394 Note 17: theory of Cavendish s trial plate 



NOTE 17, ART. 194. 



Theory of the Experiment with the Trial Plate. 

 Let A and B be the inner, a and b the outer coatings of the Leyden jars. 



Let C be the body tried and D the trial plate, M the wire connecting A 

 with C, and N the wire connecting b with D. 



Let be the electrometer with its connecting wires. 



Let the coefficients of induction be expressed by pairs of symbols within 

 square brackets, thus, let [(A + C) (C + D)] denote the sum of the charges of 

 A and C when C and D are both raised to potential i and all the other con- 

 ductors are at potential o. 



First Operation. The insides of the two jars are charged to potential P , 

 the outsides and all other bodies being at potential o. 



The charge of A is [A (A + B)] P , and that of b is [b (A + B)] P . 



Second Operation. The outside coating of b is insulated, the charging wire 

 is removed, and the inside of B is connected to earth. The charges of A and 

 of b remain as before. 



Third Operation. A is connected to C by the wire M, and b is connected 

 to D by the wire 2V. 



The charge of A is communicated to A , C, and M , and the potential of this 

 system is P lt and the charge of b is communicated to b, D, and 2V, and the 

 potential of this system is P g . 



Hence we have the following equations to determine P 1 and P 2 in terms 

 of PC, 



[(A + C + M) (A + C + M)] P l + [(A + C + M) (b + D + 2V)] P 2 



= [A(A+B)]P (i) 



[(A + C + M) (b + D + N)] P l + [(b + D + 2V) (b + D + 2V)] P 2 



= [b(A+B)]P (2) 



Fourth Operation. The wires M and 2V are disconnected from C and D 

 respectively, and the jars A and b are discharged and kept connected to earth. 



The charges of C and D remain the same as before. 



Fifth Operation. The bodies C and D are connected with each other and 

 with the electrometer E, and the final potential of the system CDE is observed 

 by the electrometer to be P 3 . 



Equating the final charge of the system CDE to that of the system CD at 

 the end of the fourth equation, 



[(C + D + E) (C + D + E)] P 3 = [(C + D)(A + C + M)] P l 



+ [(C + D)(b+-D + N)]P, (3) 



