THE INTERNAL CONSTITUTION OF BODIES. 465 
is done by substituting the volume v for [f, didnd Zé, the term 
which stands ander the sign = in the first of the equations (II) will 
dT 
b i 
e represented by a v a 
If we now write in their places all the expressions just found for 
the integrals which constitute the first of the equations (II), we shall 
have 
By similar substitutions the second and the third equation will give 
respectively 
Rk res a >» 
a Ady a dy 
dq _ dd _ dT, 
pie hy ae nee 
These three equations must hold good for the particular values x, y, 
Be Ray Vis Zi se-e seen X5 Vp 2, &e-, which answer to the centre of the 
molecules in their state of equilibrium ; and as each molecule furnishes 
three similar equations, the whole collectively will be sufficient to enable 
us to determine the unknown quantities. 
If from the formule marked (III)", (IV)', (V)’ we derive, by means 
of the changes already indicated, the expressions for 4, anes: 
x dx? dx’ 
we find 
( ) —a2ar 
ae. l+anrn)e » Xy— X 
~ =| ainda abe (gz, + f4,) 5 ota SE a 
— @r 
a2 _ 8 2, (gm +fq){Gtewe _+_ 1) xy — x 
dx Ty? ry 
— be ay (y ay +9) — 1 = 
dq d® dT dq ane 
ae tan dy’dy"s mae Cc. 
x into y and into z. 
y changing in these formule 
If we introduce these expressions into the foregoing equations, re- 
collecting that, according to the hypothesis of Franklin and A‘pinus, 
we must make f = g, and take y a little less than g, the result will be 
