MR. K. A. SAMPSON: A NEW TREATMENT OF OPTICAL ABERRATIONS. 185 
From these we get at once 
d'^^S^G, and d(3^S2H., 
and thence 
}LdSf+^(FSiG + ^d/3^SsG and d^/SSJl. 
Also for the case /3 = 0, 
§^2 — ^dSJ^^ ^d^SiG ; 
thus we get d^^S^G, and when the adopted value of Sf' is used, also, which 
completes the solution. 
We see that we can use the rays (A)—3, 5 exclusively, or (B)—2, 4, 6 exclusively. 
Making separate determinations by these roads, 
( A .) ( B .) 
d^^^2G . 
+-00678 +-00709 
KdSf'+^d%G+^d^%G . . . 
--00593 --00627 
^d^f + ^d\G-v^d^^ (4G + 24 H) 
. 
--01279 --01295 
d2/3((^iH + 4G)+^®4H. . . . 
+ -01401 +-01422 
. 
. . -00000 
2Y^d8f'-^d%G . . . 
. . --00071 
2Kd^f' . 
. . +-00260 
Hence 
(A.) (B.) 
(A.) (B.) 
p. 179. 
d%G 
. . --00331 
^jG . 
--0766 
— 
-0730 
d^^^2G 
. . +-00678 +-00709 
4G . 
. + -3941 + -4121 
+ 
-4130 
d^^S^G 
. . --01115 --01183 
4G . 
. -1-6292 -1-7285 
— 
1-7099 
d^^SJl 
. . +-00723 +-00713 
SJl. 
. + -4202 + -4144 
+ 
-4130 
d/3%B. 
. . --00686 --00668 
4H . 
. -1-0023 - -9760 
— 
-9891 
nn 
. . -00000 
SsR. 
-0000 
— 
-0060 
There 
is no doubt, from the checks on 
p. 179, 
that the numbers put 
in 
the last 
column for comparison are correct to the last digit, and we see that the numbers (A) 
which rest upon the ray (5) are decidedly less consistent with them than the 
numbers (B) which do not. 
r ^ 
FiiLi 
l) 
2 B 
2 
YOL. CCXII.—A. 
