~ — 2 sm % K l sin 2kx, 



a sin 2/cl cos 2tf#, 



— q l 



If 0<^<Z 

 and sin ql = 0. 



Interference Phenomena. 525 



sin 2*7.27 = - 1 -7t — 5 sin 2 a:/ cos 2kx. 



9 2 f " 



cos 2qx = - I - 



A i fcd/c 



= - l ~o o sin 2 /eZ sin 2/e#. 



^Jo* -9* 



The first two integrals will hold for x = 0, as the left-hand 

 side vanishes at that point ; the right-hand side will therefore 

 vanish for indefinitely small positive values, and consequently 

 also for indefinitely small negative values. The third equation 

 will also hold for # = 0, as both sides give the same value for 

 positive and negative values of x. The fourth equation, how- 

 ever, does not hold at the same point. Putting x = in the 

 first and third integrals, we obtain 



= 1 a — 2 sm2 K h 

 Jo 2 *~ K 



2 C™ /cdfc . 



- \ ~~2 2 S1 



Combining these with the previous results, we easily 

 deduce the following : — 



4 f °° icdk 



1 + cos 2qx — — \ -5 o sin 2d 



^Jo K -T 



-\ 



COS z KX 



IT 



4 f 00 koIk 

 1 — cos 2gx= -- J -j 2 s i n % K l ^n 2 *&, V 



If 0<#</, and 

 sin ql = 0. 



in 2tf# = — I ~ ^ sin 2 kI cos 2 k;#. 



* ^Jo 9 -* 



I; -J, ?=?»»« 



= l -h r, sin 2k£ sin 2 /e#, y 



Jo * -v r 



COS KX, 



7T 



4 



= 



gd/c 

 q^ — fc 2 



sin 2 *;Z cos 2 ##. 



If x>l and 

 sin^=0. 



PA//. Mag. S. 5. Vol. 37. No. 229. Jm^ 1894. 2 



