12 THE DIFFUSION OF GASES THROUGH 



Now, the above velocity corresponds to a pressure gradient dyne/cm., i. e., 

 to a loss of energy of i erg per cubic centimeter for a transfer of the cubic 

 centimeter of gas along i cm., i. e., to a resistance of F= i dyne. Thus for 

 the stated value of v 



77 = 68Xio~ 6 



The viscosity of hydrogen at 22 , according to Puluj, is 91.5 X io -6 . Hence 

 if the present method of computation, which ignores the air influx, were cor- 

 rect, it would follow that the molecular transpiration of hydrogen through 

 the intermolecular pores of water takes place at a rate corresponding to the 

 order of its viscosity. The experiments of the sequel (§§19, 20), however, 

 show that this simple method of computation is not admissible for hydrogen- 

 air diffusion, or at least not until the pressure gradients due to the heads of 

 water quite hold in check the further influx of air due to diffusion. 



14. Continued. Transpiration Depending upon Barometric Pressure. — 



If, again, the initial influx of air into the swimmer be ignored, while the 

 efflux of gas due to diffusion gradients is alone considered, the gradients 

 take the form 



dp (B-T) Pm +h" Pw ,,, 



dl g h"+2h"' W 



where B is the height of the barometer and p m and p w the densities of mercury 

 and water, -k the vapor pressure of water vapor (referred to mercury), h" 

 the effective head of water, h"-\-2h'" the length of the diffusion column. 

 The mean temperature was 22 , the mean barometer 76.21 cm., and the 

 vapor pressure 2 cm. Thus 



dp- o 74-21X13-6+ 1 1X0.998 . 



— = 981 *2 „ + „ =45,500 dyne/cm. 



whence, since <z= 12 cm. 2 and w' = 6.29Xio -10 , the auxiliary 



* = m'/a(dp/dl) = 1.15 X io" 15 



If these coefficients be taken per cubic centimeter instead of per gram of 

 hydrogen transpiring per second, under normal conditions, the volume 

 coefficient will be 



K = £/82.3Xio~ 6 =i.4oXio~ n 



Hence the velocity of transpiration for a dyne/cm. gradient is v= 1.4X10""" 

 cm./sec. 



Finally the virtual viscosity of the medium through which the single 

 molecule is dragged by the gradient would be, since the resistance F=i, 



t]= i/67riVn; = 6,3ioXio -6 



In other words, the viscosity under the tentative hypothesis stated would be 

 about 70 times as large as that of hydrogen. 



