122 Prof. Clausius on the Nature of the Motion 
consideration in determining its intensity ; the second, however, 
whose magnitude is represented by ucos$, will be changed by 
the shock into an equal velocity in the opposite direction. The 
action of the side upon the molecule, therefore, consists in de- 
priving it in one direction of the velocity wcos5, calculated 
according to the normal, and of imparting to it an equal velocity 
in an opposite direction; in other words, of imparting to it a 
velocity of 2w. cos in the latter direction. Hence the quantity 
of motion imparted to the molecule will be 
Qinu.. COB Dy.',c) di. sna oa RECS) 
where m is the mass of the molecule. 
Applying this to all molecules which correspond to the inter- 
val between $ and $+ dS, we obtain during the unit of time, 
nu 
2n 
times the same action, hence the quantity of motion imparted to 
these molecules during the unit of time is 
cos $ sin SdS 
nmu? 
i Con? So mn SS!) Onis ee 
Integrating this expression between the limits 5=0 and 
wa 5 we find the motion imparted by the side to all the mole- 
cules which strike against it during the unit of time to be 
nu? 
Sarit intiiet acindicp od eae 
Let us now conceive the side to be capable of moving freely ; 
then in order that it may not recede before the shocks of the 
molecules, it must be acted upon on the other side by a counter 
force, which latter may in fact be regarded as continuous, in con- 
sequence of the great number of shocks and the feebleness of 
each. The intensity of this force must be such as to enable it, 
during the unit of time, to generate the quantity of motion re- 
presented by the above expression. Since all forces, however, 
are measured by the quantity of motion they can produce in the 
unit of time, the above expression at once represents this force 
as well as the pressure exerted by the gas, the latter being equi- 
librated by the former. 
If « be the superficial area of the side, and p the pressure on 
the unit of surface, then 
_ mnu? 
ee. Nahe 
The product «A here involved gives the volume of the vessel or 
