Thus it is certain from the simple notion of an aplanatic system that pencils of different obliquities must yield identical images of every plane object or of a single layer of a solid object. However large an aperture may be, the resultant image of the object cannot therefore be composed of dissimilar images, and the wide aperture cannot be the cause of confusion, &c.

We see also at the same time that the delineation of an object through the Microscope does not exhibit differences of perspective according to the obliquity of the delineating pencils to

a

A*

BA

FIG. 4.

a

B*

a the entire pencil starting from the axial point A of an object, and collected to the axial point Â* of the image.

B the entire pencil starting from an excentrical point B collected to the excentrical point B* of the image.

aa and am an axial and a marginal elementary pencil from A which are contained within the pencil a.

Ba and Bm corresponding axial and marginal elementary pencils of the whole pencil 8.

The two axial pencils a a and B a pass through the central part, a, of the clear opening: the marginal pencils a m and 8 m touch the margin of the opening

at m.

The limiting diaphragm of the clear opening is assumed to be at the plane of the posterior principal focus (as is always the case approximately with high powers) in order to obtain the corresponding rays of the two pencils a and B parallel in front of the system, or the same obliquity of a m and ẞ m.

the plane of the object, as is the assumption of the all-round vision theory. The image of any plane surface A B (e. g. the upper surface of the minute die) is always the same whether the rays are admitted to the Microscope in perpendicular or in any oblique direction. If that theory was right, the image of A B, by the oblique pencils am and Bm ought to be shorter (according to the perspective shortening of the lines in oblique projection) than the image by the axial pencils a a and Ba, as we should of course have a shorter image of AB if we observed it through a low-power Microscope with inclined axis.

This absence of perspective shortening of the lines according to the obliquity of the rays exhibits therefore an essential geometrical difference of microscopic vision, which renders it uncomparable to macroscopic observation.

Secondly, consider the delineation of a solid object such as a minute die.

This is of course perfectly defined by determining the delineation of the upper plane surface A B, and of the lower A, B, (fig. 5). The result of the previous consideration must apply to both plane surfaces successively, pro

the whole aperture, i. e. by the wide pencils a and B, and the ocular focused to the lower layer as before. The points of the upper image, which is not exactly focused, will now give much broader dissipation circles projected on the sharply seen points A1* B1* but the centres of the two sets of points will still coincide.

What is the difference between these two cases? The small dissipation circles in the first case may still be capable of affording a pretty distinct vision of the upper layer at the same time as the lower, and we say that the depth of the object is within the range of the depth of distinct vision for pencils of narrow aperture. The broad dissipation circles resulting from the wide pencils of the full aperture will in all probability render the image of the upper layer very indistinct, so that the image of the whole object will appear indistinct also. The causa efficiens of this indistinctness is simply too great a depth of the object compared with the small depth of vision attendant upon a wider aperture. If we take a similar solid object, but of much smaller depth, we should see its upper and lower layers in sufficient distinctness, notwithstanding the wide aperture.

Consequently the indistinctness of an object which is not quite flat if observed with a wide aperture, does not arise from any dissimilarity of the images by axial and by oblique pencils, but solely on account of the reduction of the depth of vision.

Suppose now (3) an image projected by narrow oblique pencils am and 8 m through a marginal or intermediate part of the aperture. The sharp images of both layers A B and A1, B1, will be exactly the same as the sharp images by the axial pencils a a and Ba, or the sharp images by the whole pencils a and B. But as these images occur at different planes they will show a parallactic displacement. If the ocular and the eye are focused to the level of A, B,*, the points A and B will appear projected to the points a* b* and will be seen as dissipation circles with those points as centres. We have once more always similar images, only displaced horizontally.

This must give rise to a mode of projection of solid objects which is essentially different from the ordinary perspective projection under oblique vision. Suppose the die (fig. 1) delineated at an oblique direction of 60°. A true perspective image, such as

FIG. 6.

would be obtained by an eye receiving it in the direction r, or if the Microscope were directed to it in this direction, would give the projection on a ground plane perpendicular to the line r. But the image of the die as depicted by the oblique pencils in an objective of 120° aperture-angle will be a projection to a ground plane perpendicular to the axis of the Microscope (fig. 6), and not to the rays r. Both surfaces, a b and c d, will therefore be projected with their true diameter, but displaced horizontally, and not shortened as in fig. 1.

C

If we compare now the image of the solid object by the oblique

pencils am and 8 m to the image by the axial pencils a a and Ba, or to the image by other oblique pencils (say of opposite obliquity), we have dissimilar images. But this dissimilarity relating solely to the projection of successive layers, and being nothing else but different parallactic displacement of successive layers, cannot be effective in microscopic vision unless these images are produced by different portions of the aperture separately, that is, if the effective pencils (or the effective portions of the aperture) are separated, and the one conducted to one image and the other to another image, as is done by the various arrangements for stereoscopic vision. As long as various portions of the aperture are effective at the same time, producing one image, we have only an increase of the dissipation circles at those planes which are not exactly focused, and a reduction consequently of the depth of distinct vision. We have no "all-round vision" because vision ceases as soon as the "all-round" becomes effective.

The result of the whole consideration therefore is :-(1) In a well-corrected (or aplanatic) objective the images of a flat object by pencils of different obliquity are always strictly similar. The obliquity of the rays at the object does not produce any difference of perspective, as it does in ordinary vision, or when the same object is observed by a Microscope in an oblique direction. The Microscope therefore does not delineate solid objects perspectively, and has no capacity of all-round vision, either as a drawback or a

benefit.

(2) The images of solid objects arise from the projection of their successive layers in perfect similarity, however large the aperture may be (refraction of the rays by structural parts within the layers disregarded). As long as the depth of the object is within the limits of the depth of vision corresponding to the aperture and amplification in use, we obtain a distinct parallel projection of all successive layers on one common plane perpendicular to the axis of the Microscope (a regular ground plan), either strictly orthogonal (fig. 7) when the delineating pencils, narrow or wide, are axial, or with a certain obliquity of projection if these pencils (i. e. the axes or principal rays of the pencils) are inclined

FIG. 7.

日

to the axis of the Microscope. If the depth of the preparation is greater than the depth of tolerably distinct vision, this projection must become indistinct, because the layers above or below the range of distinct vision give rise to broad dissipation circles confounding with the distinct portion of the image. Since the depth of vision, other circumstances being equal, decreases with increasing aperture, good "definition" of wide apertures is confined to thinner objects than good definition of narrow apertures.

(3) Dissimilarity of the images of solid objects by different parts of the aperture is solely difference of projection (orthogonal projection versus oblique projection-or one degree of obliquity by axial pencils against an opposite obliquity by oblique pencils). It relates therefore exclusively to the manner in which successive layers are seen projected to the common ground plane (perpendicular to the axis of the Microscope) or to the perception of the depth, and not in any way to the delineation of the plane layers themselves. The effectiveness of this dissimilarity for microscopic vision is confined to the case of an actual separation of the images by stereoscopic apparatus; for if this dissimilarity should be perceptible and the partial images not separated (viewed by distinct eyes), the out-of-focus layers would appear confused, and no vision of the depth could be possible, as explained just above. We have, then, no advantage from the said dissimilarity.

(4) Stereoscopic vision in the Microscope is entirely based on the said dissimilarity of projection exhibited by the different parallactic displacements of the images of successive layers on the common ground plane of projection. There is no true perspective difference of the images by different portions of the aperture, because the microscopic image does not admit of a perspective shortening of the lines, which are oblique to the direction of the delineating pencils.