spherical Wave of Light. 6y 



from which it appears that the last term of the expansion 

 will be that for which q = n. 



As an example we may take a case of vibration along 

 the parallels of a system of spheres referred to a pole on 

 the axis of x. 



n= ^sin;^(^/-r)-^3C0S/(^/-r) ' 



^ - - ^sin/(^/ - r) ■^j^,f.o^p{bt - r) 



in which the vibrations are accurately on the spheres. And 

 if we perform the expansion for a case of vibrations which 

 are to a first approximation along the corresponding meri- 

 dians, we get 



»= - {f -j|^}=in/(^'-'-)+|^cos/(*/-'-) 



In accordance with this solution and the previously 

 considered form for the displacement in a secondary wave, 

 representing, on Huyghens' principle, an elementary por- 

 tion of a plane polarised wave, we must have in the assumed 

 form of such a secondary disturbance. 





2?^-i = - ^,.+1 



r 



ru-i = 2- ^,,^1 



•(2) 



r" 



We have now, if possible, to find the values and relations 

 between the constants in this expression, and to limit the 

 values of n. 



j\rote.—lt is impossible to treat the diffraction question 

 without reference to Professor Stokes' work on the subject. 



