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TWO SIMPLE APERTOMETERS FOR DRY LENSES. 



By Frederic J. Cheshire, F.R.M.S. 



{Read October 2$th, 1913.) 



Figs. 5 amd 6. 



In dealing with questions of apertometry it is very important to 

 inquire, in the first place, as to what order of accuracy it is 

 desirable to work. No useful purpose would be served by giving 

 a carpenter a foot-rule, divided to hundredths of an inch, with 

 which to measure the length of a plank. The measurement, 

 if made to such an order of accuracy, would be useless and 

 meaningless. 



Prof. Abbe, in " Some Remarks on the Apertometer" {Journal 

 of the Roy. Jlic. Soc. 1880, p. 20), after stating that the error of 

 measurement in his well-known apertometer is limited to about 

 | per cent., goes on to say that "an exactness of reading 

 to this extent is evidently more than sufficient. An unavoidable 

 amount of uncertainty resulting from the nature of the object, 

 and many other sources of slight error, will always limit the 

 real exactness of observation beyond 1 per cent, of the unit, 

 different observers and different methods of equal reliability 

 being supposed. In low powers slight variations in the length 

 of the tube, in high powers slight alterations of the cover- 

 adjustment, will admit of much greater difference than the 

 error of reading will introduce. It should be observed that 

 in high-angled objectives the aperture has not the same 

 value for different colours, owing to the difference of focal 

 length (or amplification), even in objectives, which are perfectly 

 achromatic in the ordinary sense. In the case of very large 

 angles, the aperture, angular or numerical, will be greater for 

 the blue rays than for the red, generally by more than i per 

 cent. Last, not least, there is no possible interest, either 

 practical or scientific, appertaining to single degrees, or half 



