Some Remarks on the Apertometer. By Prof. E. Ahbe. 31 



figured by Professor H. L. Smith in the paper quoted above. But 

 I soon abandoned this method as being inconvenient, because a 

 very shght deviation of the focus or apex from the centre of the 

 lens must introduce a perceptible error, owing to the refraction of the 

 spherical surface, unless the lens were very large. Since 1871, for 

 measuring great apertures I have used a 7^ectangular plate of 

 crown glass 100 mm. in length and 60 mm. in breadth, three edges 

 ground, and one, on the long side of the rectangle, polished to an 

 angle of 45"^, for allowing the plate to be applied on the stage of an 

 ordinary Microscope. The scale of numerical aperture was en- 

 graved along the three perpendicular edges according to previous 

 computation, and index-pointers used as now. In this shape (which 

 is briefly described and figured in Nageli and Schwendener, ' Das 

 Mikroskop,' 2nd ed. p. 170) the apparatus has been used for a long 

 time by Mr. Zeiss and myself; many microscopists have seen, and 

 some of them have the appliance. I explained and demonstrated 

 its use at the meeting of the Gesellschaft fiir Medicin und Natur- 

 wissenschaft of Jena, November 1, 1872. On the basis of measure- 

 ments made by this rectangular plate Mr. Zeiss in his catalogue of 

 August 1872 stated his immersion objectives to yield an aperture 

 of 108 degrees water angle, thus exceeding the maximum air angle 

 by several degrees. 



The only part of the apparatus, besides the name, which is of 

 more recent origin, is the circular shape of the glass disk, which 

 was adopted by Mr. Zeiss when he began to make the apertometer 

 for sale. 



The description of my arrangement has been delayed for so 

 long a time because I proposed to explain the method of aperture- 

 measurement and allied methods for measuring focal lengths, amplifi- 

 cations, &c,, in connection with a more exhaustive discussion of the 

 aperture theme. Now, as priority results from literary publicity 

 only, the application of the glass disk for measuring apertures 

 belongs to Mr. Tolles, of course. But as to those parts of my 

 arrangement which have not been described by others, the fore- 

 going remarks will show them to be independent of jMr. Tolles' or 

 any other apparatus. 



