in producing Expansion of Fluids and Solids. 25 



bable that the attraction between the minute particles, which is 

 the counter-agent to this elastic force, is also equal. Conse- 

 quently this attraction, being greater as the weight of the atom 

 is greater, and as the distance between the atoms is less, there- 

 fore in general mp^t'P is equal for any given temperature 

 throughout all bodies. To apply this in the present instance 



mP'T'^=:mp' f, and dividing by m; P' T^ =zp' f :. 



P'^ T rz p^ t, and substituting for T and t their values as be- 



supposing 



9 



3 - 1. 



fore, P^^'^jmi a—S^) __ p^+^(m3^ g — s^). Now, 



the attraction between the minute particles to follow the law 

 of gravity, or m P^ 7^ = mp^ f , then <p = 2, therefore 



piirn^a- i)^ P^{m^a-^n , Hence we arrive at a va- 

 S^—m^P 1.^—m^p 



lue of P in terms of p, a, S, 2, and m, which four latter 

 being known by observation and calculation, we thus obtain 

 the relative proportion of P to p. It is obvious, however, 

 that we can again compare in like manner two other equal 

 cubic bulks of the same matter, so that calling now^ the equal 

 side of their square surfaces q^ the absolute weights of these 

 equal bulks (7, u, we thence obtain a new equation for the 

 values of P and ;?, or 



pi (jn^ q _ t/s ) pi {m^ q — J) 

 i I — ] I ' 



C/s — m^ P u^ — m^ p 



in which equation, substituting the value of P derived above 

 in terms of jo, a, S, 2, and m, we find a value of p in terms of 

 a, q, S, 2, U, u, and m, all quantities already supposed to be 

 known. It is manifest also, that, if we compare the solid to 

 which p belongs with different solids, we should still find al- 

 ways the same value for p. The same result also ought to be 

 obtained from comparing this solid with any one other solid at 

 different temperatures. In this way, then, we can put the cal- 

 culations to the test of experiment. With this view, there- 

 fore, I submit them, as presenting, it appears to me, a some- 



