THE INDUCTION MOTOR. 



minal volts. Thus the vector of the primary current for any external 

 resistance is determined by the locus of the point A, Fig. i, which is 

 the straight line A D parallel with the vector of the impressed e. m. f. 

 The energy consumed by the transformer is given by the equation 



(i) & = e . i cos fi 



4. The introduction of leakage into the transformer changes the dia- 

 gram as follows : The total number of lines of induction passing 

 through the primary coil must remain constant as long as the terminal 

 voltage remains constant, neglecting for the moment the ohmic re- 

 sistance of the coil. The magnetomotive force of the main current 

 produces a stray-field proportional to the driving current; this field 



added vectorially to the main magnetic field, generates the constant 

 magnetic field included by the primary coil. The result of these ac- 

 tions and reactions is that A does no longer move in a straight 

 line, but in a semi-circle described upon the prolongation of O D C). 



*A historical remark may not be out of place here. The present writer worked 

 out the theory here given in the summer of 1895, and sent the paper to the 

 Elektrotechnische Zeitschrift, Berlin, where it was published in February, 1896. 

 Meanwhile Mr. A. Heyland, in some letters to the above-named paper, used the 

 same diagram without, however, giving any proof. When Mr. Heyland's letters 

 were published I inserted a note in my MS. referring to them. I have since, 

 whenever I had an opportunity, given Mr. Heyland ample credit for his priority, 

 and I have done it with satisfaction, as I really admired some of his later papers 

 very much. Mr. Steinmetz informed me some time ago that he had found this 

 relation as early as 1893, but that commercial reasons prevented him from pub- 

 lishing. 



