on this subject about three months before the appearance of your notice of my book in February last; but the latter remains uncompleted, as I have not been able to satisfy myself on an investigation upon which I entered to determine whether there were any other exceptions than that presented by the sphere.

2. Having said thus much, I will now discuss the proposition. The object I had in introducing it I state in the previous article of my book. It was to refute a wrong notion which has of late years appeared in print, that the law of gravity at the surface of the earth can be obtained theoretically without any reference to the arrangement of the mass. The original investigation from which this result was supposed to flow is referred to at p. 190 of Mr. Airy's Mathematical Tracts,' fourth edition; and the following is an extract from the investigation itself::

"Without assuming the earth's original fluidity, but merely supposing it consists of nearly spherical strata of equal density, and observing that its surface may be regarded as covered by a fluid, inasmuch as all observations relating to the earth's figure are reduced to the level of the sea, Laplace has established a connexion between the form of the surface and the variation of gravity, which in the particular case of an oblate spheroid agrees with the connexion which is found on the hypothesis of original fluidity. The object of the first portion of this paper is to establish this general connexion without making any hypothesis whatever respecting the distribution of matter in the interior of the earth, but merely assuming the theory of universal gravitation."

In a note at p. 83 of my book I point out a false step in the reasoning of this investigation, and in art. 86 show that when this is corrected the investigation is in no respect more general, nor assumes less, than Laplace's. But I was anxious, besides showing where that particular investigation broke down, to prove à priori that the notion which it was attempted to establish is not true. For this purpose my proposition under consideration was produced, which, for this single object, would better have been worded as follows:

PROP. To prove that if the form of the earth's surface is a spheroid of equilibrium, the arrangement of the earth's mass cannot be independent of that form.

For "suppose some [arbitrary] change were to be made in the arrangement of the earth's mass without altering its external form. It is evident that, although the resultant attraction of the whole mass might possibly be unaltered by this change at particular points of the surface, it could not remain the same as before at every point of the surface," unless the arbitrary change happen to satisfy the precise equations of condition for the external attraction of the mass to remain the same. In the first

case the change would alter the force acting at the surface, which would therefore cease to be a surface of equilibrium; in the second case the external surface retains its form only under the condition that the arrangement of the mass is one of certain definite arrangements determined by equations of condition. In neither case, therefore, is the form of the external surface independent of the internal arrangement of the mass. To arrive at this conclusion was the object of my proposition.

3. But though I have in the last paragraph changed the wording of the proposition to meet the case I was considering, I have no intention whatever of abandoning the proposition itself in its bearing upon the question of the fluid-arrangement of the earth's mass, further than that I would change the words "must necessarily be arranged" into "is undoubtedly arranged;" for the first words would seem to exclude the mathematical possibility of any other arrangement; but the second exclude only the physical probability of a different distribution. I should be wrong to assert that it is impossible for a pyramid to stand balancing on its apex; but I should be safe in saying that it would be physically impracticable. So in the case before us, as I hope now to show, any other than the fluid-arrangement-whether or not the earth is or ever was fluid, in whole or in part-appears to me to be physically improbable in the highest degree; so that I regard the mass as being undoubtedly so arranged. My critic thinks that I have very much over-estimated the force of the evidence for the fluid-arrangement; and he considers that it does not rise above a slight probability. I am not conscious of being actuated by a spirit of retaliation; but I consider that he has very much underrated the evidence, and I am tempted to think that he has not dwelt upon it sufficiently to see its full nature. Some of his expressions have led me to this conclusion. To this I now address myself.

4. The state of the case is this:-that (1) the fluid-arrangement of the mass, whatever its past or present circumstances as regards fluidity and solidity, precisely meets the condition that the surface is a spheroid of equilibrium; (2) any general or arbitrary change of the arrangement of the mass will lead to a violation of this condition; and (3) only a class of precise changes in the distribution of the mass, limited by the condition that the external attraction shall remain unchanged by the redistribution of the mass, will leave the form of the surface unaffected.

For convenience we may represent any redistribution of the mass of the earth, in the removal of materials from one part of its volume to another, by the algebraical addition or superposiof an Imaginary Body, parts of which are of positive and other

before us this body is to possess the property that its external attraction is zero, and its surface is to lie wholly within the earth's surface. For brevity I shall henceforth call such a body "the Imaginary Body."

The conclusion, then, to which the above statement of the case leads is this-that the arrangement of the earth's mass must be either

(1) The fluid-arrangement, or

(2) The fluid-arrangement + the imaginary body.

The high physical improbability of this latter I am now to show.

5. It will be observed that it is impossible altogether to get free from the fluid-arrangement. In any arrangement of the mass which differs from it and suits the problem, still that arrangement consists of the fluid-arrangement with some other precise arrangement superadded. I will take the example which my critic produces, and will make use of his diagram (p. 149, Phil. Mag. for February). The distribution of the materials in this particular case is this: everywhere it follows the fluid-law, except along the surface of two spherical shells C and D; but even there the fluid-law has a controlling influence; for the distribution along those surfaces is that of the fluid-law in the case of C, minus a precisely equal quantity of matter from every equal elementary portion of the surface and from exactly the same depth (i. e. the thickness of the shell), neither more nor less from any part of the whole spherical surface all round, and in the case of D plus precisely the same amount of matter which is taken from C, and this to be distributed uniformly all over the surface of D and to a uniform depth all round. Such a local and, I will call it, freakish departure from the law of the rest of the mass may be mathematically possible, as it undoubtedly is; but I regard it as physically inadmissible. For this reason it was that I rejected the thought, as already related, as soon as it occurred to me.

If a

vera causa could be shown for such a singular distribution, I would at once yield the point, strange as such a distribution would be. It is, however, a mere analytical figment, which in my opinion is of no value in this problem.

But the incongruous result to which the hypothesis of this single pair of complementary shells leads may no doubt be disguised (but only disguised) by imagining the superposition of countless numbers of pairs of complementary shells, of all sizes, intersecting and crossing in endless variety, so as to reduce the mass, in the view of an imaginary eye which could survey all its parts, to a complete medley, and yet the external attraction would be unaffected and the surface-spheroid undisturbed, while the fluid-distribution was to all appearances utterly destroyed. But

that supposed distribution would be no medley and without a law; its law, however, would be so singular as to make the hypothesis on which its existence depends utterly untenable. The matter at the various points of the earth, in excess or defect of that required by the fluid-law, must be of that precise amount that by its imaginary transference by complete spherical concentration or expansion, and by no other process, the fluid-arrangement would be exactly attained, no matter left in excess in any point throughout the whole mass, and none in defect. My critic seems to lose sight of the extreme peculiarity of this departure from the fluid-law of distribution, when he says that "it need not be inconsistent with the ascertained variations of gravity if there were distributed irregularly through the earth very dense masses of matter, and likewise cavities filled with very light forms of matter." But his readers will probably not suspect, after reading these words, that those "dense masses must consist of matter following the fluid-law plus masses lying in complete and uniformly thick and uniformly dense spherical shells, and that those "light forms of matter" also must follow the same precise law, viz. the fluid-law minus complete spherical shells, as before. Any departure from this singular distribution which analysis (hardly nature) has devised, would at once be fatal to the hypothesis. It may perhaps be said that these shells need not be precisely spherical; that is, they need only be nearly spherical, so as to introduce no sensible effect on pendulum experiments. But though this may appear to modify the case, it by no means removes the difficulty which the peculiarity of the arrangement presents. To my own mind these hypothetical departures from the fluid-distribution, which are possible according to the integral calculus, cannot be entertained for one moment in the face of the physical curiosities they would introduce.

Should there be any other varieties of the imaginary body besides spherical shells, the same remarks will apply.

6. Let me conclude by making some remarks on my reviewer's observation, "We do not see the need of having any theory at all." If this refers to any theory of the earth's origin, I do not see any reason to object to his remark; because it must be a matter of speculation, so far as science can feel its way. But if he refers to the theory of the earth's having been once in a fluid state, I would say (1) that if the earth's mass is now distributed in a manner which coincides with the arrangement it would have were it a fluid mass, it is so very easy and innocent an induction to pass from the one to the other, without incurring the charge of wild speculation, that it seems allowable; and (2) that not a single step has been made, that I am aware of, towards determi

mean axes.

less spherical body) without the help of the fluid-theory. Newton's first notions regarding the oblate form of the earth were derived from reflections on fluid-pressure. The geodesist measures the lengths and amplitudes of his arcs, and, assuming that they are of an elliptic form, determines on that hypothesis the But whence has he derived his conception that the form of the earth may be an oblate spheroid? From the fluid theory, and nowhere else. We cannot do without the fluid theory; and to my own mind the evidence, especially from pendulum experiments, and more particularly the influence of the bulging out of the internal strata upon the pendulum (see from p. 85 to 97 of my Treatise), is quite overwhelming in favour of the conclusion that the distribution of the mass at present is proximately according to the fluid-law.

Calcutta, March 24, 1866.

§ 4.

LXV. On Calorescence.

J. H. PRATT.

By Professor J. TYNDALL, LL.D. Camb., F.R.S. &c.

[With a Plate.]

[Concluded from p. 396.]

IN N the combination of bisulphide of carbon and iodine we find a means of filtering the composite radiation from any luminous source. The solvent is practically transparent, while the dissolved iodine cuts off every visible ray, its absorptive power ceasing with extraordinary suddenness at the extreme red of the spectrum. Doubtless the absorption extends a little way beyond the red, and with a very great thickness of solution the absorption of the extra-red rays might become very sensible. But the solution may be employed in layers which, while competent to intercept every trace of light, allow the invisible calorific rays to pass with scarcely sensible diminution.

The ray-filter here described was first publicly employed in the early part of 1862*. Concentrating by large glass lenses the radiation of the electric lamp, I cut off the visible portion of the radiation by the solution of iodine, and thus formed invisible foci of an intensity at that time unparalleled. In the autumn of 1864 similar experiments were executed with rock-salt lenses and with mirrors. The paper "On Luminous and Obscure Radiation," already referred to, contains an account of various effects of combustion and fusion which were then obtained with the invisible rays of the electric light and of the sun†.

*Philosophical Transactions, 1862, p. 67, note.

To the experiments there described the following may be added, as