ADDITION TO THE MEMOIR 



ON THE 



ACHROMATISM OF EYE-PIECES. 



If the object-glass be supposed very distant, the equations 

 for different forms of the achromatic eye-piece {Cambridge Trans- 

 actions, Vol. II. p. 243, &c.) are symmetrical with respect to the 

 first and last lenses, the second and last but one, &c., as well as 

 for the distances. If, then, the eye-piece were turned end for 

 end, the equation would still be true, and, therefore, the eye-piece 

 thus formed would also be achromatic. 



If we put t for the tangent of the visual angle, the chromatic 

 variation of this tangent, or ^t, expresses the angular extent of the 

 coloured line, which is the apparent image of a point : and if, in 

 this expression, we suppose one of the distances, as b, increased 

 by db, the alteration in the expression will shew the eifect on 

 the chromatic dispersion, produced by altering the distance of 

 the lenses. But, as it is impossible (from the nature of the in- 

 vestigation) to determine whether t is to be taken with a positive 

 or negative sign, it will be impossible to say whether the value 

 of d.l.t shews that, upon increasing b, the image formed by the 

 most refrangible rays, is brought nearer to, or farther from, the 

 center of the field of view. To avoid this difliculty, divide by t -. 



d ^ t 

 then, it is plain that if -^-^— be positive, it shews that, u[)on 



increasing b, the image formed by the most refrangible rays is, 

 with respect to that formed by the mean rays, moved from the 



H ^ f 



center of the field ; or towards that center, if "^ — be negative. 



H 2 



