GRAVITATION AS AFFECTED BY TEMPERATURE. 
351 
4. In looking for a method to continue and extend these researches it should be 
observed that a weight of, say, 1 gr. can be determined by a first-rate balance to 
l/lO 8 , under favourable conditions,* whereas in a gravitation apparatus (e.g. that of 
C. Y. Boys) the attraction of one mass to another cannot be found to be better than 
l/lO 5 at the utmost. Thus, apart from other reasons, it would be futile on the latter 
type of apparatus to look for a temperature effect (at least between 100° C. and 
— 186° C.) on the small mass m, since the above negative results have established the 
result with the greatest possible accuracy. 
But in these balance experiments of Poynting and Phillips the large mass M (in 
this case the earth) is unchanged in temperature. Now M is incomparably larger 
than m and may have a preponderating influence, whereby change of its temperature 
alone would affect the mutual attraction. In the paper quoted Poynting and 
Phillips suggested (though without any a priori grounds) the feasibility of some 
such expression as the following :— 
Mm I 
~¥' . 
/=G 
1+i 
( M t + mt') 
M + m 
where k is a temperature coefficient and t, t' are 
M and m. 
When M/m is very great, this reduces to 
/ = G [1+itf] 
increments in temperature of 
II. 
so that, on the above supposition, the mutual attraction would be influenced by change 
in temperature of the large mass only. 
Admitting the possibility involved in II., we must abandon weight experiments, 
and proceed to the use of a full gravitation apparatus, having both masses (M and m) 
under control as regards temperature. 
It is supposed by some that Kepler’s 3rd law establishes the constancy of G, but 
I have tried to showf that this is false, and that the common practice of obtaining 
the masses and densities of heavenly bodies (sun, earth, planets, &c.) by assuming the 
invariability of G is at fault. 
5. The above appears to me one case in which Kepler’s laws have been strained 
beyond their legitimate use; another case was pointed out long ago by M. Vicaire.J 
He showed that when one of two attracting gravitative masses, M, is very large 
compared with the other, m, the fact that the acceleration of the latter is independent 
of its mass follows in all cases where the law of attraction is of the form 
* See Poynting’s paper, ‘Phil. Trans.,’ 1891. 
t See ‘Nature,’ 7 Oct., 1915. 
\ ‘ Comptes Rendus,’ vol. 78, pp. 790 to 794. 
3 B 2 
