184 Mr. 0. Heaviside on the 



of fixing L 2 and L 3 , viz. either by x 1 = x 3 and x 2 = x^ or by 

 x x =x 2 and x s =x 4: ; but if so that x 1 =x 4: in the first place, then 

 they must also = x 2 = x B . 



Similarly the choice of L 2 and L 3 so as not to make x 2 =x z 

 gives two ways of fixing L x and L 4 , by vertical or by hori- 

 zontal equality of time-constants, as before ; whilst x 2 =x s 

 produces equality all round. 



The special case of all four sides equal in resistance may be 

 also noticed. Balance is given in two ways, either by hori- 

 zontal or by vertical equality in the L's. 



Leaving the mathematical treatment for a little while, I 

 proceed to give a short general account of my experience of 

 induction-balances. I did not originally arrive at the method 

 of equal ratio just described through the general theory, (20c) 

 to (27c), but simply by means of the general principle of 

 balancing by making one line a copy of the other, of which I 

 obtained knowledge through duplex telegraphy, and inves- 

 tigated the conditions (25c) to (27c) more from curiosity than 

 anything else, though the investigation came in useful at 

 last. In 1881 I wished to know what practical values to 

 give to the inductances of various electromagnets used for 

 telegraphic purposes, and to get this knowledge went to the 

 quadrilateral. Not having coils of known inductance to start 

 with, I employed Maxwell's condenser method *, with an 

 automatic intermitter and telephone. Let 1, 2, and 3 be 

 inductionless resistances, and 4 a coil having self-induction. 

 Put the telephone in 5, the battery and intermitter in 6. We 

 require first the ordinary resistance-balance, R 1 R 4 = R 2 R 3 . 

 But the self-induction of the coil will cause current in 5 when 

 6 is made or broken. This will be completely annulled by 

 shunting 1 by a condenser of capacity S 1? such that 



Rjbi = L4/R4, 

 signifying that the time-constant of the coil on short-circuit 

 and that of the condenser on short-circuit with the resistance 

 Bj are equal. 



The method is, in itself, a good one. But the double 

 adjustment is sometimes very troublesome, especially if the 

 capacity of the condenser be not adjustable. For when we 

 vary B l5 to approximate to the correct value of RjSj, we 

 upset the resistance-balance, and have therefore to make 

 simultaneous variations in some of the other resistances to 

 restore it. But the method has the remarkable recommenda- 

 tion of giving us the value of the inductance of a coil at once 

 in electromagnetic units. 



* Maxwell vol. ii. art. 778. 



