280 
MR. G. T. WALKER OK REPULSION AND ROTATION 
In the case of self-induction causing a lag, shift, or retardation of phase in the 
secondary current, the circumstances are described by Professor Elihu Thomson as 
follows :— 
“ It will be noticed that the period during which the currents are opposite, and 
during which repulsion can take place, is lengthened at the expense of the period 
during which the currents are in the right direction for attractive action. 
“ But far more important still in giving prominence to the repulsive effect than 
this difference of effective period, is the fact that, during the period of repulsion, both 
the induced and inducing currents have their greatest values, while, during the 
period of attraction, the currents are of small amounts comparatively. There is then a 
repulsion due to the summative effects of strong opposite currents for a lengthened 
period against an attraction due to the summative effects of weak currents of the same 
direction during a shortened period , the resultant effect being a greatly preponderating 
repulsion.” 
The diagram for this is given in fig. 2. 
Professor Thomson has proved experimentally that two circular coils, whose planes 
are perpendicular to the line joining their centres, repel one another when an 
alternating current traverses one of them. 
If the coils consist of circular wires of radii A, a, and the planes be distant h, while 
the current traversing the primary is of strength I sin pt, then I have shown that the 
force of repulsion is 
r [2F - (1 + COS’ y) F] [2F - (1 + sec 2 y) E], 
where 
S = resistance of secondary circuit, 
N = its coefficient of self-induction, 
_ _ (Aft) 
‘ Sm 7 ~ \/{(A + af + lr) ’ 
and F, E are complete elliptic integrals to modulus sin y. 
