formed by a Plane Digraction- Grating. ary: 
Those in which we are specially interested are the two 
nearest to a principal maximum. The ratios of their inten- 
sities to the intensities of the principal maxima are given 
below for a few cases :— 
| 212 | 
| . | Secondary 
| = | mG | Principal. 
| a | 1 
| a | pnw+270 9 
| 1 : 
| 2620971 i — 
| 4 | pnt + 263°°37 | DS 
| e | ¢ 
| 5 bee agar: Gila her - 
. ~ | Pe JR70.R()/ 1 
| re pnt +257°°50 ne 
| 1 | pam +257°27/ _! 
Thus, the ratio is nearly the same whatever the number of 
openings provided it is greater than a good dozen; and this 
ratio is never very small. 
The question arises as to the reason of the evanescence 
of the secondary maxima for ordinary gratings. For gratings 
of half-a-dozen openings they are quite conspicuous, and there 
is no striking difference in the ratio for such a grating and 
for one of 10,000 lines for which they are invisible. It 
cannot be attributed to the lines being closer together ; for 
provided the gratings compared with one another have the 
same total aperture, the secondary maxima are very nearly 
indeed the same angular distance apart for all values of n if n 
is fairly large ; for the number between two principal maxima 
is n—2, and the distance between two principal maxima. is 
proportional to n. 
The true cause of evanescence would seem to be simply 
that in spectra as usually obtained even the principal maxima 
are only feeble. In support of this it is sufficient to mention 
that the secondary maxima are quite conspicuous in the 
neighbourhood of the direct image formed by a grating of 
14,000 lines to the inch (xn = 20,000) provided that a sufficiently 
strong source of illumination, such as the electric arc, is 
employed. 
ProsLeM C.—The precise position of the principal maxima. 
The maxima usually considered are the maxima of F3; 
in reality, however, it is the maxima of y” that are required ; 
thus a slight error is here committed, for wand v are dependent 
upon one another, and the two factors of y? cannot therefore 
be separately discussed. Although the modification pro- 
duced by the correct consideration of the problem turns out 
Phil. Mag. 8. 6. Vol. 8. No. 44. Aug. 1904. N 
