164 Transactions of the Society. 
tlie radii r" s", r s } r s, the thicknesses t", t, l', and the foci /", /, f of 
the lenses. 
Example 11. — Taking then for an example (Case 5, Example 7, 
fig. 18) of two diverging menisci of flint enclosing an equi-convex of 
crown, we have r" = • 830, s' = • 413, &c. : /i = 1 • 5179, f = 1 • 6202, 
we may call the thicknesses of the menisci t" = • 1 = t', and determine 
t, the thickness of the eqni-convex, by calculation (see Example 9) as 
*387, assuming the diameter of the lens to be *7. 
We first have to find the principal points p" and q" of the flint 
diverging meniscus, and its focus f" ; this is accomplished by going 
through the following arithmetical computation, which is quite 
straightforward, and may be quickly accomplished by the help of a 
slide rule. Great care must be exercised with regard to the signs of 
the quantities throughout. In fig. 19 the lenses have been separated 
for the sake of clearness. 
Fig. 19. 
0 Q F 
r" = -830 r = -413 r' = - -413 t" = -3 
s" = -413 s = - -413 s' = - -830 t = -387 
fj = 1-6202 /t = 1*5179 t' = • 1 
« 1 = 'I 
9 // 1-B202 
•06172; 
(jj! - 1) g" = -6202 x '06172 = -03828; 
- g" r" = - -06172 x -830 = - -05123 ; 
-rj" s"=- -02549; r"s"=-3428; 
s" - r" 4- O’ - 1) g" = - -3787 = h" ; 
O' - 1 )h" = - -2319 = k" ; 
