176 MR. R. A. SAMPSON; A NEW TREATMENT OF OPTICAL ABERRATIONS. 
* 
* 
+ 5-14196 
- -98228 
- -02057 
+ -00393 
-8-41708 
+ 1-60793 
f 
I - -85005 
- - 20175 
[ - 1-05780 
" 1 
- -005Jf^ 1 
+ -61018 
+ -60536 
-99752 
2-21269 
+ -00392' 
+ -99379 
2-93655 
1-00000 
-54509 
+ 1 - 00000 . 
+ -00400' 
+ 1-63694 
■99669 + -00636' 
•20775 + -61078 
- -85287 
+ 1-00000 
_ 
01112 
— 
- 00005 
- 
00885 
+ 
•00398 
02057 
+ 
-00393 
-4 
19501^ 
- 
-01884 
-s 
62204. 
+ 1 
•62611 
-8 
41708 
+ 1 
-60793 
J- 
01175 
+ 
-00400 "I 
1-4 
80696 
+ 1 
-63694J 
f 
* 
^ , 1 
1 
- -85005 
- - 00542 1 
1 
- -20115 
+ -61018 j. 
1 
1 
- 1-05780 
+ - 60536 J 
The schemes in the middle columns which precede and follow those belonging to 
the surface are the same for « and They should be written down independently 
and read against one another to guard against errors of transcription. 
Now, for any surface (r), in accordance with (14), 
= 1(1- n,) + c/), (/37 + y';- -/Ig - 
to. 
where 6,., c,., y,., /3',., y\ are read from the normal schemes on pp. 172, 173 in terms of 
^ 0 ) (do, yo, the specification of the original ray. We now calculate these, noting 
that since exclusively together, as do also c,., y,., y^, we need speak 
explicitly of the former only. 
We require to form from the original data 4(l—that is — iv><|‘B,.. There 
is no check upon these values and they should be examined with care like other 
fundamental numbers. Their values are shown in the fable below. 
We have then as regards w:— 
b, 
br^. 
il) 
r* 
1 
r. 
Co- 
Co- 
Co- 
Co- 
Co- 
Co- 
Co- 
Co- 
Sum 1 
efficient 
efficient 
efficient 
efficient 
efficient 
efficient 
efficient 
efficient 
of CO- 
bo. 
/lo. 
bo^. 
bof^o. 
bo^. 
bol^Q. 
efficients. 
0 
+1 - 00000 
♦ 
1•00000 
* 
* 
+ -24630 
+ -24630 
* 
+ -24630 
2 
+ -99752 
+-00392 
+ -99505 
+-00782 
+-00002 
- 2-37488 
-2-36312 
- -01857 
- - 00005 
-2-38174' 
4 
ibid. 
ibid. 
ibid. 
ibid. 
ibid. 
+ 1-68120 
+ 1-67288 
+-01315 
+ -00003 
+ 1-68606: 
6 
+ -99669 
+-00636 
+ -99339 
+-01268 
+-00004 
#■ 
- -23245 
- -23091 
- -00295 
- -00001 
- -23387J 
1 
