(F) 



Mr. G. J. Stoney on Polarization Stress in Gases. 419 

 of only. Doing this, and writing fi for cos 6, we find 



p,= | • f^ivy^, 



whence, since k, the polarization stress, =P, r — P y , we have 

 finally 



rrw-iHu (G) 



-£ 



TAis, Merc, ts Me complete matliematical expression for 

 Crookes's stress. It could be integrated if we knew the law 

 of the polarization of the gas ; for then TV 2 would be a known 

 function of p. 



22. Clausius, in investigating the diffusion of heat across 

 the layer of gas, makes the assumption (Phil. Mag. vol. xxiii. 

 pp. 425 and 524) that the numbers and velocities of the mole- 

 cules " emitted " by a thin stratum of the gas (i. e. that have 

 passed out of the stratum after having encountered other mo- 

 lecules within it) may be adequately represented " by assuming 

 at first motions taking place equally in all directions, and then 

 supposing a small additional component velocity in the direc- 

 tion of positive x to be imparted to all the molecules." In 

 other words, it is assumed that the motions of these molecules 

 may be represented by radii vectores from a slightly excentric 

 origin to points equally distributed over the surface of a sphere. 

 It will be instructive to trace the consequences of this hypo- 

 thesis, both because of what it will do and what it will not do. 



Upon this hypothesis Clausius finds the following convergent 

 series for V 2 and I (he. cit. pp. 434 and 516) : — 



V 2 = u 2 + 2uq f i€ + (2ur + q 2 l )f J L 2 6 2 + ..., 



I = (1 _i /e2 + ...)_£.^ + , Ve . + _ ? 



where J<?e (J 00 - c ^' P* 525) is the small component velocity 

 spoken of above, u is the mean velocity of molecules moving 

 in the plane yz, and the other letters have the meanings 

 assigned to them by Clausius. Multiplying these together, 

 going to the second order of small quantities, and arranging 

 by powers of fi, we find 



IY 2 = u 2 (l-^e 2 ) + A lf jLe + A 2H , 2 <?, . . (12) 

 where 



A 2 =-2? 2 + 2ur + r/f + w V (13.) 



2E2 



