416 Mr. Howard Grubh [April 2, 



bers to draw up tables for the use of opticians, giving the curves 

 required to satisfy the conditions of both corrections for all refractive 

 and dispersive indices. 



A considerable amount of labour was expended on this work, but 

 in the end it was abandoned, for it was found that the calculation of 

 these curves was founded on the supposition that all surfaces produced 

 by the opticians were truly spherical ; while the fact is, a truly 

 spherical curve is the exception, not the rule. The slightest variation 

 in the form or figure of the curve will produce an enormous variation 

 in the correction for spherical aberration, and it •was soon apparent 

 that the final correction for spherical aberration must be left to the 

 optician and not to the mathematician. Object-glasses cannot he 

 made on pa'per. When I tell you that a sensible difference in cor- 

 rection for spherical aberration can be made by half an hour's 

 polishing, corresponding probably to a difference in the first place 

 of decimals in radii of the curves, you will see that it is practically 

 not necessary to enter upon any calculation for spherical aberration. 

 We know about what form gives an approximate correction ; we adhere 

 nearly to that, and the rest is done by figuring of the surface. 



To illustrate what I mean. I would be quite willing to undertake 

 to alter the curves of the crown or flint lens of any of my objectives by 

 a very large quantity, increasing one and decreasing tlae other so as 

 to still satisfy the conditions of achromatism, but introducing theo- 

 retically a large amount of positive or negative spherical aberration, 

 and yet to make out of the altered lens an object-glass perfectly 

 corrected for spherical aberration. 



I am now speaking of ordinary sizes. For very large sizes it is 

 usual to go more closely into the calculations ; but I may remark 

 that it is sometimes possible to make a better objective by deviating 

 from the curves which give a true correction for spherical aberration 

 and correcting that aberration by figuring, rather than by strictly 

 adhering to the theoretical curves. So far then as any calculation 

 is required, the ordinary formulae given in the text-books may be 

 considered amply sufficient. 



Having now determined on the curves, we have to consider the 

 various processes which the glass has to undergo from the time it 

 is received in this form from the glass manufacturer to the time when 

 it is turned out a finished objective. 



The work divides itself into five distinct operations : — (1) Eough 

 grinding; (2) Fine grinding; (3) Polishing; (4) Centering; 

 (5) Figuring and testing. 



1. The rough grinding or approximate shaping of the glass is a 

 very simple process. The glass is cemented on a holder, and is held 

 against a revolving tool supplied with sand and water, and of a 

 shape which will tend to abrade whatever portions are necessary to 

 be removed to produce the required curves. These diagrams will 

 illustrate the various operations. 



2. Fine grinding. The tools used for fine grinding are of this 



