Aperture, Angular and Numerical. 285 



means that a cone of rays, issuing from the objective at an angle 

 of 144", is contracted when it enters the slide to an angle of 77.5° 

 (PL XVII., Fig. 11). The balsam angle of a dry objective is the 

 extreme angle at which the illuminating ray strikes the object 

 mounted in balsam, and is transmitted to the objective. This 

 angle is limited by the critical angle, and cannot be greater than 

 about 82°. Owing to the fact that the full cone of rays passed by 

 a dry objective cannot be measured directly through glass, we 

 are obliged to determine the reduced angle and calculate the air 

 angle from this. 



It appears from the experiments of Prof. Smith (this journal, 

 page 203), that the highest air angle we have is not much above 

 163'^. Mr. Mayall, in his communication to the present number, 

 has made a very just stricture upon the tendency to apply the 

 terms air angle and balsam angle indiscriminately to dry and im- 

 mersion objectives, without reference to the necessary conditions 

 of perfect definition. It is useless to express the air angle of an 

 objective that works only as an immersion. When the combina- 

 tion is closed there is no air angle. If, however, it is desirable to 

 calculate the air angle corresponding mathematically to a certain 

 immersion aperture, it can be done by means of the equation: 



sin. 7v y, n ^ sin. ^ air angle ; 

 7C' being the semi-aperture in glass and n the refractive index. 



We think Prof. Smith's demonstration on page 196, is liable 

 to mislead. It is assumed that 82° in balsam corresponds to iSo** 

 in air ; but Prof. Smith shows that an objective of only 144** 

 in air can "pass" 87° in balsam. We have to regard practical 

 conditions of work, and must not only follow the rays without the 

 objective, but also their course within it. In Prof. Smith's example, 

 the angles given do not correspond to the same excellence of 

 definition in the two cases. As regards immersion objectives, it is 

 possible to increase the aperture far beyond 82°, for the upper 

 surface of the cover is, optically, abolished, and the incident light 

 passes in direct lines to the objective. 



As Prof. Abbe's apertometer is an instrument that is bound to 

 have extensive application, and has not yet been fully described 

 in this country, the following account may prove acceptable : It 

 consists of a semicircular disc of crown-glass of 45"""' radius and 

 1 2°"°- thick; the back is beveled, along the diameter, to an angle 

 of 45°, so that when the glass lies horizontal, a beam of light en- 

 tering the curved edge, strikes the back surface and is reflected 



