Neiu Apertometer . 273 



resolution is possible, can also be measured with the shutter, and 

 gives, substantially, the same angular value as is obtained in the 

 other way. 



Now, Professor Abbe has made one modification in this appa- 

 ratus which I certainly think is an improvement. He attaches an 

 achromatic convex lens of suitable focal length to the draw-tube 

 of the microscope, and slides it into the proper position to convert 

 the microscope into a terrestrial telescope, by which erect (but 

 quite small) images of distant objects are sharply defined. With 

 this he looks through the central point of the flat surface of a 

 semicylinder of crown-glass at surrounding objects, and measures, 

 by two shutters or indices (which slip on the curved surface of the 

 semicylinder), the extreme angular limits of the telescopic field. 

 This represents, as in the case of the Tolles apparatus, the angle 

 formed by the most oblique rays that can pass through the semi- 

 cylinder of crown-glass and enter the objective ; but it has the 

 advantage that the reading is sharper, and no reasonable person 

 can dispute that the rays thus measured are " image-forming," 

 since it is precisely the position of the images formed that is 

 measured. 



But Professor Abbe has made two further modifications of 

 the Tolles apparatus, the advantages of which are doubtful. In 

 the first place he has cut away the surface that corresponds to the 

 diameter of his semicylinder at an angle of 45°. The object of 

 this was to enable the apparatus to be used on the stage of an ordi- 

 nary microscope, placed vertically after the German fashion. 

 This rendered it necessary to fix the point on the upper surface of 

 the semicylinder, by a silvered cover glass, with a clear circular 

 spot in its center, which should correspond to a path of the rays 

 to the oblique surface, and thence by reflection upwards just equal 

 to the radius of curvature. It is clear that an error in select- 

 ing this point will render the reading inaccurate, and I am in 

 doubt whether the increased convenience in using the apparatus 

 compensates for this ; unless, indeed, one is to be content with read- 

 ings v.hich, on each side, may vary a degree or two from the true 

 measurements. 



In the second place, instead of dividing his semicylinder 

 into degrees, and so reading at once the aperture in the crown- 

 glass. Professor Abbe has graduated it into divisions corre- 

 sponding to an arbitrary scale of his own invention ; each 

 number engraved on the glass representing the product of the 



