318 Intelligence and Miscellaneous Articles, 



and have a progressive motion* — if taken in conjunction with certain 

 facts confirmed by experiment. 



In accordance with the said assumption, the pressure of the gas is 

 found to be the sum of all the impacts which the molecules of gas effect 

 upon the adjacent bodies in virtue of their progressive motion. The 

 pressure on the unit of surface will depend, therefore, (1) on the mass 

 of each individual molecule of gas, (2) on the velocity of the mole- 

 cules, (3) on the volume of the gas, (4) on the number of molecules. 



Let us, on the one hand, take the mass of a molecule as m, and its 

 velocity c ; on the other, the mass M and the velocity C. Then the 

 force of the individual impacts is directly as the masses and the ve- 

 locities j it is therefore proportional to the product of the two so- 

 called magnitudes of motion — that is, == mc . But the number of 



MO 



impacts effected by a molecule in equal times is proportional to 

 its velocity — that is, = — ^ Hence the pressures as regards masses 

 and velocities are 



p _ mc = 2 ([ \ 



P MC 2 m7^ W 



Hence, if we suppose that in the volume v there are n molecules at 

 equal distances and in a state of rest, in the unit of volume there are 



n x = - molecules ■ hence in a path equal to the unit of length there 



3 3 _ 



are /=♦ /*, and in the unit of surface f=(±/z\ molecules. If, 



now, the number of molecules being the same, the volume v is 



changed to the volume V, in the unit of volume there will be 



n 

 n 2 = — molecules, and there are therefore in the unit of length 



3 3 



L= A /*, and in the unit of surfaceF = ( A f n j molecules. In 



V V V V vJ 



a state of motion the pressure upon the unit of surface must be pro- 



* In favour of this conception of the gaseous condition, we have, as 

 coming most immediately within the cognizance of the senses, the recent 

 microscopic observation (Fick, Die NaturJcrdfte in Hirer Wechselbeziehung, 

 Wiirzburg, 1869, p. 27) that fine particles floating in the air are animated 

 by a tremulous motion, and, further, the observation (O. E. Meyer, Pogg. 

 Ann. vol. cxxv. pp. 177, 401, 564) that the friction of gases is independent 

 of the density, but increases with the temperature, as is required by a pro- 

 gressive rectilinear molecular motion increasing with the temperature 

 (loc. eft. pp. 584-598, compare also p. 1/9). 



