PROFESSOR ABBE'S NOMENCLA TURE. 1 2 5 



the apparatus in question. There has scarcely been time 

 to thoroughly test the apparatus while this sheet is passing 

 through the press the author has, however, tried it upon 

 a ^-inch objective of wide aperture, and this was cut down 

 in such a manner as to enable it to be used with the 

 Wenham binocular without producing any distortion. 



The working distance of the front lens was not in the 

 least altered by the contraction of the diaphragm, so that 

 the objection to most wide-aperture lenses still remains, 

 when distance from the object, either for illumination or 

 for use of dissecting instruments, is required. 



Having become somewhat confused in our nomenclature 

 of apertures, on account of the unequal value of the same 

 as expressed in degrees, Professor Abbe introduced a 

 system based on his own experiments and used in harmony 

 with existing but older optical laws. Under his hand the 

 air angle of 180 was identical with the water angle of 97 

 and the balsam angle of 82, but instead of giving them 

 three separate values he introduced the term " Numerical 

 Aperture," equivalent to I o in each of the three above 

 instances. The numerical aperture is easily obtained by 

 multiplying the sine of the semi-angle by the refractive 

 index of the fluid in which that angle has been measured : 

 this is the meaning of the formula : 



n sm u = a, 



where n = the refractive index of the medium ; sin u = 

 the sine of the semi-angle, while a = the numerical aper- 

 ture. 



A table of natural sines for each degree from i to 90 

 may be found in Chapter IX. 



The following table has been printed for many months 

 upon the cover of the ' Journal of the Royal Microscopical 

 Society ' (see next page). 



