282 Transactions of the Royal Microscopical Society. 
III. — Appendix to the Paper on the Identical Characters of 
Spherical and Chromatic Aberration. 
By Dr. Royston-Pigott, F.R.S., &c. 
( Taken as read before the Royal Microscopical Society, Nov. 3, 1875.) 
The actual calculation of the difference between the spherical 
aberrations of the extreme red and violet rays may easily be 
obtained as follows, for an equi-convex lens. 
For the spherical aberration of any ray whose refractive index 
is jx is 
— " — 7 • - 4 0* - 1) + (3m + 2) Gu - l) . «* + -£-} 
fi . fi — 1 K/i — 1 fj. — 1) 8 J 3 
In the case of an equi-convex lens, a = 0 and x = 0 in this 
expression and the spherical aberration becomes 
1 fj. 3 y 2 /x 2 y 1 
M 0-1) * ‘ 8? = (M-l) 2 ‘ 8/ 3 ’ 
y being the semi-aperture and / the focal length of the equi-convex 
lens. In order therefore to get the spherical aberration for coloured 
rays, the refractive index of the particular ray is substituted for fx 
in this expression, viz. 
m 2 
(m - 1) 2 ' 
Now take the rays B and H in the solar spectrum representing 
the extreme red and violet rays from Fraunhofer’s celebrated table 
of refractive indices for crown and flint glass : 
Kind of Glass. 
Red Ray B. 
Violet Ray H. 
Crown glass, No. 9 
Flint glass, No. 13 
/x = 1-52583 
/x = 1-62775 
1-54657 = /x 
1-67106 = /x 
Hence the spherical aberration of the red ray for the crown is 
y 3 
proportionate to the coefficient of ~ , viz. 
yfi ( 1 - 52583) 2 2-328157 
80- l) 2 8C0-52583) 2 2-211976 
or red aberration in crown .. .. = 1-05252 
so violet „ „ ....=!" 00082 
Difference in aberration 
•05170 
