33 2 ACCESSOEY APPARATUS 



powers, where there is plenty of room for the light to pass between 

 the objective and the object. The ingenious use of the bull's-eye 

 employed by Mr. James Smith, as detailed above, increases the possi- 

 bility of magnification, but it needs practice and care. With the 

 great improvement which has been effected in objectives and con- 

 densers the need of a bull's-eye which should give the minimum of 

 aberration has become a desideratum ; and Mr. Nelson has calculated 

 and had constructed a doublet bull's-eye which gives admirable 

 results. There are described in most treatises on optics doublets 

 devised by Herschel which are said to be of ' no aberration.' Mr. 

 Nelson has shown ('Journ. Q. M. S.,' vol. vi. ser. ii. p. 197, 1896) 

 that they are by no means free from spherical aberration, and that 

 their forms are such as will not even yield a minimum amount of 

 such aberration ; also that there is a numerical error in the focal 

 length of the high-power doublet. He has computed that the spheri- 

 cal aberration in the Herschel doublets amounts to * 296^, and 

 he gives the following formula for a combination, the spherical 

 aberration of which is *207^ ; or 30 per cent, less than in either of 



JF 



those proposed by Sir John Herschel. 



Boro-silicate glass, Jena catalogue No. 5 ; /z=T51 . 



1st lens crossed, r=+ 2*359) ,. 



s=-15-078j dlameter2 ' 1; 

 2nd lens meniscus, r=+ 1;280 Jj.^^. ^ 



Distance between the lenses *05, equivalent focus 2*0, working 

 distance or back focus 1*55, total aberration *1035, clear aperture 

 2*0, angle 62. The second Gauss point of the combination is close 

 to the posterior surface of the crossed lens. 



As there are some microscopists who might require a combina- 

 tion of this kind, but with a different focal length, and who are 

 unable to transpose the formula, the following rule may be of use. 

 Halve all the radii and diameters and multiply the results by the focal 

 length that is required. Example. Required a doublet on this 

 formula with 3^ inches of equivalent focus. Halving the data for 

 the crossed lens in the given formula, we have r= + l*1795, 

 s= 7*539, diameter 1*05; multiplying these results by 3i we 

 obtain r= +4*128, s= 26*386, diameter 3*7. Treat the meniscus 

 in the same way ; the lens distance may with advantage be kept 

 05. 



The following bull's-eye is not so expensive to manufacture, and 

 may on that account be preferred to the doublet of minimum aber- 

 ration just described. Its form, though of minimum aberration for 

 two plano-convex lenses, possesses 43 per cent, more aberration than 

 the former. It will on this account not be possible to obtain such 

 an even and unbroken disc of light with this form of bull's-eye as 

 with the other. The data are as follows. 



