54 ELECTRICAL EQUILIBRIUM. 



The remark made above (67) shows that all the coefficients a are 

 positive, and that a coefficient such as a qp is never greater than a pp 

 or a qq . 



69. If we solve equations (i) in reference to the charges, we 

 shall have n equations of the form 



(3) M p 



containing 2 coefficients, the signification of which is at once 

 manifest. 



The coefficient jpp expresses the charge which must be given to 

 the conductor A p to raise it to unit potential, all the others being at 

 zero potential. This coefficient, which plays a conspicuous part in 

 the theory of electricity, is called the capacity of the conductor A p ; 

 we shall revert to it in a moment. A coefficient such as y qp expresses 

 the charge acquired by the conductor A q in connection with the 

 earth ; it might be called the coefficient of electricity induced by 

 A p upon Ag. 



The application of Gauss' theorem in the case of two successive 

 states, in which each of the conductors A p and A^ is raised to unit po- 

 tential, the others being in communication with the earth, shows that 

 these coefficients are also equal in pairs, and that we have the ratio 



(4) 7pq 



which is only an extension of the theorem demonstrated above (63) 

 for two conductors. 



If we refer to the observation in 66, it is easy to see that while 

 the coefficients y^, which express the capacities, are all positive, the 

 coefficients of the induced electricity, such as y pq , are all negative ; 

 moreover, that the sum of all those which relate to the induction 

 exerted by the same conductor, is never higher in absolute value 

 than the capacity of this conductor itself. For instance, we have, 

 necessarily, 



7PP> -[71P + 72P ..... +7np\> 



unless one of the conductors in connection with the earth A q , for 

 instance completely envelopes the conductor A p . In this case, we 

 should have 



7pp= ~7qp> 



