44 



THE DIFFUSION OF GASES THROUGH 



To compute /g, a suitable value of D and F must be assumed. Let Z? = 4 

 cm. and Fin succession 10^, io^Xi.41, io*Xi.86, 10^X2 volts. Since 



/,= FV2.262Xio'(4-0' 



the successive curvilinear lines of the diagram are obtained. The lowest 

 have two intersections each; the one corresponding to stability being at 5 

 and the unstable one at us. For at s, a lowering of the disk means an 

 excessive upward electric force, while any rise of the disk means an excessive 

 downward and mechanical force. Just the reverse is true at us. The two 

 upper curves have one contact and no contacts, respectively. Hence, when 



F=io^Xi.86 and D = ^, the disk will just be on 

 the point of rising without interruption. The maxi- 

 mum rise com.patible with stability would be 4/3 

 cm. The rise for F= 10'* and io^Xi.41 would be 

 roughly 0.18 and 0.43 cm., respectively. 



To compute the potential of the maximum point of 

 stability for Z) = 3/ = 4, equation (3) becomes 



F^ = 2.262 X 10^ -r^ Pg — D^=i.86XioHolts. 

 R^ ^ 27 



The values of / for the stable positions of the disk in 

 case of different values of D and F are not so easily 

 found, in view of the cubic equation (3). When / 

 is very small, however, i. e., for values of F less 

 than 10^ volts, / maj'- be neglected in comparison 

 with D and the equation becomes 



Fig . 1 4 . — Chart sho wi ng 

 the forces actuating 

 disk for different po- 

 tential differences and 

 displacements of disk. 



F'' = 2.262X10^ 



R' 



pgDH 



(9) 



Hence, if F=io^ the disk would only rise about 0.018 centimeter. For 

 F=io^ to 0.00018 cm., etc., so that even the interferometer could not 

 indicate more than about 10 volts. If, however, D is also reduced, say to 

 0.5 cm., or 8 times, the rise will be / = 0.0000092 cm., per volt; for D = o.i 

 cm., / = 0.00115 cm., etc. 



Hence with the use of the interferometer and small values of D, there is 

 no reason why ultimately single volts should escape measurement except 

 for the capillary forces involved in flotation, where the stem penetrates the 

 liquid, as in case of the above apparatus. By decreasing the diameter of 

 the stem, however, as in the float fig. 12, sensitiveness may be further 

 increased. 



30. Constants of the Conical Float (Capsule). — When the float is of 

 the form given in fig. 1 2 and a suitable window is provided in the tube gg, 

 fig. II A, or other vessel, so that the zero position (disk e flush with the 

 guard ring dd) may be accurately determined by lens or telescope, another 



