272 Mr. A. Campbell on the Measurement of very 



circuit should be closed and shou]d besides be highly inductive. 

 In practice this was found to work with perfect success, the 

 primary current being proportional to the secondary current, 

 which latter was measured by an ammeter. 

 To find the most favourable conditions, let 



J 1? I 2 be the primary and secondary currents respectively ; 

 E 2 the resistance of the secondary circuit ; 

 N its inductance ; 



M the mutual inductance between primary and secondary. 

 Let p=2wn, where n is the frequency of alternation. 

 Here M and N are constant, while R 2 may be variable with 

 temperature. 



At first let us assume that the P.D. follows a simple sine 

 curve. Then ^ = ^n^ + p^' 2 



I 2 Mp l ; 



Now let the inductance of the secondary circuit quite swamp 

 its resistance, so that we may neglect the term R 2 2 m com- 

 parison with y 2 N 2 . In this case we obtain 



^ - - (2) 



I 2 M' W 



i.e. the ratio of the primary current to the secondary current 

 is independent of the frequency of alternation and the resistances 

 of the coils. We shall see below to what extent this valuable 

 result can be realized in practice. It is clear that in the 



above case, since ^— = c© f the secondary current I 2 is in exactly 



opposite phase to I lB 



Now suppose the primary P.D. to be no longer a pure sine 

 function of the time but to follow any periodic curve. The 

 curve of primary current can then be decomposed into a 

 number of sine curves of various frequencies ; each of these 

 will produce a secondary of opposite phase, and the ratio of 



N 

 each primary component to its secondary will = ^> . 



Accordingly the total secondary current curve will be of 

 the same wave-form as the primary and in opposite phase to 

 it, while the ratio of current transformation will be the same as 

 for a pure sine-curve alternating current*, 



* In this I have assumed that the Fourier series for the wave-form 

 contains no constant term, i. e., that there is no constant component in the 

 current. If there is such a component, nothing corresponding- to it will 

 appear in the secondary circuit, and the ratio of current transformation 

 will be by no means the same as if the current were purely alternating. 

 In fact an air-core transformer affords a good means of separating out the 

 purely alternating part of any periodic current. 



