MR. R. A. SAMPSON: A NEW TREATMENT OF OPTICAJ. ABERRATIONS. 175 
r -99669 
... . 
1 - *20775 
+ -99669 
+ 
-00636] 
+ -24359 
- 
- 71615 
1-24028 
_ 
-70979 
r 1-00000 
^ \ 
+ -85005 
+ 
-00542 
L+ -85287 
+ -20775 
- 
-61078 
+ 1-05780 
-60536 
+ - 99 GOO 
+ 
-00636] 
+ -24359 
- 
- 71615 
+ -006361 
+ 1-24028 
_ 
-70979 
+ -61078 J 
+ -85005 
+ 
-00542 
+ -20775 
- 
- 61078 
+1-05780 
- 
- 60536 
- 1-172511 
- 1-00000 / 
In the case of the first and last, the combination consisting of only two terms, the 
check calculation is a mere duplicate, and is, therefore, less searching than the others. 
The signs, in particular, should be examined to guard against a double error. 
We next form the corresponding schemes for the function again in accordance 
with the formulae (ll). Owing to the occurrence of two zeroes in the scheme at the 
surface the calculation is somewhat simpler. 
•— 
+ -01161 + -OOOTS' 
+ 1-82012 + 1-52556 
+ 1-19308 +1-00000. 
1-00071 + •00973' 
- -25398 + 1-52556 
+ -01161 
+ 1-82012 
+ -00973'! 
+ 1-52556 J 
f * 
I -2-98866 
\ - -41285 
-3-40151 
- -00830 
-3-39694 
" 1 
- -01174 I 
+ -65S97 
-I 
+ - 64223 J 
+ -00157'! 
+ -64137/ 
-99752 
-41285 
+ -00392' 
+ -65397 
-2-99609 +1-00000. 
+ 1-00458 + -00244' 
+ 1-32922 + -99866 
- -00729 
- -00101 
- -00830 
-2-98466 
- - 412 SO 
- 3-39696 
- -00731 
- 2-99208 
- -OOOOS' 
+ -00160 
+ -00157 
- -01173 
+ - 65309 
+ -64136 
+ -002441 
+ -99866 / 
