21. It has been shown by Newton, that if any mass of matter be distributed in a uniform sphere, or in uniform concentric spherical shells, the total attraction on a point without the sphere, will be the same as if the whole mass were collected in that single point, the centre. Now, proceeding upon the supposition of such a distribution of the matter in a nebula, (which is a reasonable average supposition,) we may say, that if our sun were expanded into a nebula reaching to the extreme bounds of the known solar system, namely, to the newly-discovered planet Neptune, or even hundreds of times further; the attraction on an external point would remain the same as it is, while the attraction on points within the sphere of diffusion would be less than it is; according to some law, depending upon the degree of condensation of the nebular matter towards the centre; but still, in the outer regions of the nebula, not differing much from the present solar attraction. If we could discover a mass of luminous matter, descending in a spiral course towards the centre of such a nebula, that is, towards the sun, we should have a sort of element of the spiral nebulæ which have now attracted so much of the attention of astronomers. But, by an extraordinary coincidence, recent discoveries have presented to us such an element. Encke's comet, of which we have just spoken, appears to be describing such a spiral curve towards the sun. It is found that its period is, at every revolution, shorter and shorter; the amplitude of its sweep, at every return within the limits of our observation, narrower and narrower; so that in the course of revolutions and ages, however numerous, still, not such as to shake the evidence of the fact, it will fall into the sun. 22. Here then we are irresistibly driven to calculate what degree of resemblance there is, between the comet of Encke, and the luminous elements of the spiral nebulæ, which have recently been found to exist in other regions of the universe. Can we compare its density with theirs? Can we learn whether the luminous matter in such nebulæ is more diffused or less diffused, than that of the comet of Encke? Can we compare the mechanical power of getting through space, as we may call it, that is, the ratio of the inertia to the resistance, in the one case, and in the other? If we can, the comparison cannot fail, it would seem, to be very curious and instructive. In this comparison, as in most others to which cosmical relations conduct us, we must expect that the numbers to which we are led, will be of very considerable amount. It is not equality in the density of the two luminous masses which we are to expect to find; if we can mark their proportions by thousands of times, we shall have made no small progress in such speculations.