Methods for Imj^roving Spherical Correction. By Prof. Ahhe. 821 



the very short focal lengths, which are so inconvenient in use and 

 scarcely less difficult in workmanship. 



According to this consideration, the plan in question has been 

 applied practically to the production of an objective of very large 

 aperture on the homogeneous immersion system. The formula has 

 been computed on the condition of equal spherical correction for 

 two different colours (D and F) for a focal length of 3-0 mm. 

 (~), and an aperture of 1'40 numerical = 138^ balsam angle — 

 the widest angle, probably, which has been hitherto attained, as 

 it already exceeds by several per cent, the utmost aperture for 

 water immersion, and approaches within 7 per cent, the possible 

 maximum, which is consistent with balsam-embedding and crown- 

 glass covers. The system is planned on the duplex-front con- 

 struction. In order to use a moderate curvature (shortest radius 

 1"30 mm.) the front has been tasked in an unusual way: it has 

 been made active up to 6^ beyond the equator of the sphere, a 

 surface exceeding the hemisphere by about ^^ o^ ^^"^ radius thus 

 being applied as a clear lens.* The angles of incidence of the rays 

 increase up to 44^ on the air side of the front lens, but do not 

 exceed this amount at the anterior surface of the second lens. The 

 anterior part of the system (corresponding to the lens M of the 

 diagram) is made as a quadruple system, two binary lenses above 

 the duplex front ; the over-corrected posterior part (N) of rela- 

 tively great focal length is a triple lens, the flint cemented between 

 two crown lenses, and the distance between the opposite surfaces 

 of both parts is approximately three times the focal length of 

 the entire system. Though it would have been possible in this 

 case to make shift with three separate lenses in the front part, I 

 preferred to take four, in order to deal with lower curvatures ; the 

 good success of the quadruple systems having practically proved 

 that the slight loss of light and the slight increase of difiused light 

 by one lens were more than counterbalanced by the advantage of 

 surfaces of lower curvature. The computation of the formula was 

 based on the supposition of an immersion fluid of a refraction 

 exactly identical with that of the covering glass, 1 • 518 to 1 • 520 for 

 the D ray. 



* As a hyper-hemispherical lens cannot be set into tlie brasswork in the 

 ordinary way, it was necessary to fix it by means of a parallel plate cementefl on, 

 fixing the slightly prominent edge of this plate — a device applied already by 

 Mr. R. B. Tofles, as I am told. Avoiding the difficulties connected with this 

 unusual shape of the front lens, would have needed a much stronger curvature of 

 this front for obtaining a focal length of 3 mm. But then its focal length would 

 have been considerably less than the focal length of the entire system, and the 

 objective would have been siiuilar to a much stronger one in all practical respects. 

 The advantage of a lower power depending only on the greater focal length of 

 the front leus, the aim must be to keep this focal length as great as possible. 

 By the construction considered above it is obtained only slightly less than the 

 focal length of tlie entire objective. 



