THE RA1MU)\V DUE TO A CIRCULAR SOURCE OF LIGHT. 17 



/"; nevertheless it does not follow tluit the niaximu for /" always 

 remain as maxima for F. 



For the consideration of the general character of F, we 

 shall begin with that of /'"'. By Stokes's expression 



,,,, 2 1 „ C.x^^ 17 1 ^"-Ks) 



f- is composed of two terms : tlie mean term ,^ , ^ , and the 

 ^ ^ y .3 y /.a 



oscillating term, whose amplitude is limited by the same numer- 

 ical factor — .-- .-^ : therefore at maxima /"'- increases to 2x 



VaVxH 

 (mean term) and at minima decreases to zero. But the character 



of F is slightly different, since 





The first term is equal to 



and leads to the same mean term so far as the first order of 

 -7^ is concerned. But the second term, after putting ~y ~ra 



-1/ (y/^V 7"" 



the mean value of — K'_^ — — , and integrating with respect to 

 a new variable 1~y-^—^ — j'^ , becomes 



Thus the amplitude of the oscillating term is limited by 

 M V^'>^^^Vy-d) i^i 1^ i j„u(.Ij smaller than ,~ ,~ ; and, more- 



over, this may be positive or negative according to the sign of 

 sin(-j/3-;f^i/;f^). For the smaller value of a>, -y—^ becomes 



