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III. — Oil the Characters of Spherical and Chromatic Aberration 

 arising from Excentrical Refraction, and their relations to 

 Chromatic Dispersion. By Dr. Eoyston-Pigott, M.A., F.R.S,, 

 F.C.P.S. 



The paj)er which I last had the honour of submitting to the Eoyal 

 Microscopical Society treated of the characters of sjoherical and 

 chromatic aberration, which are identical. In that paper, none of 

 the statements of which need correction, the peculiar spherical 

 aberrations of red and blue light were scrutinized and their actual 

 spherical (i. e. their marginal) aberrations calculated approximately.* 



On referring to Professor Littrow's paper on " Double Object- 

 glasses," the reader will see at pages 240, 241,t that he says, 



" The principal of these properties (in a proposed double 

 object-glass) is that all rays, red as well as violet, incident near to 

 or far from the axis shall all unite after tLe fourth refraction in 

 one j)oint of the axis." That is to say, that these coloured rays, 

 whether marginal or central, shall at last have a common focal 

 point. 



He then proceeds to test in section (7) this union of all the 

 rays considered, namely, violet, red, and mean rays by his formulae. 



He takes the case of crown glass and flint glass with indices 

 1 • 53 and 1 • 58 respectively and | for the ratio of their dispersions. 

 He then calculates the points at which the violet and red rays cut 

 the axis by means of the formula for spherical aberration depending 

 on the radii of the lenses and their refractive indices. 



In order to find whether the dispersion of colours has been 

 destroyed, he determines the points at which the red and violet 

 rays cut the axis. 



He gives several examples of determining the points at which 

 the red, violet, and mean rays cut the axis after refraction through 

 the object-glass, of which I beg to subjoin an example in which the 

 aperture of object-glass is 9 ' 62 inches and focal length 5 feet 

 (a most extraordinary short focal length). 



For this construction he says, page 249, " I found the focal 

 length (projjortions used) 



For mean rays incident at an angle of 10'' 2 -"0375 chromatic 



For mean rays incident ne;ir axis (i. e. geo- abeiration. 



metrical focus) 2-30379 CO-OOOOO^ 



For violet rays 2' 30379 Sa ^n/mix 



-C 1 O on.vrro (0 UOOOl) 



For red rays 2 • 30378 ^ ^ 



* The principal focus varies with each change in the refractive index, i. e. 

 with the colour, and this would introduce further small changes neglected in the 

 Appendix to the last paper. 



t Vol. ill,, ' Mem. Roy. Astr. Soc' 



