398 SUMMARY OF CURRENT RESEARCHES RELATING TO 



probably due to the practically enlarged aperture caused by the rolling 

 motion of the eye from side to side." 



It will also be noticed that the diaphragm to be used with the 

 apertorneter is made convex on one side, and if the convex side is put 

 into the larger aperture of an eye-piece — or other — diaphragm, it rests 

 steadily in position. 



Two Simple Apertometers for Dry Lenses.* — These are due to 

 F. J. Cheshire, who begins his description by quoting Abbe's authority t 

 that it is useless to attempt an accuracy greater than 1 p.c. in an aper- 

 torneter. Fig. 86 shows a plan of the author's form of an apertorneter 

 for dry lenses, which for simplicity in use and for the accuracy of its 

 results probably leaves nothing to be desired. A strip of vulcanite A 

 (the right-hand end is shown broken off) is so divided that the distance 

 D of any line from the zero of the scale is given by the equation J 



D = 2 A tan (sin" 1 N.A.) 



The graduations are marked with the corresponding N.A. values for a 

 value of A equal to 25 mm. In use the apertorneter 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 apertorneter 

 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 C on the scale is that of the lens tested. The gradua- 

 tions from to • 9 N.A. proceed by steps of • 02 and from • 9 to 

 0-96 N.A. by steps of 0-01. 



Fig. 37 shows a modification of the form of apertorneter described in 

 the author's original paper in 1904. He has substituted for the con- 

 centric 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 apertorneter 

 scale is thus a simple linear scale upon which N.A. values can be read 

 directly. The scale runs from - to 0*9 N.A. by steps of 0*05, 

 i.e. the divisions starting from the centre have the values 0, 0'05, 0'10, 

 0*15, 0*20, etc., of N.A. The short curved lines of the scale should 

 strictly be hyperbolas, but such curves are very difficult to draw accurately, 

 and it was not until the author's son, R. W. Cheshire, suggested to him 

 that they might be replaced by arcs of circles with curvatures equal to 

 those of the corresponding hyperbolas at their vertices, that the aperto- 

 rneter described became a practical construction. 



The author is of opinion that there are several objections to Nelson's 

 form§ of his apertorneter which was introduced by him in 1904. These 



* Joum. Quekett Micr. Club, xii. (1914) pp. 283-6 (2 figs.). 



t See this Journal, 1880, p. 20. 



X Journ. Quekett Micr. Club, ix. (1904) p. 1. § Vide supra. 



