nute that they may be neglected. Also, corresponding to these two latter equations, there will be the term in the radius vector dr.=213" cos (73−4p2−33+45°. 57′) -2.13" cos (743-442-343+101°. 11') Amount It must be mentioned that t is supposed here to com of the Earth's displace sent time. mence with the year 1800. It may be worth while to see how the present position ment at of the Earth is affected by the above inequality. This the pre- will be done by substituting for na, es, etc., their numerical values. The values of e,, etc., for the year 1800 are ε3=230°.49′.50", &=100.23.32, &=81.52.10, then 8, = 1862°. 38′ 40′′, 4ɛ2 = 401.38.8, 3ɛ, 245.32.30, by means of these values and those of n,, etc., previously given 80, 7.293" sin (729.39t+210°. 46′), or-7.293" sin (729.39t+30°. 46′), from which we see that the Earth is at present behind its mean place; and by making t=57, we shall find that for the beginning of this year 80-7.293" sin 43°. 58'= -5.06", which gives the quantity by which it is in arrear of its mean place. The time when it was at its mean place will be found by making 729.39′′t+30°. 46′ =0, which will give t= -151.8, that is, it was at its mean place about 151.8 years before the year 1800, or about 209 years ago; since which time it would appear to have fallen back about 5′′, and it will attain its greatest negative value in about 240 years after this, and the motion will then begin to be accelerated. As the period of this inequality is very long, and its amount small, it will take a long course of the most careful observations to determine the circumstances of it, or even to detect its existence at all: nevertheless, if it is correct, it may ultimately be done with quite as much certainty and accuracy as any other inequality of the same amount in which the period was shorter. Of the three bodies which are principally affected by it, that in which it will probably be by far the most considerable, is the Moon; and, consequently, it would seem that this is the body in which it will be most easily detected by observation. Before going to the calculation of any other inequalities which exist, it may be well to make a few remarks upon the one which has been just examined. It is remarkable not only for the facts that have been mentioned, such as its effects upon the motion of the Moon, etc., but for the extreme smallness of the quantities which produce it. Mars is one of the smallest of the planets, and the inequalities in its motion, which give rise to it, are very minute. There appears to be a small inequality of long period in the Small motion of the Earth produced by the long inequality of inequality in Jupiter and Saturn, which, though it does not appear to the moamount to more than about the third of a second, as its tion of period is about 900 years, may have a sensible effect on the the motion of the Moon. It is needless to give the calculation at length; but the following terms, taken from M. Pontécoulant, are the principal ones which produce it. In the coördinates of Jupiter, we have 80=-1187" sin (5-2p,+3° 40′) -161′′ sin (54,-3-58°. 11') -.00202 cos (55—34,—58°. 7'); and in those of Saturn, 80=-2906" sin (54.-24.+3°. 38') Earth. +652.59" sin (4p-2p,-59°.34') dr-.00095 cos (545-24,+32°.32′) +01479 cos (44-24.—59°. 28′). The values of dr here given are expressed in parts of the radius of the Earth's orbit. All these quantities together appear to produce the inequality in the orbit of the Earth 80.354" sin (5-24.—34°.50′). (5.) There are many other combinations of terms like these, which produce small divisors, but no others that I have found in the case of the Earth, which seem to be of importance. As, for instance, the terms depending upon 34-7p+403, and upon 54, -642—403. These, as well as others which there are, may perhaps produce an inequality of a few seconds in the Moon's motion, and so, perhaps, may be worth examination; otherwise they are of no importance. The former appears to amount to about one-fourth of a second; the latter is still less. The principal steps in the calculation of the terms depending on 24.-6p,+3p, mentioned above, and upon 45-40+20,, as well as one or two involving the coördinates of four planets, will be given in a future number. The figure of the Earth proves it to have been once in ART. II. On the Physical Structure of the Earth. By THAT HAT our planet was once in a condition of complete fluidity, is clearly indicated by what Alexander von Humboldt has so happily called the greatest of all geognostical phenomena, the flattening of the earth towards its poles, and its outswelling towards the equator. While the labours of mathematical investigators, since the time a state of of Newton, have rendered more evident the explanation of fluidity. this phenomenon by the fundamental principles of mechanics, the estimate of its absolute amount has been found more and more coincident with the results of observation. Playfair and Sir John Herschel have, it is true, pointed out the possibility of the earth acquiring a sphefect at- roidal shape from the abrading action of its liquid coattempts to ing; but neither of these philosophers have followed out explain all the consequences flowing from the mechanical condiEarth's tions of the problem they had stated. The prominent figure position given to their views, in connexion with certain the by- geological theories, and especially by one of the ablest pothesis writers of the present day,' induced me some years ago to of fluid- give some attention to the question. By the aid of deveity. Imper without 'See Lyell's Principles of Geology, chap. 18, seventh ed.; chap. 31, ninth ed. 2 Proceedings of the Royal Irish Academy, vol. iv., p. 333. 1 lopments in series of Laplace's coefficients, I obtained a mathematical expression for the equilibrium of the watery coating of the abraded spheroid. This expression contains terms depending on the density of land and water, and on the mean density of the earth. Among other results deduced from it, it appears that on the abrasion theory, the difference between the equatorial and polar axes of the fluid covering of the earth, could not exceed of its mean radius. Observation shows that 104.6 its true value is about, and thus we are compelled to regard the abrasion theory of the earth's figure as inadequate to satisfy all the requirements of a perfect theory. In proceeding to consider the general structure of the The earth, it may thus be fairly assumed that it was at one fluid time in a fluid state, in other words, that it was in a state of fusion from intense heat. It is difficult to conceive the any other means of satisfying the condition of fluidity; Earth and direct observations, in every instance that they have from inbeen made, clearly prove the existence of a temperature, tense at points not far below the surface of our planet, which heat. would suffice to melt nearly every substance coming under our notice. former state of resulting fication of the Earth. If the physical properties of the substances existing in the Process earth's interior do not essentially differ from those which of solidicome under our observation, it is possible to arrive at an approximate knowledge of the internal structure of our planet by studying the physical and mechanical changes which would take place during the solidification of substances in a fused state. The fused matter composing the earth would at first evidently consist of a series of spheroidal layers of equal pressure and density, arranged symmetrically around their common centre, the density of each layer increasing with the pressure from the surface to the centre. If pressure were very effective in solidifying the matter of the earth, it might be possible that solidification would commence at the centre. But as yet we have no reason to conclude that great pressure and great density of fused matter may not be inconsistent with its state of fluidity. This is rendered still more manifest by certain conclusions deduced from the dynamical theory of heat, which I have communicated to the British Association. The experiments of M. Cagniard de Latour show that certain gases and vapours may acquire the density of 3 See Athenæum, September 5, 1857, p. 1120. liquids, while still retaining their aeriform condition, provided that the temperature continues extremely high. But, even allowing the possibility of the formation of a solid nucleus from the influence of pressure at the centre of the Earth, where the pressure on the fluid would be greatest, it will soon appear that this nucleus could not long exist under the conditions accompanying the solidification of the superficial parts of the fluid. If we define the solid crust of the Defini- Earth as that portion of it which would be laid bare by tion of stripping off all the rocks evidently deposited as sedimencrust of tary formations, experiment proves that when the rocks the composing the crust of the Earth, as thus defined, are Earth in reduced by heat to a fluid condition, and then allowed the to solidify, they contract in volume to a very considerable inquiry. extent. The density of the solidifying portions will be the solid present Why solidification should thus considerably increased, and the first effect of refri geration on the superficial stratum of the fused mass will therefore be, to cause portions of that stratum to sink downwards through the next adjoining stratum, until they arrive at another of equal density with themselves. The extremely small conducting power of such fused matter will permit us to entirely neglect the direct influence of conduc tion between such portions of the fluid as are not in close contact; consequently the cooling of the remaining strata will take place chiefly by the influence of the descending solidified portions. The portions of the fluid so cooled by contact would also tend to change their positions and to descend in a similar manner. A process of convection would thus take place at the surface of the fluid, but the following causes would tend to impede its propagation towards the interior of the mass: 1. The fluid rendered dense by refrigeration would descend into strata successively denser from compression. 2. The passage of the cooled matter through these strata would tend to make them still more dense. 3. The densities of the portions descending from the surface, would be diminished by the increase of their own temperature from contact with strata nearer to the centre. From these actions, not only would the cooled portions of the superficial strata of the fluid come more quickly in contact with strata of the same density, below which they could not further descend, but also, their motions would be more resisted in proportion to the density of the strata the sur- passed through; and thus the energy of the process of conface so as vection, unlike the same process in a perfectly homogeneous com mence at |