Transpiration and Radiometer Motion. 381 



leaving the fixed surface after their first encounters with the 

 moving and with the fixed have velocity (l—f)fw; but 

 without following up this process any farther we see that it 

 implies that when the steady state has been reached the 

 molecules leave the moving plane with velocity w 2 and the 

 fixed plane with an average velocity w u and these must be 

 connected by the relations 



(1— f)w 1 ±fw=w 2 , and (1— f)iv 2 = w 1 ; 



whence Wi = w{1 - f)/{2 -f h lV2 = w /(2-f), 



which give (wi + w 2 )/2 = w/2, as of course they ought. 



Each molecule that encounters the moving plane gains 

 momentum m(ic 2 —w^) or mwf/(2—f), and ni?/4 molecules 

 encounter unit surface in unit time, so that the friction 

 between solid and gas is 



F = nmvivf/4;(2-f); (11) 



if f—1/2 this becomes nmvw/12, it is a limiting value of 

 rjic/T) (1 + 2%/D) when D is negligible in comparison with f, 

 and it is independent of the distance between the moving and 

 fixed planes. We see therefore that we can carry the ex- 

 pression 7j/(D + 21) into the consideration of cases either where 

 D is made very small or f very large. 



The expression (11) shows that in capillary tubes whose 

 diameters are only a fraction of the mean free path — that is 

 with very fine tubes such as the passages of porous plates and 

 gas at ordinary pressures, or with ordinary capillary tubes 

 and gas at low pressures, or in any tubes at low enough 

 pressures — the flow of gas under pressure will not obey 

 Poiseuille's laws ; indeed in a line or two we can show that 

 (11) leads at once to Graham's laws of transpiration of gases 

 through porous plates verified and extended by Reynolds. 

 For if the gas is passing through a fine tube of radius II with 

 velocity w at distance x from one end, then when the flow is 

 steady 



7rB.nm.vwf/ 2 (2 — /) = wWdp/da, 



and taking account of the conditions at the two ends of a 

 tube of length I by suffixes 1 and 2, 



irBPwnm = irWw^m = irR 2 w 2 n 2 m = 2(2 — f)7rW(p 2 —p\)/lv ; 



thus the time of transpiration of unit volume measured at the 

 pressure^ being l/7iWw 2 is Jn 2 mv£/(2 — /)7rR 3 (p 2 — P\). 



Now Reynolds made some experiments in which px—p* 

 was kept a constant fraction of p 2 , and therefore proportional 

 to n 2 , under which conditions the time of transpiration should 



