SpJierical Wave of Light. 69 



and as far as this term is concerned 



d't, dn d'C ^ 



T- + y + V = 0- 

 dx dy dz 



d^ /27r^V. 



''t, (27rb\\ 



and a^-r naust be written , • as explained in Article 9 of 



Professor Stokes' paper. 



If we had considered the full form of the equation on 

 the elastic solid principle, we should have been led to add 



to £.)].? terms -^, — , -~ where d> has the form 

 ax ay dz ^ 



a . 2Trbt I'x + my + n'z . zizbf 

 -sin—— + ^ sin^— 



^ f (P + ^ + r) _ :,(px' + £y- + rr + /lyz +jzx + Lxy) } ^-^^M _^ ^^^ 



(or rather such part of it as has the form yf(x,r), the 

 terms being final terms in the form of expansion, which I 

 have used throughout. 



I 3- 



I have as yet spoken of a plane polarised wave of light, 

 but obviously any expression which can, on Huyghens' 

 principle, represent a secondary wave corresponding to an 

 element of a plane wave, can equally well represent the 

 secondary wave corresponding to an element of any wave 

 front whatever, provided only the radii of curvature at the 

 element considered are large compared with the wave 

 length. I shall accordingly attempt to find the conditions 

 that we must have in order that a disturbance in a spherical 

 wave of radius c (where X/<: is an infinitesimal quantity), 

 may be reconstructed by the integral disturbances of certain 

 secondary waves arising from all points upon its surface. 



