236 
MR. STOKES ON THE THEORY OF CERTAIN 
• • cl 
proper multiplier of is -• This may be shown to be a necessary consequence of 
the principle mentioned in the preceding article, that light is never lost by inter- 
ference ; and this principle follows directly from the principle of viva. In proving 
that is the proper multiplier, it is not in the least necessary to enter into the con- 
sideration of the law of the variation of intensity in a secondary wave, as the angular 
distance from the normal to the primary wave varies ; the result depends merely on 
the assumption that in the immediate neighbourhood of the normal the intensity 
may be regarded as sensibly constant. 
In the expression (a.) we have 
PM= [x—pY-]- {y — qY'] = V ~ —2qy}— f— jox -f 53/) , near I y , 
if we write f for It will be sufficient to replace outside the cir- 
cular function by We may omit the constant /’under the circular function, which 
comes to the same thing as changing the origin of t. We thus get for the disturb- 
ance at M due to the unretarded stream, 
or on performing the integrations and reducing. 
2 chl Xf . 2 ' 7 rql Xf . mph 
— /Sin -ri -r Sin Sin 
xf 2-K(il xf irph Xf 
A 
ph\ 
2f)' 
{b.) 
For the retarded stream, the only difference is that we must subtract R from vt, 
and that the limits of x are g and g-\-k. We thus get for the disturbance at M due 
to this stream. 
2 ckl xf . 2 'nql Xf . 'Trpk . 
Tr" 7 r /Sm -rj — / sin^-sm 
xf 2 i^ql Xf -Kpk Xf 
(c.) 
If we put for shortness r for the quantity under the last circular function in (b.), the 
expressions (b.), (c.) may be put under the forms u sin r, v sin (r— a), respectively ; and 
if I be the intensity, I will be measured by the sum of the squares of the coefficients 
of sin r and cos r in the expression 
so that 
u sin 7-\-v sin (r — a), 
lz=yf -Y'^UV COS a, 
( 10 .) 
which becomes, on putting for u, v and a, their values, and putting 
A// 
I = Q.^{(sm^y-h(sin^^y-f2sin-^-sin^cos[f-^(4g-f-/i-l-/i’)]|. (11.) 
12. Suppose now that instead of a point we have a line of homogeneous light, the 
