202 Mr. 0. Heaviside on the 



sion that he has obtained experimental evidence of the exist- 

 ence of induced currents therein. Now, although when it 

 is considered that although induced currents in wires were 

 known to exist, yet the possibility of their existing in metal 

 not in the form of wires was only a matter of the wildest 

 speculation, Professor Hughes's conclusion must be admitted 

 to be very comforting and encouraging. 



Leaving now the question of cores and the balance of 

 purely electromagnetic self-induction, and returning to the 

 general condition of a self-induction balance Z 1 Z 4 =Z 2 Z 3 , 

 equation (23c), let the four sides of the quadrilateral consist 

 of coils shunted by condensers. Then R, L, and S denoting 

 the resistance, inductance, and capacity of a branch, we have 



Z=^S^-f(R + L ? )- 1 }- 1 ; .... (55c) 

 so that the conjugacy of branches 5 and 6 requires that 

 {Stf + flE^ + Ltf)-!} \SiP + (R 4 + L 4 p)-i} 

 ^{^P + (^2 + ^2p)- 1 }{^p + (R 3 -rL 3 p)-'} y (56c) 



wherein the coefficient of every power of p must vanish, 

 giving seven conditions, of which two are identical by having 

 a common factor. It is unrecessary to write them out, as 

 such a complex balance would be useless ; but some simpler 

 cases may be derived. Thus, if all the L's vanish, leaving 

 condensers shunted by mere resistances, we have the three 

 conditions 



xiiR^ = R2R3J 



8 1 fR 4 +&JR 1 = 8 a /R i + S s /R 3 , I . . . (57c) 



8x84=8283, 



which may be compared with the three self-induction condi- 

 tions (25c) to (27c) . 



If we put RS=y, the time-constant, the second of (57c) 

 may be written 



yi+3/4 = y 2 + ?/3 ? (58c) 



which corresponds to (26c). If S 2 = = S 4 , the single con- 

 dition in addition to the resistance-balance is */i=y 3 . If 

 S 1 = = 8 2 , it is y 3 =# 4 . 



Next, let each side consist of a condenser and coil in 

 sequence. Then the expression for Z is 



Z=R+I J p+(S P )-i, (59c) 



