ANGULAR APERTURE FOR BINOCULAR OBJECTIVES. 



39 



Fig. 25. 



bands b b', a spot v v' may be found by mathematical computation, 

 which may be designated the visual centre of the whole Semi-lens ; 

 that is, the spot which, if all the rest of the semi-lens were 

 stopped-off, would form a picture most nearly corresponding to that 

 given by the whole of it. This having been determined, it is easy 

 to ascertain what should be the Angle of Aperture (opq, Fig. 25) of 

 the entire Lens, in order that the angles v p v between the ' visual 

 centres ' of its two halves should be 15°. The investigation of 

 this question having been kindly undertaken for the Author by his 

 friend Prof. Hirst, the conclusion at which he has arrived is, that 

 the angle of aperture of the entire Lens should be about 36*6°. This, 

 which he gives as an approxi- 

 mate result only (the requisite 

 data for a complete Mathe- 

 matical solution of the ques- 

 tion not having yet been 

 obtained), harmonizes most 

 remarkably with the results 

 of experimental observations 

 made upon objects of known 

 shape, with Objectives of dif- 

 ferent angular apertures ; so 

 that the Stereoscopic images 

 produced by the several objec- 

 tives may be compared, not only 

 with each other, but with the 

 actual forms which they ought 

 to present. No better objects 

 can be selected for this pur- 

 pose, than those which are 

 perfectly spherical ; such as 

 various globular forms of the 

 Polycystina (Plate xix.), or 

 the Pollen-grains of the Mal- 

 vaceae and many other Flowering-plants (Fig. 230). Now when either 

 of these is placed under a Stereoscopic Binocular, provided with an 

 Objective of one-half or four-tenths of an inch focus having an an- 

 gular aperture of 80° or 90°, the effect of projection is so greatly 

 exaggerated, that the side next the eye, instead of resembling a 

 hemisphere, looks like the small end of an egg. If, then, the 

 aperture of such an Objective be reduced to 60° by a diaphragm 

 placed behind its back lens, the exaggeration is diminished, though 

 not removed ; the hemispherical surface now looking like the large 

 end of an egg. But if the aperture be further reduced to 40° by 

 the same means, it is at once seen that the hemispheres turned 

 towards the eye are truly represented ; the effect of projection 

 being quite adequate, without being in the least exaggerated. 

 Hence it may be confidently affirmed — alike on theoretical and on 



