124 Prof. Clausius on the Nature of the Motion 
metre—to be given. Then 
g=9™80896, 
p=10388, 
7a. 
To determine v, we know that, according to Regnault, a kilo- 
gramme of atmospheric air under the pressure of 1 atmosphere, 
and at the temperature of melting ice, occupies 0°7738 cubic 
metre. Hence p being the specific gravity of the gas under 
consideration, its volume at the temperature of melting ice will be 
0°7733 
Egat 
and at the absolute temperature T, assuming 273° to be the abso- 
lute temperature of melting ice, it will be 
0:7733 TT 
p 273° 
Hence we deduce 
u?=3 . 9°80896 . 108383 .0°77338 . se alt 
273 .p 
T 
=235130 575 
and consequently 
u=485™ qT 
BB pt tee) eH) 
As particular cases, we obtain the following numbers corre- 
sponding tothe temperature of melting ice :— 
for, oxygen «-. ..\, 461, 
for nitrogen. . . . 492™, 
for hydrogen .. 1844™, 
These numbers are the mean velocities which, for the totality 
of molecules, give the same vis viva as would their actual velo- 
cities. At the same time, however, it is possible that the actual 
velocities of the several molecules differ materially from their 
mean value. 
19. By means of the equations above established, we will 
lastly examine what relation exists between the vis viva of the 
translatory motion and the whole vis viva, or heat, in the gas. 
In doing so we will conceive the quantity of heat to be mea- 
sured, not by the ordinary unit of heat, but by the mechanical 
unit of vis viva, or what is equivalent, by the unit of work. To 
this end we have only to divide the quantity of heat measured 
in the ordinary manner by the thermal equivalent of the unit of 
