On the " Lag " in Microscopic Vision. By E. M. Nelson. 417 



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Looking at the figures in the Table, which deals with 14 objectives, 

 we see that the " lag " is increased in every instance by deeper eye- 

 pieces. In the first lens, an apochromatic of 1^ in. focus, the " lag " 

 is increased from — 87 to + 10 by changing the eye-piece from 6 to 

 12. The achromatic 1^ with an A or 5 eye-piece does not perform so 

 well as the apochromatic, its order of merit being 13 '0 against 13*9 

 of the apochromatic with a 6 eye-piece. The fall in the merit of an 

 apochromatic 1 in. with eye-pieces ranging from 4 to 12 is as much as 

 from 14*7 to 9 "4. The apochromatic 1/2 shows a similar result, viz. 

 from 14*7 to 9*5. The XII eye-piece has an advantage of about 

 1 • over the compensating. The GKfford screen also raises the order 

 of merit about 1 ' 0. The difference in the performance between an 

 apochromatic 1/2 and an achromatic of nearly the same aperture in 

 resolving the same band with the XII eye-piece, is about 2 ■ 0. An 

 achromatic 1/2 with a very low optical index can only score 11*5 points 

 with an A eye-piece — in other words, it is about 3 behind the apo- 

 chromatic. 



The apochromatic 1/4 falls off more rapidly than the 1/2, its merit 

 with the 8 eye-piece being only 8 ■ 7 ; but the achromatic on the 

 other hand is only 7 ■ 8, and that too upon a lower band. The position 

 maintained by the semi-apochromatics in the table is most interesting. 

 Take for example the 1/4; it begins with an order of merit only a 

 little behind that of the apochromatic, and holds its own remarkably 

 well under the deeper eye-pieces ; it resolves 55,000 with 11 • marks 

 as against 11*6 for the apochromatic, and 7*8 for the achromatic. 

 An achromatic 1/5 with some uncorrected spherical aberration falls as 

 low as 5'6 for 60,000 lines. Two semi-apochromatic l/6ths come 

 next, the one which has the lower optical index being the better cor- 

 rected lens of the two. The above 13 objectives may all be described 

 as picked lenses in their respective classes, but a bad achromatic 1/6 

 is put last by way of comparison ; it can obtain only 6 ' 1 marks in 

 resolving 45,000 lines per inch. 



The last point shown by this method of testing lenses is an impor- 

 tant one, for it demonstrates that the advantage lies with short-tube 

 objectives. It is to be regretted that the table is not as complete as 

 it might have been, but a sufficient number of short-tube lenses were 

 not at hand for comparison. 



We see then that lenses which hitherto were thought capable of 

 bearing the deepest eye-pieces without showing the least sign of 

 breaking down are proved incapable of standing even medium power 

 eye-pieces without loss ; and we also learn that all super-amplification 

 of the objective image, whether by eye-piece or tube-length, will be 

 accompanied by a fall in the number of marks ; and lastly we note the 

 very high place taken by cheap semi-apochromatic objectives. 



Assuming that there is no " lag," the power sufficient to resolve 

 any given number of lines to the inch may be found by multiplying 

 v by t and dividing the product by 100. Example : — What is the 



