54 M. J. Frohlich on a neiv Proposition in the 



because in the above-mentioned position of the system of co- 

 ordinates fti and ft are very nearly -^-; 



sm «! cos y 1 



COSY! 



Hence we get for the kinetic energy of the diffracted light 

 proceeding from "d¥ and falling upon the entire screen: — 



cK'ajpja-, 3A -J- f + "r ''""*(«, /9)a«3T. . (i.) 



'!j— 00 «^— GO 



2. The variables are c^ft ; then 



a = («i — « ) sin « , £ = ft — £ 

 (for the same reason as before), 

 ■n B« "dec 



cos7 



Therefore the kinetic energy of the diffracted light proceeding 

 from the entire luminous surface FF, but falling only upon 

 the element "df is 



CK'2l^«o9&^£ +0 °j^J *(«, /9)3«3/9. (II.) 



The limits of the integration could be extended to — o© and 

 + oo , since indeed <E>(a, ft) remains finite only when the values 

 of «i — « , fti—fto are very small, but otherwise vanishes. 



Now, if we call the two elements ~d¥ and ~df conjugate when 

 their spherical angles in the aperture ^ are equal (conse- 

 quently 3« d# = d«i3&, and thus expressions I. and II. 

 become identical), -expressed in words this leads to the follow- 

 ing proposition : — 



The kinetic energy of the diffracted light emanating from a 

 large , uniformly luminous spherical surface FF, and falling on 

 the element "df of the screen, is equal to the kinetic energy of the 

 diffracted light proceeding from the conjugate luminous element 

 dF, and falling on the entire spherical surface of the screen ff 

 — provided that the line joining the conjugate elements goes 



