NOTES ON THE THEOBY OF THE TRANSFORMER 279 



work of hysteresis becomes -=- a which is thus the formula of Stein- 



</ 



metz. 



In the case where a secondary exists the number of turns of wire 

 being n 1 and the current y 1 , we have simply to replace ny in the above 

 formula by ny -}- n^y 1 and change the phase of the hysteresis term so 

 as to be 90 from the combined magnetizing force, ny -f- n^y 1 . The 

 equations of the currents will then be, by Maxwell's formula, 



E=Ry + n 



which suffice to determine both y and y 1 . The result is too complicated 

 to be attractive. The equations show, however, that the odd harmonics 

 must appear in either the electromotive forces or the primary or second- 

 ary currents, if not in all of them at once. The exact distribution is 

 only a case of complicated calculation. 



It is to be specially noted that all formulae by which self induction is 

 balanced by a condenser will not be correct when applied to an iron 

 transformer but only to an air transformer. They will, however, apply 

 approximately to iron transformers in which the magnetization is small 

 and thus probably will apply better to transformers with an open 

 magnetic circuit than with a closed one. 



Also an iron transformer should not be compared with an air trans- 

 former or two iron transformers with different magnetizations with 

 each other. 



In conclusion I may add that the mathematical difficulties might be 

 overcome by another mode of attack but other work draws me in 

 another direction and I leave the matter to be worked up further by 

 others. 



