SpJierical Wave of Light. 

 They will be given by the scheme 



71 



cos9 . sin0cos0 . sinOsin^ 

 sin0 . — COS0COS0 . — cos0sin0 

 . sin0 . - cos^ 



be 



Then the co-ordinates of P, referred to these axes, wi] 

 given by X = pcos9 - c 

 Y = psme 



and r^ = f- 2rpcos0 + c^. 

 We must now express the amplitude and direction of 

 displacement at O in terms of a, 0, and 0. 

 P Let the angle AOO be written 7, 



and the angle between the meridian 

 planes ^. Then 



sincsiny — sinasin^; 

 cos^siny = cosasin6l - sinctcosOcos^; 

 cosy = cosacosO + sinasin0cos(;f.. 

 The first approximation to the resul- 

 tant displacement at O is 

 cos"*ysiny 

 ~c '' 



^ resolving this along the new axes of 



Y and Z as Q, we get 



C05>sinysina ^^^ cos'-ysinycosg ,g3p,,ti,.g, 

 c c 



and applying to each of these the formulae (i) obtained as 

 the necessary form of displacement in the secondary wave, 

 and writing x and y for X and Y, we get 

 ^1 = cos'"ysinysinc^(.T./')y - cos'"ysinycosc/^(jv:.r)_y 

 7?i = cos'"ysinysin30i(^.r) 



4i = cos"*ysinycosc|0i(.T.r) + <^ii{x.r)y^^ + cos"'7sinysinc^4(^.?')j^- ; 

 all being divided by c. 



We must now resolve these parallel to the axes, and get 

 t, = ticos0 + 7/isin0 ; 

 r] = ^isin0cos0 — t;iCos9cos0 - Cisin0 ; 

 ^ = ^isin0sin0 - rjiCOsOsincj) + 4icos0. 



