4 THE DIFFUSION OF GASES THROUGH 



pressure gradient (P — p), I, when 77 is the viscosity and f the slip of the gas. 

 Hence the value )j/(i +4$"/ r) = 4.8 X 10 6 would have to obtain, a resist- 

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

 (tj= 180X io -6 ), even if the part of the section of the channel which is open 

 to capillary 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 p and k p respectively 



p Rr adp.dl ' jj 



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 v — mRr/p is the correspond- 

 ing loss of volume at t and p, 



p Rt aRrdp/dl {3 ' 



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

 or tn = m/t; if 



it h "p«& 



dl ti'+2h!" 



where p w is the density of water, h" and h'" 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 m Hi+2k'"/h" , 



k = 



Vp„, pJ 



Rt t a Pu 



k p = k p Rr (5) 



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

 pendent of Rt. The coefficient k P , however, is more perspicuous. 



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

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



_Mp ! » H 

 v tRap, 

 and similarly for h" = 



reduces to 



m = k p ap w g 



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

 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 



?(i-i) (6) 



T \D,„ pj 



