LIQUIDS AND ALUED EXPERIMENTS. II 



I may remark in passing that from equation (4) 



m' = kap,g/{i-\-2h"'/h") 



the individual values of m' from day to day should vary with p„, or with 

 temperature; but this amounts to but 0.02 per cent per degree and is thus 

 insufficient to explain the zigzag passage of some of the curves obtained; 

 for instance, that of the transpiration of air into air through water (§19), 

 or of hydrogen into hydrogen (§20) , quantitatively. Moreover, the zigzag is 

 of a positive and negative character and hence quite beyond the reach of 

 such a discrepancy. It has been referred partly to the effect of vortices 

 due to convection (frictional pull of water on the swimmer), or again to an 

 actual evolution and absorption of the imprisoned gas from the water below, 

 as temperature rises and falls. Finally, since the true mass rate, m, for 

 mixed gases is obtained from m', by 



m = m — (5) 



Po 



where pg refers to hydrogen and therefore for the given mixture, ccBt. par., 

 m is constant, w'p must also be constant. In other words, m' as computed 

 will vary inversely as the actual density p of the gas, i. e., m' will increase 

 as temperature rises and decrease as temperature falls. The effect of 

 temperature is not, however, marked in these experiments. It is so, how- 

 ever, for an air-air system, for which the latter explanation does not apply. 

 Hence the cause of the irregularity is probably absorption and release, as 

 specified. 



13. Continued. Apparent Frictional Resistance per Molecule. Virtual 

 Viscosity. — The above coefficient, k, nominally shows the grams per second 

 of hydrogen which transpire molecularly for a pressure gradient of one 

 dyne/cm. at 22°. As the density of hydrogen at 22° is about 82.3X10"® 

 the volume coefficient will be 



K = V82.3 X io~® = 1.30X 10"' 



Here k is the true coefficient of transpiration by volume. 



It may be interesting to inquire in passing what the virtual viscosity would 

 be under which the molecule transpires for a pressure gradient of d3'ne/cm. 

 when 1.3X10"^ c.c. of hydrogen transpire molecularly between opposed 

 faces of a cubic centimeter, or the velocity of the molecule is i'= 1.3X io~" 

 cm. /sec. If the resistance, which is really kinetic, be regarded as due to a 

 continuous medium of virtual viscosity rj, we may write the force / urging a 

 single molecule of radius r with a speed v 



f=6Trr]rv 



Thus the force which urges A^ = 6oX 10^^ molecules (O. E. Meyers's estimate 

 of the number per cubic centimeter, if the effective diameter of each is 

 2f = 2Xio~^ cm.) will be 



F = 37r77X2Xio"*X6oXio'^X» 



