ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
87 
Ji - (A - 1) m- 2Q„, - Q,-(i - A) - <wi - >) 
8Q1 \n 0 nj ( n x \?q n 2 J \n 2 ) 
+ 
+ 
8 d 2 0-3 Q 3 2 - l) - 4 d t 9?t (1 _ I) 
\n 2 J n 2 \n x n 2 ) 
K + , 2 )(i_ i ) Q 33 + 4 , i ^_ 1 )^ v ] 
(1- 4^0-0 
L j = (i ) ra^_ (i _ x )n 
Q 2 \ n L U V ( L n i \ n 2 / J 
+ 8 d 2 cr 3 Q3" (i - l) - 4 rf 2 Q 3 3 (1 - l)[ . 
= (1 - 1) {3Q 3 - 2 0- s } Q 3 (l - 4 c * i0 - 2 - 4^0-3). 
These magnitudes occur as coefficients in the following equations: 
A Ql ^2 + A Q 2 + A a 3 --a - | 
S cr' 
8Q1 
sr 
So-', 
S 0+ 
o~ o — <r 
sr 
sr 
A«, I -„- + M, rQ - + A«, rQ - ; --r. 
From these the three quantities A Q are to be calculated, and, when 
added to the Q, define the Q : wherefrom, as before, follow the new radii, 
which, combined with the assumed thicknesses, produce a system free 
from spherical and chromatic aberration at the given working distance 
and tube-length, and satisfying the sine law. 
Example : n 0 = 1. 
n l = 1-57332. dn x = + 0-00998 (heavy barium silicate crown). 
n 2 = 1*62059. dw 2 = + 0-01714 (ordinary silica flint). 
o-j = — 0*027778. 
log^ = 7-8023. 
log N 2 = 7-6265. 
logN 3 = 8-0243. 
h x = + 0-03307. 
h 2 = - 0-00185. 
= + 0-00213. 
+3= + 0-005556. 
log Lj_ = 9 • 5616 n. 
log L 2 = 8*2681 n. 
log L 3 = 9-5831. 
Jc L = +0-2319. 
h 2 = + 0-0047. 
Jc 3 = — 0-2366. 
