OF ARTS AND SCIENCES: NOVEMBER 11, 1863. 175 



inches. The ratio of the aperture to the focal length has been taken 

 larger than can be adopted in practice, in order to exaggerate the 

 amount of curvature. It will be seen that the curves in the systems of 

 Gauss and Frauenhofer may be nearly represented by the two solutions 

 of Herschel's equations.* 



It follows that Gauss's form, originally designed to secure a more 

 complete elimination of the chromatic dispersion, must be also rather fa- 

 vorable than otherwise as regards the correction of the aberration of 

 figures. It may be remarked, further, that his investigation, neglect- 

 ing the thickness and distance of the lenses, leads to an equation of 

 the fourth degree, which has no solution corresponding to V., nor to the 

 above values of the radii used by Frauenhofer. On the other band, if 

 the curves in III. and V. have been derived from substantially the same 

 theory, which seems a probable inference, it is scarcely possible that 

 Frauenhofer should not have had at some time under consideration the 

 system represented by the other solution of the equations, which would 

 have conducted to forms approximating very nearly to the system of 

 Gauss. 



Five hnndred and tweiitj'-seventli Meeting. 



November 11, 1863. — Statute Meeting. 



The President in the chair. 



Professor Cooke reported that no purchases of books for the 

 Library had been made since the annual meeting. The Acad- 

 emy voted to continue without change the list of periodicals. 



The President presented the following report from the 

 Council : — 



* The refractive and dispersive powers in III., and probably in II., differ by small 

 amounts from those used in computing IV. and V. ; moreover, in the latter, the effect 

 of the thickness of the lenses and of their distance from each other has not been in- 

 cluded, so that the numbers to be strictly comparable would require a small cor- 

 rection. The values V., computed with the elements of refraction and disper- 

 sion used for III., neglecting only the correction for thickness, become 



ft. 

 + 14.212 



-f 6.349 



— 6 488 



+ 25.375 



21.00 



