order of magnitude as the excess itself. Without dwelling, however, on inferences which have not received the sanction of accurate analysis, we may observe that whatever influence we allow to centrifugal force and that of gravity acting on a mass of great dimensions, we cannot still consider the present form of the earth as a modification of any very different form resulting from the action of those forces on a mass originally solid, without having recourse to particular hypotheses. It would seem necessary, for instance, that the axis of rotation in the initial motion should have been at least nearly coincident with a permanent axis of rotation; and also that there should be some particular law of density of the mass in its original form, to ensure in its final form a density which should have a certain symmetrical relation to the axis of rotation, such as doubtless exists in the actual density of the globe. It is the absence of the necessity for all such additional restrictive assumptions that constitutes the great recommendation of the hypothesis of the earth's former fluidity, and which enables us to account, on that hypothesis, in so simple and satisfactory a manner, for the present form and density of the earth, as the results of mechanical causes.

13. Another mode has also been suggested of accounting for the spheroidal form of the earth, independently of the hypothesis of its former fluidity*. Suppose, for instance, its original form to have been spherical, and the period of its rotation the same as at present. The equatorial region would form one continuous ocean, while the land in the polar regions would rise above the level of the ocean, attaining its greatest height at either pole. But these polar tracts of land would be slowly removed by that constant operation on its shores by which the ocean is now wearing away the land which protrudes above its surface, and an approximation to the spheroidal form would doubtless thus be produced if sufficient time were allowed for the operation.

I am not aware that any one has advocated this view of the subject as a probable one, and the distinguished author of the work just referred to, in suggesting it, has made the following remark :-"We are far from meaning here to trace the process by which the earth really assumed its actual form; all we intend is, to show that this is the form to which, under the condition of a rotation on its axis, it must tend; and which it would attain even if originally and (so to speak) perversely constituted otherwise." It may also be observed that geological observation has afforded no indication, as I conceive, of any greater accumulation of sedimentary deposits in the equatorial than in the polar regions. Still this mode of accounting for the earth's spheroidal form might be appealed to (as, in fact, it has been by a distinguished geologist) as one not inconsistent with physical principles and admissible conditions, and therefore as tending to diminish our confidence in the theory which presents the spheroidal form of the earth as a proof of its former fluidity. It is therefore desirable to submit this idea of the possible origin of the spheroidal form to as accurate a test as we are able. But for this purpose it will be necessary to make some hypothesis respecting the internal constitution of the earth as well as its external form. It may perhaps be deemed the simplest supposition, that the primitive matter of the earth would have been of uniform density under a uniform pressure. Adopting this hypothesis in conjunction with that of the earth's primitive sphericity, it would follow that the interior surfaces of equal density would be spherical, having for their common centre the centre of the earth. After the earth had been thus constituted, we must suppose it to have received its spheroidal form by the denudation of its polar regions, and the deposition of the transported matter to

Herschel's Astronomy, page 120,

the region of the equator. To test the truth of this hypothesis, we may appeal to the phænomena already mentioned (art. 11) of precession and nutation, and the corresponding inequality in the moon's motion.

If the density of the earth were uniform, the resultant attraction of the moon or sun on the portion of the terrestrial mass contained within a sphere having its centre coincident with the centre of the spheroid, and its radius equal to the earth's polar radius, would manifestly pass through the centre of gravity of the earth, and would, therefore, have no effect in producing precession and nutation. In such case these phænomena would be due solely to the attraction on the protuberant equatorial mass which forms the excess of the spheroid above the sphere just mentioned. In like manner the corresponding inequality in the lunar motion would also be due entirely to the attraction of the same protuberant portion of the earth's mass on the moon. Supposing the earth's mass and external form to be the same as at present, the annual precession of the pole, as due both to the action of the moon and of the sun, would amount to nearly 58"; and the coefficient of the term expressing the inequality in the moon's motion would amount to about 10".

Again, if we suppose the removal of the superficial mass from the polar to the equatorial regions to take place without affecting the density of the remaining portion of the mass, the resultant attraction of the sun or moon on that portion would still pass through the earth's centre of gravity, and would consequently have no influence in producing the phænomena in question, which would therefore depend entirely, as in the former case, on the equatorial protuberance. Hence, the mass of the earth and its ellipticity being the same in the two cases, the calculated lunar inequalities would be proportional to the densities of the equatorial protuberances, and the calculated precessional motions would be proportional to the densities directly, and to the moments of inertia inversely. In the first case the density is the mean density of the earth; in the latter, it is the superficial density; and these densities (art. 10) may be taken in the ratio of nearly 24 to 1. The moments of inertia may be taken in the ratio of about 6:5, taking the variable density as above (art. 10). Consequently, if the spheroidal form of the earth were due to the cause to which it is here assigned, the annual luni-solar precession would only be about 28", and the coefficient of the lunar inequality about 4". Their actual values, as established by observation, are respectively about 51" and 8", presenting the discrepancies of about 23" and 4" respectively.

In calculating the above amounts of the precession and the lunar inequality, assuming the hypothesis we are considering respecting the earth's spheroidal form, it has been supposed that the general interior mass would retain its primitive density. This would manifestly not be strictly correct, since the density must necessarily be more or less affected by the removal of so large a mass from the pole, and its deposition about the equator. Let E, denote the modulus of elasticity for the solid matter of the earth before being subjected for an indefinite period of time to any more considerable pressure than that to which it would be subjected on the surface of the earth; and let E denote the modulus for the same matter after having been subjected for an indefinite period of time to that enormous pressure to which all matter at considerable depths below the earth's surface must be subjected. Then, without entering into the intricacies which would be involved in the general problem, it may be easily shown, at least for points not too remote from the surface, that if E = Eo, the surfaces of equal density after the change in the earth's form would be approximately similar to the external surface; but if, on the contrary, E be much greater than E, the surfaces of equal density would remain approximately spherical, notwithstanding the change of pressure

due to the change of external form. If this latter be the true supposition, as it will probably be thought to be, the above calculated results will be approximately true, and will furnish unquestionable evidence of the inadmissibility of the hypothesis we have been considering respecting the origin of the earth's spheroidal form; for though the quantities we have to compare as the results of observation and the results of calculation are so small, the limits of error in the determination of them are too narrow to admit of even very much smaller discrepancies than those exhibited in the results stated at the close of the preceding paragraph, if the hypotheses on which the calculations are founded are true.

These particular discrepancies, however, only prove the inadmissibility of the above mode of accounting for the earth's spheroidal form, when we adopt the hypothesis above made respecting the primitive density of the terrestrial mass. If we should adopt some other hypothesis respecting that density, we might undoubtedly account by this theory, not only for the earth's actual form, but also for the other phænomena above mentioned. But it is to the necessity for such particular assumptions that I would here again direct attention, as I have already done at the close of the preceding article. In any theory which assumes the earth's primitive solidity, it is necessary to make some arbitrary hypothesis respecting its primitive law of density; so that, in such theories as those discussed in this and the preceding article, while we admit the general principle of reasoning before laid down (art. 7), in seeking for some secondary cause to which the earth's form may be attributed, we reject in a great measure the application of that principle with reference to the earth's density; since we can only profess to account for it in such theories, by means of some particular and independent hypothesis adopted for the purpose. In the theory which admits the former fluidity of the earth, there is no such inconsistency. No assumption is there made respecting the primitive constitution or density of the terrestrial mass, for the fluid state is only assumed to have been some antecedent, and not necessarily its primitive state; and the present density of the earth becomes as much the necessary consequence of physical causes as its form. The results also of this theory are all in perfect harmony with each other; and we can assert the undoubted adequacy of the causes assigned by it to produce the observed phænomena; while, in the other theories we have discussed, a similar adequacy of causation is, I conceive, extremely doubtful.

If then we admit the general principle of reasoning above alluded to, it appears to me that the theory which asserts the former fluidity of the globe has a much stronger claim to our preference than any other. If, on the contrary, we reject that principle as a guide in our speculations in these remoter regions of geological science, it would seem more consistent, in assuming the earth's original solidity, also to assume that its present spheroidal form was originally impressed upon it, as being that form which would alone admit of an admixture of land and sea in all latitudes, and which thus best adapts its surface to be the habitation of those animate beings which it has been destined to support. But it must be incumbent on those who adopt this view of the subject to explain why, in thus denying that the earth's form and density are to be referred to secondary causes, they reject, with reference to these phænomena, a principle of reasoning and interpretation which they admit with reference to geological phænomena in general, and without which, in fact, geology could have no existence as a physical science.

14. Refrigeration and Solidification of the Earth's Crust.-We may now proceed to consider the process of refrigeration and consequent solidification of the terrestrial mass; and for this purpose I shall beg leave to quote a part

of the preliminary observations from my paper entitled 'Researches in Physical Geology,' published in Part II. of the Transactions of the Royal Society for 1839.

"In the first place, we may observe that there are two distinct processes of cooling, of which one belongs to bodies which are either solid or imperfectly fluid, and is termed cooling by conduction, and the other to masses in that state of more perfect fluidity which admits of a free motion of the component particles among themselves. In this case the cooling is said to take place by circulation or convection. The nature of the former process has been ascertained with considerable accuracy by experiment, and the laws of the phænomena have been made the subject of mathematical investigation, but of the exact laws of cooling by the latter process we are comparatively ignorant. It is manifest, however, that since time must be necessary for the transmission of the hotter and lighter particles from the central to the superficial parts of the mass, as well as for that of the colder and heavier particles in the opposite direction, the temperature must increase with the depth beneath the surface; and, moreover, that this increase will be the more rapid, the more nearly the fluidity of the mass approaches that limit at which this process of cooling would cease, and that by conduction begin, since the rapidity of circulation would constantly diminish as the fluidity should approximate to that limit. But still, even in this limiting case, it seems probable that the tendency to produce an equality of temperature throughout the mass will be much greater, and consequently the rate of increase of temperature in approaching the centre much less, than if the cooling of the mass had proceeded by conduction during the same time, the conductive power being very

small.

"If the matter composing the globe was originally in a high state of fluidity from heat, the process of cooling would undoubtedly, in the first instance, be by circulation. The manner in which the transition will take place from this mode of refrigeration to that by conduction, depends on certain conditions, of which, in our speculations on this subject, it is important to form a distinct conception.

"Since the heat increases with the distance from the surface while the mass is cooling by circulation, the tendency to solidification, so far as it depends on this cause, will be greatest at the surface and least at the centre; but, on the other hand, the pressure is least at the surface and greatest at the centre; and consequently the tendency to solidify, as depending on this cause, will be greatest at the centre and least at the surface. To estimate this tendency under the joint influence of these causes, it would be necessary, in the first place, to know the law according to which the temperature increases in descending from the surface to the centre, while the mass is cooling by circulation; and secondly, the influence of the temperature in resisting solidification, as compared with that of the pressure in promoting it. These, however, are points on which we possess at present little or no experimental evidence, and therefore the only conclusion at which we can arrive is this,— that if the augmentation of the temperature with that of the depth be so rapid, that its effect in resisting the tendency to solidify be greater than that of the increase of pressure to promote it, there will be the greatest tendency to become imperfectly fluid, and afterwards to solidify in the superficial portions of the mass; whereas if the effect of the augmentation of pressure predominate over that of the temperature, this transition from perfect to imperfect fluidity, and subsequent solidity, will commence at the

centre.

"If we suppose the former of these cases to hold, it would appear that no

incrustation of the surface could take place so long as any inferior portion of the mass retained its perfect fluidity, because as the superior particles should become condensed they would continually descend into the perfect fluid beneath, always supposing the mass in that state in which an increase of specific gravity would result from a decrease of temperature. The process of circulation would thus go on till every part of the mass should have lost that degree of more perfect fluidity, which admits of a motion of the particles among themselves being excited by their unequal refrigeration. The circulation, therefore, would cease nearly contemporaneously in every part of the mass, which would then begin to cool by conduction, rapidly at the surface exposed to the low temperature of the planetary space, and extremely slow in the central parts, on account of the small conductive power of the matter composing the earth. Consequently the globe would consist, after a certain time, of an exterior solid crust, and interior fluid matter, of which the fluidity would increase in approaching the centre, where it might still approach to that more perfect fluidity which admits of cooling by convection. With reference, however, to the mechanical action of any forces producing either motion or hydrostatic pressure in the interior mass, the whole of it might, as an approximation, be considered perfectly fluid. No attempt has yet been made to determine the present probable thickness of the earth's crust, assuming it to have been originally in a state of fluidity, on account of the difficulty already mentioned, arising from our ignorance of the influence of high temperature in resisting solidification, compared with that of great pressure in promoting it. All that has hitherto been determined on the subject is, that the present state of the earth's surface may be consistent with the existence of a solid crust, of which the thickness is small compared with the earth's radius.

"Let us now recur to the other case above mentioned, that in which the increase of pressure in descending towards the centre of the mass is supposed to have a greater effect in promoting solidification than the increase of temperature in preventing it. Supposing the mass to have been first in a state in which every part was cooling by convection, this process would first cease, and that of cooling by conduction begin at the centre, while the superior portion would still continue to cool by convection, so that these two processes would for a time be going on simultaneously in different parts of the mass. It is manifest, however, that the central portion, cooling by conduction, would constantly increase, while the exterior portion, cooling by convection, would constantly diminish, so that at length no part of the mass would be cooling by the latter process. Before it should reach this stage of the refrigeration, the central portion of a mass so large as the earth might become perfectly solid, so that at the instant when the circulation should entirely cease, the whole might consist of a solid central nucleus, surrounded by the external portion still in a state of fusion, and of which the fluidity would vary continuously from the solidity of the nucleus to the fluidity of the surface, where, at the instant we are speaking of, it would be just such as not to admit of circulation.

"When the mass should have arrived at this stage of the cooling, a change would take place in the process of solidification, which it is important to remark. The superficial parts of the mass must in all cases cool the most rapidly, and now (in consequence of the imperfect fluidity) being no longer able to descend, a crust will be formed on the surface, from which the process of solidification will proceed far more rapidly downwards, than upwards on the solid nucleus. Consequently, then, our globe would arrive at that state, according to the mode of cooling we are now considering, in which it