1 82 Prof. J. Perry on the 



The higher harmonics diminishing more and more rapidly, 

 and having greater and greater lag. 



In the light of our general expressions (2), it will be seen in 



LL'-M 2 



the third statement and (6) that ji represents a re- 

 sultant coefficient of self-induction in the primary coil, unless 



M 2 R' 



for exceedingly small loads, and the resistance is R-\ — ^72"- 



Hence, unless the leakage is very small indeed, or very great, 

 it is obvious that the primary current cannot be a periodic 

 function of the same kind as the primary voltage. The 

 Tables and expressions show that this is also the case with the 

 secondary current. They also show that the secondary and 

 primary currents are nearly the same functions of the time, 

 although opposite in sign, and that they are nearly propor- 

 tional to one another. 



All necessary general rules suggested by the Tables are 

 easily worked out from the formula. But the suggestions 

 are such that it is evidently worth while to treat the subject 

 more generally, and those who are interested in symbolic 

 methods, as employed in linear differential equation work, 

 may prefer to see the equations written as 



V=(R + L<9)C + M<9C', .... (11) 



O = M0C + (R' + L'0)C', .... (12) 



rather than in the usual way. Hence 



0' — — Mfl y /iq\ 



RR'+(RL' + R'L)0+(LL'-M 2 )<9 2 ' ' [ } 



0= ( B, + L, *> V (14) 



RR'+(RL' + R'L)0+(LL'-M 2 )0 2 ' ' ^ J 



d d 2 



where stands for — , and 6 2 for -^ . 



These values are true for all kinds of currents, and any two 

 circuits, whether there is iron present or not. We know 

 that on a transformer L and U are practically proportional 

 to P 2 and S 2 , and M is nearly == vT37. 



From (3) and (4) at every instant, 



L - me °-{m + wr- • • ■ (15) 



This result is of course derivable at once from equation (2). 

 If R' is small, 



-c- L V 



