In like manner, in regard to the question of fluids in the moon, unless such observations, as those of Schroster cited above, be sufficient to prove their existence, or new facts came to light, we cannot scientifically assert it. But as little can we scientifically deny it, unless observations have been such as no small quantity could in any circumstances elude.

In such a case, all we have a right to say is, we do not know ;—just as previously to the invention of the microscope, men could not, without denying fact, have denied the existence of infusoria; fact is fact, whether known or unknown; but they could truly have asserted that the existence of these was unknown.

But may not fluids exist on the moon, even in large quantity, and yet elude terrestrial observation? Attempts to establish this have been made. It was some time since announced that Professor Hausen, a Danish astronomer, had determined the moon's centre of gravity to be towards the side remote from the earth. Supposing this demonstrated, the inference at once is, that the fluids, being accumulated round the centre of gravity, are drawn to the further side of the moon, and not at all, or only a small portion of them, exposed to human view. In an out-station of India, I have no means of access to the paper of Hausen, nor the

period. Then, and then only, will believers in the recent origin of the human race have a case to consider. And let those innovators who assign a pre-Adamic origin to our race, and determine man to be the only rational being, bethink themselves how they will settle the controversy with an opposite class of innovators, who, instead of ignoring all rational beings of higher or lower order except Adamites, allege no less than some seventeen progenitors of so many independent races now walking the earth under the common designation of men.

To this a friend adds the following very suggestive fact: "The conclusion from Horner's discovery of pottery is most untenable. The Nile, I have no doubt, from my own observations, shifts its bed not perhaps so rapidly as the Ganges, yet in a similar way. A few years ago a brick house stood high on the very brink of the Hoogly, and was deserted; a part of it fell down into the river, which, however, approached no nearer, but threw up a bank to the level of the plain, and receded to a considerable distance. The Ganges does not make an annual deposit equal to that of the Nile; yet if Mr. Horner will go to that old ruin, and bore on the east side of it, he will find bricks and broken lotas 30 or 40 feet deep, indicating the peopling of the Sunderbunds 15,000 years at least."

In like manner, the famous human skeletons of the Guadaloupe limestone prove nothing until the antiquity of the stone is definitively established. And when we are told of two human foot-prints in old red sandstone on the banks of the Mississipi, we cannot but ask, why are they not shown in situ? and why only two? And from a print given in a work before me I would ask, are they human? I have looked at impressions of the soles of the fect of natives of this country, and find them different.

least idea of the nature of his reasoning.* But the statement that such a demonstration had been produced, and appeared to have stood uncontroverted, induced me to renew, and trace to results, some speculations I had made years before. Finding no satisfaction from astronomical works, I have been thrown on the first principles of celestial mechanism. I have thus been led step by step to the conclusion that— The Moon is ovoidal, with the prolate axis permanently directed to the earth, or in the line of the moon's radius vector, the more oblate end remote from the earth, and the dynamical or oscillatory centre nearer that end. In explanation I may remark that I use the word axis here, not as an axis of rotation, for the idea of rotation enters not into the proposition, but in the same way as the word is used in Spherical Trigonometry and Conic Sections, to denote a diameter vertical to a given great circle, or the greatest and least diameters of an ellipse, and as the author of the last note has appropriately used the word. Ellipse and ellipsoid, though practically, are not mathematically exact. I therefore use the word ovoidal, though, under the dynamical law referred to in the demonstration, the figure is doubtless proximate to

On this point, one of my friends referred to has favoured me with part of the requisite information: "Theoretical considerations lead to the conclusion, that the moon must either be ellipsoidal, with its major axis nearly parallel to the radius vector, or that its interior is heterogeneous (or both), and its centre of gravity not corresponding with its centre of figure. The first is not confirmed by observation, unless it has recently been so by the photographic labours of De la Rue, who has taken some careful stereoscopic views; and I have a sort of indistinct recollection of having heard that they tended to confirm the idea of an ellipsoidal figure. Hausen's propositions are:

"1. If the moon's centre of gravity and the centre of its figure do not coincid», then must all the co-efficients of the inequalities in mean longitude be multiplied by a constant factor, which is a function of the distance between the two centres projected on the radius vector. And, 2. If the centre of the moon be further removed from us than the centre of gravity, then is this factor less than unity; but if, on the contrary, the former be nearer to us than the latter, the factor will be greater than unity.

"Airy's Greenwich Observations (1750-1850) show that the theoretical co-efficients must all be increased or, according to Hausen, multiplied by 1·0001544, in order to reconcile them with observation; which makes the distance of the centre of gravity behind that of figure to be 33.5055 English miles."

This, let me add, is quite a distinct inquiry from that which I institute; but it is all the more satisfactory when the results are found to harmonize. It shows inductively that the moon is not of uniform density, the denser matter being on the further side, and therefore the centre of gravity being towards that side, while I propose to investigate the moon's oscillation, in one particular, so as to show that, even if the density be uniform, the centre of oscillation is on the remoter side.

an ellipsoid, or more correctly, perhaps, prolate spheroid, since the oblate and the prolate spheroids or ellipsoids are equally related to the ellipse, the one being formed by its revolution round the minor, and the other round the major axis.

To prove the proposition, it might be sufficient for those intimately acquainted with mechanical philosophy to refer to the law of oscillation, and to exemplify in the fact that a body moving in a curve, as a carriage turning a corner, has the centre of gravity constant, yet a certain velocity will make it upset and fall outwards. In this case, the centrifugal or oscillatory force is concentrated in a centre more remote than the centre of gravity from the centre of motion. On the same principle, in the case of the moon, the earth is the centre of motion, and if the mass be uniform, the centre of a great circle or ellipse in the plane of the line joining the centres of the two bodies is the initial centre of gravity, that is, before it has acquired centrifugal force. But the centrifugal force gives it a centre of circular motion more remote than this centre of gravity. The mass of the moon being considered as concentrated in this centre, that mass balanced by the equal forces of terrestrial gravitation, and centrifugal or tangential force, has its orbitual distance the radius vector, from which it cannot vary. But it is otherwise with molecules of that mass. Those on the side nearer the earth have a tendency to greater velocity, and therefore more of tangential force, than those on the remote side.

We must, to estimate this difference, consider the figure of the moon as produced by gravitation, and modified by centrifugal force; in other words, we must view it statically and dynamically.

centre.

1. Statically.-Let A (Fig. 2) be the earth's and в the moon's Join AB, and produce it to E. Make CD perpendicular to AB. Supposing the moon primarily spherical, or of a form approaching sphericity, all the matter in the hemisphere CED, by gravitating towards the earth, would have a force additional to its lunar gravity and augmenting its weight. The matter, for example, at any point I would have its attraction to the earth's centre A, if represented by IK, resolved into the forces IJ and JK, of which 1J would give an impulse towards the earth, while JK would be so small as to be inappreciable in adding weight in the direction CB. The aggregate of such forces would combine with the moon's gravitation to increase the weight of all the matter in the hemisphere CED; and thus the regions about E would become oblate, like those about the earth's poles. The contrary would take place in the hemisphere CFD, since the moon's own gravitation draws the matter towards B. Therefore the hemisphere CFD would become prolate to the

earth. Thus the moon, flattened at E and elevated at F, would tend to the ovoid form,-as the dotted curve. In such a form, the centre of gravity would be nearer E than F.

This may be more concisely expressed thus: at 1 the weight of a molecule is increased by the earth's attraction, and all the ordinates to CD in the hemisphere CED shortened, while at L the weight is diminished, and all the ordinates to CD in the hemisphere CED lengthened. The lunar gravitation in the direction CB, and DB. is not increased or diminished.

2. Dynamically.-Suppose the moon to be put in motion in its orbit, and suppose the part of it from E to F to be or become* firm or solid, as those who deny the existence of fluids in the moon allege her whole body to be. Consider now a molecule or mass of the matter at F and another at E as simultaneously beginning to move, i. e. to share in the moon's orbi tual motion. Both revolve round the centre of gravity of the earth and moon. But F is nearer to that centre than E, therefore (by Kepler's third law), the mass F would, if free, move with greater velocity than the mass E. Being more powerfully attracted by the earth, it must do so, to produce a sufficient centrifugal force to balance the greater centripetal, else it would fall to the earth. But, by hypothesis, it is not free, but fixed, as to distance from E. Its tendency to greater velocity must therefore add to the velocity of E, while E must retard it in like proportion; and the resultant of both be in the centre of oscillation or orbitual motion. Also F's greater centrifugal force will give all its particles a tendency away from A, and towards E; and this holds of particles on the surface on each side of F.

Now if, besides the firm matter making the distance FE a fixed quantity, there were also at F a quantity of fluid matter that would immediately obey its greater centrifugal force, which is not like the

It has been suggested that "the hypothesis of plasticity or rigidity must be the same both for the dynamical and statical proof." But for the statical proof it is enough that the initial figure be spherical, whether by gravitation acting for a time on a plastic mass, or by the creative fiat. The same hypothesis as to being fluid or firm would only be necessary if applied to the same instant of time. The words "primarily spherical” refer to the form (in whatever way impressed) antecedent to the lunar revolution. At the instant when that begins, and not earlier (whether or not we suppose previous lapse of time in giving the sphericity), I can correctly start, as I do, my dynamical hypothesis of the body of the moon from F to E being of firm texture,-as it is admitted to be in fact,-in order to demonstrate the form and position which must be assumed by fluids, if existent on its surface.

+ Ift and t' be the times of revolution of two bodies, and d and d' their distances, then t2: t' 2:: d3: d'3. Hence, the smaller the distance the smaller the time, and therefore the greater the velocity.

centrifugal force of the firm parts connected with the like force at E; and thus this fluid at E would seek equilibrium by flowing towards E, at which the fluid would rise to such level as to produce equilibrium. There would thus be, not a tide which fluctuates, but a constant conflux or elevation of fluid at E, while, though F be, as previously shown, elevated towards A, it is not with fluid but solid matter. Its tendency is in proportion to its intensity to counteract the statical force of the earth's attraction, and produce a somewhat nearer approximation to the spherical form. It may be thought that it should completely do so, since the centrifugal and centripetal forces are equal; but this equality is true only of the centre of gravity, not of the matter at the nearer and remoter sides of the moon.

This communication of the centrifugal force from F to E tends to remove the centre of oscillation nearer to E than the statical centre of gravity. If the moon were all fluid, the surface molecules at F would perpetually tend towards E, and tend to impel the molecules at E towards the centre; and in this case also an equilibrium would be produced. The matter in the nearer half of the moon would have a constant impulse towards E, and, according to this impulse, the fluid must seek equilibrium in that direction.

Thus the moon is in a state of stable equilibrium, with the hemisphere CFD always towards the earth. For, as the law of centrifugal force gives a tendency to protuberance on the moon's remoter half, so the centre of gravity lies nearest the aggregate of matter, according to the law of the centre of gravity. There are more molecules of matter beyond the bisection of the prolate axis than on the nearer side of it. If we conceive these aggregates balanced on the arms of a lever, the centre of figure, or even of gravity being fulcrum, the remoter arm, being loaded with the aggregate of oscillatory force, must be the shorter. Now, if the moon were only statically posited, it would tend to fall to the earth, and the centre of gravity would assume the maximum of nearness to the earth. The portion of its mass nearest the earth would tend to maintain that position as being most attracted. Thus the statical equilibrium would be stable; but this depends not on the position of the centre of gravity, and would hold equally whether the moon's density were uniform or not.* But the moon is actually moving in her orbit, or revolving round the earth's and her centre of

This is different from the consideration of the centre of gravity of a body on the earth's surface, because in the latter case no account is taken of the gravitation of the parts of the body towards oue another. The aggregate of gravitation to the earth is considered as united in the centre of gravity.