676 
LORD RAYLEIGH ON THE VALUE OF THE BRITISH 
tan +1 W f R + Lw tan tan \ x sec 
iG'K'w 
+ R /3 + L /3 w 
o {R/+I/&J tan 0+R' tan /x sec 0} 
When the wire circuit is open the equation determining the angle of deflection (0 O ) 
is 
00 
WIG*) 
tan 0 O -f r “ s ^ ( — ! R/ + L ' w tan ^o+R' tan /x sec 0 O } 
Since r is an extremely small quantity it is unnecessary to keep up the distinction 
between t0/ cos 0 and r tan 0, By subtraction 
(1 -j-r)(tan 0— tan 0 O ) 
= {tt~hLw tan 0+R tan /x sec 0} 
M'K' 
O) 
"*"E' 2 + I/ i V ! 
{L 'o>(tan 0— tan 0 o )-f-R / tan /x (sec 0— sec 0 O )} 
The last term is small, and we may neglect (sec 0— sec 0 O ) in combination with 
R' tan /x. 
Moreover 
iGTC'o) _ (1 4 -t) ta/n 0 O 
R' 3 -f L' 3 w 3 R' + L 'co tan 0 O 
so that 
(1 -f r)(tan 0— tan 0 O ) = pa ^ {B-j-Toj tan 0+R tan /x sec 0} 
+(l+r)(tan tan 4) 
If now we write (GK) for GK/(1+ r) , we get 
tan 0— tan 0 O = -^^^ Q> {R-J-La) tan 0-hB tan /x sec 0} {1+qy tan 0 O } 
JL\a T 1/ 
The effect of 1/ would therefore be to increase disproportionately the deflections at 
high speeds, i.e ., contrary to the effect of L. It appears, however, that in these 
experiments it could not have been sensible. At the highest speed tan 0 O was about 
-qYq, and co about 26 per second, so that co tan 0 O would be about - 2 \. The value of 
L'/R 7 is difficult to estimate with any accuracy. But the value of L/R for the wire 
circuit is about ’01 second, and that for the ring circuit must be much less, so that the 
terms involving L 7 may safely be omitted. 
The quadratic in R then becomes 
R«_K, i(GK>(l + tan ^ sec 4 +L 2 m s_l( GK )La) !! 
tan 0 — tan 0 O 
tan 0 
tan 0— tan 0 O 
:0 
