30 
THE ASTRONOMER ROYAL, W AYE-LENGTHS 
in. 
Fr f = Length of wave for F, in Paris inch, =0-00001794, 
Fr g = „ „ G „ =0-00001587. 
The lines are not designated, in Kirchhoff’s tables of measures, by the received 
letters ; the letters, however, as well as Kirchhoff’s scale-numbers, are attached to his 
engravings of the spectrum, which appear to be carefully drawn. From these I took the 
following numbers : — 
K c =Kirchhoff’s scale-measure for C= 694-1, 
Kd 55 55 
D=1004-8, 
K E = ,, „ 
E=1527-7, 
II 
& 
M 
F =2080-0," 
K g — „ ,, 
G=2854-3. 
The next step was to construct a formula, which, when applied to Kirchhoff’s values 
for C, D, E, F, G, should produce Fraunhofer’s values for the same lines. I know no 
physical reason for adopting one formula in preference to another; and I therefore 
adopted the simplest algebraical formula. Putting ^^x^roK,, and f \—\ 00000000 x Fr„ 
T QccnTYiPfl 
f,=a+l . k,+c(k y+d(Jc,Y +e(ky, 
and formed five equations numerically by putting successively on the left side/ c , f D , &c., 
and on the right side fc c , y& D , &c., giving to those symbols the numerical values derived 
from the small tables above. Solving the equations, I found 
/,= 3596-688 
-2582-018 x h 
+1587-046 x (Jc) 2 
- 476-676 x (£,) 3 
+ 52-959 x(^) 4 . 
From this formula, values of f and Fr^ were tabulated for every 0-01 of k h or for 
every 10 '0 of Kirchhoff’s scale. It will be sufficient to give here every tenth number. 
KircKhoff. 
Fraunhofer. 
in. 
0-0000 
Eirchhoff. 
Fraunhofer. 
in. 
0-0000 
Eirchhoff. 
Fraunhofer. 
in. 
0-0000 
0 
35967 
1000 
21780 
2000 
18148 
100 
33539 
1100 
21199 
2100 
17888 
200 
31400 
1200 
20697 
2200 
17625 
300 
29525 
1300 
20262 
2300 
17358 
400 
27887 
1400 
19879 
2400 
17087 
500 
26462 
1500 
19538 
2500 
16814 
600 
25227 
1600 
19229 
2600 
16539 
700 
24162 
1700 
! 18942 
2700 
16269 
800 
23244 
1800 
18671 
2800 
16007 
900 
22456 
1900 
18407 
2900 
3000 
15760 
15535 
Between the numbers computed for every 10-0 of Kirchhoff’s scale, the numbers 
were interpolated for every one of Kirchhoff’s line-measures by simple proportion of 
