316

Dr. G. J. Stoney on the Limits of Vision:

57 and 59), or 27-3 times as much. If the proportion of increase of temperature to that of surface were known, the average magnitude of the particles of the finest insoluble powder might perhaps be calculated.

The evolution of heat by the mere contact of solids and liquids which do not in the ordinary meaning of the term "chemically unite," must to a minute extent affect the determination of the specific heats of insoluble powders by the method of mixing them with water. And if contraction of volume follows immediately upon its loss of heat, then the specific gravities of insoluble powders when arrived at by the process of weighing them, first in air and then in water, are probably also slightly influenced.

The heat produced by the mere contact of insoluble solids such as silica, alumina, &c. with water and aqueous solutions of salts, may account for that produced by spring-water, seawater, mineral-water, &c., filtering through geological strata, and for that developed in other cases of underground temperature where ordinary chemical action is absent.

XXVIII. On the Limits of Vision: with special Reference to the Vision of Insects. By G. JOHNSTONE STONEY, M.A., D.Sc., F.R.S., Vice-President, Royal Dublin Society *.

THE

Introductory Remarks.

Page

316

317

325

HE President of the British Association, at the recent meeting of that body in Nottingham, mentioned in his opening address that the image formed by the compound eye of an insect had been photographed. This suggests the inquiry how the image is formed, and what is the limit of the vision of which it is the physical basis. The investigation of this point shows that insects cannot see very minute objects, and the whole inquiry seemed of sufficient interest to be laid before the Royal Dublin Society, especially as it suggests much further study which the author could not attempt, but which there are other members of the Society most competent to undertake.

From the Scientific Proceedings' of the Royal Dublin Society of the 20th December, 1893. Communicated by the Author.

SECTION I.-Of Vision in general,

Fig. 1.

As preliminary to the inquiry it is well to consider what are the causes that limit the amount of detail that can be seen by the instrumentality of eyes such as our own, the kind of eyes of which we know most. That there is such a limit to human vision may be easily seen by placing a well-illuminated ruling of parallel lines at different distances from the eye of a person whose vision is good. Let us suppose black lines ruled, as in fig. 1, on a white surface at intervals of one millimetre from the middle of one line to the middle of the next. If an observer with keen vision views these from a distance of eleven or twelve feet, he is able barely to make out that they are a ruling; beyond that distance, they seem one uniform grey surface, while from stations nearer to them he perceives the individual lines distinctly. Now, at a distance of eleven feet a millimetre subtends an angle of 1' (one minute). Hence we learn from observation that in order that two objects may be seen as two, they must, at least, subtend an angle of about 1' at the eye. If they subtend a less angle than this they are seen as one object.

Millimetric Ruling.

Now there are three distinct causes, any one of which is by itself competent to put a limit of this kind to our power of distinguishing minute objects; and in persons with the best vision each of these three seems to put nearly the same limit as the other two. This adjustment between them is, no doubt, the result of development, since any further improvement on the lines of any one of these causes would be useless, unless it were accompanied by a simultaneous improvement in both the others.

One cause is the spacing of the cones that occupy the fovea lutea, into the small area of which about 7000 are packed. The fovea lutea is that spot in the retina which furnishes us with the exceptionally distinct vision which we have in the middle of the field of view. The cones are here without accompanying rods, and are at intervals of about 4μ*, measuring from the middle of one to the middle of the next. This interval is about half the diameter of the red corpuscles

*The micron μ is the millionth part of a metre. This is the same as the thousandth of a millimetre, or the 1/25400th of an inch.

of human blood, an object familiar to every microscopeobserver. Again, the "optical centre" of the eye lies a centimetre and a half in front of this part of the retina; and at this distance the interval between adjoining cones subtends an angle of nearly 1'. Hence, in order that the images of two points of light may fall on the corresponding parts of different cones, their distance asunder must subiend an angle of, or exceeding, 1' at the optical centre of the eyes; in other words, the interval between the objects in external nature that are being examined must subtend this angle at the eye. Thus we fail to see with the unassisted eye much detail which is revealed to us by the microscope. This happens if at a distance of ten inches, the distance of most distinct vision, the intervals at which these objects are spaced subterd an angle of less than 1'. Such objects may, however, be seen with optical aid, provided it is such that the little interval subtends an angle exceeding 1' at the optical centre † of the object-lens used in the microscope, a point which, with the higher powers of the instrument, lies close to the object on the stage. But beyond this limit, and therefore beyond the reach of the microscope, there are still worlds of events in nature which we can never see, although we may infer the existence of some of them in other ways.

We have found that the spacing of the cones in the fovea lutea is competent to put a limit to the minuteness of the detail that can be seen with the naked eye. Now, the small size of the pupil of the eye also, and independently, determines such a limit. Astronomers are familiar with the fact that the image of a star (which is virtually the image of a point of light, since no telescope is competent to show the true disk

*From each point of a visible object a cone of rays, starting from that point as its apex, falls on the pupil. In passing through the eye this cone of rays is made to converge, and finally becomes a cone of rays advancing towards that point of the retina where the image is formed. The apex of the second cone is accordingly at this point. Most of the rays of the first cone are bent in passing through the cornea and optic lens, and advance in a new direction in the second cone. But there is one among them, which, in the second cone, continues in the same direction, or at least parallel to the direction which it had in the first cone. This ray is called the undeviated ray. It is easily seen that there is one such ray in the light coming from each point of the object. Now all the undeviated rays very nearly pass through a certain point which is situated close behind the optic lens, and 15 centimetre in front of the middle of the retina. This is the point which is called the "optical centre" of the eye. †The optical centre of the object-lens of a microscope is the point where the "undeviated rays" cross (see last footnote). In compound microscopes this point lies in or in front of the object-lens, and with high powers is close to the object.

of a star) consists of a small round central patch called the spurious disk, surrounded by coloured rings which very rapidly fall off in brightness. This phenomenon is due to the interference of the light coming from the two halves of the object-lens, and is susceptible of mathematical treatment. It thus appears that the angular radius of the first dark ring, estimated from the middle of the object-lens, is

λ 0 = (1·22) },

where is the wave-length of the light, and A the aperture, i. e. diameter, of the object-lens. This furnishes a boundary within which the central spurious disk lies, and up to which its faintest outlying portion barely extends. It also fixes the minimum visibile with that aperture, since two points would have begun to be blurred into one another if so close that the middle of the spurious disk of each lay on the first dark ring of the other. Let us then put into this formula, 0=1'='00029 in circular measure (this is the limit already fixed by the rods and cones), and λ=6 of a micron (which is the wave-length of yellow light). We thus find

of an

whence A2524 microns, which is very nearly inch. This, then, is the diameter of the pupil of the eye when of such size as to put the same limit on the visibility of small objects as the rods and cones do. Now, this is about the size to which the pupil of the eye shrinks when we scrutinize well-illuminated objects, and is the smallest to which it can be allowed to shrink without interfering with the vision of minute detail, by placing a further restriction beyond that imposed by the layer of rods and cones*.

Again, the eye viewed as an optical instrument is far from perfect. Its chromatic defect may be detected by placing the finger horizontally in front of the eye, and looking just over it at the bar of a window. In this way the window-bar is viewed through the upper half of the pupil, and is then seen

* It might be thought that with the more dilated pupil which we have in faint light, we could see more detail. But the reverse is the case; for instance, the two small double stars e, and e, Lyræ are more than 3' asunder, and yet, in consequence of their faintness, are nearly at the limit of what a very good eye can see distinctly as two objects. To eyes that are fairly good they appear as one object elongated, while persons may have tolerably good sight and not even see the elongation.

320

Dr. G. J. Stoney on the Limits of Vision:

to be bordered with colour. Finally, the spherical aberration* of the eyes becomes conspicuous when we view a considerable star or planet with one eye. Instead of being seen as a point, it is seen as a small irregular patch with short tails from it, and of somewhat different shape according as it is viewed with the right or with the left eye. Now this is due to spherical aberration co-operating with another defect which it is difficult to disentangle from spherical aberration, and which is caused by the light having to pass through the other layers of the retina before reaching the rods and cones. These layers, however, do little harm in the fovea lutea, as here they are either absent or thin, so that the irregular image seen when we look directly at a planet is chiefly due to pure spherical aberration.

Now these defects, viz. the chromatic and spherical aberrations, including under the latter that further defect which arises while the light is crossing the retina, are dealt with in nature in the same way in which a photographer deals with them in his photographic camera, viz. by limiting the aperture, which diminishes the effect of these imperfections. We have already found that the aperture of the pupil is contracted as much as is compatible with the other conditions to be fulfilled. Now it is evident that a certain amount of the defects with which we are at present dealing, especially when rendered less operative by the limited aperture of the pupil, may be allowed to remain in the eye without rendering it incapable of distinguishing objects separated by 1' of angle, the limit already fixed by the rods and cones; and there can evidently be no tendency in evolution to effect any further improvement of the eye as an optical instrument. Accordingly, in persons with the best vision, the eye seems to have been just improved up to this point, leaving its outstanding defects still very conspicuous when searched for; and it is shortcoming in respect to these defects which is chiefly what makes one man's eyesight less perfect than another's.

We shall next deal with another preliminary remark, which it is well to make, as it will dispel the oft-repeated error that there ought to be some connexion between our vision and the position of the image formed on the retina. It is pertinent to point this out when engaged in inquiring into the vision of insects, for, as we shall see presently, the

*If a sphere be drawn round a point of the image formed by light of one wave-length, to represent the crest of one of the luminous waves advancing towards that point, the whole of the crest should reach that sphere at the same instant of time. There are, however, usually little deviations of some parts of the crest of the wave from this sphere, which defect is called spherical aberration,