Continuous-current Transformers. 159 



The theory of alternate current-transformers has been in- 

 vestigated by various authorities. It was first shown by 

 Maxwell that where there is mutual induction between two 

 circuits, the effect upon the secondary circuit of the presence 

 of the primary circuit is threefold : — (a) to transform in a 

 certain ratio the electromotive force ; (b) to add to the resist- 

 ance of the secondary circuit an apparent resistance equal to 

 that of the primary multiplied by the square of the same ratio; 

 (c) to deduct from the coefficient of self-induction of the 

 secondary circuit a quantity equal to the coefficient of self- 

 induction of the primary circuit multiplied by the square of 

 the same ratio. The ratio in question was found to be the 

 quantify 



2imM 



where M is the coefficient of mutual induction, n the number 

 of alternations per second, L x and R x the coefficient of self- 

 induction and the resistance respectively of the primary 

 circuit. In a communication made last year to this Society 

 I showed how, assuming the proper conditions of good con- 

 struction to have been observed, this ratio was equal to the 

 ratio of the number of secondary windings to the number of 

 primary windings in the transformer ; which ratio is known 

 as the " coefficient of transformation." 



The object of the present paper is to show that in continuous 

 current-transformers effects of the same kind exist. The 

 investigation is of an elementary character, secondary reac- 

 tions being assumed to be negligibly small. 



Consider a motor-generator, with double-wound armature 

 of ring or drum type, arranged to rotate between the poles of 

 a common fixed field-magnet. The magnetism of the latter 

 may be considered for present purpose constant : the effect of 

 variation in the magnetization will be afterwards considered. 

 Let the number of armature-conductors of the primary or 

 motor part, as counted all round the periphery, be called Q l9 

 and that of the secondary part be called C 2 . The ratio of C 2 

 to Ci we may call the coefficient of transformation, and we shall 

 use k as the symbol of this ratio. 



Now let i n r 1; and E x stand respectively for the current, 

 the resistance, and the induced electromotive force in the 

 coils of the primary armature, and i 2 , r 2 , E 2 for the corre- 

 sponding quantities for the coils of the secondary armature. 

 Write N for the whole number of magnetic lines passing 

 through the armature-core. Also write e x and e 2 for the 

 respective differences of potential at the terminals of the 

 primary and secondary parts. 



