compound lenses and object-glasses. 
261 
Table 3. Values of r , r ' &c. deduced from equations (x), (A). 
/ ^ =1524 
1 i *'= i - 5*5 ' 
■CTZZ 
r or r — 
I 
r 2 
/ or r — 
3 
r rz 
4 
L— 
L '= 
0-50 
0-55 
060 
+ 1-4818 
1-4885 
1-4910 
— 2-3350 
2- 7524 
3- 2800 
—2-4053 
2- 7772 
3- 2637 
—06959 
06880 
0-6996 
+ 2 0000 
2-2222 
2 5OOO 
1-0000 
1-2222 
I-5000 
0-65 
0-70 
1+855 
1-4646 
3- 9670 
4- 8967 
3 ' 9‘ 1 5 
4-8005 
0-7369 
0 8120 
2-8571 
33333 
I- 857 I 
2 3333 
0-75 
I + 121 
6 *22I5 
6 0790 
0-9508 
4-0000 
1 
3-0000 
24. These values once obtained, it is easy to calculate the 
radii and focal lengths of the respective lenses, which I have 
accordingly set down, for the convenience of those who may 
be inclined to make trial of this construction, as follows. 
Table 4 Dimensions of an aplanatic double object-glass, indices of refrac 
tion 1-524 (crown) and 1585 (flint). Compound focal length io-oooo. 
Ratio of the 
Radius of 
Radius of 
Radius of 
Radius of 
Focal length 
Focal length 
dispersive 
the 1st. 
the 2d. 
the 3 d. 
the 4 th. 
of the 
of the 
powers. 
surface. 
surface. 
surface. 
surface. 
crown lens. 
flint lens. 
+ 
— 
— 
— 
+ 
— 
0-50:1 
6 7485 
4-2827 
4-'575 
14-3697 
5-0 
lO'COOO 
0 55 
67184 
3 " 633 2 
36006 
H 5353 
45 
8 1818 
0 60 
6 7069 
3 0488 
3-0640 
14-2937 
40 
66667 
0 65 
6-7316 
6-8279 
25208 
2-5566 
13-5709 
3'5 
5 - 3 s 46 
0 7c 
2 0422 
2-0831 
12 3154 
3 *° 
4-2858 
0-75 
7-0816 
1-6073 
1-6450 
10 5186 
2'5 
3 3333 
To reduce these values to those required for any other pro- 
posed focal length of the compound lens, a simple proportion 
is all that is necessary. 
25. This table and the preceding afford room for one or 
two remarks of some moment. And, first, with regard to the 
