524 Mr. R. J. Sowter 



on 



second principal focus invariable for a small change in the 



index is marked ^ =0. 

 dfx 



It is an hyperbola whose asymptotes make an angle of 

 45° one with the other. One of these asymptotes is the 

 straight line already considered marked " Focal Length a 

 minimum." 



The curves obtainable from such conditions as j = n.d. 

 i. e. for lenses in which the focal length has a specified rela- 

 lation to d^ are rectangular hyperbolas w^hose major axis is 

 the line 



?/ + ^=0. 



The numbers corresponding to n are marked along this 

 line. The points are the centres of the corresponding hyper- 

 bolas. 



The semiaxes of these hyperbolas are given by the expres- 

 sion 



v 



2n + 3?/2 



6 



The second diagram shows the shapes and the general 

 optical properties of certain lenses which have been con- 

 structed on these principles. 



The conditions selected are described above, and the re- 

 lations of the radii of curvature and the focal length to the 

 thickness below^ each lens. 



The uniform scales indicated along, above, and below the 

 axes give the magnification values for any point, the upper 

 scale for light before, the lower for light after, passage 

 through the lens. 



It should also be mentioned that the value of ju selected 

 for the computation of the actual quantities was not always 

 1*5, but depended apon the glass selected. 



The first, third, and fourth make very good eyepieces, 

 especially the first, which has all the advantages of a Huyghens' 

 eyepiece, to which it bears a close analogy in its ruling 

 conditions. 



LXIII. On Astigmatic Aberration. 

 By E. J. SowTEE, B.Sc, A.R.C.S* 



THE paper affords a simple explanation for some of the 

 shadow phenomena observed by Prof. S. P. Thompson 

 in his experimental researches on the aberration of lenses f, 



* Commumcated by the Physical Society : read December 12, 1902. 



t '• Some Experiments on the Zonal Aberration of Lenses." Extrait 

 des Arch. Neerland des Sc. and Traill Taylor Lecture, 1901. " Shadows in 

 Astigmatic Beams," Prof. S. P. Thompson, Proc. Phys. Soc. June 12, 1903. 



