THE SPECTRUM OF NOVA PERSEI AND THE STRUCTURE OF ITS BANDS. 271 
a=0:07 they increase to 2 times the amount for a=0°04. For double the exposure 
the degrees of blackness 1, 3, 5 and 10 become respectively 1°9, 5°3, 8°4 and 15. 
Let the intensities of radiation 7, . . . 2, give respectively the blacknesses of degree 
m,... ™, when exposed time ¢# The question is, what is the degree m if a 
radiation of intensity 27 be exposed the same time t? Formula (5) gives 
1, (m,) = F(m,)2i where Rn) Fm), therefore 
(7) E(m) = ZF(m,). 
An extract of the F-Table is given below. 
TaBLe IX. 
F(m). F(m). 
Qo | ———— || 0g os 
(n= WO |) Os 4, j= ie] OH UZE |e 
0+} 0-00 0:00 8 1:08 1:06 
1 O'1l 0-19 9 127 1:20 
YW) 0:23 0°52 10 1:47 1:34 
3 0°35 0-44 11 1:68 1:49 
4 0-47 0°56 12 1-92 1°65 
5 0-61 0°68 13 PANT 1°82 
6 0-75 0°81 14 2°45 2°00 
7 0-91 0:93 
For instance, radiations which would singly give the degrees 1, 2, 3, 4 produce when 
Superposed m,=8°4 for b=1:08 (by Table [X., F(m,) = 0:11 + 0°23 + 0°35 + 0°47 = 1:16) 
| and 11:1 for b=1°4, as compared with 2m = 10. 
The difference m,—2m depends on 2m and the number of radiations which are 
superposed. It varies most for the intensity curve which shows the greatest range 
between maxima and minima, and which has a different number of superposed bands at 
different places. On this account the calculated intensity curve, 2m, belonging to photo- 
plate No. 4, which on hypothesis B has from 3 to 6 superposed radiations in the region 
| between H, and H, is the most likely to differ from an intensity curve m, calculated by 
| formula (7). I assume the same bands, and in first approximation the same degrees m 
which contribute to the 2m-curve of Plate I., but I compound them according to formula 
(7). The resulting m,-curve is then brought to agreement with the observed intensity 
| curve by suitable changes of the intensities of the bands, and the question is whether 
| this curve satisfies the observed curve as well as the =m-curve does. Table X. contains 
the calculation in detail at an interval of 10 tm., while it was made for every 5 tm. 
The first columns show, under the heading m, the degrees of blackness at each point which 
the radiations would singly produce on the film. 2m is the ordinate of the calculated 
intensity curve on Plate I., which was made to agree as near as possible with the 
observed intensity curve (see § 8); m) is the resultant if the degrees m be compounded 
