THE DIFFUSION OF GASES THROUGH 



ancy which will be felt in the lapse of time, 

 in the next chapter. 



The question will be discussed 



4. Equations. Manipulation. — Let h be the difference of level of the impris- 

 oned water and the free surface in the reservoir R. Then it follows easily that 



Rm r 



7 i jt r m 



p w ~ gM (i+m/M)- Pw /p 



(i) 



Fig. 2. — Cylin- 

 drical diver. 



where 7/ is the corrected height of the barometer (from which the mercury 

 head equivalent to the vapor pressure of water is to be deducted), p m , p w , p a , 

 the densities of mercury (o° C), water (2° C), and glass, 

 respectively, m the mass of the imprisoned air at v , R its 

 gas constant, and t=/ + 273° its absolute temperature. 

 M is the mass of the glass of the swimmer and g the acceler- 

 ation of gravity. 



The equilibrium position of the swimmer is unstable. 

 To find it R may be raised and lowered for a fixed level of 

 the swimmer ; or R may be clamped and the proper level of 

 the swimmer determined by suction and release at C. The 

 dropping of the swimmer throughout the column of water 

 may occasion adiabatic change of temperature of 0.23 . It was my practice 

 in the present experiments to use the latter method and to indicate the 

 equilibrium position of the swimmer by an elastic steel ring encircling A. 

 In this way the correct level may be found to about 1 mm. and afterwards 

 read off on the cathetometer. 



After making the observations, the hose ab is to be separated at a, so that 

 the swimmer falls to a support some distance above the bottom, admitting 

 of free passage for diffusion. Clearly this diffusion is due to the difference 

 of level, h", between the water in v and at the free surface of the liquid 

 (see fig. 2). Increase of barometric pressure has no differential effect. A 

 large head h'", however, means a longer column for diffusion. 



5. Data. — In table 1 a few of the data made in 1900 are inserted, chosen 

 at random. 



In the intermediate time I did not return to the measurements until quite 

 recently (January 191 1), when a second series of observations was made. 

 As much as one-fourth of the air contained in 1900 had now, however, 

 escaped, in consequence of which the above method had to be modified and 

 all heads measured in terms of mercury. Hence if H denotes the height 

 of the barometer (diminished by the head equivalent to the vapor pressure 

 of water) and if m/M be neglected in comparison with 1 (about 0.06 per 

 cent), the equation becomes 



Mg Pm H(i/p m -i/ Pg ) 



m --R- ; ^ 



in which the first factor of the right-hand member is constant. If the 

 observations are made at the instant the swimmer sinks from the free 

 surface in A, fig. 2, H must be increased by the mercury equivalent of the 



