THERMAL EFFECTS OF FLUIDS IN MOTION. 
355 
To compare with the absolute scale the indications of a thermometer in which the 
particular fluid (which may be any gas, or even liquid) referred to in the notation p, v, t, 
is used as the thermometric substance, let p 0 and p l00 denote the pressures which it has 
when at the freezing and boiling points respectively, and kept in constant volume,*;; 
and let v 0 and v 100 denote the volumes which it occupies under the same pressure, p , at 
those temperatures. Then if d and 9- denote its thermometric indications when used 
as a constant-volume and as a constant-pressure thermometer respectively, we have 
6 =100 J L Po . 
P 100 Po 
( 9 ) 
100 - 
v 
100 — v o 
( 10 ) 
Let also e denote the “coefficient of increase of elasticity with temperature*,” and 
g the coefficient of expansion at constant pressure, when the gas is in the state defined 
by (v, t ) ; and let E and E denote the mean values of the same coefficients between 
0° and 100° Cent. Then we have 
dp 
€ Po dt 
£ 
dp 
dt 
v 0 x- 
dp ’ 
dv 
■c> .Pioo Po 
100po 
(11) 
( 12 ) 
( 13 ) 
E= 
100 V 0 
~ 100 
( 14 ) 
Lastly, the general expression for - quoted in Section II. from our paper of last 
year, leads to the following expression for the cooling effect on the fluid when forced 
through a porous plug as in our air experiments : — 
5 =i{J"(*|-p)*+( p ' v '- pv )} do 
(p,v) (P',V) (P,V), as explained above, having reference to the fluid in different 
states of density, but always at the same temperature, t, as that with which it enters 
the plug. 
From these equations, it appears that if p be fully given in terms of v and absolute 
values of t for any fluid, the various properties denoted by 
JK-JN, 
<Z(JN) 
dv ’ 
6, S-, e, £, E, 
E, and &, 
may all be determined for it in every condition. Conversely, experimental investiga- 
* So called by Mr. Rankine. The same element is called by M. Regnault the coefficient of dilatation of 
a gas at constant volume. 
2 z 2 
