in terms of coefficients of induction 395 



Eliminating P 1 and P 2 from equations (i), (2) and (3), 



P 3 [(C + D + E) 2 ] {[(A + C + M) 2 ] [(b + D + N)*] 



- [(A + C + M) (b + D + N)]*} 



(\A(A + B)} {[(C + D)(A + C + M)] [(b + D + N)*] \ 



-l(C + D)(b + D + N)]((A + C + M)(b + D + N)}} \ 

 [b (A + B)] {[(C + D)(b + D + N)][(A + C + M)*} 



-[(C + D)(A + C + M)] [(A+C + M)(b + D + N)]}) 



By means of his gauge electrometer, Art. 249, Cavendish made the value 

 of P the same in every trial, and altered the capacity of D, the trial plate, 

 so that P 3 in one trial had a particular positive value, and in another an equal 

 negative value. He then wrote down the difference of the two values of D as 

 an indication to guide him in the choice of trial plates, and the sum of the two 

 values, by means of which he compared the charges of different bodies. 



He then substituted for C a body, C', of nearly equal capacity, and repeated 

 the same operations, and finally deduced the ratio of C to C' from the equation 



C : C' : : D, + D t : >/ + >,_'. 



The capacities of the two jars were very much greater than any of the 

 other capacities or coefficients of induction in the experiment, and of these 

 [b (B + b)] was less than half the greatest diameter of the second jar, and may 

 therefore be neglected in respect of [b 2 ] or [Bb]. We may therefore put 

 [Bb] = - [ft 2 ], and in equation (4) neglect all terms except those containing 

 the factors [A*] [b 2 ] or [A 2 ] [Bb]. 



We thus reduce equation (4) to the form 

 P 3 [(C + D + E) 2 ] = P {[(C + D) (A + C + M)] - [(C + D) (b + D + N)]} 



- [>*] - [D (b + N)] + [D (A + M)]} ....... (5) 



The bodies to be compared were either simple conductors, such as spheres, 

 disks, squares and cylinders, and those trial plates which consisted of two con- 

 ducting plates sliding on one another, or else coated plates or condensers. 



Now the coefficient of induction between a coated plate and a simple con- 

 ductor is much less than that between two simple conductors of the same 

 capacity at the same distance, and the coefficient of induction between two 

 coated plates is still smaller. See Note 16. 



Hence if both the bodies tried are coated plates, the equation (5) is reduced 



^3 ([C 2 ] + [Z> 2 J + [ 2 !) = P ([C 2 ] - [fl 2 ]), ...... (6) 



so that the experiment is really a comparison of the capacities of the two 

 bodies C and D. 



But if either of them is a simple conductor, we must add to its capacity its 

 coefficient of induction on the wire and jar with which it is connected, and 

 subtract from it its coefficient of induction on the other wire and jar. These 

 two coefficients of induction are both negative, but that belonging to its own 



