4 THE DIFFUSION OF GASES THROUGH 



pressure gradient {P — p)/l, when rj is the viscosity and f the slip of the gas. 

 Hence the value 77/(1 +4f/>) = 4.8 X lo*^ would have to obtain, a resist- 

 ance which would still be enormously large relative to the viscosity of air 

 (t) = 180X io~^), even if the part of the section of the channel which is open 

 to capillar}' transpiration is a very small fraction. 



7. Coefficients of Transpiration. — To compute the constants under which 

 flow takes place the concentration gradient dc/dl may be replaced either by 

 a density gradient dp/dl or a pressure gradient dp/dl. If the coefficients 

 in question be k^ and kp respectively 



' Rt adpdl ^-"^ 



where the section a is equal to the area of the mouth of the swimmer, R is 

 the absolute gas constant, r the absolute temperature of the gas, and m the 

 loss of imprisoned air in grams per second. If z; = mRr/p is the correspond- 

 ing loss of volume at r and p, 



" Rt aRrdp/dl ^-^ ' 



If in equation (3) the full value of m is inserted, and t denotes current time 

 or m = m/t; if 



dp _ h"p„g 



dl h"-\-2h"' 



where pw is the density of water, //" and //'" the difference of level (see fig. 2) 

 of the surface in v below the free surface in A and above the mouth at d, 

 the relations are 



Mp^ Hi + 2h'";jr 



k„ = 



( " - ~) (*' 



Rt T ap„ 



K=KR^ (5) 



The acceleration of gravity g has dropped from both equations; k^ is inde- 

 pendent of Rt. The coefficient kp, however, is more perspicuous. 



If h'" is made very small in comparison with h" (care being taken to 

 avoid loss of air during manipulation), //' will also vanish; or for h" = 0, 



^ tRapy, T \p 



^ (^ - ^) (6) 



. „ T \p,„ pj 



and similarly for h" = o 



I 



reduces to 



in = kpap^g 



Thus the apparatus is most sensitive if a is as large as possible and h'" jh" 

 as small as possible and the length of the column in A is eventually without 

 influence on the result. Hence if for a cylindrical swimmer the internal 



