318 Mr Pritchard on the Aberration of a Diamond Lens. 



at large, owing no doubt to the want of a simple comparison of 

 its spherical aberration with that of glass and other substances 

 of lower refractive power, I have in the present paper endea- 

 voured to demonstrate in a familiar and tangible manner its 

 real longitudinal aberration. 



Plate III. Fig. 8, represents a section of two semi-lenses. 

 They are both convexo-plane. The upper one D is the form 

 of a diamond lens of the same magnifying power and semi- 

 aperture with the lower one G, which represents one formed of 

 glass. * F is the principal focus of the two lenses for inside 

 rays : d and g are the focal points of their outside rays. Hence 

 the space F d,.will be the longitudinal aberration of the dia- 

 mond lens, and g F that of the glass lens. This geometrical 

 illustration will, I hope, address itself with sufficient force to 

 the eyes of those least initiated in such matters ; but I have 

 availed myself of the work of Mr Coddington to compute the 

 spherical aberration according to an expression given by him 

 in page 93 of his work, which is as follows : — 



t J i . (/^+l)( ^~-l) 1 / 



^ t/^U/^-i)' "^^ i^\ 3 7* 



If we assume the refractive index of diamond to be 2,5 (/a) 

 as a mean, (it ascends as high as 2,755) then the above for- 

 mula, executed in numerical computation, will stand as follows : 



-{ 



1 , (2,5 + 1) (2,5- 1)1 f_ 3 y 



+ 



2,5)2(2,5 — 1)2^ ^ 2,5)^^ J/ ""7/ 



nearly, or about f of its own thickness, while it is well known 

 that the aberration of a glass lens of the same form, and in the 

 same position, is I of its own thickness. But as the thickness 

 of a diamond lens will be considerably less than that of a glass 

 one of the same power and aperture, it will be necessary to 

 compute them respectively ; and it will be found, by taking the 

 proportions given in the geometrical illustration, to be for the 

 diamond 9.55, while the thickness of the glass one will be 758. 



• In the construction of the figure I have assumed the radii as 8 to 3, it 

 having been found by careful experiment, that the powers of a diamond 

 and plate glass lens of the same radii are to each other as 8 to 3. These 

 proportions will of course vary a little according to the refractive indices of 

 the stones employed. The lenses in the figure are slipped a little for cor- 

 rection of thickness, to make the focus F fall in the same point. 



I 



