Astronomical Society. 67 



an indirect numerical, solution, by the well known and ready method 

 of trial and error, a method perfectly correct in theory as well as 

 easy in practice. 



M. Littrow exemplifies this theory by applying it to that parti- 

 cular case when the indeterminate problem is limited by the condi- 

 tion of Kliigel, viz. that the refractions at the first two surfaces 

 shall be as small as possible, in which case the first or crown lens is 

 in fact wholly given, and it only remains to determine the radii of 

 the flint. He takes into consideration the thickness of the former, 

 but not the latter, lens, and neglects also their distance inter se. 

 As a numerical instance, he supposes the indices of refraction 1*53 

 and 1*58, the dispersive ratio l,and the thickness of the crown lens 

 one hundredth part of its focal length, when, by applying the pro- 

 cess described, he finds the following radii : 



Crown lens. . 1st surface (convex) 0*186823 



2nd surface (convex) 0*608170 



Flint lens . . 1 st surface (concave) 0*407996 



2nd surface (concave) 0*445808 



Focal length of the compound lens ;= 1 ; aperture 0*06495 

 M. Littrow, however, is by no means of opinion that the condi- 

 tion of minimum refraction here assumed is the best, or in any way 

 essential to a good object-glass ; only it facilitates calculation. He 

 regards it as more advisable to aim at increase of aperture, and for 

 this purpose to assume the first or crown lens equiconvex, which 

 he affirms to be the condition requisite for the attainment of that 

 end. He therefore explains his method of proceeding in this case, 

 and applies it to the same numerical data with those last mentioned, 

 which give for the final results : 



Crown lens (equiconvex) Radius of each surface. ... 1*06 

 Flint lens (biconcave) Radius of 1st surface .... 1*04394 



of 2nd surface 3*296512 



Focal length 3*702231 

 Aperture. . . . 0*09973 x focal length 

 or nearly T v of the focal length, being a much larger proportional 

 aperture than it has been usual hitherto to give to achromatic 

 telescopes. 



The author concludes by stating the reason of his entering into 

 these investigations : viz. an application made to him by an artist of 

 Vienna. 



A paper was also read from M. Slawinsky, containing the fol- 

 lowing observations, made at Wilna. (Longitude l 1 ' 4i m 12* East 

 of Greenwich). 



1. Eclipses of Jupiter s Satellites. 

 Sidereal time. 

 . 4 b m 23 s ,7 good observation. 

 8 51 51 ,9 very good. 

 10 44 25 good enough. 

 12 29 38 ,7 very good. 



15 31 56 ,1 middling. 



16 46 ,1 middling. 

 16 I 14,9 a little doubtful. 



, 16 46 15 ,2 passable. 



K2 2. Oceu 



