264 Mr. J. F. W. Herschel on the aberrations oj 
|a'= 1*585, the resulting curvatures and radii will be as in the 
two following tables, to which we have also subjoined the 
values of the coefficients of (2) to save the trouble of recom- 
putation, should any other equation beside (A) be thought 
preferable to use with it. 
Table 5. Values of.r, r 1 , &c. j **, 1 
5 1/* = i *585 
Z3 ZZ 
r or r — 
I 
r 2 = 
r ' or r — 
3 
r 4 
0 50 
0*55 
o*6o 
+ 1*5041 
1*5220 
15217 
2*4642 
2*887 1 
3.4386 
— 2 5168 
2*8880 
3-3916 
— 0*8074 
07988 
0-8275 
065 
0*70 
1*5 108 
1 4791 
v-n 4 ^* 
04 ^ 
_p>. CO 
ON N 
4*0636 
4 9 8 93 
0*8890 
1-0007 
0*75 
1*405 2 
6 ’ 53»3 
6 3259 
1 ' * 977 
and the radii being calculated from these in the same manner 
as before, will come out as follows : 
Table 6. Radii of an aplanatic object glass. 
Focal length rr io*ocoo. Refractive indices 1*504 
and 1*585. 
Ratio of 
Radius of 
Radius of 
Radius of 
Radius of 
dispersive 
the 1st. 
the ‘ 2 d. 
the 3d. 
the 4th. 
powers. 
surface. 
+ 
surface. 
surface. 
surface. 
0-50 
6-6485 
4 058 1 
3-9733 
12*3854 
0-55 
6-5703 
3+637 
3-4626 
12*5193 
o*6o 
6 57-6 
2-9082 
2-9484 
12-0839 
0-65 
66190 
2-4049 
24608 
1 1*2481 
0*70 
6-7609 
1-9476 
2-0043 
9 99 2 7 
0-75 
7-1164 
!-53ii 
00 
0 
00 
t/-\ 
8 - 349 * 
