396 Note ij: theory of Cavendistis trial plate 



wire and jar is probably greater than the other, so that the correction on the 

 whole is negative. 



Hence in Cavendish's trials the capacity deduced from the experiment will 

 be less for a simple conductor than for a coated plate of equal real capacity. 



This appears to be the reason why the capacities of the plates of air when 

 expressed in "globular inches," that is, when compared with the capacity of 

 the globe, are about a tenth part greater than their computed values. See 

 Art. 347. 



It would have been an improvement if Cavendish, instead of charging the 

 inside of both jars positively and then discharging the outside of B, had charged 

 the inside of A and the outside of B from the same conductor, and then con- 

 nected the outside of both to earth, using the inside of B instead of the outside, 

 to charge the trial plate negatively. In this way the excess of the negative 

 electricity over the positive in B would have been much less than when the 

 outside was negative. 



With a heterostatic electrometer, such as those of Bohnenberger or Thomson, 

 in which opposite deflections are produced by positive and negative electrifi- 

 cation, the determination of the zero electrification may be made more accu- 

 rately than any other, and with such an electrometer P 3 should be adjusted 

 to zero. But the only electrometer which Cavendish possessed was the pith 

 ball electrometer, in which the repulsion between the balls when at any given 

 distance depends on the square of the electrification, and in which therefore 

 the indications are very feeble for low degrees or electrification. Cavendish 

 therefore first adjusted his trial plate so as to produce a given amount of separa- 

 tion of the balls by positive electrification, and then altered the trial plate so as 

 to produce an equal separation by negative electrification. In each case he has 

 recorded a number expressing the side of a square electrically equivalent to 

 the trial plate, together with the difference and the mean of the two values. 



He seems to have adopted the arithmetical mean as a measure of the charge 

 of the body to be tried. It is easy to see, however, that the geometrical mean 

 would be a more accurate value. For, if we denote the values of the final 

 potential of the trial plate by accented letters in the second trial, we have 



P,' ([C*] + [D*] + [ 2 ]) - P ([C] - ["]) (7) 



Since P 3 + P,' = o, we find by (6) and (7) 



[C*\ ([C] + [*]) - [D*] [D'"] + J [E*] ([/>*] + (D'*}). 



If we neglect the capacity of the pith ball electrometer, which is much less 

 than that of the bodies usually tried, this equation becomes 



[C 2 ] 8 = [> 2 ] [D'*}, 



or the capacity of the body tried is the geometrical mean of the capacities of 

 the trial plate in its positive and negative adjustments. 



