OF ARTS AND SCIENCES: OCTOBER 13, 1863. 171 



nearly seventy per cent. Steinheil has stated, that, with the Gaussian 

 objectives, ratios of the aperture to the focal length as large as ^\y 

 can be used for the largest refractors.* It must be remembered, that, 

 owing to the strong curvature of the surfaces, the light has to traverse 

 a greater thickness of the glass, and must experience more than ordi- 

 nary loss from extinction. Perhaps, also, there will be a sensibly 

 greater loss from reflection, from the greater inclination of the incident 

 ray to the surface near the margin. The gain in area will, therefore, 

 not represent precisely the increase in illuminating power. 



There are two other objections to the new construction which may 

 be thought in some measure to counteibalance its special advantages : 

 one of these is the much greater depth of its curves, suggesting, per- 

 haps without sufficient foundation, practical difficulties of workmanship. 

 That they have been actually overcome in lenses of moderate size is 

 certainly the best reason for anticipating success when the trial is made 

 on a larger scale. It is further evident, from the peculiar form of the 

 lenses, each of which is a meniscus, that, if they are worked out of flat 

 discs, as usual, greater thickness of material will be required. Tliis 

 would increase the difficulty, ali'eady so great, of procuring suitable 

 glass. It is possible that the material could be accommodated nearly 

 to the ultimate form of the lenses, just as, in the present process of 

 manufacture, an irregular mass is moulded into a flat disc, approxi- 

 mating to the shape required. It does not appear that either of these 

 obstacles would long remain in the way of the general adoption of the 

 new system, if its advantages were distinctly recognized, and sufficient 

 inducements were offered to artists and to the manufacturers of optical 

 glass to turn their efforts in this direction. 



The contrast presented in the character of the curves in the two 

 combinations, which is so decided that the eye at once distinguishes 

 between them without any occasion for measurement or exact com- 

 parison, is very remarkable ; for if the superiority of Gauss's com- 

 bination be admitted, it shows that the practice of opticians has been 

 confined to a region altogether removed from that in which the best 

 system is to be found. In this they have only adopted the recommen- 

 dations of the many eminent mathematicians who have treated of the 

 theory of the achi'omatic object-glass. 



The question proposed in this theory is to ascertain that form and 



* Sitzungsberichte der konigl. bayer. Akad. der Wiss., 1860, V. 663. 



