and Radiometer Motion. 145 



The fact that a gas or any body can be at rest, and at the 

 same time be transmitting energy, presented a paradox 

 which caused the property of conduction to be the last of the 

 general properties of matter to receive kinetic explanation. 

 This was not for want of perception of the latent motions of 

 the molecules, but for want of a recognition of the only 

 characteristic in such latent motion, or any motion of agitation, 

 which could cause such transmission — the failure to realize that 

 the only means by which matter can transmit energy while 

 in a mean state of rest is that in which the latent motion con- 

 sidered with respect to any plane consists of two streams of 

 matter crossing the plane from opposite sides, the velocity of 

 the one stream being greater than that of the other, and the 

 ratio of the densities being inversely as their velocities. 



Clausius seems to have first recognized this. After reading 

 Maxwell's paper and pointing out his errors, he frames a 

 theory of conduction, the same as Maxwell's in so far as the 

 energy carried across the plane by the molecules is taken to 

 represent the heat conducted, but differing in so far as he 

 recognizes the necessity for a difference in the velocity of the 

 opposite streams, such that their velocities shall be inversely 

 proportional to the densities. And taking into account the 

 principle that the mean velocities of molecules after encounter 

 are the same as before, he infers that the characteristic velocities 

 of the two opposite groups of molecules, leaving an element 

 in the direction in which the temperature varies, are such as 

 they would have, if the gas were uniform, plus a velocity in the 

 direction of the fall in temperature depending on the slope 

 of temperature and the mean path of the molecules. 



From this start Clausius develops the theory of conduction 

 for gas at rest, using the condition of rest to define the 

 velocity common to the two groups, through a layer of gas of 

 any definite thickness, but only in the case of indefinite 

 lateral extension. Thus he only studies the action in one 

 dimension, and he nowhere refers to the existence of any 

 solid surfaces. 



Maxwell followed with his classical paper of 1866"*, in which 

 he acknowledges Clausius's corrections, and then obtains the 

 equation of continuity, the equations of motion and of energy, 

 and also the equation for the state of conduction of energy, for 

 gas in three dimensions in terms of the logarithmic-decrements 

 of the inequalities, having obtained the constants for these 

 rates for a particular law of force between the molecules. 



These equations are applicable to any varying condition of 

 gas provided there is no discontinuity, but they afford no 

 * Phil. Trans. Roy. Soc. 1867, p. 49. 



