Upon this second image the same experiment may be repeated so as to make a third image still smaller and nearer the eye at d"e" and from

the third even a fourth

and still smaller image may be formed at e"". The position of these successive planes are indicated by the dotted lines; but in this figure the position of the axes is only adapted to vision on plane No. 2. For the higher planes, the optic axes must converge still more. For the 4th plane Ie and IId will represent the visual lines. Standing

2.

erect and looking down upon the regularly checkered carpet on the floor of my room, the figures of which are 4 inches from center to center, I can with the greatest ease bring out successively four distinct images one above the other, the nearest being but seven inches from my eyes, and the figures (which are two inches in diameter in the carpet) reduced to about 4 inch in diameter. If while looking at the image on the 4th plane the convergence of the optic axes be suddenly relaxed the image drops and may be caught on No. 3. Again by relaxing the convergence it may be dropped and caught on successive planes until it falls to its natural position.

I have made similar experiments on a great variety of patterns of wall papering, oil-cloths, calicos, &c., with the same results. Of a regularly checked oil-cloth on my hall, the lozenge-shaped figures of which are 10-2 inches across, I make successively three perfectly distinct images, the nearest being but 4 inches from the eyes.

Those who are not accustomed to experiments of this kind can probably most easily succeed as follows. If we look on the floor, and place the finger between the eye and the floor the finger will of course be seen double. Now move the finger up or down until we find a place in which the two images of the finger will exactly fall on contiguous figures of the pattern: the finger now indicates the position of the first plane. Now look steadily at the finger instead of the floor, until the image of the floor rises to it and becomes distinct, then withdraw the finger. To get the second plane, look again at the floor and

raise the finger until its images fall upon figures separated from one another by an intervening figure and then look steadily at the finger. The other planes may be obtained in a similar manner. The position of the several planes may be also easily calculated; the data being the inter-ocular line, the distance of the object and the interval from center to center of the figures. Both by measurement and calculation I determined the planes in the case of the carpet to be 21.5, 13·05, 9.37 and 7.3 inches respectively. In the case of the oil-cloth they were 11.8, 6·54 and 4.5 inches.

If the distance between the centers of contiguous figures be less than the inter-ocular line, then still other images may be seen beyond the real object and very much enlarged. The position of the eyes and the place of the image in this case also

3.

is easily explained. If da b c (fig. 3) be the plane of the real object, and the eyes I and II be directed toward contiguous figures a and b but not crossed, then the image of a and b will combine and be seen at a' the intersection of the visual lines. So also a and d will be seen at d' and b and c at c', and the dotted line will represent the position of the image plane. In order to make this image we must gaze through and beyond the pattern until we observe the double images come together and coincide, and then fix the eyes steadily. The enlarged image gradually becomes distinct.

This experiment is much more difficult than the preceding. The pattern should not be too small, otherwise the difficulty is very great. In former years I had often performed the experiment with perfect success, but the wall papering I had used

for this purpose, had been destroyed and I found difficulty in again obtaining a suitable pattern. I therefore constructed a pattern by ruling black lines on a large sheet of paper so as to make perfectly equal squares 1 inches wide. With this simple diagram my success in all the preceding experiments was really marvellous. The colored patterns before used form far more beautiful images, but for scientific purposes the ruled diagram is far preferable. With this diagram standing upright before me at the distance of sixteen inches, I got with great ease seven successive images on this side of the object and one beyond. All the images on this side were defined, with great ease and perfect distinctness although the nearest, both by measurement and by calculation, was but three inches from my eyes, i. e., far within the limits of my distinct vision. With great effort I could obtain others still nearer. The nearest I actually retained and measured, was but 1 inches from the root of the nose, but I afterward found that there was no limit except the root of the nose itself. Within three inches, however, the

4.

images were no longer perfect, not from any want of distinctness of the lines, but because the horizontal lines of the two images were no longer parallel but crossed one another as shown in the figure (fig. 4), and therefore could not be made to coalesce perfectly. The explanation of this will be given in its proper place. The still nearer images, as for instance those within 14 inches could not be retained; the strain on the interior recti muscles of the eye was too great.

The image beyond the object is much more difficult to obtain with clearness, especially if the object be near the eyes. At the distance of two feet from the object, I obtained the image very clearly and without much difficulty, but on approaching to within ten or twelve inches it was only by patient trial for some time that it could be brought out with perfect distinctness. When the object was twelve inches from the eyes the image by calculation was found to be about thirty inches distant. By turning the diagram so that the diagonals were horizontal and similar points therefore more than two inches apart, the image was seen at the distance of about six feet. It had

the exact appearance of a tesselated marble pavement made up of squares nine inches on a side.

In all these experiments the least irregularity in the pattern shows itself very conspicuously in the image, not by indistinctness of outline of the figures, but by apparent inequality in the plane of the image. Thus in the carpet it shows itself by an apparent wrinkle; in the lined diagram by some of the lines rising like black threads stretched above the general surface of the image. This phenomenon is a familiar one in stereoscopy, and is used for detecting the slighest difference in two apparently similar patterns; as for instance between a genuine and a forged bank bill.

I believe any one, and particularly any young person with good eyes, can with practice succeed in all the experiments detailed above. Several of my family have tried them with success. Yet in all cases it requires some practice to succeed well. I can, even yet, always detect some difficulty on first trial after an interval of a few days. But after several hours practice the illusion is so complete that it is almost impossible to dispel it. The image is so real that in attempting to recover the real object by relaxing the convergence of the optic axes, the doubling of the lines causes the eyes instinctively to return to their former position and thus to restore the image. I have sometimes been actually obliged to look away in order to recover the real object.

The experiments detailed above, have an important bearing on some points in the theory of vision. It is the universally accepted doctrine among physiologists that the axial and focal adjustments of the eye cannot be dissociated. Helmholtz speaking of the consensual movements of the eye says, "We cannot turn one eye up, and the other down; we cannot move both eyes at the same time outward; we are obliged to combine always a certain degree of accommodation of the eye to distance [focal adjustment], with a certain angle of convergence of the axes [axial adjustment]."" He proceeds, however, to give certain peculiar conditions under which the first two laws may be violated, but none in which the last is violated. For many years I regarded these experiments as confirming the ordinary doctrine. I had observed in my first experiments on the carpet that each successive plane became more and more indistinct. accounted for this by supposing that both the optic axes and the lenses were adjusted for vision on the plane of the image, while the light diverged from the floor five feet distant. It seemed to me a crucial experiment proving the necessity of

* Helmholtz, Croonian lecture, Proc. Roy. Soc., April, 1864.

focal adjustment, and the inseparable association of it with axial adjustment. On re-commencing these experiments a few weeks ago, however, I was struck with the fact that the figures of the images were far more distinct than the real figures were when a small object was viewed in the position of the images. To test this point fairly I placed two bone buttons in similar positions and on similar spots on the pattern and then brought their images in coincidence. At first the united image was indistinct but gradually it became perfectly defined-every thread-hole as clear and distinct as it is possible to conceive. I succeeded, though with greater difficulty, in getting a perfectly distinct image of the buttons on all the planes. It was evident therefore that the indistinctness of the figures of the image on the higher planes, was not the result of the want of focal adjustment but of imperfection in the pattern. The subsequent experiments with the ruled diagram proved this beyond the possibility of doubt. The images in this case were obtained with much more ease and the lines were defined with the most perfect sharpness even when the image was brought nearly to the root of the nose.

In all cases, however, the image when first obtained was a little indistinct, and then gradually became clear. With unpracticed eyes this interval of indistinctness is considerable, but becomes shorter and shorter with practice, until it almost disappears. When the image once becomes clear, it remains so, but there is then a sense, while looking at the image, of gazing beyond it, or rather perhaps, there is a difference between the image and a real object which we cannot account for, but which is not a difference of distinctness. There is evidently an unnatural condition of the eyes which produces strain and fatigue.

There is but one possible explanation of these phenomena, viz., that the optic axes and the lenses are adjusted to entirely different distances. The three adjustments of the eye, viz the axial adjustment, the focal adjustment, and the contraction of the pupil, have been so associated through successive generations, and the association so confirmed and strengthened in each individual by constant practice from the earliest childhood, that a single act of volition accomplishes them all. Under ordinary circumstances they are so indissolubly associated that neither can be accomplished without the others. But the experiments described above prove that under certain circumstances the first two, at least, may be completely dissociated. In these experiments when the image is first obtained the optic axes, the lenses, and the pupil, are all consensually adjusted for vision at the distance of the image: and hence