IO THE DIFFUSION OF GASES THROUGH 



12. Continued. Coefficients Depending upon Water Heads Only. — It 



will be expedient to compute the coefficients of molecular transpiration, 

 tentatively, under a variety of hypotheses, before making a more careful 

 examination of the case. There are at the outset two points of view from 

 winch the coefficients of transpiration may be calculated, since in fig. 3 the 

 gas at v (hydrogen), is different from the gas at/ (air). Thus the pressure 

 gradient may either be taken as the mere excess of pressure at v over that 

 of/, i.e., 



dp _ h"p w g _ Pw g 



dl h"+2ti" i+2h'"/h" {2) 



since both gases hydrogen and air are saturated with moisture ; or the gradient 

 may be taken as the full barometric pressure plus the head, i.e., 



dp _ H+h"p 9 g 



dl h" + 2h'" {3) 



since there is no hydrogen above / and both gases, hydrogen and air, are 

 saturated with water. To decide between these and other hypotheses it 

 will ultimately be necessary to introduce for comparison an artificial atmos- 

 phere of hydrogen at/, as is done in §20 below. Moreover, if the diffusion 

 takes place subject to equation (3), air must in like manner diffuse from/ 

 into v, and a phenomenon of considerable complication result, as is actually 

 the case. 



Leaving the theoretical discussion for more adequate treatment below, it 

 is interesting preliminarily to examine equations (2) and (3) separately. 

 Postulating equation (2), the (virtual) coefficients k for a pressure gradient 

 are respectively, if a is the area of the mouth of the swimmer, and m' the 

 loss of imprisoned air per second for tl e gradient dp/dl, 



m! m' i+2h'"/h" 



k = — : — 7-7, = (4) 



adp/dl a Pw g 



Here 2h'" = 1 1 cm., h" '=11 cm., therefore \-\-2k'" jh" = 2. The mean tem- 

 perature may be taken at 22 or p w = 0.998; # = 981, a= 12 cm. 2 , thus 



2 



k = m' — — . . _ = i7oXio -f W 



12X0.998X981 



The pressure gradient dp/dl is 489 dynes/cm. Hence, since 



m = — 6.29 X io _10 g/sec. 



the value of the initial coefficients is at 22 , for hydrogen, if the air influx 

 is ignored, 



£ = i.07Xio~ 13 



Here k is the rate in grams/sec, under the hypothesis stated, at which 

 hydrogen transpires molecularly between opposed faces of a cubic centi- 

 meter of water, when the gradient is one dyne/cm. 



