178 Mr Lister on the improvement of the 



and to prove in what manner it was applicable to another most 

 simple form of the object-glass, having made a magnified 

 tracing of the curves of one of Utzschneider's, and drawn a ray 

 through it from its longer aplanatic focus, which was ascertained 

 after cementing the lenses ; I laid down a figure of the Aim 

 lens inverted, and by means of the angles of the other diagram 

 projected a plano-convex z, Fig. 5, to be joined to its flat side. 

 The new glass proved as achromatic as the original, though the 

 single radius of the plano-convex was more than one-third 

 longer than corresponded with the curves of the former dou- 

 ble convex lens : the two aplanatic foci showed themselves as 

 before ; the longer, however, not in the place indicated by the 

 ray drawn : but at a point F, about two-thirds more distant 

 from the glass, and from which both surfaces of the flint lens 

 bent the pencil outwards ; the shorter focus F" too becoming 

 about half the length of the other, and the angle of incidence 

 of its rays not equalling that of their emergence. 



The longer aplantic focus may be found when one of the 

 plano-convex object-glasses is placed in a microscope, by short- 

 ening the tube if the glass shows over-correction, if under-cor- 

 rection by lengthening it, or by bringing the rays together 

 should they be parallel or divergent, by a very small good tele- 

 scope. The shorter focus is got at by sliding the glass before 

 another of sufficient length and large aperture that is finely 

 corrected, and bringing it forwards till it gives the reflexion of 

 a brio-lit point from a globule of quicksilver, sharp and free 

 from mist, when the distance can be taken between the glass 

 and the object. 



The longer focus is the place at which to ascertain the ut- 

 most aperture that may be given to the glass, and where, in 

 the absence of spherical error, its exact state of correction as 

 to colour is seen most distinctly. 



The correction of the chromatic aberration, like that of the 

 spherical, tends to excess in the marginal rays ; so that if a 

 glass, which is achromatic with a moderate aperture, has its 

 cell opened wider, the circle of rays thus added to the pencil 

 will be rather over-corrected as to colour. 



The same tendency to over-correction is produced, if, with- 

 out varying the aperture, the divergence of the incident rays 



