458 



Prof. J. Perry. 



[May 12, 



solenoids in centimetres. The curve which, on squared paper illus- 

 trates the magnetic law is a straight line, and I = oA. 



2. If the curve is not a straight line, that is, if there is some in- 

 dication of saturation, and there generally is some saturation where 

 /3 the induction per square centimetre exceeds 2 X 10~ 6 (or 2000 

 C.Gr.S. units), it will be found that a good approximation to 

 actual facts is obtained by assuming that when I = I sin x, A = 

 A (sin x — b sin3a? + msin 503 + &C.) where Io/A© = <?, aconstant, and n 

 is any quantity which increases continuously. Thus it will be found 

 that taking only one harmonic, b = 0*2 gives a close approximation to 

 what may be the actual case in transformer problems. Taking two 

 harmonics, b = 0*2 and m = 0*05, gives a better result. There is no 

 hysteresis in such cases. 



3. If the curve is a simple hysteresis loop such as may be obtained 

 in slowly-performed cyclic magnetisation, on the assumption that 

 I = I sin x, one of my students, Mr. Fowler, has found A in terms of 

 sin(# + ei), sin(2# + e2), &c, a rather complicated expression which I 

 need not give. But another student, Mr. Field, finds that the ap- 

 proximation A = A {sin (»+/)— b sin3x-\-msm5x} is sufficiently 

 accurate for many purposes of calculation if b = 0*2 and m = 0*05. 

 However complicated the law may be, it can be expressed in the 

 shape : — if I = 21; sin (ix + e{) then to the ^th term in I there corre- 

 spond the terms in A, (Ii/<rj){sin (ix + ei +fi) — - h sin 3ix + mi sin 5 ix + 

 Ac.}. 



Our first assumption of constant permeability applied to a trans- 

 former with one primary and many secondaries causes equation (1) 

 to become A = (l + g<r^)~ 1 N 1 V/R 1 , and hence 



-C s = (F s N 1 /R t R 1 ){*$Y/(l + q<re)}. 



I will, for sake of illustration, consider a 1500- watt transformer, which 

 is a specimen of many in use. One primary coil Ri = 27 ohms, 

 T$i = 460 turns. Internal resistance of the one secondary coil 

 = 0*067 ohm, rT 2 = 24 turns. Effective primary potential differ- 

 ence = 2000 volts or V = 2828 sin Tcb. Frequency about 95 per 

 second, or h = 600, « = 360 square centimetres, X = 31 centimetres. 

 It will be found that the highest value of /3, the induction per square 

 centimetre, is 2*755 X 10~ 5 (or 2755 C.Gr.S. units). If there are neither 

 condensers, nor self-inductions, nor magnetic leakage, and if ju, = 

 2000 (it will not much affect our results to take jx = 1500 or 3000), 

 then c — 3X10 -4 ; if there is no load on the transformer q = 7837, 

 and if there is full load, when R 2 = 6*8 ohms, q = 7922. It is 

 evident from these numbers that in practical cases 1 + q_oO is nearly 

 the same as qo0. Neglecting the 1 means neglecting an alteration of 

 l/500,000th of the amplitude and a lag of 1 /200th of a degree. We 

 see that in this case neglecting the term A in equation (1) is quite 



