The Optical Qualiiy of Mr. ToUes J. Objective. 15 



Let the lines marked E, E in Fig. 1 represent the extreme marginal 

 rays of a pencil of 60^ angle proceeding from the inner systems, 

 viz. the back and middle combinations acting as one. Angular 

 aperture of such limited extent, 60°, certainly involves no difficulty 

 as to measurement, and hoping no objection from any critic on 

 that score, I will assume the angle and focus-distance A of the 

 pencil emergent from the front surface of the middle, m, to be 

 accepted on trust. In support of the case, I will state here that I 

 can easily give more available angle to back-and-middle. 



When the front, which is a hemisphere, is in position, as shown 

 in Fig. 1, the cone of hght bounded by K, E is intercepted by it at 

 its convex surface, and brought to a focus at F directhj, the front 

 being of common-crown glass, and " immersed " in balsam of the 

 same refractive-index, assumed to be 1 • 525 for the case. The 

 focal-point F is obtained by projection, and Mr. Wenham is expected 

 to admit its correctness or show the contrary. The angle at F 

 is 90^. 



And now to discuss the case of maximum air-angle under the 

 same circumstances. 



The inner lines E' E', Fig. 1 , are drawn at an angle of 82^, or 

 4P with the axis. As this pencil of smaller angle emanates from 

 the same focal-point F in balsam, the rays E' E' must meet the 

 convex surface of the fr'ont at a less distance from the axis than 

 the larger pencil, as may be seen in the figure. But as this 

 reduced aperture of the lens at the front, and at the convex 

 surfaces, is aU that can possibly be used " dry," its limits being 

 shown by tracing the course of extreme rays for the equivalent 

 balsam pencil of the largest possible pencil transmissible to or from 

 air; it follows that that portion of the front-surface between the 

 lines E' E must be unused aperture, when the objective is used 

 dry, though the practical angle be infinitely near to 180°. 



To illustrate a little further : Let the light be considered as 

 proceeding down the tube from the eye- piece, and the objective 

 being dry at the surface, s. Obviously the extreme ray of the 

 pencil of 82°, and of balsam-focus at F, would meet the interior 

 plane and dry surface of the front at an incidence of 41°, and 

 necessarily have its course on emergence with a nearness to coinci- 

 dence with the front plane surface, involving only an inappreciable 

 difference from a direction parallel, or 180^ of angle. 



Mr. Wenham's small caps may perhaps properly enough apply 

 here to express his sensations, but the /ad becomes clear and indis- 

 putable. 



Dry, the surplus aperture from E' to E, i. e. beyond 4F of 

 incidence, gives a silvery ring by total reflexion from the plane 

 surface as should be expected. It trims the aperture hke a 

 diaphragm. 



VOL. XII. c 



