ME. R. A. SAMPSON; A NEW TREATMENT OF OPTICAL ABERRATIONS. 173 
• 997523 
831 
+ 
+ 
-003924' 
2443 
J 
-> 
5 
r 1-000000 
•0040005 
■ 1-000000 
+ -0040001 
+ 1-639121 [ 
2180 f 
•996692 
+ 
•006367 
1 
* 
1-000000J 
- -207753 
+ 
•610780 
- -545089 
+ 1-636941 J 
•996692 
+ 
•006367 1 
-+ 
6 
- -51^3286 
- -340532 
+ 1 
-003471 
-001142 
■ ^ 
' 1-000000 
, - -545089 
■ } 
1-639121J 
- -883818 
+ 
•997671J 
It may be well to repeat what these scheDies imply. Take the scheme 16. If 6 , /3 
refer to any ray where it meets the tangent plane to the surface (O) after crossing 
that surface but before crossing the space 1, and V, /3' refer to the same ray where it 
meets the tangent plane to the surface ( 6 ) after crossing that surface, then the 
scheme 16 states that 
6 '= +r0007126+ •009735;8, 
/3'=- •2539906+1-525572/1, 
and mutatis mutandis the same holds for c, y, c', y . 
We conclude, from the expressions on p. 151, that for the whole combination the 
cardinal features of the normal combination are given by 
HF = -ri31455 = -H'F', OF = -ri28820, 6 F'= + ri27712. 
We next work out the schemes multiplied into each of the aberrational functions w, 
as given in (ll), p. 157. The schemes {g, h, ...}, {g', h\ ...} which respectively 
precede and follow the surface to which w refers are read at once from the computation 
of the normal system just completed. As the surfaces are supposed to be spherical, 
we have e = 1 . The general arrangement is as above, and the check consists in 
forming the combination first forwards and then backwards. Again every figure is 
shown, but now the decimal places may be reduced to five. 
•—■ 
r 1-00000 
\ - 1-19308 
1-00071 
+ -83876' 
- -01161 
- -00973 
f 1-00071 
+ -83876 
- -01161 
- -00973 
+ •83816j 
+ -98910 
+ -82903 
- 1-00000 J 
- -28398 
- 21288 
-1-82012 
-1-52556 
_ -2-07410 
- 1-73844 
•98910 
- -25398 
-1-82012 
+ -82903 
- -21288 
-1-52556 
r 1-00071 + -00974 
-25398 +1-52556 
-2-07410 
- 1-73844 
