LIQUIDS AND ALLIED EXPERIMENTS, 37 



nearly absent in case of the diffusion of hydrogen and is thus not a direct 

 temperature effect. To state the case analytically, the volume v of the 

 imprisoned gas is, in terms of its gas constant R, absolute temperature t, 

 pressure p, and mass m, as usual given by 



p = R —T = RpT 



V 



Now, since 



m = 



it follows that 



Rt \pto Pff/ 



P ^Pw Pg^ 



where v is the volume which would be contained in the diver and p the 

 corresponding density of the gas, at any selected fixed or fiducial atmos- 

 pheric pressure and absolute temperature p and r, under which the experi- 

 ment is supposed to take place. If the latter be given in centimeters of 

 mercury, the barometric height being B, 



H /I i\ 



-D \Pw Pa / 



It follows that if we divide m by p, the density of the gas originally in the 

 diver under the specified normal conditions (density being known for a single 

 gas but not at once given in case of a mixture), we refer all data to these 

 conditions and temperature and pressure discrepancies are excluded. More- 

 over, V and the corresponding diffusion coefficient, k = v/a(dp/dl), can be com- 

 puted for any gas, m.ixed or simple. Under the form Bv/II-\-M / Pg = M ' p^, 

 the above volume equation is obvious directly, as the approximate condi- 

 tion of flotation at the manometric pressure //. 



Finally, it is not improbable that the irregularities of graph in question 

 may be actually used as a means of measuring the variation of the solu- 

 bility of a gas in the liquid, with temperature. 



In conclusion I may point out the extreme sensitiveness of the above 

 method. With the same apparatus, relative data should be determinable 

 with an accuracy comparable to that with which the barometer can be read ; 

 i. e., much within o.i per cent, since, finally, 7; = '^'///jB, where v' is the nearly 

 constant volume on flotation. Absolute data, however, require a determi- 

 nation of the constants of the apparatus, which is less accurately feasible. 

 It has already been intimated that to secure this sensitiveness, temperature 

 must be kept constant in the lapse of time. Furthermore the rigorously 

 pure gases must be introduced under their own atmospheres and there must 

 be no foreign gases dissolved in the liquid. Moreover, all observations 

 must be made with the artificial atmosphere kept in place. Indeed, it is 

 a question whether the effect of diffusion in rendering gases stored over 

 water impure has generally been adequately guarded against. 



