4 F. J. CHESHIRE ON ABBE'S TEST OF APLANATISM, 



and the magnification, the radius of curvature of the equivalent 

 refracting surface and the point at which the latter cuts the axis. 

 Abbe's Test of Aplanatism. — In the year 1879,* Abbe, wishing 

 to ascertain to what extent objectives, made before the formulation 

 of the sine-law, satisfied that law, invented the test diagram 

 shown by Fig. 2. The problem was to find the nature of the 

 curves, which, drawn upon a flat surface placed normal to the 

 axis of a microscope and at a given distance below the lower 

 focus of the objective to be tested, should project into the upper 

 focal plane of the objective as a rectangular network of equi-thick 



Fig. 2. 



ABBES TEST FOR APLANATISM 

 (a = 12'5 mm.) 



and equi-distant parallel straight lines, in the event of the sine- 

 law being fulfilled. These curves, by a method to be subsequently 

 described, can be shown to be hyperbolas. To use the diagram, 

 it should be placed upon the stage of the microscope, and the 

 object to be tested focussed upon the middle point of the bottom 

 line. The body of the microscope^ carrying the objective with it, 

 should then be racked back through 12 5 mm. Upon removing 

 the eye-piece and looking down the tube, one-half of the back of 

 the objective will be found to be occupied by an image of the 

 diagram, in the form of the net-work referred to, if the objective 

 is a good one. 



* See Gesammelte Alhandlungen von Ernst Able, p. 226, 



