118 On a neiv Formula for a Microscope Object-glass. [Jan. 16_, 



small errors can be detected. The work should be commenced at the 

 back from a long conjugate focus, which, not being a constant distance, 

 may be taken as very near to parallelism. The high powers all have the 

 means of correction within this distance, and perform better with a long- 

 posterior focus than with a very short one. The relative indices for the 

 two or more rays should be marked on a large pair of proportional com- 

 passes, the long limb representing the sine of the angle of incidence, and 

 the short one that of refraction. Both the sines ought to be set off in 

 the diagram behind, and neither of them in front of the ray in course of 

 projection ; this leaves the way clear, with the least confusion of lines. 



At the same time a second or counterpart diagram should be at hand, 

 to which the rays only are transferred as soon as their direction is ascer- 

 tained ; with these precautions a mistake is scarcely possible. 



Now it is hoped that some improvements may be effected by this in- 

 vestigation, on account of the simplicity attained in the combination, in 

 which we have two single lenses of crown, whose foci bear a definite pro- 

 portion to each other; while all the corrections are performed by one 

 concave of dense flint, the acting condition of which is not altered by the 

 influence of any other concaves acting in the combination, and hitherto 

 taking a share of the duty. This one flint is now to be considered 

 singly as the heart and centre of the system in reference to the correction 

 of the rays entering and leaving. 



This memoir is of necessity incomplete, for want of definite informa- 

 tion concerning the optical properties of various kinds of glass. Data 

 obtained from working them into small lenses furnish only a rough ap- 

 proximation to the mean dispersive power of the combined flint and 

 crown having the best apparent effect. Of the intermediate rays, little 

 can be known beyond the mere appearance of more or less of a secondary 

 spectrum. 



Nothing of importance has been published since Eraunhofer's Table, 

 containing the refractive indices for each of the seven primary colour- 

 lines of the spectrum for ten kinds of glass : great advance has been 

 effected since that date in the manufacture of optical glass, a most com- 

 plete collection of which of every variety has been made by the Rosses up 

 to the present date. Selected specimens from this will be worked into 

 prisms, and the relative spectra mapped out by the Fraimhofer lines, 

 leading, it is hoped, to the discovery of a combination of crown and 

 flint glass which shall be free from secondary spectrum or absolutely 

 achromatic. The result of this investigation will be the subject of a 

 future communication . 



