164 Adams — Electromagnetic Effects of 



The value found was accurate to at least one-half of one per 

 cent, which is sufficient for this purpose. 



The charge of the spheres is the most uncertain element in 

 the quantitative determination, and it is this uncertainty 

 especially which makes the method of revolving spheres far 

 less suitable for quantitative work than the method of rotating 

 disks, particularly as employed by Rowland in his second 

 experiment. If a single set of spheres had been used, charged 

 to the same potential, an equal opposite charge would have 

 been induced on neighboring conductors which would have 

 travelled with the charges on the spheres. It would have been 

 difficult to determine just what the resultant effect should be. 

 For this reason two distinct sets of spheres were used, charged 

 oppositely, the spheres always keeping the same relative posi- 

 tions. It was then assumed that the only moving charges 

 were those carried on the moving spheres. The capacity of 

 the spheres was calculated on the assumption that they were 

 the only conductors present. The charge on any one sphere 

 was calculated by the method of images, the charges on all the 

 other spheres being regarded as concentrated at their centers. 

 We then have (Maxwell, volume i, section 159): 



± q — charge of each sphere. 

 ± P = its potential. 

 a = its radius. 

 f x ,fv etc. = the distances of the centers of the spheres 

 from one another. 



Then the charge on any sphere is given by : 



s = Pa Mj\ + 7^ • ■ ■ ■) + Hk + 7. + ■ ■ ■ ■)■ 



where the odd subscripts refer to spheres of the same set and 

 even subscripts to spheres of the other set- 

 Numerous determinations have shown that the potential of 

 the individual cells making up the battery averages almost 

 exactly two volts when freshly charged. On this basis, assum- 

 ing perfect insulation, the potential used was 20,000 volts. It 

 was thought best, however, to get a closer estimate of the 

 potential, since the insulation was not perfect. This was 

 measured by means of a guard-ring electrometer. If the 

 radius of the movable disk is R, the inside radius of the guard- 

 ring R', D the distance between the moveable disk and the 

 fixed disk, W the weight required to balance the attraction of 

 the two disks, and g the acceleration of gravity,* 



* Maxwell, volume i, section 217. 



