z8 
fT.0FES8(JK A. E. H. LOVE OX THE TXTEOKATIOX OF THE 
the (listiirbaiice is estimated. The difficulty could not be evaded by adopting a 
diffei'ent law of disturbance in secondary waves, and one aspect of it has Vjeen noticed 
by 8 ir G. Stokes'" in connexion with tlie law obtained by him. The difficultv would 
not aiise if we took a system of diverging sph'rical waves, and resolved the disturb¬ 
ance at a point (J, outside some particular s})herical wave front, into secondary waves 
due to a distrilaition of sources over this ti'ont. The difficulties of integration are, 
liowever, in this case considerable ; when the point O is at a great distance from the 
Sj)here, the integrals can be evaluated approximately, and it can be verified that the 
distuid)ance corresj)ondiug to the primary wave is reproduced. 
Passar/e of llffircs through an Apert are. 
24. The general problem of the passage of radiation across an aperture in a screen 
would involve a solution of the general ecpiations (4) or (12) of § 9, subject to 
boundary conditions holding all over both faces of the screen ; and, unless the 
incident radiation and the shape of the edge have very simple characters, this 
cannot at present be attempted.! In the theory of diffraction, it is customary to 
assume that the disturbance at points of the aperture, to which the disturbance 
on the furtlier side is due, is that wliicfi would be found at tliose points if there were 
no screen, and also that the elements of the surface of the screen contribute 
notiling to the distuiTance on tlie further side.;]; In the Theory of Sound, Hetai- 
HoL'PZ^ lias justified tlie use of a somewhat similar assumption in the problem of the 
open jiipe. In the present theory the (juestion may be forimdated as follows ;—A 
train of radiation is propagated on one side of a surface S tov'ards the surface : 
there is an aperture in the surface, and the transmitted radiation is to be represented 
as due to sources situated in the aperture ; how must such sources be distributed? 
[25. {Pc-wntteii 2Jajch, 1901.)—We sim})lify the general question by means of two 
suppositions:—(1.) that the incident radiation is represented by simple harmonic 
functions of the time, with period 27r/KO; ( 2 .) that the surface 8 is plane. The 
first of these enables us to eliminate all vector potentials, Iiy the rule 
(F, G, H) = /v“'(/, p, h) ....... . (59). 
It will appear later that the second supposition constitutes a jiractically unimportant 
restriction, when the aperture is small. We shall take the plane 8 to be given by 
the equation 2 : = z\ and shall suppose that the incident radiation is propagated on 
the nearer side (2 < 2 '). The transmitted radiation, ou the further side (2 > 2 '), 
‘ Fa|)ers,’ 2, p. 288. Of. IjouI IEvylekui, ‘ tVave Theory of Light,’ p. 429. 
t t'/’. A. .SOMJiEiirELD, ‘ 4Lith. Theorie d. DitfVaction,’ ?ilath. Ann., vol. 47 (1896). 
I Loi'd It.VYLEiGll, ‘Alive Theoi'v of Light,’ }». 430 ; or ‘Theory of Sound,’ vol. 2, § 291. 
§ ‘ J. f. Math. (Crelle),’ 57 (1859) ; or ‘ Viss. Abh.,’ vol. 1, p 303. 
