22 MOLECULAK MOTION AND ITS ENEKGY 12 



interior pressure can be calculated by the following method, 

 which is carried out with greater strictness and generality 

 in the Mathematical Appendix No. 1, l*-7*. 



Consider the space occupied by the gas to be divided by 

 a plane into two halves, a right half and a left half, and 

 mark off a bit of this plane of unit area. On this unit area 

 the one half of the gas presses with the same intensity from 

 its side as the other half from the opposite side. For the 

 right half would be moved from left to right by the pressure 

 exerted on it by the left half, if it did not itself exert an 

 equal and opposite pressure. Now, we measure a continuous 

 force by its impulse in a unit of time ; in the meaning of 

 our theory, therefore, the pressure is nothing else than the 

 momentum which is transferred in unit of time through 

 the unit area of the plane from one half of the gas to the 

 other, or, rather, as need hardly be specially specified, it is 

 the component of this momentum in the direction of the 

 pressure. To find the value of the pressure we have there- 

 fore to calculate the momentum perpendicular to the unit 

 area which is transferred from one half of the gas to the 

 other by the molecules that cross the unit area in a unit of 

 time. 



If for simplicity we retain Joule's conception of break- 

 ing up the motion into three components, we have to assume 

 tKat one-third of all the molecules move perpendicularly to 

 /the plane. One-half then of this one-third i.e. one-sixth 

 of the whole move at any moment from left to right, while 

 an equal number move from right to left. 



In a unit of time those molecules only can cross the 

 plane whose distances from it at the beginning of the time- 

 unit are less than the length of path travelled during the 

 time-unit. Hence all the molecules which cross the unit 

 area from left to right in a time-unit come from the cylinder, 

 whose base is the unit area, and whose height is measured 

 by the speed G, and whose volume therefore is numerically 

 equal to G. The number of molecules therefore which cross 

 unit area of the plane in unit time from the left half of the 

 gas to the right is %NG, if JV, as before, represents the 

 number of molecules in the unit of volume. 



