570 DR. J. W. CAPSTICK ON THE RATIO OF THE 
neglecting squares of the differential coefficients, or, since 

z Rt = pv —f, 
therefore 
es 1 df 
C,-G=R(i— oo) ese 
ex df df 2 oy ah 
SR ba gach each anaes - + (8). 
If 67 is the increase of the kinetic energy of translation of the molecules in unit 
mass of the gas for a rise of temperature dt, we have 

C, dt = 67 + B dr 
=2(1+ 6) R&, 
since 
ae SS Ree 
Hence 
g Ce 
ke as: 
and dividing out C,, equation (3) becomes 

- 2 1 df Ik Gh 2 df if 
91S gel + ARSE Ch ie. ae =a) Bee YA 
p dv 
If the form of f(p, v, t) were known we could readily put equation (4) into a form 
fitted for calculation. Unfortunately we cannot use the characteristic equations 
proposed by CLausius, VAN DER Wats, Tart, and others, for the constants of these 
equations are not known except for a few gases. 
There is however not much lost by taking an approximate value of the term in 
brackets, for from the nature of the equation the experimental error in y is consider- 
ably increased in £. 
By differentiating the approximate equation 

Bib Ns aon 
we get 
68 / 8 2y 
B/ 4 (y — 1) (5 — 3y) 
Hence, if 
68 / dy 
== 1/c3} = — 8 
y B/ ¥ 
wile, = 
