290 
MR. G. T. WALKER OK REPULSION AND ROTATION 
In fig. 28, cl — 135°; in fig. 29, a = 165°. 
Pig. 28. Fig. 29. 
For general principles I have derived assistance from the paper by Professor C. 
Niven, in the ‘Philosophical Transactions’ of 1881, “On the Induction of Electric 
Currents in Infinite Plates and Spherical Shells.” 
The Mechanical Effects of the Currents Induced in One Coil hy those in Another. 
1. Adopting Maxwell’s notation and taking y lf y 2 , as the currents in the two 
circuits, we have 
2T = Ly* + 2My 1 y. 2 + % 2 a . 
If It and S be the resistance of the primary and secondary circuits, and the current 
in the former be I sin pt, then for the second circuit 
whence 
where 
J t (Myi + N y 2 ) + S y 2 — 0, 
y 2 = A cos pt -f B sin pt, 
A B - I 
SMp “ MNp 2 — p 2 N s + S 2 ' 
Thus the “lag” due to self-induction in the secondary coil is tan 1 Np/S, and the 
electromagnetic force tending to increase a coordinate x is 
• • dM 
y dx ’ 
the mean value of which is 
, I 2 MNp 2 c!M 
~ ¥ S 2 + N y dx • 
If the coils consist of circular wires of radii A and a, and their planes be perpen¬ 
dicular to the line of length h that joins their centres, then Maxwell shows (§ 701) 
that 
