A B E 



Cor. When Q E and Q F are given, aberration vnvi<>.> ;\% A N varies as 

 R N 8 nearly. 



The following series for aberration is a little different from the pre- 

 ceding; but amounts nearly to the same thing; putting / II E A. 



Aberrat. - ^- / (sec. 6 - 1) - - /, (sec. G - 1) + &c. 



Cor. Wlien the incident rays are parallel, aberration A T . 

 II. Aberration in refraction at spherical surfaces. 



Let A & A' be the perpendicular distances of Q and 9 from the refract- 

 ing surface, m the ratio of the sine of incidence : sine of refraction, v = 

 ver. sin. A N (see preceding figure j) then 



Aberrat. = ( A' r)* ~ --- ~) o 



is .*. positive, if A be less than (m -f 1) r, & negative when A is above 

 that value. When A (m -f- 1) r, there is no aberration. 



When the incident rays are parallel, or = o, this reduces to 



(A' -r)z 

 i v j or if F be the principal focal distance, it is 



F 

 III. Aberration in a lens. 



We may consider this as consisting of two parts : 



(1.) The variation in the second focal distance arising from the aberra- 

 tion in the nrst (a.) 



(2.) The additional aberration in the refraction at the second surface 

 08). 



Let A" be the distance of the focus after the 2d refraction, the re<st as 

 before ; then 



For the 2d part we must alter our formula, by putting for m, V for 

 .4', A' for A, A" for A', r' Jor r ; 



,^ A ,, _,.,.(' ' ),., 



' \?/>A' A" / 



