88 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
a x = + 0-09904. ci 2 = - 0*1485. 
8 1 = + 0-05561 Q 3 + 0-00355. 
S 2 + 0 • 07788 Q 3 2 + 0 • 009479 Q 3 + 0 • 0002835 = 0. 
One root of the equation S 2 = 0 is Q 3 = — 0 • 05293, and 
Q 2 = - 0-2014. r A = + 54-56. 
Q 1 = + 0-04611. r 2 *= — 7-195. 
S x = + 0-0006072. r 8 = - 21*11. 
On the assumption that d x = 4 - 1*5, d 2 = + 1-0, we get from the 
working out of the paraxial ray <r' 3 = + 0*006176, r = + 0*00001279, 
S 2 = + 0-000001416, and the correction-equations with logarithmic 
coefficients 
+ 7-4042 A Q x + 7-1257 A Q 2 - 7-4325 A Q 3 = - 4-1511. 
+ 7 • 7721 AQ 1 + 7- 6383 A Q 2 — 8-0500 A Q 3 = - 5-1069. 
+ 9-5343 A Q x + 8-2555 A Q 2 - 9-5832 A Q 3 = - 6*7928. 
Whence 
AQ X = ■+ 0-000893, 
Q x = 4-0-04700. 
AQ 2 = + 0-00237, 
Q 2 = - 0-1993. 
AQ 3 = + 0-002529, 
Q 3 = _ 0-05102. 
r = + 0-00000029, 
S 2 = - 0-00000254. 
I KQ . HQ 
**! = + 52-03. 
r 2 = - 7-291. 
r 3 = - 22-00. 
A calculation of the rays proceeding from the object, and inclined to 
the axis at 6°, 4°, 2°, and infinitely slightly, gave 
hay. 
Intersection 
Logarithmic 
distance. 
sine ratio. 
C-axis 
180-39 
0-6869 
F-axis 
180-37 
0-6868 
D-axis 
179-93 
0-6858 
D2° 
179-98 
0-6857 
D 4° 
180-67 
0-6867 
1)6° 
184-17 
0-6936 
C 6? 
183-72 
0-6926 
F 6° 
187-78 
0-7009 
By a slight trigonometrical adjustment, the aberration residue can be 
rendered negligible. The calculation for the second root value of Q 3 
is carried out similarly ; finally, both evaluated systems have to be 
investigated in their relation to extra-axial rays. 
Centering of Lenses.* — Dr. Hugo Schroeder commences his paper 
on this subject by pointing out the obvious importance of accurate central 
* Ccutral-Zeit. f. Optik, 1898, pp. 161-2, 172-3, 182-3. 
