292 EDWARD M. NELSON ON 



should be understood that the apertures of objectives are designed 

 for an integral number of degrees, and not for a rounded-ofi N.A. 

 Example : — A lens would not be made N.A. 0-33, which is 38° 32', 

 but would be constructed with an angle in air of 38° or 39°. 



Now to pass on to Apochromats. Apochromatism is an inven- 

 tion which enables opticians to enlarge the ratio of aperture to 

 focus. In the lower powers it is not needed, because a sufficiently- 

 large ratio can be obtained without it. Objectives of 3 in., 2 in., 

 and IJ in. were made sixty years ago of excellent quality, with 

 large optical indices ; but when the powers are increased to the 

 1/3 in. and upwards, the advantage of apochromatism will be 

 evident, and consequently the curve need not begin to bend up so 

 soon. Three curves have been drawn ; two, on one chart, 

 showing the existing apochromats. The low-power apochromats 

 are freak lenses : for example, a 1 in. of N.A. 0-3 is useless ; no 

 microscopist who had a 2/3 in. of N.A. 0-3 would ever use the 

 1 in. of N.A. 0-3. The same may be said for the 1/2 in., a 

 1/3 in. of the same aperture is by far a more useful object-glass. 

 A 1/4 in. of N.A. 0-95 is much more of a freak ; if its aperture 

 were reduced to N.A. 0-8 it would be a very serviceable lens ; 

 while a 1/6 of N.A. 0-95 is a most useful glass, and is the limit 

 for a dry lens. If you will examine these two curves you will see 

 the usual kick about the 2/3 in. ; it indeed seems a strange practice 

 to underdo the 2/3 and overdo the 1/3, when there can be no 

 possible reason for it. Now, if you will kindly examine the 

 apochromatic curve (fig. 4), you will see that, like the previous one 

 for achromats, it is a smooth curve without any kick, and by 

 comparing these two you will find that the apochromats and 

 achromats have both the same " jumping-ofi " ground, but that 

 the apochromats have far more " staying " power. The last 

 curve is one I have drawn for oil immersions (fig. 5). Here we 

 encounter very much reduced optical indices. It begins with a 

 1/7 in. of N.A. 1-0 (optical index 14-3) and practically ends with 

 a 1/12 in. of N.A. 1-4 (optical index 11*7), but as some micro- 

 scopists use a 1/16 in. of N.A. 1-3 (optical index 8-1) the curve 

 is continued to show its backward march. 



A 1/18 in. of N.A. 1-3 (optical index 7-2) is made, but it is 

 difficult to see the use of such a lens. The curve for it would 

 follow on vertically two squares above the 1/16 in. It is often 

 said that there is not much difierence between the fluorite l/12th 



