156 PROFESSOR KELLAND, ON THE 



Supplying these values, we obtain, 



1 r" v 1 — cos 2x 



f M 5 * 5 ) -if* 3 



a? 



7T 



= — (1 — e' ia ), a being always = 



7T 



2 ; 



. •. the intensity on this supposition is He — , or as we will write it, to 



denote that e stands now for the semi-aperture, HE 



TV 



We find then, that the whole quantity of light incident is exactly 

 that which corresponds to the open space between the bars, no effect 

 being produced by interference, or its destruction. 



2. Next, as a particular case, in order to make the process intelligible, 

 we will find the illumination when the breadths of the wires are equal 

 to the openings between them. 



If, for instance, there be two wires, the general formula gives 



J \ x ) Vsin %xi 



„ r» fsmx\ 8 . , „ , 

 = He (— — I 4cos 2 2#a# 



= 4iHef — (sin 8 a; — 4 sin 4 a; + 4 sin 6 a?) 



= 4 He f -, (- — ;rCOS 2x + tcos 4>x - -cos 6x ) 

 Jo x* \4 8 4 -8 / 



-*ra.(*-i+§) 



= it He. 



