OPTICAL PRINCIPLES OF THE MICROSCOPE. 37 



For, supposing the pictures taken through the bands b V to be suffi- 

 ciently dissimilar in their prospective projections, to give, when com- 

 bined in the Microscope, a sufficient but unexaggerated Stereoscopic 

 relief, those taken through the bands a a' on either side of the centre 

 would be no more dissimilar than two portraits taken at a very small 

 angle between the cameras, and their combination would very inade- 

 quately bring out the effect of relief; whilst, on the other hand, the two 

 pictures taken through the extreme lateral bands c c', would differ as 

 widely as portraits taken at too great an angle of divergence between the 

 cameras, and their combination would exaggerate the actual relief of the 

 object. Now, in each of the lateral halves, a spot v v r 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 (op q, Fig. 30) 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 Dr. 

 Hirst, the conclusion at which he arrived was that the angle of aperture 

 of the entire lens should be about 36.6. This, which he gave as an 

 approximate result only (the requisite data for a complete Mathematical 

 solution of the question not having yet been obtained), harmonizes most 

 remarkably with the results of experimental observations made upon 

 opaque objects of known shape, with Objectives of different angular 

 apertures; so that the Stereoscopic images produced by the several 

 objectives 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 purpose than those which are perfectly spherical ; such 

 as various globular forms of the Polycystina (Plate xix.), or the Pollen- 

 grains of the MalvacecB and many other Flowering-plants. When either 

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

 objective of half-inch or 4-10ths inch focus having an angular 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 exaggera- 

 tion is diminished, though not removed; the hemispherical circle 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 hemi- 

 spheres turned towards the eye are truly represented; the effect of 

 spherical projection being quite adequate, without being in the least exag- 

 gerated. Hence it may be confidently affirmed alike on theoretical and 

 on practical grounds that when an objective of wider angle than 40 is 

 used with the Stereoscopic Binocular, the object viewed by it is repre- 

 sented in exaggerated relief, so that its apparent form must be more or. 

 less distorted. 1 There are other substantial reasons, moreover, why 



1 This position has been contested by observers who have used high powers 

 binocularly with transparent objects, and who, in thir zeal for large angles of 

 aperture, affirm that no exaggeration of Stereoscopic effect is produced by the 

 combination of the two pictures thus obtained. Bat it seems to be forgotten 

 that such objects cannot afford the actual measure of Stereoscopic effect, which 

 is given by opaque objects of known form us above described. And, so far as the 

 Author's experience extends, every competent observer who makes use of a good 



