of the Eye-pieces of Telescopes. 



Substituting, the proportion of the tangents becomes 



b( f, , a-\ B + b-B( f — aS 



Be b-B c-C f , , a') 



The quantity c — C may be thus calculated. By the known formula; 

 for aberration at refraction by one surface {Cambridge Trans. Vol. II. 

 p. 110), 



1 _ M- 1 1 



X ~ : 



r nb^ 2' n' \r ^ B/ ' \r "B"/ 



Rejecting the thickness, the same formula, putting -s for r, ~x for /y. 



c for X, and - for n, gives 



71 ° 



1 r I n a- „ /I ix^ ^1 n + l\ 



c s X 2 \s X/ \s nX / 



Substituting for - the value just found, and for -. in the small term the 



X A. 



value before set down, we find 



1 /I 1\ 1 



- =■ n-\ (- +-)-T 

 c Vs r/ 



a' n-\lf\ ix- 1 w + i 11- 1 „+i^ 



Substituting for - , - , ^ , and ^ the values found above, and putting 



fi = B + b - B, we liave 



1 /I l\ 1 b-B 



c \s r/ B B- 



I b-B a- ( n-p f \ 



