120. Prof. Clausius on the Natwre of the Motion 
first deduce the expression which shows in what manner the 
_pressure of the gas on the sides of the vessel depends upon the 
motion of its molecules. 
As the shape of the vessel is indifferent, we will select that 
which is most convenient for our purpose. We will assume the 
vessel to be very flat, and that two of its sides consist of parallel 
planes so close to one another that their distance asunder 1s infi- 
nitesimal when compared with the other dimensions of the ves- 
sel. Hence we need not consider the cases where the molecules 
strike against one of the narrow strips of sides, and we may 
assume that each moves in a right line until it either strikes 
against another molecule or against one of the large parallel sides. 
In fact, to take the small sides into consideration would change 
nothing in the final result, and would only make the develop- 
ment more prolix. 
Let us consider one only of the two large sides; during the 
unit of time it is struck a certain number of times by molecules 
moving in all possible directions compatible with an approach 
towards the surface. We must first determine the number of 
such shocks, and how many correspond on the average to each 
direction. 
15. Hereafter we shall always assume the gas to be an ideal 
one; in other words, we shall disregard the irregularities pro- 
ceeding from an imperfect gaseous state, so that in determining 
the pressure we may, with Krénig, introduce certain simplifica- 
tions in place of considering the motion exactly as it takes place. 
The whole number of shocks received by the side remains un- 
changed when we assume that the molecules do not disturb each 
other in their motion, but that each pursues its rectilineal path 
until it arrives at the side. 
Further, although it is not actually necessary that a molecule 
should obey the ordinary laws of elasticity with respect to elastic 
spheres and a pertectly plane side, in other words, that when 
striking the side, the angle and velocity of incidence should equal 
those of reflexion, yet, according to the laws of probability, we 
may assume that there are as many molecules whose angles of 
reflexion fall within a certain interval, e. g. between 60° and 61°, 
as there are molecules whose angles of incidence have the same 
limits, and that, on the whole, the velocities of the molecules are 
not changed by the side. No difference will be produced in the 
final result, therefore, if we assume that for each molecule the 
angle und velocity of reflexion are equal to those of incidence. 
According to this, each molecule would move to and fro between 
the large parallel sides, in the same directions as those chosen 
by a ray of light between two plane mirrors, until at length it 
would come in contact with one of the small sides; from this 
