Rainbow due to a Circular Source of Light. 605 
taken as nearly true. From this it follows that the effect of 
the breadth of the slit is more manifestly shown than for that 
of a circular source. Especiaily, the maxima and minima 
not only interchange places at certain points, but the interval 
between the maxima and minima slightly increases, as a con- 
sequence that the first maximum displaces towards 6=0, 
while the higher maxima, showing the same tendency, 
displace by smaller amount. In Pulfrich’s experiment *, 
where he takes third maximum as standard, the first and 
second displace slightly towards 6=0, and the other to the 
opposite side, as compared with Airy’s values of 7%. This 
displacement may be due to the breadth of the slit. 
7. For numerical calculation we must have recourse to 
mechanical quadrature. The method of procedure is as 
follows :—Draw a circle having the centre at K@ and radius 
equal to K®, then plot a curve whose ordinate is equal to 
the product’ of the value of f* into the corresponding 
ordinate of this circle ; the area of the new curve divided by 
the area of this circle is the value of F at K@. The following 
table was constructed by this method. 
2@=apparent diameter of the sun=32’. 
K@: (except 0) max. and min. of Airy’s value. 
Pee —0:025 cm; X= 5093 x 107° em. K= 120-95. 
ae e——0 Oo en.’ @ A-=o690 X 10° em. '  K= 192-00. 
| 
ke f2. F, 1 
0 0:443 0-447 0:465 
1-084 1-008 0-930 0-840 
2-495 0-000 0-103 0:228 
3-467 0:617 0:497 0:362 
4-363 0-000 | 0-124 0:237 
5145 0-510 | 0:378 (0:260 
5892 0-000 0133 0:235 / 
6-A78 0-450 0:300 0:206 
7-244 0-000 0-140 0:223 
7868 0:404 (254 7 
8-479 | 0-000 0:145 | 0-208 
9-060 0-384 0:230 | 0-164 
9-630 0:000 0:148 0-199 
10:17 0:362 0:207 0-155 
10-716 0:000 0-150 0-195 
The graphical representation of this ‘table is given at the 
end of the paper, where /* is represented by the broken line 
and EF’, F, in full lines (fig. 1, p. 609). 
# yeh abi XxXxill. pp. 205, 206 (1888). 
Phil. Mag. 8. 6. Vol. 8. No. 47. Nov. 1904. 2U 
