f>0 Professor Airy oti the Spfierical Aberration 



And this applies as well when the equation St = o is satisfied, as 

 in any other case: and we can, therefore, determine with ease 

 the effect of altering one distance of the glasses of an achromatic 

 eye-piece, while the others remain unaltered. 



Using, then, the same notation as before, we find 



In the eye-piece of two glasses, 



d.S.t hi , 2 



= . da , - . 



t n- 1 a 



In the three-glass eye-piece, 



d.o.t_ Sn ,, 3 a-2.p + q 



t n—\' ' bp + a + b.q + ar—2ab 



In the four-glass eye-piece, 



d.ti.t _ Sn ,, (2 .r+s-3c) (2.p+q-3a) -ac 



I M— 1 ' 'ac (q + r-2b) + {bc-rs) (p + q) + {ba-pq) {r + s)' 



(The denominators of these fractions have been simplified by means 

 of the equation H = o.) 



If, upon substitution in these expressions, the fraction is 

 positive, it indicates that an increase of a or 6 makes the image 

 formed by the blue or most refrangible rays, exterior to that 

 formed by the yellow rays : if the fraction is negative, the yellow 

 image, on increasing a or b, will be exterior to the blue image. 



Practical Rules for the Construction of Eye-Pieces. 



For a single eye-glass. 



1. For distinctness, the lens should be equi-convex. 



2. If it be rather more convex on the side next the object-glass. 



