254 REPORT—1885. 
tion normal to the incident light, but in one inclined at an obtuse angle 
to that in which the light is travelling. Tyndall observed this effect 
when the particles scattering the light cease to be very small. 
Chapter II.—Hetmnoirz’s THxory. 
§ 1. Helmholtz looks at the problem of the propagation of an 
electro-magnetic disturbance in a somewhat different manner, and a com- 
parison of the two theories is given by the author of this Report.! 
The electro-magnetic effects in the medium depend, according to 
Maxwell, on the values of F, G, H, the components of the vector potential, 
or, as Maxwell also calls it, of the electro-kinetic momentum, and if 
we integrate round a closed curve, the values of F, G, H satisfy the 
equation 
[Fae-+ Gay ~ Hade=|["S8* ade oil eo ya 
Tr 
where ds is an element of the curve, 7 the current at any point at a 
distance r from ds, do an element of the curve in which the current 7 is 
running, ¢ the angle between ds and do, and the integration on the right 
extends round the two curves s and o. 
From this we can show that 
K= ‘a da! dy' dz! dx 
aff) gidgide Ok ee 
And if we put 
ifisde gil so levig 
delay ert etd ® . ‘ ; . (12) 
we find that 
dJ : Pe 
= lle cig le 
ad da TT tt dadt — ; 7 
dF , db , dH 
h =o — + — 4+-—_ 
where J i cent qa 
Helmholtz, starting from the equation 
{ Fda + Gdy' + Hde = (Ae wide 
ij 
investigates,the most general form which F, G, H can have. He shows 
that we must write for a of equation (11) the value 
1 (_-k) @?o,, 
a Fall >t Taal dz'dy'dz’ yx. ; . (14) 
where & is an unknown constant. Hence 
; ao ‘ 
2 — — ry — ik )——_ 
V?F = — 4cpf + pb qa k) andi (15) 
and by comparing this with (13) we see that 
a 
' Glazebrook, Proc. Camb. Phil. Soc. vol. vi. pt. ii, See also J. J. Thomson, 
« Report on Electrical Theories’ p. 133 of this volume. 
