OF ARTS AND SCIENCES: OCTOBER 13, 1863. 173 



the resemblance referred to is merely accidental, or whether it expresses 

 an affinity involved in the nature of the problem. But the latter seems 

 the more probable explanation. The numerical values of the radii in 

 his system, computed for a special case,* are here transcribed from his 

 orio;inal memoir, after reducinsr them to a focal length, for the two lenses 

 combined, of twenty-one French feet, for the sake of comparison with 

 the large Munich refractors. 



I. Gauss's Curves. 



ft. 

 1st surface of the crown lens, convex, radius = -}- 2.535 



2d " " " concave, " = — 7.521 



1st " " flint lens, convex, " =4-3.123 



2d « " " concave, " = — 2.084 f 



Compound focus, = 21.00 



In No. 1289 of the Asd'onomische Nachrichten Oudeman has given 

 the following measurements of an object-glass made by Frauenhofer 

 for the Equatorial of the Observatory at Utrecht. The numbers have 

 been reduced to the same unit as before, assuming the focal length 

 from Astr. Nach. 1281. 



II. Frauenhofer' s Curves. 



ft. 

 1st surface of the crown lens, convex, radius, ^ -|~ 14.157 



2d " " " " " =-1- 5.635 



1st " " flint lens, concave, " = — 5.775 



2d " " " convex, " = + 25.945 



Compound focus, = 21.00 



Another of his object-glasses, probably computed from a similar for- 

 mula, but for glass of slightly different refractive and dispersive powers, 

 has values of the radii as follows + : — 



III. Frauenhofer'' s Curves. 



ft. 

 1st surface of the crown lens, convex, radius, = -[" 15.430 



2d " " " " " =4- 6.144 



1st " " flint lens, concave, " = — 6.262 



2d " " " convex, " = -[- 22.461 



Compound focus, = 21.00 



* Zeitschrift fiir Astron., IV. 350. 



t This number has been corrected to accord with the erratum noticed at the end 

 of the volume cited. 



t Zeitschrift fur Astron., IV. 352. 



17* 



