Interference Methods to Spectroscopic Measurements. 341 



This for ra=l reduces to 



-y cos nir 



~ I -An 2 ' 



IV. <£(#)= cos 2 mnr— , or sin 2 m7r— 



= 1+ cos2m7T— . 



— a 



sin?27r x Tsin (m + n)7r sin (?n — ?i)7r~| 



V- 7l7r ~~ 2 (^-f-ft) 7 *" (m—n)7r J 



sin m7r 

 m7r 

 The following cases are of interest : — 



T? A TT Sin7l7T 



Jbor ra = or go , v ft = , 



u n7r 



„ m=l,3,5,&c, V=V (l±-^), 

 „ m=2,4,6,&c, V =V (l+ -^-j). 



V. 4>M = COS P 7T — . 



This case deserves special notice, as many of the others may 

 be accurately or approximately represented by it. 



In this, as in all symmetrical functions, the term S vanishes, 

 and 



v=-° 



C a x 



\ cos p 7r — cos XirDxdx 



L a 



COS P 7T— dx 



j; 



X 



Putting 7T- =iv and 2Da = q, this becomes 



f 



J 



cos p io cos ^ iy clcv 

 Y= ' 



[T(ip+l)f 



For V = we have 



P/w7. J%. S. 5. Vol. 31. No. 191. Jjm'J 1891 2 B 



