302 Rot/al Astrdnomical Society. 



course of the axis of each pencil, considered as a single ray subject 

 to chromatic separation, through all the lenses to the eye, when, if 

 they enter the pupil in any relative direction, except that of paral- 

 lelism, they will produce the sensation of chromatic separation in the 

 direction of the radius of the field of view. In this micrometer eye- 

 piece such a defect is wholly inadmissible, and therefore the first 

 condition is, that the eye-piece shall be (without reference to the 



fault describe4^ aii'd«v^dttt t^ai^ to separation of ima£t«^'y 



achromatic. ". !^wTort')n-H,„..e,f, ,, .,,_^ F -B.f^ 



The theory of achromatic eye-pieces was given by the author in 

 the Cambridge Transactions, vol, ii., and the first divided eye-glass 

 micrometers which he. constructed were made of four-glass eye- 

 pieces in which the equation of achromatism was satisfied, subject 

 to the condition already mentioned, that the distance between the 

 first and second lens should be equal to the focal length of the first 

 lens. But in the use of these a new inconvenience soon manifested 

 itself. The separation of the images is produced by so moving a 

 segment of the divided lens that the pencils of light are received upon 

 a part of the segment where the surfaces are inclined, so that there 

 is introduced in this part of the eye -piece a prismatic refraction and 

 consequently a prismatic dispersion. In general, the dispersion thus 

 produced will not be so modified by the passage of the rays through 

 the two remaining lenses that the rays of all colours (as separated 

 by the motion of the segment of the second lens) will enter the eye 

 in a state of parallelism ; and therefore the separated images will 

 appear coloured from this cause without respect to the part of the 

 field of view in which they are seen. iiiuoiu u-i ./ m. ■ms io 



This failing is, perhaps, more important than tli^ '6tiif^j for it' 

 affects the estimation of the scale of the micrometer as well as the 

 ordinary use of the micrometer. The only practicable method of 

 ascertaining the scale of the divisions is to place a wire in the me- 

 ridional direction across the centre of the field ; to make two images 

 of a single star by separation through a known number of divisions 

 in an equatorial direction, and to observe the transit of these two 

 images across the wire. If one or both images are coloured, so as 

 to present the appearance of a spectrum in the direction of separa- 

 tion, these transits are uncertain, and the estimation of the scale- 

 divisions derived from them will be uncertain. 



It was not till long after this inconvenience had been perceived 

 that it occurred to the author that it was possible to ascertain, in an 

 algebraic form, the theoretical equation upon which the removal of 

 this chromatic dispersion would depend, and thereby to discover 

 whether the two equations (of achromatism in the ordinary case of 

 no separation of images, and achromatism as regards only the disper- 

 sion produced by the separation of images) could be satisfied simul- 

 taneously, and without disturbing the assumption that the distance 

 between the first and second lenses should be equal to the focal 

 length of the third lens. On forming the equations, and substi- 

 tuting trial numbers, he had the gratification of discovering that 

 numbers could be found for the distances and focal lengths which 



