hend by what means some of tbe most extraordinary conclusions have been arrived at,—is within the reach of many who shrink from the task, appalled by difficulties, which, perhaps, are not more formidable than those incident to the study of the elements of every branch of knowledge; and who possibly overrate them from disregarding the distinction between the degree of mathematical acquirement necessary for making discoveries, and that which is requisite for understanding what others have done. That the study of mathematics, and their application to astronomy, are full of interest, will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at the truths they disclose, whether it be in the discovery of a world or of a new property of numbers.
Section II.
It has been proved by Newton, that a particle of matter, placed without the surface of a hollow sphere, is attracted by it in the same manner as if the mass of the hollow sphere, or the whole matter it contains, were collected in its centre. The same is, therefore, true of a solid sphere, which may be supposed to consist of an infinite number of concentric hollow spheres. This, however, is not the
