18 Object-glasses and their Definition. 



aperture is 130°, and the rays will not enter beyond this litnit, 

 therefore the ray after refraction by the flat front must occupy a 

 fixed position which cannot be exceeded, and so on during the whole 

 course of the ray through the entire combination, till it converges to 

 the long conjugate focus at the back. These lines being unalterable, 

 it must be evident to the merest tyro in optical science that if the 

 front lens is immersed in Canada balsam, but little or no refraction 

 can take place at the flat surface, and the rays from this, instead of 

 meeting at 130^, will proceed straight on, as shown by the dotted 

 lines, at an angle of about 74"^, showing the loss of aperture in 

 balsam. I am here assuming for the sake of simplicity that there 

 is no thin glass cover intervening in the mass of balsam between the 

 object and lens, as its presence would not materially influence the 

 result. 



I may, now that the diagram is under consideration, make a few 

 remarks concerning this ith, as its performance is known to many. 

 Comparisons were often made, and it held its own for some years. 

 This is not adduced for the sake of exalting it as a model of per- 

 fection, but for the discussion of possible defects, and the direction 

 in which improvements might be anticipated. Commencing with 

 the front lens. The simplicity of this, and also the determination 

 of the radius by the intended power of the lens, leaves but httle scope 

 for alteration. The correction for thickness is obtained by trial, as 

 I have explained in my paper. The diameter is hmited by the pro- 

 posed aperture. For 130^ rather more than this segment of the 

 circle must be allowed. For 170^ we approach near to a hemi- 

 sphere. We now come to the middle ; it will not do to make this 

 of too long a focus, or we cannot command our aperture, therefore 

 the curves are deep and the lens thick. A short radius in the back 

 emergent surface is not material, for the bending of the rays is here 

 gradual ; but in all achromatics it is important to get the contact 

 surfaces of as long a radius as possible, hence the value of the triple 

 back. Now in the middle here delineated these surfaces are deep, 

 so far, that were it not for the Canada-balsam film that cements 

 them together, which allows the transmission of the outer rays, 

 these would be lost from total reflexion from the concave surface of 

 the flint, as shown by the dotted line. As such abrupt courses are 

 prejudicial both for the correction of chromatic and spherical aber- 

 ration, the question is, how can this be remedied ? 1st, by making 

 the lower surface of the concave deeper. This can only be done to 

 a limited extent, or we have an excess of outward coma that is after- 

 wards difficult to cure ; indeed if the quality of the glass were suit- 

 able I would prefer to make this surface flat. Another way would be 

 to make the middle a triple. Andrew Koss employed this, but aban- 

 doned it eventually, probably on account of its complexity. If the 

 first and most abrupt bending of the rays were sustained by two 



