Self-induction of Wires. 187 



any position. Now make r 1 = r 2) and ^ = Z 2 ; this reduces 



Z = ir+i(l + m)p; (31c) 



whilst, when in sequence, we have 



Z=2r + 2{l+m)p, (32c) 



thus proving the property stated. We may therefore make 

 one inductometer serve as two distinct ones, of low or high 

 resistance. 



There does not seem to be any other way of making the 

 two coils in parallel behave as a single coil as regards external 

 electromotive force. Any number of coils whose time- 

 constants are equal will, when joined up in parallel, behave 

 as a single coil of the same time-constant ; but there must be 

 no mutual induction. (An example of the property * that any 

 linear combination whose parts have the same time-constant 

 has only that one time-constant.) This seriously impairs the 

 utility of the property. This reservation does not apply in 

 the case of the equal-coil inductometer. 



Having got the inductometer calibrated, we may find the 

 inductance of a given coil, or of a combination of coils in 

 sequence, with or without mutual induction, nearly as rapidly 

 as the resistance. Thus, 1 and 2 being equal, put the coil to 

 be measured in 3, and the indoctometer in 4. We have to 

 make R 3 =R 4 and L 3 = L 4 , or to get a resistance-balance, and 

 then turn the inductometer till silence is reached, when the 

 scale-reading tells us the inductance. This assumes that L 3 

 lies within the range of the inductometer. If not, we may 

 vary the limits as we please by putting a coil of known 

 inductance in sequence with branch 3 or 4 as required, putting 

 at the same time equal resistance in the other branch. 



Or, the inductometer being in 4, and 1, 2 being induc- 

 tionless resistances, put the coil to be measured in 3. If it has 

 a larger time-constant than the inductometer's greatest, insert 

 resistance along with it to bring the time-constants to equality. 

 The conditions of silence are B- 1 E>4 = E 2 B, 3 and L 3 /R 3 = L 4 /R 4 . 

 Here a ratio of equality is not required. The method is 

 essentially the same as one of MaxwelFst, and is a good one 

 for certain purposes. 



Or, 1 and 2 being any equal coils, put one coil of the 



* This property supplies us with induction-balances of a peculiar kind. 

 Let there be any network of conductors, every branch having the same 

 time-constant. Set up current in the combination, and then remove the 

 impressed force. During the subsidence all the junctions will be at the 

 same potential, and any pair of them may consequently be joined by an 

 external conductor without producing current in it. 



t Maxwell, vol. ii. art. 757. 



02 



