ON CERTAIN DIFFRACTION PHENOMENA. 305 



Thu.s, the intensity (A' diffracted light at D is given by 



or uioYd briefly by 



(II) I = MocPfdn c ' ^ (^^^ + ^^')- 



Tlie abo\(' expressiijn gives tlie intensity of diffracted light for 

 Fresnel's diffraction phenoinena. 



To evaluate the integrals given in (I) and (II), assinne as the 

 origin oï three rectangular c<3-ordinate axes x, ij, z. Let the coordi- 

 nates (jf the points L, 1>, i^ referred to these axes be denoted thus : — 



L : a, h, c, 

 D : a , b', c, 



P : X, y, z, 



and let the ecjuation of the surface referred t(.) the same axes be 



F (x, y, iij —const. 

 Thus, we have 



LO = ^ a^ + h- + c' = II, 



OD = ^ a'+ 6"-+ c- = W, 



LP ^ V (^» - ^f + (^ - Vf+ (^- - =2)' = 1^ - ^^^^ 



PD = ^ (rt'- xf^- {b'- yy'-{- {c'- y.)- = W - âli\ 



Expanding the expressions for LP and PD Ijy means of the binomial 

 theorem, we have 



LP ^ E j^ - -^yfj^iax -Vby ■]r cz)--\- ^, + , 



T„ ax + b'y + c'z 1 , , ,, , ,., ./;-+?/-+ 12'" . 



PD = K ^^-jf^ ^j^a^«'^+^^+^'^^)''+ ^-^4^^ — +■ 



or 



