EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 57 



porarily disturbed (series 8). Apart from flexure of the pier, long waiting 

 (50 minutes in series 9) does not further change the position of equilibrium, if 

 the slight swinging is taken into account. The cause of the gradual motion 

 may reside in the viscosity of air, as indicated in the next paragraph. 



If we compare the results of fig. 330 (system not in metallic contact) with 

 the present (system metallically connected) the results appear as follows: 



System not in 

 metallic contact 



2 A AT = 0.02 1 

 22 



38 

 38 



37 



Mean 2&N =0.038 



System metallically 

 connected. 



H 

 .015 



12 



13 



IO 



II 

 Mean 2AJV =0.013 



The disks were usually about a millimeter apart. Metallic contact has 

 thus apparently made the repulsion smaller; but it is not certain that the 

 distance apart of the plates is quite identical. Moreover, data obtained at 

 different times vary considerably. In the present case the repulsion observed 

 for the disks 20 cm. in diameter is 2F R = 6$.2&N = 6$. 2X0. 013=0. 85 dyne, 

 at about d i mm. of air-space. 



32. Retardation due to viscosity of air. It will next be necessary to ex- 

 amine the above suggestion, that the very gradual approach of the suspended 

 disk to its position of equilibrium may be due to the viscosity of the interposed 

 film of air, in view of the small forces and small displacements involved. 

 The case may perhaps be treated in terms of Poiseuille's law, assuming that 

 the flow is from the center of the two nearly contiguous parallel disks radially 

 toward the circumference. Let y be the initial distance apart of the disks, 

 and the time t = o second, measured from the fixed toward the movable disk. 

 Let y' be the final position of equilibrium of the movable disk, so that its 

 excursion is yo y' . Let a small impulsive force P act normally on the outside 

 of the movable disk, by which it is put into the position y. The pressure 

 generated will cause a flow radially outward, and if p is the pressure in the 

 fluid at a distance r from the center, Poiseuille's law may be written 



-QL j r ^(2irr-y)* dp 

 dt ' STTT dr 



(\ 



for the flow through a ring whose section is y.dr, if >? is the viscosity of the gas 

 and V the volume of fluid crossing per second. If the flow is steady, so that 

 dp/dt = o for all distances from the center, and if the liquid is virtually 

 incompressible, i.e., V independent of r, the problem may be solved without 

 difficulty. Neither of these conditions is quite true. The second, however, 

 inasmuch as the average pressure increment is exceedingly small relative 



