182 
Transactions of the Society. 
(ii.) When the eye is held at the back principal focus of the lens 
d 
(iii.) For real images, calling the screen-distance d, 
d i 
” = 7 _1 - 
This last formula shows that in our example above, the image on 
the screen would be 9, and not 10. 
From these formulae it may be seen that in the case of a low 
power it makes a greater percentage of difference whether the eye is 
held close to the lens, or at its principal focus, than when a high 
power is used. Thus with the same minimum accommodation 
distance of 8 in. and a 4 in. lens there is a difference of 50 per cent., 
but with a lens of 1 /2 in. focus only 6 per cent. 
The following is a table of magnifying powers for simple Micro- 
scopes of various foci, from 1/4 to 6 in., and with various least 
distances of accommodation, worked out according to the first formula, 
which assumes the eye to be held close to the lens. 
Least Distances of Accommodation. 
Foci. 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
i 
13 
17 
21 
25 
29 
33 
37 
41 
45 
49 
53 
57 
1 
10 
13 
16 
19 
22 
25 
28 
31 
34 
37 
40 
43 
1 
7 
9 
11 
13 
15 
17 
19 
21 
23 
25 
27 
29 
2 
3 
51 
7 
81 
10 
14 
13 
141 
16 
171 
19 
201 
22 
i 
5 
61 
n 
9 
101 
H* 
±X 3 
13 
141 
15f 
17 
181 
19f 
l 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
U 
3 
3| 
41 
3 
5 
5| 
61 
7 
72 
1 3 
81 
9 
101 
2 
21 
3 
31 
4 
41 
5 
51 
6 
61 
7 
71 
8 
n 
21 
2| 
3 
3f 
31 
4 ! 
4 ! 
5 
5f 
54 
61 
6-1 
3 
2 
21 
2f 
3 
Ql 
3§ 
4 
4 i 
4 ! 
5 
5 1 
5| 
H 
1 7 
21 
21 
21 
3 
31 
31 
3f 
4 1 
n 
4 f 
5 
4 
1} 
2 
21 
21 
21 
3 
31 
3^ 
- 
3 T 
4 
n 
H 
5 
If 
4 
2 
2a 
5 
2£ 
5 
2f 
2 1 
3 
34 
3f 
34 
31 
6 
4 
n 
4 
2 
21 
2-1 
3 
21 
2| 
2f 
3 
31 
To find the power when the eye is held at the back principal 
focal point, subtract 1 from the values given in the table, but if the 
magnification of a real image on a screen is required subtract 2, the 
accommodation distances being of course in this last case screen- 
distances. Thus with a lens of 1£ in. focus, and a minimum distance 
