390 Mr. W. Sutherland on Thermal 



obtained by putting surface-den si ty and axial density in 

 place of p s and p c in the last formula. 



It is easy also to obtain an expression for the average density, 

 but as it is evident that for a given tube at a given tempera- 

 ture the average density remains proportional to the density 

 at the axis, which is the same as if there was no attraction 

 between gas and solid, we see at once that the effect of sur- 

 face condensation on our investigation of thermal transpiration 

 is to multiply the density by a factor which remains nearly 

 constant for a given tube or to divide X by the same factor, 

 and the effect of ignoring this factor as we have done is to- 

 produce values of WWyJm 2 which ought to be divided by 

 the factor before they should be expected to be constant for 

 any one plate. Now experiment has shown that hydrogen is 

 much less condensed on solid surfaces than other gases, so 

 that with hydrogen the factor will be nearly unity (probably), 

 and therefore, from the last little table, that for air between 2 

 and 3 ; the factor for C0 2 ought to be larger still, as this gas 

 is much more liable to surface condensation than air, while 

 the last table would make the factor to be 137/68 or 2 ; but 

 too much reliance must not be placed on the value of W for 

 C0 2 , as Reynolds found the trouble caused by the condensa- 

 tion of the C0 2 to be so great as to discourage him from 

 making any further experiments with it. Thus the apparent 

 discrepancy in the last table has furnished some new evidence 

 in connexion with condensation of gases in the passages of 

 porous solids. 



As to the values of A', which stands for 



9R 2 R lVo 2 /V fe + ^i) 4 , 



we see that as a is nearly 1 the value of B ,2 /16A' ought to be 

 nearly equal to (R 2 + Ri) 2 /4R 2 R 1 , and of course the value of the- 

 ratio B /2 /16A x is not affected by our ignoring condensation in 

 the establishment, of the fundamental equations. In the case of 

 hydrogen, the values of B' and A x for stucco I. lead to an unreal 

 value of R 2 /Ri, an d ^ nus vve see that the formula (19) lor conical 

 passages is too much of a refinement for present purposes ; 

 and therefore abiding by the formula (17) for cylindrical 

 passages we may say that B /2 /16A' ought to be not much 

 different from unity. For stucco I. the values of B /2 /16A' 

 are *86 for hydrogen and 25 for air, while for meerschaum II. 

 and C0 2 the value is 1*8 ; these values are near enough to 

 l'O to give satisfactory evidence of the general soundness of 

 the details in the theory. 



Reynolds, guided by his theory, formulated his experimental 



