On Magnetic Lag. 35 



In the view I shall put forward I shall assume : — 



(1) That the variations are harmonic. 



(2) That the only induction in the secondary coil is derived 

 from the core, and is therefore, as regards phase, in quadrature 

 with the magnetization. As the current in the secondary coil 

 will be considered as producing one of the components of the 

 stress producing magnetization, itself reacting upon the coil, 

 the necessity of introducing a special E.M.F. of self-induction 

 is obviated. 



(3) That each turn in either coil embraces the same number 

 of magnetic lines. 



I shall also make use of the following symbols : — 



E, the maximum electromotive force of the machine ; 

 I ly the maximum value of the current in the primary 



circuit ; 

 I 2 , the maximum value of the current in the secondary 

 circuit ; 

 7T—0, the angle of phase-difference between the currents ; 

 ?n, the number of turns of wire in the primary coil ; 

 n, „ ,, „ secondary coil ; 



(/>, 'the angle of magnetic lag ; 

 ?*!, the resistance in the primary circuit; 

 r 2 , „ „ secondary circuit ; 



Ul I are the readings of two dynamometers placed respec- 

 * 2 * lively in the primary and secondary circuits, their 



1 2 1 2 



constants being A and B, so that -^- = A«j, -|- = Ba 2 ; 



a 3 is the reading of a dynamometer one of whose coils 

 is in the primary, the other in the secondary 

 circuit. Its constant is C. 



M is the maximum magnetization. 



The magnetic stress produced by each coil is proportional 

 to the current in that coil multiplied by the number of turns 

 in the coil, and is here taken to be that product, called very 

 often the ampere-turns. Its maximum value in the primary 

 coil is jjiIj and in the secondary coil it is nJ 2 . 



Now the observations on the dynamometers A and B furnish 

 us with a knowledge of I x and I 2 in any case ; and m and n 

 are details of the construction of the transformer. Thus we 

 are in possession of the two quantities ml l and nl 2 . 



But the three dynamometer observations enable us to de- 

 termine the angle of phase-difference between the currents, as 



D2 



