138 BULLETIN OF THE 



mechanical " perpetual motion :" the average velocity hi' any appre- 

 ciable volume of gaseous molecules subsists only so long as no work 

 is effected. By whatever amount any considerable number of flying 

 particles impart motion to slower groups, or to a solid mass, by this 

 amount do they reduce their own speed, and thus represent a dimin- 

 ished temperature. By whatever amount they receive any average 

 increase of velocity from repeated impacts or from compression 

 within a contracted inclosure, by this amount do they represent an 

 elevation of temperature, at the expense of the bodies from which 

 such additional energy is derived. 



The Kinetic interpretation of the Laws of Gases. — It has been 

 shown by Clausius that the number of collisions of a molecule in a 

 given time is proportional to the mean velocity of all the molecules, 

 to their number in a given volume, and to the square of the dis- 

 tance between the centers of two molecules when at nearest ap- 

 proach,* or at what has been called their dynamic contact. 

 By the mathematical investigations of Kronig, Clausius, Loschmidt, 

 and Maxwell, the foundations of a molecular physics have been 

 successfully established ; and the laws of gaseous action thus far 

 experimentally ascertained, have been found to result deductively 

 as the necessary consequences of the kinetic theory. 



Thus the kinetic energy of any volume of molecules (which rep- 

 resents the temperature of the gas) being the product of molecular 

 weight or mass by the mean square of the velocity, it follows that 

 the relative rates of effusion and diffusion must both be inversely as 

 the square roots of the masses, — that is of the gaseous densities ; — 

 the law of Graham. 



It also follows that in the case of diffusion, by reason of the 

 proportional retardations due to more numerous collisions from 

 the presence of other gas, the coefficient must be lower than in the 

 case of effusion. 



In any mixture of gases, since from the mutual encounters of 

 molecules of different mass, the average kinetic energy will be the 

 same for all masses, or the mean squares of the velocities will be 

 inversely as the respective masses, it follows that in different in- 



*" It is to Clausius that we owe the first definite conception of the free 

 path of a molecule and of the mean distance travelled by a molecule be- 

 tween successive encounters." James Clerk Maxwell. (Encyclopced. 

 Brit. 1875: vol. in, p. 41.) 



