210 Lord Rayleigh. On the Bridge Method in its [Feb. 19, 



available for ordinary resistance testing, they should be combined, 

 that their resistance is equal to that (i) of the corresponding coi 

 bination of wires in parallel. Periodic currents may be conceived 

 arise from the rotation of a coil in a magnetic field of given streng 

 If the space occupied by the windings of the coil be supposed to 

 given, their number m will be determined by the condition of eqi 

 impedances. Thus, if 



(q + c) (b + d) _ 



(14) 



Mod (/i + t/i) = Mod (*,+ ,) (15) 



in analogy with (13). 



The above is the solution of the problem, if the coils of the sendii 

 and receiving instruments represent the whole of their respectii 

 branches, and are limited to occupy given spaces. The inductanc 

 and resistances cannot then be varied independently. But tht 

 would often be no difficulty in escaping from this limitation. Tl 

 inclusion of additional resistance, external to the instrument, 

 only do harm ; but the case is otherwise with inductance, positive 

 negative. If the inductance of the instrument added to r 2 , or to 

 be positive, the total inductance may be reduced to zero by the ins 

 tion of a suitable condenser, and this without material increase 

 resistance. If the inductance be already negative, the remedy is 

 so easily carried out; but, theoretically, it is possible to add 

 necessary inductance without sensible increase of resistance, 

 greater the frequency of vibration, the more feasible does this COT 

 become. We may, therefore, without much violence, suppose tl 

 the inductances of two branches can be reduced to zero with< 

 additional resistance. Thus, 



, = 0, 



and the condition of maximum efficiency of the transmitting 

 receiving coils is then given by Schwendler's rule, 



*i = fit fi = *i (!' 



These suppositions form a reasonable basis for further investif 

 tion ; but conclusions founded upon them will be subject to 

 examination, especially in extreme cases. We may also now introdi 

 the promised simplification, 



a = c, b - d (II 



in accordance with which (8) becomes 



d-b 



46 



(19) 



