26 Mr. G. F. Fitzgerald on the Mechanical 



Sir 



R 2 



represented by a pressure p = ~— when R 2 = X 2 + Y 2 + Z 2 in 



the direction given by 



/x : v 1 — yi 2 sin <£ : s/ 1 —/A 2 cos (/> : : X : Y : Z : : I : m : n, 



and an equal diminished pressure in every direction at right 

 angles to this line. Double this pressure will be the Crookes's 

 force, which is consequently in this case 



and it is in the direction whose direction-cosines are propor- 

 tional to I : m : n; so that, if we put 



l=vy, m=vs/l— yJ sin<£, n = vVl- yl cos<£, 



The direction-cosines of the line of transference of heat are 

 evidently ot:/3:y, and so far there is no reason why these two 

 lines should coincide, although of course in most cases they 

 probably differ but little in direction. 



The only other distribution I shall consider is one suggested 

 by Mr. Stoney's investigation (Scientific Transactions of the 

 Royal Dublin Society, p. 39) of the nature of the distribution 

 of the velocities in the gas between two large parallel surfaces 

 at uniform unequal temperatures. He has shown that it tends 

 towards a distribution which would be represented by two 

 streams of unpolarized gas moving in opposite directions across 

 the layer. Now the actual distribution is never exactly this, 

 and possibly, as he has mentioned, departs in various degrees 

 from it as you pass across the layer. If, however, we assume 

 the distribution to be the same all the way across, and that 

 consequently the mean temperature of each stream is that due 

 to the surface it is leaving, we can calculate the resultant pres- 

 sures. 



If v x and v 2 be the mean velocities of the molecules in each 

 stream respectively relatively to the centres of mass of the 

 molecules, and if % and u 2 be the velocities of the streams 

 (i. e. of these centres of mass), and /^ and p 2 their densities, 

 the pressure upon a fixed plane normal to the direction of the 

 streams is 



