: CP+2 
K, ©, K6) 2 [hs Y — l sin 2n{ 3 
9 9 = QZ {ob 25 se a 
( ee —Ko ee) | ee V3 AV WO+2 
cos 2ar ( 
Fe) = Se 00S 
Rainbow due to a Circular Source of Light. 603 
5. For the consideration of the general character of F, we 
shall begin with that of 7’. By Stokes’s expression 
5 TK = y ae Fike PU ea 
f? is composed of two terms: the mean term aes and 
WEWAT. 
the oscillating term, whose amplitude is limited by the same 
numerical factor ; therefore at maxima /? increases 
1 
hon IO 
to 2x (mean term) and at minima decreases to zero. But the 
character of F is slightly different, since 
The first term is equal to 
2 E 
7K?) _ dev (Kg)—2 ere aKa * =) 
and leads to the same mean term so far as the first order of 
~ 
Ka is concerned. But the second term, after putting 
K® 1 x 
= “7 Ke the mean value of Vv “ie - a and integrating 
with respect to a new variable 27 (a 
2. becomes 
Ké@—K@®\i : K6+ K®\3 
—) —cos 27 eee 
sin 2 Dat Ee a 
y 
Ké 
sin tn (= =. sin (V3rKbV Key 
67 K®KO Pe 37 KDKG 
Thus the amplitude of the oscillating term i A limited by 
sin y ee K6) much smaller than ANAC ae A and, 
moreover, this may be positive or negative according to 
the sign of sin (,/37K@,/K@). For the smaller value 
if ; 
of O, 3oK OKO gradually increases and the period of 
sin f4/ 30 K@\/ Ke} prolongs; in the limiting case ®=0, 
sin {./37K®/ KO} becomes equal to — ==, as 
aT KOKO n/3/ KO 
