTE I.

I am happy to be enabled to put before the reader extracts from two letters of Sir J. Herschel, which show, that though my early friend is extending the boundaries of our system, by his observations in the southern hemisphere, his active and indefatigable mind has yet found time to throw its comprehensive glance over some of the highest questions which perplex other sciences. I feel, that the almost perfect coincidence of his views with my own, gives additional support to the explanations I have offered ; whilst the reader will perceive, from the different light in which my friend has viewed the subject, that we were both independently led to the same inferences by different courses of inquiry. I. The first of the letters to which I allude, and of which I shall extract the greater part, is addressed to Mr. Lyell.

" Feldhausen, Cape of Good Hope, Feb. 20, 1836. " MY DEAR SlR,

" I am perfectly ashamed not to have long since ac-" knowledged your present of the new edition of your

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" Geology, a work which I now read for the third " time, and every time with increased interest, as it " appears to me one of those productions which work " a complete revolution in their subject, by altering " entirely the point of view in which it must thence-" forward be contemplated. You have succeeded, too, " in adding dignity to a subject already grand, by ex-" posing to view the immense extent and complication " of the problems it offers for solution, and by unveiling " a dim glimpse of a region of speculation connected " with it, where it seems impossible to venture without " experiencing some degree of that mysterious awe " which the sybil appeals to, in the bosom of ^Eneas, " on entering the confines of the shades—or what the " Maid of Avenel suggests to Halbert Glendinning,

'He that on such quest would go, must know nor fear nor failing; To coward soul or faithless heart the search were unavailing.'

" Of course I allude to that mystery of mysteries, the " replacement of extinct species by others. Many " will doubtless think your speculations too bold, but " it is as well to face the difficulty at once. For my " own part, I cannot but think it an inadequate con-" ception of the Creator, to assume it as granted that " his combinations are exhausted upon any one of the " theatres of their former exercise, though in this, as " in all his other works, we are led, by all analogy, to " suppose that he operates through a series of inter-" mediate causes, and that in consequence the origina-

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" tion of fresh species, could it ever come under our " cognizance, would be found to be a natural in con-" tradistinction to a miraculous process—although we " perceive no indications of any process actually " in progress which is likely to issue in such a " result." " Now for a bit of theory. Has it ever occurred to " you to speculate on the probable effect of the trans-" fer of pressure from one part to another of the earth's " surface by the degradation of existing and the for-" mation of new continents—on the fluid or semi-fluid " matter beneath the outer crust? Supposing the " whole to float on a sea of lava, the effect would " merely be an almost infinitely minute flexure of the " strata; but, supposing the layer next below the " crust to be partly solid and partly fluid, and com-" posed of a mixture of fixed rock, liquid lava, and " other masses, in various degrees of viscidity and " mobility, great inequalities may subsist in the distribution of pressure, and the consequence maybe, " local disruptions of the crust, where weakest, and " escape to the surface of lava, &c. If the obstructions " to free communication among distant parts of a fluid " be great, no instantaneous propagation of pressure

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can subsist, the hydrostatical law of the equality of pressure being only true of fluids in a state of undisturbed equilibrium. If the whole contents of the fissures, pipes, &c., into which we may consider the interior divided, were lava, it is true no increase of pressure on the bed of an ocean, from deposited matter, could force the lava up to a higher level than the surface, or so high. But if the contents be partly liquid, partly gaseous, or partly water, in a state to become steam, at a diminished pressure, then it may happen that the joint specific gravity of lava + gas, or lava+ steam occupying any given channel may be less than that of water ; or of the joint column of water + newly deposited matter—which may be brought to press upon it by any sudden giving way of support, and the effect will be the escape of a mixture of lava and gas, either together, as froth and pumice, or by fits, according as they are disposed in the channel. This (taken as a general cause of volcanoes) would account for the great quantity of gaseous matter which always accompanies eruptions, and for the final blow out of wind and dust with which they so often terminate. It has always been my greatest difficulty in Geology to find a primum mobile for the volcano, taken as a general, not a local phenomenon. Davy's speculations about the oxidation of the alkaline metals seems to me a mere chemical dream, and the fermentation of water and pyrites as utterly insignificant on a scale of any

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magnitude. Poulett Scrope's notion of solid rocks flashing out into lava and vapour, on removal of pressure, and your statement of the probable cause of Volcanic Eruptions, in p. 385, vol. ii. 4th Ed. when you speak of the effect of a minute hole bored in a tube, in which liquefied gases are imprisoned, both appear to me wanting in explicitness, and as not going high enough in the inquiry, up to its true beginning, and also as giving, in some respects, a wrong notion of the process itself. The question stares us in the face—How came the gases to be so condensed ? Why did they submit to be urged into liquefaction? If they were not originally elastic, but have become so by subterranean heat, whence came the heat ? and why did it come ? How came the pressure to be removed, or what caused the crack ? &c. &c. " It seems clear that if the gases, or aqueous vapour, were once free, at so high a degree of elasticity as is presumed, there exists no adequate cause for their confinement,—the spring once uncoiled, there is nowhere a power capable of bending it up to the pitch. We are forced therefore to admit, that the elastic force has been superadded to them, during their sojourn below, by an accession of temperature. Now, though I cannot agree with you in your view of the subject of the Central heat, p. 373, vol. ii. 4th Ed. (because I see no reason why the heat may not

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go on increasing to the very centre without necessitating such disturbance of equilibrium as to give rise to any circulation of currents, which you there seem to regard as the necessary consequence of such a state*), yet I agree entirely with what you observe in p. 376, —that the ordinary repose of the surface argues a wonderful inertness in the interior, where, in fact, I conceive that every thing is motionless. Under these circumstances, and debarred from that obvious means of boiling our pot, the invasion of a circulating current, or casual injection of intensely hot liquid matter from below, the question, ' Whence comes the heat T and ' Why did it come ? remains to be answered on sound theoretical grounds. Now, the answer I conceive to be as follows :—

" Granting an equilibrium of temperature and pressure within the globe, the isothermal strata near the centre will be spherical, but where they approach the surface will, by degrees, conform themselves to the configuration of the solid portion ; that is, to the bottom of the sea and the surface of continents. Suppose such a state of equilibrium, and that under

* " Heated liquids circulate not because the lower parts are hotter, but because they are lighter, than the upper. But in the interior of a heated globe, the density depends not only on the temperature, but on the pressure (i. e. the depth) of each stratum ; so that nothing is easier than to imagine a law of increasing temperature which shall co-exist with increasing density.

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" the bottom B of my great ocean D E, the isother-" mal strata are as represented by the black lines.

Now, let that basin be filled with solid matter up to A. Immediately the equilibrium of temperature will be disturbed. Why ?—because the form of a stratum of temperature depends essentially on the form of the bounding surface of the solid above it, that form being one of the arbitrary functions which enter into its partial differential equation. Immediately, therefore, the temperature will begin to migrate from below upwards, and the isothermal strata will gradually change their forms from the black to the dotted lines. The lowest portions at B will then (after the lapse of ages, and when a fresh state of equilibrium is attained) have acquired the temperature of the stratum C, corresponding to their then actual depth, while a point as deep below B as C is below the surface, will have

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acquired a much higher temperature, and may become actually melted, and that without any bodily transfer of matter in a liquid state from below. But if C be already at the melting point, B will now be so— i. e. the lower level will attain B, and the bottom of the new strata will melt, water included, with which, from the circumstances of the case, they must be saturated. " Now, let the process of deposition go on, until, by accumulation of pressure on the bottom or sloping sides, or on some protuberance from the bottom, some support gives way—a piece of the solid crust breaks down, and is plunged into the liquid below, and a crack takes place extending upwards. Into this the liquid will rise by simple hydrostatic pressure. But as it gains height, it is less pressed ; and if it attain such a height that the ignited water can become steam, the case before alluded to arises, the joint specific gravity of the column is suddenly diminished, and up comes a jet of mixed steam and lava, till so much has escaped that the deposited matter takes a fresh bearing, when the evacuation ceases, and the crack becomes sealed up. " In the analysis I have above given of the process of heating from below, we have, if [ mistake not, a strictly theoretical account of that great desideratum of the Huttonian theory—' Let heat,' says he,

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' invade a newly deposited stratum from below.'— But why ? Not because great currents of melted matter are circulating in the nucleus of the globe— not because great waves of caloric are rushing to and fro, without a law and without a cause in the subterranean regions—but simply because the fact of new strata having been deposited, alters the conditions of the equilibrium of temperature, and they draw the heat to them, or, which comes to the same thing, retain it in them in its transit outwards (the supply from the centre being supposed inexhaustible, and its temperature of course invariable).

" According to the general tenor of your book, we may conclude, that the greatest transfer of material to the bottom of the ocean, is produced at the coast line by the action of the sea ; and that the quantity carried down by rivers from the surface of continents, is comparatively trifling. While, therefore, the greatest local accumulation of pressure is in the central area of deep seas, the greatest local relief takes place along the abraded coast lines. Here, then, in this view, should occur the chief volcanic vents. If the view I have taken of the motionless state of the interior of the earth be correct, there appears no reason why any such influx of heat should take place under an existing continent (say Scandinavia) as to heat incumbent rocks (whose bases retain their level) 5 or 600° Fahr, for many miles in thickness. (Princ. of Geol.

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vol. ii. p. 384.4th Ed.) Laplace's* idea of the elevation of surface due to columnar expansion (which you attribute, in a note, to Babbage,) is in this view inadequate to explain the rise of Scandinavia, or of the Andes, &c. But, in the variation of local pressure due to the transfer of matter by the sea, on the bed of an ocean imperfectly and unequally supported, it seems to me an adequate cause may be found. Let A be Scandinavia, B the adjacent ocean (theNorth Sea), C a vast deposit, newly laid on the original bed D of the ocean ; E E E a semi-fluid, or mixed

mass, on which D D D reposes. What will be the effect of the enormous weight thus added to the bed DDD (rock being heavier than sea)? Of course,

* " Nisi Mitscherlich's. I remember well to have read it somewhere other."

[This was written before my friend had received the abstract of the paper on the Temple of Serapis, forwarded to him by Mr. Lyell. The reader will perceive, by Note G. of the Appendix, that isothermal sur..es form the prominent feature of both our views of this question.— B.]

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to depress D under it, and to force it down into the yielding mass E, a portion of which will be driven laterally under the continent A, and upheave it. Lay a weight on a surface of soft clay : you depress it below, and raise it around the weight. If the surface of the clay be dry and hard, it will crack in the change of figure." " I don't know whether I have made clear to you ray notions about the effects of the removal of matter from above, to below, the sea. 1st. It produces a mechanical subversion of the equilibrium of pressure. 2dly. It also, and by a different process (as above explained at large), produces a subversion of the equilibrium of temperature. The last is the most important. It must be an excessively slow process, and will depend, 1st, on the depth of matter deposited ; 2dly, on the quantity of water retained by it under the great squeeze it has got ; 3dly, on the tenacity of the incumbent mass—whether the influx of caloric from below, which must take place, acting on that water, shall either heave up the whole mass, as a continent, or shall crack it, and escape as a submarine volcano, or shall be suppressed until the mere weight of the continually accumulating mass breaks its lateral supports at or near the coast lines, and opens there a chain of volcanoes.

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" Thus the circuit is kept up—the primum mobile is the degrading power of the sea and rains (both originating in the sun's action) above, and the inexhaustible supply of heat from the enormous reservoirs below, always escaping at the surface, unless when repressed by an addition of fresh clothing, at any particular part. In this view of the subject, the tendency is outwards. Every continent deposited has a propensity to rise again ; and the destructive principle is continually counterbalanced by a re-organizing principle from beneath. Nay, it may go farther—there may be such a tendency in the globe to swell into froth at its surface, as may maintain its dimensions in spite of its expense of heat ; and thus preserve the uniformity of its rotation on its axis, in spite of the doctrines of refrigeration and contraction, (which, by the bye, had occurred to myself, and been rejected, as inadequate to give a general formula of explanation of volcanoes, &c.) Perhaps I shall recur to this subject on some future occasion ; but really the stars leave me very little time to lick into form any geological theories, or even to examine them with any degree of scrupulous severity." II. The following is the copy of a letter from Sir John Herschel to Mr. Murchison, in explanation of the views expressed in his previous letter to Mr. Lyell.

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" Feldhausen, Cape of Good Hope, Nov. 15,1836.

" In the letter you allude to as having been written by me to Mr. Lyell, there were some speculations about the effect of central heat on newly-deposited matter, which, judging from some expressions in his answer to that letter, I am inclined to think must have been put obscurely, since he appears disposed to regard the view I took of the subject as identical with some theory ascribed to Mr. Babbage (but, I believe, before propounded by Mitscherlich) about the elevation of strata by pyrometric expansion of the subjacent columns of rock, by an invasion of subterraneous heat. Granting the heat, there is no difficulty in deducing expansions, disruptions, tumefactions, &c. ; but this was not my drift. Will it be trespassing too much on your patience if I here state, in brief, what I really had in view—which, so far as I can recollect, has not hitherto been duly, or not at all, considered ? If you like to call it my ' theory,' you may do so ; but it is not so much ' a theory,' as a pursuing into its consequences, according to admitted laws, of the hypothesis of a high central temperature, which many geologists admit, and all are familiar with. " Granting, then, as a postulate, a gradation of temperature within the globe, from the observed external temperature at the surface, up to a high state

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of incandescence at the centre : I say, that when solid matter comes to be deposited to any considerable thickness on any part of the bed of the ocean, by subsidence, (or even on the surface of a continent, by volcanic ejection, as in great volcanic plateaux and table-lands, or by the action of the wind,.as in sand hills,) the mere fact of such accession of materials, without requiring any other condition, or concomitant cause, will, of itself, in virtue of the known laws of the propagation of heat through a slowly-conducting mass, immediately subvert the equilibrium of temperature, and induce a change in the form of the isothermal surfaces (curves of equal temperature) in the whole region immediately beneath, and surrounding the point of deposition—causing all those surfaces (which, you will observe, are only imaginary mathematical ones, like lines of equal variation in a magnetic chart—not real strata) to bulge outwards, and recede from the centre in that part. The direct consequence of this will be, that any given point of the surface on which the deposit took place will, when a new state of equilibrium is attained, (supposing it to be so) have a temperature corresponding to an isothermal surface of a deeper order : i. e., it will have become hotter than it was previous to the new deposit ; and the same is true of every point in the vertical line drawn from that point downwards. Supposing, as before said, a new state of equilibrium to be attained, (the deposition ceasing, by the filling up

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of the sea in that part) then the temperature of the lowest parts of the newly-formed strata will be that of a point situated beneath the surface of an old continent in the same latitude, at a depth equal to the thickness of the deposited matter. The thicker, therefore, the deposit, the hotter will its lower portions tend to grow; and, if thick enough, they may grow red hot,or even melt. In the latter case, their supports being also melted or softened, may wholly or partially yield, under the new circumstances of pressure, to which they were originally not adjusted; and the phenomena of earthquakes, volcanic explosions, &c., may arrive—while, on the other hand, if no cracks occur, and all goes on in quiet, the only consequence will be, the obliteration of organic remains, and lines of stratification, &c.—the formation of new combinations of a chemical nature, &c. &c.—in a word, the production of Lyell's ' metamorphic-' rocks. " The process described above is precisely that by which a man's skin grows warmer in a winter day by putting on an additional great coat ; the flow of heat outwards is obstructed, and the surface of congelation carried to a distance from his person, by the accumulation of heat thereby caused beneath by the new covering. " You see, therefore, that my object is to get at a geological ' primum mobile? in the nature of a vera

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causa, and to trace its working in a distinct and intelligible manner. In future, therefore, instead of saying, as heretofore, 'Let heat from below invade newly-deposited strata (Heaven knows how or why), then they will melt, expand,' &c. &c., we shall commence a step higher, and say, ' Let strata be deposited.' Then, as a necessary consequence, and according to known, regular, and calculable laws, heat will gradually invade them from below and around ; and, according to its due degree of intensity at any assigned time, will expand, ignite, or melt them, as the case may be, &c. &c. &c. ; and, I mistake greatly, if this be not a considerable reform in our geological language.

" According to this view of the matter, there is nothing casual in the formation of Metamorphic Rocks. All strata, once buried deep enough, (and due time allowed ! ! !) must assume that state,—none can escape. All records of former worlds must ultimately perish. " P.S.—If you think it worth while to read the above speculation whenever a discussion may arise, naturally leading to it, at any meeting of the Geological Society, (not as a formal communication, for I have not time to put it into shape, or work it out in detail, but incidentally) you are quite at liberty to do so ; and I shall be glad to know your own opinion of it."

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Since the first edition of this work was published, Mr. Lyell has received another letter from Sir John Herschel, explanatory of his views on this subject ; and I am happy to place before the reader the following extracts, not because there is any necessity to prove that my friend arrived independently at the same conclusions with myself, but because they afford additional illustrations of a view which we both think deserving of further inquiry. This letter was written by Sir John Herschel previously to the receipt of the first edition of this volume, which I had forwarded to him at the Cape of Good Hope.

" Feldhausen, June 12, 1837.

" I reply to your note, however, immediately, " because there are points in it, and in a letter of " Murchison's I lately received, but especially in " yours, which call for immediate notice on my part, " lest I should be supposed to have willingly and " knowingly, what our French neighbours call, " ' emprunté des idées,'—appropriated the ideas of " Babhage ; to which charge should any one feel " disposed to bring it (B. I am sure will not), I plead " not guilty. Till the arrival of Murchison's letter, " in fact, I was utterly unaware that Babbage had (or " any body else) speculated on that peculiar mutual

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reaction of the surface and interior of the globe, which consists in what, I think, we 'must now call ' the secular variation of the isothermal surfaces ' of the latter. The idea I considered as entirely my own ; and I was never more taken by surprise, than when to-day, directed for the first time by an express mention in your letter of a paper of Bab-bage's, abstracted in the Geological Notices, I hunted up all those notices in my possession, and found in an uncut Number (No. 36,)—as I am sorry to say many of these, and other not less interesting brochures which have reached me, still are— an abstract of a paper on the Temple of Serapis, at the end of which a theory identical with mine in that leading point, undoubtedly stands printed. " Convinced as I feel of the great importance of this general view of geological revolutions, in contrast with all the arbitrary, local, and temporary expedients which have hitherto been resorted to to explain particular phenomena, and to the recourse had to ' the volcano and the earthquake,' as the great explaining powers ; whereas in this view, these are only symptomatic phenomena, natural and necessary concomitants of systems of action much more extensive, which are constantly going forwards. ...But as I do, at all events, lay claim to absolute independence of speculation on the subject, it is quite right that I should make clear to you and to

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' him the progress of my own ideas, and also account ^: for what must have appeared singular in my own ^; mention of his speculations in my letter to Murchison. And to take the last first :—The fact is, that I never was aware that Babbage had made any communication to the Geological Society on the subject, till Murchison's letter first led me to suppose, and yours expressly stated, by referring to the Proceedings for an abstract, that such was the case. The passage in your book and note appended, (Vol. II. p. 383, 4th Edit.) contain no allusion to the cause of rocks becoming heated from below. The employment of the pyrometric expansion of rocks as a motive power, was, I feel confident, suggested by some one (and the name of Mitscherlich or Laplace, has somehow got connected in my memory with it) many years ago, certainly before 1833. Of this B. must have been as ignorant as I was of his views, as he appears to have based his ideas on Colonel Tottens'* experiments (when made I know not). And I only remembered to have read Babbage's paper on the Temple of Serapis, published in one of the quarterly journals not long after his arrival from the Continent, in which, so far as I recollect, this point is not touched upon ; nor is it in your speech from the chair, where alternate pyrometric expansion and contraction, without reference

The origin of my view is stated in the first paragraph of this Note.

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to the cause of the invasion or abstraction of heat, are alone alluded to.

" However, discussion of points of this sort is of little moment in itself; as, if a theory be founded in sound views, it matters little to the world whether A. or B. or A. and B. first entertained it, or whether it arose in the whole alphabet when its seeds were ready to germinate. As regards the course of my own ideas, it was simply this. When I first read your book, I was struck with your views of the metamorphic rocks, and I began to speculate how and why the mere fact of deep burial might tend to raise their temperature to the required point. Three modes occurred :—1st. Development of heat by condensation ; but this cause seemed somewhat feeble, and not very clear in its mode of action, since at every moment an equilibrium of pressure and resistance is established. 2dly. Plunging down into an ignited pasty mass ; here however, considering the excessive slowness of the process, it occurred to me that there would be plenty of time for the ignited matter below, not merely to divide its caloric with the newly superposed mass, but to take up fresh from below, and thus to establish a regular gradation of temperature from below upwards. And this led to the 3d and more general view of the matter, which is that of the variation of isothermal surfaces, as stated in my letters to Murchison and yourself.

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" These notions had been fermenting and regurgitating in the cavities of my brain, from the moment I first read your statement of the metamorphic doctrine in your first edition ; but what determined the disruption of the incumbent stratum, and their final explosion, was the reperusal of your little 12mo. edition you were so good as to send me. " All things considered, however, I do not regret having written what I did : and I am still so far disposed to regard it as publici juris, as to wish that such passages in my letters as yourself and Mur-chison may think eligible for the purpose, might on some fitting opportunity be read at a meeting of the Geological Society. (All idea of my drawing up a regular paper is out of the question, I am so involved in other matters at present.) It will draw attention to the subject, and science will gain by the discussion. " When people think independently at different times, and excited by different original subjects of consideration, bearing on one more general object, if their ideas converge towards one view of the matter, it is a proof that there is something worthy of further inquiry ; and if they think to any purpose, it is hardly possible but that many points will occur to each, which do not to the other, and that so a theory may branch out and acquire a body much

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sooner than it would do by the speculations of one alone ;—and indeed such is in some degree the case in the present instance. Babbage, for example, has speculated not only on the heaping on of matter in some parts, but on its abstraction in others, as a cause of variation in the isothermal surface ;—and justly ; it is a case of the algebraic passage from + to — passing through 0. In envisaging (as the French call it) the question algebraically, the cases could not be separated. Again, he has confined himself to the pyrometric changes in the solid strata, while I have left these out of view, and relied on what I think to be a far more energetic and widely acting cause—the variation of pressure, and the infirmity of supports broken by weight or softened by heat, to produce tilts. Both causes, however, doubtless act, and both rriust be considered in further detail : the former alone may account for the phenomena of the Bay of Naples ; the latter must, I think, be called into account for those of Scandinavia and Greenland, and of the Andes.

" I would observe that a central heat may or may not exist for our purposes. And it seems to be a demonstrated fact, that temperature does, in all parts of the earth's surface yet examined, increase in going down towards the centre, in what I almost feel disposed to call a frightfully rapid progression ; and though that rapidity may cease, and the progression even

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take a contrary direction, long before we reach the ^; centre, (as it might do, for instance, had the earth, originally cold, been, as Poisson supposes, kept for a few billions or trillions of years, in a firmament full of burning suns, besetting every outlet of heat, and then launched into our cooler milky way) still, as all we want is no more than a heat sufficient to melt silex, &c. I do not think we need trouble ourselves with any inquiries of the sort, but take it for granted, that a very moderate plunge downwards, in proportion to the earth's radius, will do all we want. Nay, the internal heat may even be locally unequal ; i. e. great in Europe and Asia, small under America, —as it would, for example, if, when roasting at Poisson's sun-fire, the great jack of the universe had stood still, and allowed one side of our terraqueous joint to scorch, and the other to remain underdone. —A hint to those who are on the look out for a cause (if any such there be) for the ' poles of maximum cold,' and the general inferior temperature of the American climate, from end to end of that continent."

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NOTE K.

ON THE ELEVATION OF BEACHES BY TIDES.

if the earth were a spheroid of revolution, covered by one uniform ocean, two great tidal waves would follow each other round the globe at a distance of twelve hours.

Suppose several high narrow strips of land were now to encircle the globe, passing through the opposite poles, and dividing the earth's surface into several great unequal oceans, a separate tide would be raised in each. When the tidal wave had reached the farthest shore of one of them, conceive the causes that produce it to cease ; then the wave thus raised would recede to the opposite shore, and continue to oscillate until destroyed by the friction of its bed. But if, instead of ceasing to act, the causes which produced the tide were to

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reappear at the opposite shore of the ocean, at the very moment when the reflected tide had returned to the place of its origin ; then the second tide would act in augmentation of the first, and, if this continued, tides of great height might be produced for ages. The result might be, that the narrow ridge dividing the adjacent oceans would be broken through, and the tidal wave traverse a broader tract than in the former ocean. Let us imagine the new ocean to be just so much broader than the old, that the reflected tide would return to the origin of the tidal movement half a tide later than before : then, instead of two superimposed tides, we should have a tide arising from the subtraction of one from the other. The alterations of the height of the tides on shores so circumstanced, might be very small ; and this might again continue for ages : thus causing beaches to be raised at very different elevations, without any real alteration in the level either of the sea or land. If we consider the superposition of derivative tides, similar effects might be found to result ; and it deserves inquiry, whether it may not be possible to account for some remarkable and well-attested phenomena by such means. The gradual elevation during the past century, of one portion of the Swedish coast above the Baltic, is a recognised fact, and has lately been verified by

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Mr. Lyell.* It is not probable, from the form and position of that sea, that two tides should reach it distant by exactly half the interval of a tide, and thus produce a very small tide ; nor is it likely that by the gradual but slow erosion of the longer channel, one tide should almost imperceptibly advance upon the other : but it becomes an interesting question to examine whether, in other places, under such peculiar circumstances, it might not be possible that a series of observations of the heights of tides at two distant periods, might give a different position for the mean level of the sea at places so situated. If we conceive two tides to meet at any point, one of which is twelve hours later than the other, the elevation of the waters will arise from the joint influence of both. Let us suppose, that from the abrasion of the channel, the later tide arrives each time one-hundredth of a second earlier than before. After about 3,150 years, the high water of the earlier tide will coincide in point of time with the low water of the later tide : and the difference of height between high and low water will be equal to the difference of the height of the two tides, instead of to their sum, as it was at the first epoch. If, in such circumstances, the two tides were nearly

* See Phil. Trans. 1836.

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equal in magnitude, it might happen that on a coast so circumstanced, there would at one time be scarcely any perceptible tide ; and yet, 3000 years after, the tide might rise 30 or 40 feet, or even higher; and this would happen without any change of relative height in the land and water during the intervening time. Possibly this view of the effects which may arise, either from the wearing down of channels, or the filling up of seas through which tides pass, may be applied to explain some of the phenomena of raised beaches, which are of frequent occurrence. Natural philosophers are at present not quite agreed upon the mode of determining the mean level of the ocean. Whether it is to be deduced from the averages between the highest and lowest spring tide, or from the averages of all the intermediate ones, or from the means of the instantaneous heights of the tide at all intervening periods—or by whatever other process, its true level is yet to be ascertained. It may, perhaps, also be useful to suggest that, besides the actual level of the sea at any particular place, it would be also desirable to ascertain whether the time of high water at given epochs is not itself a changeable quantity, These reflections, however, are only thrown out with the view of exciting discussion on a subject involved at present in great mathematical difficulties, and possessing, at the same time, the highest practical importance.

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NOTE L.

ON RIPPLE-MARK.

the small waves raised on the surface of the water, by the passage of a slight breeze, are called Ripple ; and a series of marks, very similar in appearance, which are sometimes seen at low water on the flat part of a sea-beach formed of fine sand, are called ripple-marks. Such marks occur in various strata of stone, and at various depths below the solid surface of the globe, and are regarded as evidence of their having been formed beneath the sea. Similar appearances occur when a strong wind drives over the face of a sandy plain, and are frequently seen upon the surface of snow.

It appears that two fluids of different specific gravity, the lighter passing over the surface of the former, always concur in the formation of ripple. It seems also

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that the lines of ripple-mark are at right angles to the direction of the current which forms them. If a fluid like air pass over the surface of perfectly quiescent water, in a plain absolutely parallel, it will have no effect ; but if it impinge on the surface of the water with the slightest inclination, it will raise a small wave, which will be propagated by undulations to great distances. If the direction of the wind is very nearly parallel to the surface, this first wave, being raised above the general surface, will protect that part of the water immediately beyond it from the full effect of the wind, which will therefore again impinge upon the water at a little distance : and, this impact concurring with the undulation, will tend to produce another small wave, and thus, new waves will be produced. But the under surface of the air itself will also during this process assume the form of waves, and so, on the slightest deviation at any one point from absolute parallelism in the two fluids, their whole surfaces will become covered with ripples. If one of the fluids be water, and the lower fluid be fine sand, partially suspended in water, these marks do not disappear when the cause ceases to act, as they do when formed by movement of air over the surface of water ; but they remain and form the ridges or ripple which we observe when the tide has receded from a flat, sandy shore.

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If, after the formation of ripple-marks at the bottom of a shallow sea, some adjacent river or some current deposit upon them the mud which it holds in suspension, then the first marks will be preserved, and new ripple marks may appear above them. Such is the origin of those marks we observe in various sand-stones, from the most recent down to those of the coal measures. Dr. Fitton informs me, that the sand hills on the south of E tapies (in France) consist of ripple-marks produced by the wind on a very large scale. They are crescent-shaped hillocks, many of which are more than a hundred feet high. The height is greatest in the middle of the crescents, declining towards the points ; and the slope on the inner side of the crescent, which is remote from the prevailing direction of the winds, is much more rapid than that on which it strikes. Mr. Lyell has observed and described this mode of formation of ripple on the dunes of sand near Calais; remarking, that in that case there is an actual lateral transfer ; the grains of sand being carried by the wind up the less inclined slope of the ripple, and falling over the steep scarp. I have observed the same fact at Swansea. A similar explanation seems to present itself as the origin of that form of clouds familiarly known as " a mackarel sky"—a wave-like appearance, which pro-

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bably arises from the passage of a current of air above or below a thin stratum of clouds. The air, being of nearly the same specific gravity as that of the cloud it acts upon, would produce ripple of larger size than would otherwise occur. The surface of the sun presents to very good telescopes a certain mottled appearance, which is not exactly ripple, and which it is difficult to convey by description. It may, however, be suggested, that wherever such appearances occur, whether in planetary or in stellar bodies, or in the minuter precincts of the dye-house and the engine-boiler, they indicate the fitness of an inquiry, whether there are not two currents of fluid or semi-fluid matter, one moving with a different velocity over the other, the direction of the motion being at right angles to the lines of waves

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NOTE M.

ON THE AGE OF STRATA, AS INFERRED FROM THE RINGS OF TREES EMBEDDED IN THEM.

THE indelible records of past events which are preserved within the solid substance of our globe, may be in some measure understood without the aid of that refined analysis on which a complete acquaintance with them depends. The remains of vegetation, and of animal life, embedded in their coeval rocks, attest the existence of far distant times ; and as science and the arts advance, we shall be enabled to read the minuter details of their living history. The object of the present note is to suggest to the reader a line of inquiry, by which we may still trace some small portion of the history of the past in the fossil woods which occur in so many of our strata. It is well known that dicotyledonous trees increase in size by the deposition of an additional layer annually

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between the wood and the bark, and that a transverse section of such trees presents a series of nearly concentric though irregular rings, the number of which indicates the age of the tree. The relative thickness of these rings depends on the more or less flourishing state of the plant during the years in which they were formed. Each ring may, in some trees, be observed to be subdivided into others, thus indicating successive periods of the same year during which its vegetation was advanced or checked. These rings are disturbed in certain parts by irregularities resulting from branches ; and the year in which «ach branch first sprung from the parent stock may be ascertained by proper sections. It has been found by experiment, that even the motion imparted to a tree by the winds has an influence on its growth. Two young trees of equal size and vigour were selected and planted in similar circumstances, except that one was restrained from having any motion in the direction of the meridian, by two strong ropes fixed to it, and connecting it to the ground, at some distance towards the north and south. The other tree was by similar means prevented from having any motion in the direction of east and west. After several years, both trees were cut down, and the sections of their stems were found to be oval; but the longer axis of the oval of each was in the direction in which it had been capable of being moved by the winds.