284 F. J. CHESHIRE, TWO SIMPLE APERTOMETERS FOR DRY LENSES. 



degrees, of aperture angles ; for no microscopist in the world will 

 be able to make out any difference in the performance of objec- 

 tives as long as the numerical apertures do not differ by several 

 per cent., other circumstances being equal." 



" For these reasons I consider all attempts at very accurate 

 measurements of this kind to be useless." 



No one, probably, is likely to have the temerity to question 

 the authority of Prof. Abbe on such a question as Apertometry, 

 so that we can accept his limit of 1 per cent, with confidence. 



Fig. 5 shows a plan of a form of apertometer for dry lenses 

 which for simplicity in use and for the accuracy of its results 

 probably leave nothing to be desired. A strip of vulcanite A * 

 is so divided that the distance D of any line from the zero of the 

 scale is given by the equation 



D = 2 A tan (sin-i n.A.) 



set out in this Journal for April 1904 (Ser. 2, vol. ix. p. 1), in 

 the article on " Abbe's Test of Aplanatism, etc." The graduations 

 are marked with the corresponding N.A. values for a value of A 

 equal to 25 mm. In use the apertometer is placed upon the 

 .stage and the object plane of the lens to be tested adjusted at a 

 height of 25 mm. above the plane of the scale. The upper focal 

 plane of the objective is then observed in any known way and the 

 apertometer adjusted on the stage until the inner edge of the 

 fixed white block B is seen on one edge of the objective opening. 

 This adjustment effected, the sliding white block C is slid along 

 the strip A until its inner edge is seen on the opposite edge of the 

 objective opening to that on which the block B is just seen. 

 The N.A. value found opposite to the inner edge of the block 

 on the scale is that of the lens tested. 



The graduations from to 0*9 N.A. proceed by steps of 0*02 

 and from 0-9 to 0*96 N.A. by steps of 0-01. 



Fig. 6 shows a modification of the form of apertometer 

 described in my original paper in 1904. I have substituted for 

 the concentric circles there shown curved lines which project 

 optically into the upper focal plane of the lens being tested as a 

 number of equi-distant straight lines of equal thickness. The 

 projected image of the apertometer scale is thus a simple linear 



* The right-hand end is shown broken off. 



