compound lenses and object-glasses. 253 
pected till more rigorous means have been devised of insula- 
ting the different homogeneous rays, so as to secure their 
absolute identity at all times, and under all circumstances, a 
subject to which I have already devoted some attention, and 
not altogether without success. 
16. In the choice of media, then, for a double object-glass, 
we must be directed by the condition that their dispersive 
powers of the first order shall differ considerably. The 
equation 
0 = L/> -f Up', 
the only one we can satisfy rigorously in this case, gives 
_ _ P_ 
L — p' 
indicating that the lenses must be of opposite characters, and 
having their focal lengths in the direct ratio of their disper- 
sions. If we call l the power of the compound lens, and take 
& = y, the ratio of the dispersions, we get 
L = — ,L= — 
I — to 1 — to 
We have then only one farther guide to direct us in our 
choice of media, viz. that the dispersive powers of superior 
orders shall follow as nearly as possible the same propor- 
tion in both media, as those of the first. 
17. In triple object-glasses we have 
o = L/> + L'/+ L " p" 
o = Lq+Uq'+L"q” 
and /= L + L'+L" 
whence we obtain 
T __/ P'i"-dP" . 
* PW— q")+p\i"—q)+P"(q — ?') ’ 
T ' / P"9-3"P . 
' M— 9") +/(?"—?) +p" (?“/) ’ 
T" / Pl'—lP ' . 
(O 
(O 
(?) 
