306 Royal Astronomical Society. 
the other numerators are in their proper proportion to that one. 
Hence the mass of the earth, for instance, may be called unity, and 
the results of observation may be made to give the relative masses 
of other bodies. 
What, then, is the mechanical signification of this numerator ? 
The answer to this question belongs to the physical astronomer, 
properly so called. 
Our first idea of mass is derived from bodies at the surface of 
the earth; under the same bulk some are lighter, others heavier. 
Two explanations present themselves: either the heavier body is 
composed of matter of the same kind as the lighter, but in a state 
of greater density, or more closely packed; or else the heavier 
body is composed of particles intrinsically heavier, that is, more 
powerfully acted on by the earth than those of the lighter. Which 
of these two explanations is to be received as the true one, more 
concerns the chemist than the astronomer, but the language of the 
former explanation is always used in our science. If we have 
reason to know that water compressed into one-twentieth of its 
bulk would produce all the mechanical effects of gold, then the 
latter is, and must be, in mechanics, considered as containing 
twenty times the quantity of matter of the former, under a given 
volume. 
We are in the habit of referring solid bodies to water, in esti- 
mating their quantities of matter, and the specific gravities of the 
several kinds of matter, or the ratios of the weights of given bulks 
to the weight of the same bulk of water, have been carefully de- 
termined. Now among the questions of primary interest to the 
physical astronomer comes the following:— What is the quantity 
of matter in the whole earth, from which that in the several other 
planets is so easily determined? If the earth were a ball of water, 
what alteration would need to be made in the numerator of the 
fraction which expresses its attractive power ? Both these questions 
are answered together; and it is only within the last seventy years 
that any attempt at an answer has been made on rational grounds. 
If we knew the materials of which the earth is composed, it 
would be a mere matter of calculation to answer the preceding 
questions. But, ignorant as we are, a priori, even as to the fact 
whether there is an interior to the earth at all, that is, whether it is 
a solid globe or only a hollow shell, we cannot possibly be in 
possession of the means of forming so much as a guess at the 
character of the answer. There is but one mode of proceeding, 
and that was, no doubt, suggested by the processes and results of 
the theory of gravitation. Since a comparison of the actions of 
two planets upon a third can be made to give the ratio of the 
masses of those planets, it is obvious that if we can compare the 
effect of the whole earth with the effect of any known part of it, we 
may deduce a comparison of the mass of the whole earth with the 
mass of that part of it. A mountain in one case, a large leaden 
ball in another, have been weighed against the whole earth, by com- 
