

, AND ITS CONNECTION WITH THE THEORY OF HEAT. 429 
1 dp do d 
Me ee OS 
@ dz dz 2Q ( dz * Pay + Vaz) *=9 
Lidp doa d d d 
ee aurea ok a pane : ©) 
ldp' do 

d 
ode a -2Q(a ee at Va) 1-2 
Let 7 be the radius of curvature of the path of the particles through (2, y, 2) ; 
and a’ 6’ 1’, its direction-cosines; then the above equations obviously become 

Hoge ee 2A SO 
ldp do_ Sam 
Saitek Oe a aS NB Se (3 A.) 
If these equations are siesta 
ay J eg 
must be an exact differential. Let —@ be its primitive function; the negative 
sign being used, because a’, (’, y’ must be generally negative. Then the integral 
of the equations (3) is 
log. e= => : oa =e Log Q $—#)+ constant ; 
_ or taking ¢, to denote the pressure at the bounding surface of the atom :— 
zl) Ses 
e=0,¢% BO Ae orl oaths hier iteibuil aed: ooh Ae (4). 
Our present object is to determine the Seok. density, g,, and thence 
_ the pressure p=/ @,, in terms of the mean density 7- 1 ‘and heat Q. For this pur- 
3 pose we must introduce the above value of ¢ into equation (2), giving 
2Q ee 
Or tion sf Vin dy dz 
210 mec 
i paho=hps [ff ¢ a Pig ET ae ayiayiounionl! 
1 
Let the volume of the atom be conceived to be divided into layers, in each of 
which ¢ has a constant value. Then we may make the following transforma- 
tions. 
VOL. XX. PART III. az 

