434 Prof. J. Perry on Choking Coils. 



if I is the total induction (10 8 C.G.S. units being taken as 

 the unit of induction). If 



A = NC + nc and q = W/W + n 2 /r 2 



(the term n 2 /i^ being really negligible), the fundamental 

 equation for calculating 1 is 



A+fl0I=NV/R (1) 



Given the law connecting A and I and the resistances and V, 

 I may be calculated, and consequently C and c. Now in 

 ordinary practical transformer calculations A may be neglected 

 in the equation, even with the most complex law of mag- 

 netization; and it is this that causes calculations of the 

 induction and secondary currents and voltages in the most 

 complex cases, and even the primary current, unless when 

 there is a small load on the transformer, to be exceedingly 

 easy even when the coils are curiously connected with con- 

 densers and choking coils, and when there is much magnetic 

 leakage. But in our present case, it is A itself which is 

 wanted, and another method of working must be adopted. 

 In fact, the value of C does depend very much upon the law 

 of magnetization. 



However complicated the magnetic law may be, it can be 

 expressed in the shape : — 



If I = 2^-i ",- S1D *#| 



then 



A = 5 A f { sin (ix +f { ) — b { sin 3 ix + m . sin 5 ix — &c} , 



x being any quantity which increases continually. To be 

 strictly accurate, even as well as odd harmonics of ix exist in 

 A, and one of my students, Mr. Fowler, has worked them 

 out for some of Prof. Ewing's curves ; but the above formula 

 has been found by Mr. Field to be sufficiently accurate. Of 

 course, instead of ix we may have (ix + e i )in the above general 

 expression. 



When there is no hysteresis, f { =0. When there is con- 

 stant permeability (no hysteresis and no saturation), not only 

 is /;=(), but ^=0, 77^=0 &c, and cr^a^. 



If fx the magnetic permeability of the iron is constant and 

 the magnetic circuit is altogether of iron, as it always ought 

 to be both in transformers and in choking coils, a } stands for 

 47ra//,10" 9 /X, where a is the area of cross section of the iron 

 in square centimetres, and A, is the average length of the 

 induction solenoids in centimetres, 



Equation (1) becomes in the most general case 



NV/R = 2A l .| cos/, sin (ikt + e.) + (sin/. + qilco-J cos (ikt + e.) 

 —b. sin 3(ikt + e t ) + m. sin 5(ikt + e.) j- ; 



