. Carnegie Institution of Washington publication. 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^, io*, 10^X2 volts. Since /,= '(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
. Carnegie Institution of Washington publication. 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^, io*, 10^X2 volts. Since /,= '(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^ and D = ^, the disk will just be on the point of rising without interruption. The maxi- mum rise with stability would be 4/3 cm. The rise for F= 10'* and io^ would be roughly and cm., respectively. To compute the potential of the maximum point of stability for Z) = 3/= 4, equation (3) becomes F^ = X10^-r^ Pg — D^= 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 . 14.—Chart sho wi ng the forces actuating disk for different po- tential differences and displacements of disk. F'' = ^ R' pgDH (9) Hence, if F=io^ the disk would only rise about centimeter. For F=io^ to cm., etc., so that even the interferometer could not indicate more than about 10 volts. If, however, D is also reduced, say to cm., or 8 times, the rise will be / = cm., per volt; for D = cm., / = 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 invo
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