MICROSCOPIC VISION. 149 



been frequently republished since Dr. Fripp's time. We 

 can, however, pause to discover what new views were added 

 to microscopy by it. First, as regards aperture, we have 

 seen that before the publication of the theory the angular 

 aperture of objectives had been correctly measured, and 

 the angular apertures of dry, water immersion, and balsam 

 immersion objectives had been correctly compared ; the 

 balsam angle being the then standard of comparison. 

 Prof. Abbe's very brilliant idea of using one limb of 

 Snell's equation (law of sines) as a standard to which all 

 kinds of aperture might be referred greatly simplified 

 matters, and at the same time put fresh meanings into, 

 and enlarged the ideas connected with, the term aperture. 

 We see, therefore, that both Dr. Pigott and Tolles used 

 numerical aperture in the conversion of their angles 

 (nascent angles, Pigott ; balsam angles, Tolles), but they 

 did not call it by that name. They used Snell's law; thus, 

 fji sin </> = fi' sin ^'; Abbe went further and said, /x sin (fi = 

 fx sin <^' = Numerical Aperture. Tolles, in measuring a 

 dry \^ might have observed an angle of 27f^ in his glass 

 apertometer where yu. = 1*52. He would then have looked 

 out the sin of 27J°, viz. '465, and have multiplied it by 

 1-52, obtaining the product "707; he would then have been 

 proceeding to convert this sine into an angle, when Prof. 

 Abbe would have interposed and said, '' Stop, that is Nu- 

 merical Aperture; do nothing further." If Tolles had gone 

 on, he would have found that "707 was the sine of 45°, and 

 the angular aperture of his \ would consequently have 

 been 90°. 



As to the enlarged ideas put into the word Aperture 

 by Prof. Abbe, time will only permit of an examination 

 of these in oatline. Any one wishing to pursue this inter- 

 esting subject further can easily do so by consulting current 

 publications. 



