272 Remarks on the Aperture of Object-glasses. 



it is theoretically impossible to construct an objective which shall 

 transmit from balsam a pencil greater than 80°. Each of these 

 gentlemen has written a memorandum on the subject, which, with 

 their permission, I append to this paper. 



The position taken by Mr. Wenham is certainly true for 

 objectives as ordinarily constructed ; that it is not necessarily true 

 for all possible constructions will be seen by a moment's reference to 

 his figure in the November number of this Journal (page 232). 

 The deductions drawn from that figure are in strict accordance with 

 optical theory only so long as we suppose the lines d, a, and b, e, 

 which represent the course of the extreme rays in the crown-glass 

 front of the supposed objective to remain constant. It is not 

 possible for the extreme rays to have greater obliquity if the light 

 passes from air into the glass ; but if the radiant is in water and 

 nearer than the point /, or in balsam and nearer than the point g, it 

 does not follow that the rays cannot enter the glass front, but 

 simply that they will take a course more oblique than the lines d, a, 

 and b, e. In the case of balsam of the same index as the glass front 

 there will of course be no refraction at the line of junction between 

 the balsam and the glass, and rays of any degree of obliquity can 

 enter. To what degree of obliquity it will still remain possible for 

 such rays to emerge into air from the posterior hemispherical surface 

 of the front lens, will depend upon the precise form given to it, and 

 how far it is possible to collect these rays so as to form an image at 

 the eye-piece will depend upon the construction of the posterior 

 combinations. 



In the same way in the excellent paper of the Rev. S. Leslie 

 Brakey, in the March number of this Journal (p. 108), the conclu- 

 sions drawn by the author are only true so long as we suppose the 

 direction of the ray 0, X (which precisely corresponds to the line b, e, 

 in Mr. Wenham's figure) to remain unaltered ; the same reasoning 

 applies in both cases. Mr. Brakey remarks that it follows from his 

 demonstration, "that the results are entirely independent of the 

 kind of glass used for the objective front," which is quite true as 

 far as " the results " go, but both he and Mr. Wenham seem to 

 have overlooked the fact that their demonstrations do not touch the 

 question of the angle possible to be transmitted through an objec- 

 tive from a radiant in water or balsam, but only, to use Mr. 

 Brakey 's own accurate expression, the " reduced angle " in water 

 or balsam corresponding to a fixed air-angle. Suppose, however, 

 an objective to have such a construction that, when a parallel pencil 

 of solar light is transmitted from behind, the extreme rays shall 

 finally reach the fiat surface of the front lens at an angle greater 

 than that formed by the line 0, X, in Mr. Brakey 's figure, of course 

 if there is air in front of the lens every such ray will suffer total re- 

 flexion, while if water or balsam be substituted it will be transmitted. 



