EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 69 



From the computed values of F' R , since F R is equal to 65.2 XAA/", the true 

 value of the displacement in the absence of repulsion, A/V',may be computed as 



H6.-4W 



65.2 



the result being given in the eighth column in centimeters. It shows the 

 corresponding displacement of the suspended plate in half centimeters. 



The two values of AA/" and AA/ 7 now give us the displacement due to repul- 

 sion in centimeters, 



as shown in column 10. Again, the distance apart (in centimeters) of the 

 uncharged plates d' is given in the third column, being 



and found from observation directly. Finally, the residual distance apart of 

 the plates, y, if the suspended plate had taken its true displacement AAT (in 

 the absence of repulsion), is given in the eleventh column, since 



= 



In every case, except the first, in which y is negative, the plates when charged 

 at a distance d apart were not under forces sufficient to put them in contact. 

 One must observe, however, that for a distance apart y when d<y, the forces 

 would not increase correspondingly. Only in case 5 is d = y, nearly. Thus, 

 without repulsion, the disks should have been thrown in contact when charged, 

 in all cases. In the actual presence of repulsion this was not observed, except 

 perhaps in the first. 



The substance of these investigations is contained in column 9, where the 

 ratios of F' R computed electrically and the value of F R from independent data, 

 i.e., from the given displacement AAf of the horizontal pendulum, are given. 

 It is seen that the ratio 



F' K /V'V 



decreases as the charged plates are farther apart (d), until at d>o.i^ cm., the 

 ratio is nearly i; i.e., the repulsion of plates nearly vanishes when their dis- 

 tance apart markedly exceeds i mm. Just how large d would have to be in 

 order that F' R /F R = i, I did not endeavor to find, since the suspended plate 

 vibrates annoyingly for large distances apart. In other words, definite ex- 

 periments of this kind must be left for the summer months. The constants 

 of the pendulum should then also be determined. Moreover, in a lighter pen- 

 dulum, the sensitiveness may be indefinitely increased, particularly when the 

 pendulum is provided with a float, while the error due to the inclination of the 

 pier does not simultaneously increase, an obvious advantage. It seemed wise, 

 therefore, to stop the work for the present at the point of progress reached. 



