C. Bams — Repulsion of Two Metallic Disks. 103 



d' or d + AiVT/2 



and found from observation directly. Finally the residual dis- 

 tance apart of the plates, y, if the suspended plate had taken 

 its true displacement kN' (in the absence of repulsion), is given 

 in the eleventh column, since 



y = AiV/2 - d'. 



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

 when charged at a distance d apart, were not under forces suf- 

 ficient 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 the case except perhaps in the first. 



The substance of these investigations is contained in column 9 

 where the ratios of F' u computed electrically and the value of 

 F B computed from the given displacement L]Sf of the horizon- 

 tal pendulum, are given. It is seen that the ratio 



(F' R /F R ) = (v r /vy 



decreases as the charged plates are further apart (d\ until at 

 d > *13 om , the ratio is nearly 1 : i. e., the repulsion of plates 

 nearly vanishes when their distance apart markedly exceeds 

 l mm . Just how large d would have to be in order that 

 F'-r/F^ = 1, I did not endeavor to find, since the suspended 

 plate vibrates annoyingly for large distances apart. In a 

 specially equipped laboratory and with a lighter pendulum, 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. 



Table I, however, admits of a number of preliminary 

 estimates of the decrease of repulsion (f ) with d, the distance 

 apart of plates, for we may write, 



/= 65-2 x 2.x = 130a; dynes, nearly. 



These values are given in column 12 of Table I and in fig. 6, 

 with the exception of the first, which is distorted from actual 

 contact. The second observation (2 in figure) seems to be in 

 error for some reason not detected. The others make a com- 

 patible series. The forces found in the earlier work lay 

 between 1*3 and 0*5 dynes, for distances of the same order, dis- 

 tances which were not usually the same in the two positions of 

 the fixed disks. If we take the results in fig. 4, which are 

 probably the best, 



