ol6 Ü. XAGAOKA. 



Jieturiiiiii,'' io our [H'oblciii on FrüUiihofer's ditfrnction phcnoinena, 

 we iz'tit for the exiR'ession of the iuteiisitv 



I — 4 a- — ß — (A-+ L-) 



With a hoinoo'eneouy tsonrce of Jiu'ht, the iiiteiisity always vanishes 

 whenever I h is a nuiJtipJe of -. The fringes arising i'roni the term 

 sill' lb are exactly the same as those given hy the ])lane slit. When 

 the surface on which the slit is cut is cylindrical, the additional factor 

 K- + L'' enters into the expression for the intensity of the ditfracted 

 li^dit. This factor has maxima and minimu f )r ditierent positions of 

 tlic telescope, and moreover depends on the length of the slit. Thus, 

 wlien the Hmits (jf integration lie from to -, K -■= - J°{^) and L = 0, 

 and there would be places of darkness for .such positi(His of the teles- 

 C(3pe as are determined by the values of ç corresponding to the roots; 

 uf /■>(?). 



For a great numi)er of ecpiidistant slits, the expression for the 

 intensity would be tlie same as that for ordinary grating, multiplied 

 by the factor K- + L'\ 



The case which calls f)r sjjccial attention is when the ray 

 is normally incident, and tlie telescope turned so as always to 

 lie in the plane xij. Tlicn ;c = 0, //. := 0, v = 1, and // = 0. Thus 

 I = ^^4^ sin. (0, where w is the angle made by the axis of the telescope 

 with z axis. The places of darkness are given by 



n / 



Sm (I) =- — r • — r- 



2 6 



The maxinra and minima arising from the term K- + L" must be 

 separately determined f )r the ])arlicular slit in question. 



