LIQUIDS AND ALLIED EXPERIMENTS. 57 



38. Equations. — It will be expedient in the present research to compute 

 the coefficient of diffusion by volume, relatively to standard pressure and 

 temperature, and this may always be done even in the case of mixed gases. 

 The flotation experiments thus give 



"»=T(--")-=<---)- w 



70 \Pw Pg^ 7" ^Pzo Pg^ T 



where Vq is the volume of gas in cubic centimeters in the diver, at 273° 



absolute, and 76 cm. of the barometer. M is the mass of the swimmer, 



Pg its density, p„ the density of the liquid, at the absolute temperature r. 



H is the pressure in centimeters of mercury at which flotation just takes 



place at the given fiducial level. If B is the barometric height, h the head 



(including capillary depression) of the mercury manometer communicating 



with the gas above the free surface, // the height of the bubble of gas in 



the swimmer, rr d , 7 ; ' ; r \ 



H = B+h'pjp^-h-x-Tr (2) 



where p,„ is the density of mercur>^ r the vapor pressure of water or of a 

 solution at t°, .v the surface depression of the cistern of the manometer. 

 In all the adjustments used 



// = 1^ + 0.05 — I .Ol/? — TT 



The density p,^ is easih^ found for any solution, but it is not always possible 

 to obtain -rr' the reduced vapor pressure due to solution. Methods will be 

 given for each table. Their effect is usually insignificant. 



The above equations for the interdiffusion of two gases {H initially alone 

 within the diver and finite in quantity, A without and unlimited in quan- 

 tity) are, as above shown, when the volume coefficient k refers to 0° C. and 

 76 cm. of mercury. 



2h"' + h' 



a 



- '^'0 = PhW - '^o) + *^a h"Ptc S (3) 



where //" and h'" are the heads of the liquid shown in fig. 16, a the area of 

 the dift-usion column, pf, and p^ the partial pressures of the gases within 

 the diver, k^ and k^ their volume diffusion coefficients, and p^ the density of 

 the liquid. Throughout the experiments if B is the height of the barometer 



B-^ = Pa-\-pn-h''p.S (4) 



Hence if but a single gas A is present, p^^ is zero and 



-(2h'"-\-h")v,/a^Kj.^'p,S (5) 



from which k^ may be computed from observations of Vq in the lapse of 



time. Moreover, , ,^, 



iiPo = k (6) 



the coefficient of diffusion referring to mass, which can not therefore be found 

 except in case of a single gas, where Po is given. One may observe that 



Vo/a = ho (7) 



where h^ is the height of the cylindrical air bubble within the diver at 

 standard pressure and temperature. The variations of //q in the lapse of 

 time are not, however, measurable with adequate accurac5^ 



