of exploring our own eyes, we must not forget that the screen, our own retina, is curved, nor that there may be in eccentrical parts of it a certain amount of parallax from the law of vision by normals to it, nor that the rays of light that reach it are bent by ordinary ocular refractions. Insomuch that, in obtaining absolute values from the foregoing proportions, we must not reckon beyond upon more or less approximate results. These circumstances, however, cannot be said to occasion embarrassment; because we. shall find no great difficulty in evading or correcting such aberrations. And it will transpire, as we proceed, that there are no physiological problems of any prominence, open to this mode of treatment, in which comparative results alone are not effica

cious.

Let us seek for pencils of rays of the two kinds, which may be conveniently thrown upon our retina.

The diffused light of day, from the sky, clouds, smooth sheet of water, white road, or wall of a house, admitted into the eye through a fine puncture in a card, gives a good divergent pencil; though the convergent one, in this instance lying in front of the puncture, is not available.

Nevertheless with light issuing from small luminous discs we can readily command all such pencils as we need. We may, by means of the head of a pin, or the surface of a convex lens, reflect into the eye, from the sun or a small candle-flame, very fine divergent pencils. Or use the image of the disc formed in the focus of a lens of short focal length for this purpose. If we look through a convex lens of an inch focal length towards a gas, or candle-flame, remotely (as at the length of a long room) situated, so that the image may be formed at or near the principal focus of the lens, that there may be yielded a rapidly convergent and therefore divergent pencil, the eye may receive, to more than half its depth, far enough for all practical purposes, a divergent or convergent pencil at pleasure. For nice observations we can reduce the flame to a small round disc, by fixing before it a card with a small circular aperture. By approaching the disc we can introduce the focus deeper into the eye. By placing the disc at our back at one end of the room, and viewing its image in a mirror at the other, we can double the distance of the radiant. In a word, we may consider ourselves equipped for the major part of our researches, if we are provided with an object-glass of a microscope of an inch focus. By fitting the tube in which the glass is fixed into another of card-paper, we can slide one within the other, so as to introduce the focus any measured distance into the eye.

In commencing, however, the actual application of the geometrical deductions of 3 and 4, we must take into account that all projections upon the retina will appear inverted; and that thus what has been described as being inverted will seem to be erect, and what as erect, inverted.

6. If a single pencil, then, diverge (3) from a point a little in advance of the eye, this point will be the apex, as it were, of a cone of light, the size and shape of whose retinal base will depend upon that of the pupil, of which indeed it will be an erect, and therefore apparently an inverted, luminous image; comprising apparently inverted images of all the objects that intrude upon the cone, in apparently inverted positions with respect to its own centre, and with movements seemingly diametrically opposite to those they really have, if any of them move independently of the eye itself.

If we use the lens, and carry the focal point towards, and then into the ocular media, it will arrive at a depth where the divergent pencil will no longer fill the pupil, and therefore no longer project a complete image of the margin of the iris. Still, so much of this margin, and of whatever else falls in the divergent pencil, will display the inverted effects just adverted to: while whatever has been embraced by the advancing cone of convergent rays will appear erect, in their true positions with respect to one another, and with the actual movements independent of the eye they may happen to have; presenting up to this point a complete inversion of the picture we had of the same things in the divergent pencil.

By referring to 3, and interpreting the word infinite, as applied to an image, as meaning filling the retinal field, or occupying the whole pencil of rays, we may see how the retinal shadows or images of interrupting bodies vary in size, as the focal point falls

before, upon, or behind them. Thus, by this means alone, we may immediately observe the order in distance from the retina, iris, or tear, or any known ocular site, in which such bodies occur.

7. There is a point in the axis of the eye which may be called its optic or lenticular centre, as nearly that where the rays from external visible points that hold a straight course to their destination, all cross each other. Hence, if the focus of the lens we apply to the eye be made to coincide with this point, its rays will likewise proceed undiverted by ocular refractions.

In conceiving in the diagram the screen as a straight line, we virtually represent the retina by its tangent; and we may do this for small angles, because in them the lengths of the arc and tangent do not appreciably differ from each other. Wherefore, when we introduce as far as the optic centre, a pair of foci nigh enough together to cast the corresponding points of any pair of shadows we may wish to view near each other, we adopt the best expedients for ensuring accuracy in numerical results deduced from the foregoing equations.

In attempting from 3 and 4 calculations as to size and distance, in this manner, we use an instrument which prevents our seeing with the eye which we are exploring, objects of the external world, but we can note apparent sizes and distances of the images against any surface at an ascertained distance from the eye's optic centre, by aid of the other eye.

8. We may take the eye's optic radius (making the optic centre from eye's surface) at, and its optic axis at of an inch. Whilst the depth of the vitreous humour is, of the crystalline lens, and of the aqueous humour and cornea together also of the length of the optic axis. Then an actual retinal length is to the apparent as to the remoteness in inches of the surface we measure upon from the optic centre. We may mark experimentally in a given case the distance of the focal images of the two discs from the centre of the lens we use, and calculate the separation of these images, as in the instance of the eye; or employ the usual formula for such a purpose.

9. If we now have recourse to two crossing pencils (4 and 6), of the pairs of like images projected upon the retina, those images contributed by the right-hand source of divergent rays will be seen on the right of their fellows. But when we derive our divergent pencils from the images of a couple of bright discs (6) by means of a lens, these images have respectively changed sides in regard of their discs, so that the projections by the right-hand disc appear on the left of their fellows, whilst those rendered by the convergent pencil of the right-hand disc fall, in appearance also, on the right of their fellows.

As the principal transparent structures of the eye are an alternation of solid and fluid media, a very rough application of our rules would enable us to observe in which of these media any shadow-throwing body is situated, because those of one kind will be fixed in the eye, whilst the others will float in it; those occurring anteriorly to the conjunctiva, and the iris within the globe being moveable at our pleasure, without the globe itself being disturbed. Thus, an eyelash, tear, iris, an object in the crystalline, and one in the vitreous, with a couple of divergent pencils in front of the eye, would cast pairs of shadows, subtending angles less and less in the order in which their causes are here cited. But when the same bodies are immerged in a couple of convergent pencils, the pair of shadows of the eyelash subtend the least angle, and, in order, the others greater and greater angles.. This sort of reversal is a striking event, so that the mere passing of the imaginary line that joins the two foci from before backwards, tells us at once which of two ocular bodies is deeper.

10. For the clearer understanding of a modification of the mode of investigation by two pencils, of practical moment, we may remark, that could we look with the same eye, and at the same instant, towards a distant, small luminous disc, through two side by side convex lenses with parallel axes, the right hand lens would fling its image of the disc to the right of that of the other, and all the fellow shadows thrown in the two divergent pencils would be seen in just such mutual relation, as happens in the

* These mean values are gathered from 'Physiologische Optic,' von H. Helmholtz, § 10, Encyk. d. Phys.

case of light from two punctures or two lucid points; wherefore the convergent pencils from the lenses would so project the objects lying in them that the images caused by the right-hand lens would appear on the left of their fellows.

Hence, if we gaze through a single puncture in a card at the apex of some terrestrial object visible against the sky, or a fixed spot of any luminous surface, or gaze straight forward towards a lucid disc through a lens, and move the card or lens about across the optic axis, perpendicularly to it-taking care with the lens to keep its axis always parallel to itself or the optic-we may affirm that a dark spot, owing to a blind place in the retina, or some thin object resting flat upon the visual sentient points, will not appear to move, and that the shadow of objects will seem to travel in the same direction as the card or lens with a perpetually increasing velocity, as they are situated nearer to the point of divergence. Whilst whatever objects are encountered by the convergent pencil will seem to make excursions in the adverse direction to what the lens does, with a swiftness continually decreasing as the object is further in advance of the point of convergence. We have merely to turn the lens upon its axis to rotate its contents so as to distinguish them from retinal objects.

True it is that we cannot see the remote disc through the lens. But in moving it as advised, the nearly parallel rays from the disc must keep passing every point in the substance of the lens in the same style, or all such rays for a given point in the glass would fall upon the cornea parallel to one another, and thus upon the same retinal point. So that the extremity of the short tube in which the lens is set, seen through or beyond the latter, or any of the numerous obstacles to the free passage of light, so common in glass lenses, will seem to abide quite still in their original sites, however widely the lens be borne across the optic axis, yielding fixed points for our regard to rest upon, of the most commodious sort. In other words, in these cross excursions, images due to the lens and those due to the retina suffer no displacement, whilst the rate of movement continually accelerates as the object imaged approaches the focal point, the movement being evinced in a retrograde manner with respect to that of the lens, for objects between it and the focal point, and with that of the lens for those between the focal point and the retina. Thus, in a case in which divergent pencils, especially if from points anterior to the eye, as in the usual entoptical methods, yielding parallaxes in the same direction, would produce no distinguishable difference, when there is room enough between the two bodies situated a little deeper one than the other in the eye, for a focal point to be carried transversly between them, their images appear to fly asunder. Just as when the line joining two foci derived from two lights is placed between the objects, this great opposite deflection may be witnessed by noticing on which side that image of each pair lies that vanishes when we shut off one light by the hand.

11. Yet, when we have thus provided ourselves with devices for determining the localities, sectional shapes and sizes of the bodies connected with the visual organs, which obtrude themselves upon our sight, we have not exhausted our means of research. Because the form and refractive power of a transparent body may appreciably influence the features of its image; and inflection of light occurs both at the edges of these and of opaque bodies; whilst all the bodies may reflect light. These different phenomena may happen more or less separately or mixed, may be distinct in their character, or may so far simulate another sort of phenomena as to make it difficult to distinguish them. But here, too, it will transpire that the use of the two kinds of pencils is of much greater efficacy than that of the divergent only. However, it will be more convenient to take the effects here alluded to into consideration in our actual analysis of the accidental phenomena, since we shall then be aided in our interpretations by comparing one with another. Nevertheless, it may not be amiss to premise a few words on a special topic or two claiming our attention in this study.

12. We notice, then, that the shadow of the orifice of the tube in which the lens is screwed, as seen on the distal side of the glass towards a round lucid disc, shows a series of concentric circles, or alternations of bright and dark external fringes from inflexion of light at the edge of the tube; that like external fringes surround the shadows of all the foreign particles that ostensibly stud the glass. In addition to which,

if the body be narrow, the very middle of its shadow is illuminated from inflection at its sides, even though there may be no other internal fringes strong enough to be thus visible. The central luminosity in the shadow of a small round particle being a round area of about the same brightness as the average light yielded by the lens-facts in accordance with ascertained laws of light. If we use an elongated disc, as a candleflame, these effects must necessarily be best seen in objects that are parallel to the flame's length. Inflective phenomena in the convergent and divergent pencils resemble each other.

13. Phenomena of interference, by inflection of white light, are attended with manifestation of colour, and perhaps, as Sir D. Brewster affirms, by careful scrutiny we may discern inflective colours from ocular objects. But the appearances we are to investigate are so immersed in a pervading colouration, the offspring of ocular chromatic dispersion, that no other kind merits attention. Thus the image of the pupil obtained in white light from a lucid point, within the least focal distance of the eye, is a perfect spectrum of the point, whose middle is occupied by the most, and circumference by the least refrangible colour.

14. If we look through a puncture in a card, a straight narrow object, as a pin, passed across its axis a little without the card, only appears straight when it coincides with the diameter of the pupil's image, seeming to curve continually with a more marked concavity towards the centre, as it retires from it. An effect ascribed by Dr. T. Young to ocular refraction.* It may be appended that, from the same cause, the pin passed between the eye and puncture seems straight only at the centre of the pupil, becoming more convex towards it as it leaves it. These remarks may be applied (6) to our other convergent and divergent pencils respectively.

The ocular refractions gather the rays that enter the pupil from a radiant point just before the cornea, to a less image of it than it would otherwise have, and in like manner diminish the images of all ocular bodies; and as the eye is withdrawn from the radiant this diminution goes on, until, when it is able to bring the rays to a focus upon the retina, all the images vanish. There is a point about half of an inch from the cornea, where the rays from the radiant fall upon the retina parallel to one another, and which has been named the "anterior focus of the eye." And assuming that the rays also traverse the vitreous humor parallel to each other (in § IV. I shall demur to this supposition), the images of all bodies residing in it would equal in diameter the bodies themselves. Duncan measured these bodies in this way.

Listing looked through a puncture from one fixed external point to another, and observed how the images of ocular objects shifted their places in that of the pupil, and thus judged of their depths in the eye relative to that of the iris. Brewster, by means of a lens of "very short focus," gets from two sources of light two radiant points, at an ascertainable interval near the cornea, so as to throw two images of a filament near the retina, "just in contact," in order to calculate the distance of the filament from the retina. It does not appear that he proposed to correct for ocular refractions. Donders afterwards modified the plan of these radiants just in advance of the cornea, to calculate the distances of objects more remote from the retina. He assumed the parallaxes of the iris and other objects to be respectively to each other as their retinal distances. This, however, could only really happen if the rays from each pencil passed from the iris to the retina parallel to each other.

§ II. Eyelashes, Eyelids, and Conjunctival Fluids.

15. The eyelashes, the most advanced of these, when immersed in either kind of pencil, exhibit diffractive effects like bodies spoken of in 11 and 12. The hair also reflects light into the eye, and when it does this from a small luminous disc, yields a divergent pencil, limited in one direction at least by the iris, according to the place of the disc, and more or less perfectly displaying the contents of the eye.

16. The lubricating fluids are frequently so equably diffused over the conjunctiva, that our pencils fail to disclose them; but with fitting examples present we may see with divergent rays both opaque and illuminated pictures of drops of fluid, a contrariety announcing a difference in form, both drops being transparent, to the effect that the former are elevated and the latter depressed in the middle. Thus the convex tear (the more frequent kind) brightens its image and gives shade to its areola, by abstracting from the divergency of the rays that penetrate it, whilst in the other case the areola is brightened at the expense of the image. When these drops are immersed in a convergent pencil, the illuminated image becomes dark, and the darkened image bright, the convex tear, by increasing the convergency of the rays that pass through it, causes them to diverge sooner than the mass of rays, whilst in the other case they do not meet so early.

FIG. 2.-a and b are two drops of conjunctival fluid in a divergent, a' and b' the same in a convergent, pencil.

These little lenses, if we look at a candle-flame through a lens, tend to form erect or inverted images of it, according to their own form. They average from te of an inch in diameter (7).

The rays passing by and through these tears interfere with each other, so that a series of fringes surround the light and dark images; four, five, or more alternations may be counted, or in a flattish tear in a fine divergent pencil, perhaps twenty exquisitely fine ones. The illuminated middles of the images of the tears are broader and brighter for the size of the object than in the example of an opaque body, whose image preserves a like middle both in divergent and convergent rays (12).

These tears on the otherwise naked eye display round a candle-flame a series of wide brighter and darker rings, and in this common way obtrude upon us phenomena like those described above. A convex tear by the divergent pencil which proceeds from the image of the flame formed by it a little within the cornea, manifests beautifully the contents of the vitreous humour. The chromatic dispersion of the eye, combined with that of the tear, is usually obvious in the pencil from a tear. An eyelash seen through it against a flame often seems curved, if it falls laterally to the axis of the pencil, owing to the refractions of the tear and eye (14).

When the upper eyelid is lifted, we observe to follow it (upwards in a convergent and downwards in a divergent pencil), often, a series of drops. Helmholtz notes this upward movement, adding, "that when the upper eyelid is lifted, it draws after it the viscous mucosities, ("die zähen Schleimtheile nachzeiht.")* The conjunctiva must tend to drag off some of a limited quantity of any sort of fluid carried over it by attraction into the angle between it and the upper lid.

If the eyelids be kept closed by even a slight pressure from the finger for a while, the marks of the Meibomian glands and of the inequalities of the finger, will persist in the conjunctiva for some time; the true seat of the "curdled" appearance is easily detected by 3 and 4, and the nature of its inequalities analysed, if we wish.

17. Furthermore, whilst employing the divergent pencil, let an eyelid encroach upon it, and we observe along its shadow, which is disposed to bend its middle towards the

Allg. Encyk. d. Phys. s. 151. His description of these surface-phenomena from divergent light agrees well with the above; but I had anticipated him, except in the instance quoted.