296 G. 8. Hastings — Secondary Chromatic Aberration 



aberration. Other things being equal those materials having 

 the smallest numbers under A and JB would be preferable. To 

 illustrate : suppose we take combinations 3 and 37 and 10 and 

 37, the first having a small, and the second a large, secondary 

 aberration. Take a negative binary of the second pair of 

 power — 0*553, which will give 



A, =-2*72 B 10 =l-31 k' lo(Pl =l9-& <p 10 = -0-553; 

 add to this a binary of the first pair of which 



A 3 =3-84 B,= -2-04 &> S =-19-S ^,= 1- 

 and we have a triple lens for which 



A 3 = 3*84 A 10 =— 2-72 A 37 = — 0*73 Jc'(p=0 cp^=0-U7. 

 The meaning of A 37 is obvious when we remember that B 8 and 

 B 10 both express curvature sums for the same material, flint 37. 

 To find the curvature sums for a focal length of one, we should 

 have only to divide throughout by 0*447, which yields 8 '59 

 — 6*09 and — 1*63. These are moderate curvatures, but in 

 view of the fact that 10 is not a permanent glass I should pre- 

 fer 3, 25 and 37, or 3, 27 and 37, although there are a consid- 

 erable number of such triple combinations which may be useful 

 and which may be gathered from a study of the table. 



Fourth : that by means of the table we may also find the 

 value of the secondary chromatic aberration for a binary com- 

 posed of any two materials entered in it. For example, sup- 

 pose we desire the color characteristic of a binary composed of 

 Nos. 1 and 22, which is one of the combinations recommended 

 by the makers as yielding an objective of notably diminished 

 secondary aberration. Take a negative binary of 22 and 37 

 with a power of — 0*527 ; its constants are : 



A 22 = — 2*85 B 22 =l*84 k'<p'=11-0. 

 Combining this with the binary of 1 and 37 of power one, we 

 have a binary lens of the two glasses in question (since the 37 

 eliminates) the constants of which are : 



A 1 = 3-97 A„ 2 =— 2-85 Jc'q>=— -8'5 <p=0*473; 

 or, reduced to focal length of unity, 



A^S-39 A 22 = — 6*02 &'= — 18*0, 

 whence we conclude that by this construction we only reduce 

 the secondary dispersion one-third at a cost of permanence in 

 one of the lenses. 



Other combinations recommended for the end in view are 2 

 and 24, and 3 and 28. The first of these is optically by far 

 the best, reducing the dispersion about five-sixths, but both the 

 materials are perishable ; the second pair is practically the same 

 as 1 and 22, but 28 is not permanent. If we are content with 

 a combination containing a glass which is not permanent we 

 can find much better pairs than those suggested in the cata- 

 logue. For example, 2 and 22 reduce the secondary aberration 



