points, we can in most cases consider them as one; the same is of course the case with the knot-points; and there is thus formed what is called the reduced eye of Listing (das reducirte Auge). In this way we have only a single refracting surface and two media; the first being air with the index of refraction 1, and the second, vitreous humour with that of 103. The radius of this imaginary refracting surface =5.1248 mm.; its vertex coincides with the single principal point, and its centre with the single knot-point.

77

The distance from the vertex of the cornea to the*

Second principal focus: = + 22·6470 ""

Optical centre of the eye.-All rays passing directly towards the centre of this spherical surface will strike the surface perpendicularly, and hence will not suffer any change in their direction after refraction. Thus the centre (single knot-point) of this spherical surface exactly corresponds to the "optical centre of the eye" of English authors, and to the "point of intersection of the axes" (Kreuzungs-punkt der Richtungs-linien) of German writers. The use of this optical centre is sufficiently clear from what we have already said about the knotpoints: we may, however, mention that the angle at the optical centre, formed by the axes passing from the extremities of the object, is called the visual angle.

Circles of dissipation.-If we suppose the ideal eye accommodated for infinite distance, rays parallel to one another would come to a focus on the retina; divergent or convergent rays proceeding from any point would, however, come to a focus behind or in front of that membrane, and would thus form upon it what is called a circle of dissipation. The magnitude of this circle will depend partly on the distance of the object, and partly on the size of the pupil. Let b c be the diameter of the pupil, and o its centre, a the luminous point, f the focus to which the rays are converging after refraction; let bf, cf, meet the retina in the points de; de will be the diameter of the circle of dissipation, and i may be its centre: owing to the similar triangles bƒ c, if. b c if dje, we have bc of :: de: if. de

=

bc.

of oi+if or in words, to find the diameter of the circle of dissipation, we must divide the distance of the image from the retina by the distance of the image from the centre of the pupil, and then multiply by the diameter of the pupil. This equation shows at the same time that de, the diameter of dissipation, varies directly as bc, that of the pupil. Hence, other things being the same, the smaller the pupil, the less is the size of the circle of dissipation.

We may now trace the effects of a change in the position of the

Fick, loc. cit. S. 269.

object, the ideal eye remaining adapted for parallel rays. Let us suppose that the object approaches the eye at some uniform rate of motion, its image will also move in the same direction-that is, it will be formed further and further behind the second focal plane; it will not, however, move at the same uniform rate: at first it scarcely changes its position; as the object continues to approach, it recedes with increased quickness, until at length the object, being close to the first focal point, it moves with infinite rapidity, so as to be situated at infinite distance, when the object reaches the first focal point. It is scarcely necessary to remark that the circle of dissipation and the distance of the image increase together, and that hence we may readily imagine how a distant object may pass over a great space without requiring any change (in the accommodation of the eye), whilst a very slight alteration in the position of a near object may necessitate a considerable increase in the power of refraction.

Owing to the compound nature of light, &c., a mathematically exact image is never formed on the retina; accordingly, we may readily understand that objects at different distances are seen with equal distinctness, provided their images are not attended by too large circles of dissipation. The eye is practically accommodated for a line and not for a point, a fact specially pointed out by Czermak, who has called it the line of accommodation; its length will vary inversely as the rate of increase of the circles of dissipation, the more slowly they increase, the longer it will be.

*

Listing has calculated for the ideal eye the following table: in it l' is the distance of the luminous point from the first focal point, l'' the distance of the image from the retina, z the diameter of the circle of dissipation on the retina.

It is as yet unknown to what degree the circle of dissipation can attain in the normal eye, without interfering materially with vision ;

Listing, loc. cit. p. 499. The formula for the distance of the image from the second F' F" focal point, when that of the object from the first focal point is given, is7=1"; F′ F′′ being the first and second principal focal lengths; l', the distance of the object from the first principal focus; and l'", that of the image from the second principal focus. In the ideal eye, FF" = 301·26 mm.; the distance of the pupil from the retina = 19·15 mm.; and its diameter is considered to be constant and = 4 mm.

*

very possibly this limit varies in different cases. It is at all events clear that up to a certain degree it does not interfere at all with the distinctness of vision, and thus it can be scarcely doubted that an image having the diameter 0.0011 mm. would appear to us only as the image of a point; and if we assume this to be the limit beyond which vision would suffer, the table shows that the ideal eye accommodated for infinite distance would see with equal distinctness an object at the distance of sixty-five metres: it is therefore in this sense accommodated for all objects placed between sixty-five metres and infinity, or in other words, its line of accommodation is of infinite length. Suppose again, that the retina be removed to 0.8 mm. behind the second focal plane; an object at the distance of 375 mm. from the first principal focus would now have its image formed exactly on it; objects further than 377 mm., or nearer than 373 mm., would form circles of dissipation greater than 0.0011. The line of accommodation would in this case be only 4 mm. long. It is also evident that this varies inversely in length as the size of the pupil, and thus that the less the latter, the longer will be the former. These deductions are perfectly consonant with our daily experience. Every one knows that two very distant objects can be seen with equal distinctness, and at the same time, although separated from one another by a great space; thus a star and a distant terrestrial object can be clearly seen at the same time; on the other hand, two objects placed near the observer will be seen with equal distinctness, only when they are very close to one another. We may also conclude that the changes of the eye necessary for the distinct vision of near objects will be very greater than those required for objects at a distance. A very simple experiment may serve to enforce this fact: let a thin white thread be stretched horizontally before the eye and nearly in the line of the optic axis; if now, one eye being closed, some point of the thread, for example a point ten inches distant, is fixed with the other eye, the thread will appear single for a considerable distance on the further side, and for a short space on the nearer side of that point; elsewhere the thread appears indistinct or double. points By fixing different nearer and further off, we may readily convince ourselves of the existence of lines of accommodation. These facts-that the eye is distinctly over a range of considerable length, independently any change in its accommodation, and also that in many cases it even large circles of dissipation, should never be forgotten

much

able to see

of

can disregard in estimating the range of accommodation in any given case; too much by a disregard of these points. care cannot be exercised, for numerous errors have been already caused Thus Gräfe says, with reference to employing circles of dissipation for the distinction of objects, "yet more strikingly is this the case with cata

There are some interesting remarks on vision with circles of dissipation by Prof. A. von Gräfe, in the Archiv für Ophthalm.,' Band. ii. Abth. 1, S. 170-186. His observations show that there are great differences in this respect between cases; thus, that with equal circles of dissipation the power of recognising objects varies.

The diameter of the bulbs at the macula lutea is from 0025" to 0030" 0011 mm.

to '0013 mm.

Archiv fur Ophth., Band vii. 2, 152.

ract cases which have undergone operation during youth, and have not employed sufficiently strong glasses. Such patients, although really without a trace of accommodation, may yet apparently possess a considerable range when examined by the ordinary methods with parallel lines of small print (at least, so far as refers to counting or distinguishing letters, and not as to distinctness of sight).

It would here be the place to discuss the rays that pass to the more lateral portions of the retina; as yet, however, their course has not been very exactly determined. This is of the less importance, because the rays we have considered are those that strike the macula lutea, and it is only by means of them that we really see distinctly; the more lateral portions of the retina give only a very dull qualitative sensation.

Accommodation of the eye.-The eye when at rest is, owing to its structure, the curvature of the cornea, &c., adapted for a certain distance, which is commonly called the most distant point of distinct vision; the rays from an object placed at this distance would come to a focus on the rod-layer of the retina. By the exertion of a certain power we are able to see with distinctness objects placed at a much nearer point; this is positive accommodation, in which the eye is rendered more refracting; on the other hand, it is clearly possible that the eye may be rendered less refrangible than when at rest, and thus adapted for more distant objects, or for converging rays; this would be negative accommodation. As we shall hereafter have principally to refer to positive accommodation, we shall always understand it to be positive when we merely employ the term accommodation.

Positive accommodation. For every eye there is a limit nearer than which an object cannot be brought without its becoming indistinct, a limit called the nearest point of distinct vision, and another given by the eye when at rest, the furthest point of distinct vision: throughout the space between them the eye can see distinctly. What are the changes in the eye then? Since Kepler first ventured an explanation, this question has constantly occupied both physicists and physiologists. At different times an altered position of the lens, elongation of the anteroposterior diameter of the eye, contraction of the pupil, change in the form of the lens, have been supposed to furnish a sufficient explanation, either separately or combined.

Sixty years ago, Thomas Young* convinced himself that the power of accommodation depended on a change in the shape of the lens. As an hypothesis it was already older; Young was, however, the first to advance positive proofs in its favour. The experiments of Cramert and Helmholtz have fully confirmed this opinion, and have caused a general agreement§ on this subject. Helmholtz|| says :—

* Philos. Trans. 1801, vol. xcii. p. 23; or Works, vol. i. p. 12.

Het accommodatie-vermogen, &c., Haarlem, 1853.

Archiv fur Ophthal., Band i. Abth. 2; or Physiol. Optik.

The reader will find a further account of these researches in Prof. A. Thomson's remarks On the Focal Adjustment of the Eye,' &c., Glasgow Medical Journal, vol. v. p. 50.

1858.

Gräfe's Archiv, loc. cit., p. 63.

"The changes in the eye which I have observed during its accommodation for near objects, are the following:

"1. The pupil contracts.

"2. The pupillary margin of the iris moves forwards.

"3. The periphery of the iris is thrown backwards.

"4. The anterior surface of the lens becomes more convex, and its vertex passes more forwards.

"5. The posterior surface of the lens becomes also a little more convex, but does not perceptibly change its position. The middle of the lens therefore becomes thicker" (its axis longer).

From this it appears that the lens is the essential organ in accommodation for near objects; indeed, this part would be superfluous except for that special purpose; an increase of the corneal curvature, or even other alterations, would have done all, except providing the eye with a transparent body capable of undergoing change in its form.

Accommodation for near objects is effected by increasing the curves of the two surfaces of the crystalline lens-i.e., by diminishing their radii; the vertex of the posterior surface of the lens remains in situ, that of the anterior passes forwards, and thus the space between the two becomes greater.

From the accommodation essentially depending on a change in the form of the lens, it would seem certain that it would be entirely, or almost entirely, lost after the operation for cataract. This, however, appeared to be contradicted by the well-known fact, that cases occasionally occurred in which after the operation print could be read near at hand, and at the same time distant objects could be perceived. Thus Arlt* says:

"A decisive proof of the falsity of all hypotheses that the accommodation depends on a change in the position or form of the lens, is afforded by the fact, that we occasionally meet with patients who have been operated on for cataract, and who with one and the same spectacles can see distinctly both near and distant objects, and in whom by experiment we can prove that they possess a greater or less power of accommodation."

He goes on to say that such cases have been referred to errors of the observer, to regeneration of the lens, or to the change in the form of the anterior part of the vitreous body. He quotes such cases from Home, Maunoir, Stellwag von Carion, and his own observation. He denies that during life the anterior surface of the vitreous body becomes curved forwards, and does not believe in the regeneration of the lens. Thomas Youngt made some experiments, from which he decided that no accommodation remained. He says:

"It is unnecessary to enumerate every particular experiment, but the universal result is, contrary to the expectation with which I entered on the inquiry, that in an eye deprived of the crystalline lens, the actual focal distance is totally unchangeable."

And he points out the cause:

"It is obvious that vision may be made distinct to any given extent, by means of an aperture sufficiently small, provided at the same time that a sufficient quantity of light be left, while the refractive powers of the eye remain • Die Krankheiten des Auges, Band iii. S. 227. Prag, 1856. + Loc. cit., p. 46.

57-XXIX.

2