Glancing from equation (4) to its fellow (3), and remembering that B is comparatively small, it is plain that the fraction involving the cosines in the former instance must be a very little less than unity, whilst in the latter it must be a very little greater, so that for the same observed angles a and 6, the two equations must give values of d not differing appreciably from each other. So that, altogether, the conception of an exterior point, B, being seen by a second reflection of the rays from the flame, demands for it a parallax difficult, if not impossible, to discriminate from that of a vessel placed just as far interior (speaking in terms having sole reference to the eyeball) to the sentient surface.

There is a phenomenon, which if not an example of the kind imagined, closely simulates it. For as the flame nears the optic axis from a lateral position, so that objects lying by the latter may reach their greatest parallactic deviation, the middle of the vascular effigy acquires an umbrageous complexion, and if, during a few seconds, we whirl the flame with somewhat of briskness round the eye, an abruptly defined, dark, quite circular area, whose diameter subtends with me just 4°, as if from a sentient circle of about th of an inch in diameter, comes forth; and as the flame travels round the optic axis, doing the same on the distal side of it in such a way as to show that the axis passes through its cause's own centre. In a word, it is made evident that the phenomenon is co-extensive with the foramen centrale, and is begotten by it; and recollecting the circumstance that the fovea is par excellence the retinal spot that suffers the pigment of the choroid to be visible from within, and that it has been demonstrated (28) that it is by the rays of light reflected from the internal periphery of the eyeball that the vessels are revealed, we instinctively ask ourselves whether the pigment could be seen as conjectured in fig. 6. And observing that the mean capillary patch, sweeping over the pigmentary circle, enjoys about half as much again of the scope of angular freedom that the said shady area does, whether we should assign from equations (3) and (4) the sentient surface an intermediate position to them and it.

30. However, if we adopt the opinion that the sentient surface is exposed to be excited by lucid images conveyed to it from rays traversing it centripetally, we allow that there is, prima facie, no improbability in the hypothesis that the very shadows of the vessels inspected by us may be the reflection of shadows previously cast outwardly upon a surface enclosing the sentient one; and so, whether the last be located without, at, or within the vessels.

If the reader, in imitation of the style of figs. 5 and 6, will draw four concentric circles near together, and consider the outmost one an axiform section of a reflecting mirror A BA', and the other three of sentient surfaces, passing severally without, through, and within the vessel E, whose shadow is cast by the ray A B upon the mirror at B, and reflected in в A', which cuts the three sentient circles in e', e", e'", indicating the parallaxes F C F', F C F", F C F'"', then it will be obvious that these parallaxes fall all in the direction of those which we actually witness in the vessels, and that these angles are greater, first as E is further from the mirror, and secondly, as the sentient circle is further from these. In the case in which E and e' are in one circle-the surface in which the vessel is imbedded receiving its reflected shadow posteriorly at another place-we В may simply by writing for in equation (3) find d, the distance of either sentient 2

or vessel from the mirror, or

And we have only to imagine the radii of the sentient surfaces supposed to lie within or without the vessel to vary, in order to diminish or increase this value so as to approach the value of d as estimated from equation (3).

If a= 40°, and -4°, equation (3) gives d 0.0037 of an inch, equation (4) gives d 0.0033 of an inch.

Though it is true, then, that the trials of equation (3) upon variously disposed vessels in our own eyes will be found to accord very well with the hypothesis upon which we started, that the sentient points are a little external to the vascular plexus, within the limits of their known distance from the choroid, we can scarcely feel so sure that our mode of estimation is so conformable to the conditions of the standard-much less of an individual eye-or that the angles to be observed can be so reliably taken, as to entitle us to neglect the possibilities of other textural super-impositions, as hinted at by equations (4) and (5), backed by the spectral intrusion of the foramen centrale. We should not, without some hesitation, decide between the following arrangements:

a. The sentient surface without, the causes of the dark figures, of the foramen and the vessels, both casting direct shadows.

b. The sentient surface between, receiving the direct shadows of the vessels, and the reflected rays of the foramen.

c. The sentient surface within, at, or without the vessels, and receiving their images and that of the foramen, by reflection.

d. The sentient surface and the vascular plexus intersecting each other; either partly within, at, and without the other; the sentients receiving the images of the vessels and that of the foramen by reflection.

31. In considering if there be any circumstances which tend to eliminate any of these rival claims, it occurs that if the shadows of the vessels be disclosed after their reflection from any surface, the rays from the given pencil must not only pass the vessels, but must pass them, again, and, consequently, whichever of the three positions the sentient surface hold, there must be, from the same pencil, a pair of shadows for each vessel-if the sentient surface be the inmost, a direct one, and one with a parallax happening originally in the re-passing (reflected) rays. If the vessel and sentient points lie in the same surface, a direct one reflected with a decided parallax, and one happening originally in the re-passing rays, with no, or scarcely any parallax. If the sentient points lie on the outside of the vessels, a direct one, and with a greater parallax, the same direct one reflected.

In experimenting with the candle, I find that we may actually behold a notable supplementary version of the vascular figure. As we bear the candle round the eye, all over the more sensible parts of the retina, though gradually becoming more indistinguishable laterally, we may see, in a delicate guise, shadows of vessels as fragmentary black lines, of varying breadth and length, separated by lustrous interstices, conforming to the type of the vascular phantom when begotten by a bright line, as the back of a knife, moved across its length perpendicular to the optic axis, which only shows vessels and portions of vessels that happen to have a course parallel to itself. I observe, further, that the parallelism of the lines in the example before us, for ever indicates the meridional (that through the optic axis) plane, which the flame occupies for that instant; in short, a changing picture, rotating about the optic axis, as the flame revolves round it; successively ushering in such vessels as lie over the regions of the retina that sees them, or such as happen to be parallel to the said meridional plane, without developing more than a very slight parallax, and that in the direction taken by the meridional plane. Whence the intrusive phenomenon cannot emanate at all from the pencil that occasions the dominant figure, but must be attributed to aberrant rays of light from the flame itself that permeate to the back of the eye, without touching at the tunics: as some may well do by undergoing irregular reflections and refractions in the ocular media. And there are other facts to intimate that many rays really do so.

32. But besides this, we have yet another additional manifestation of the vessels. All the time that the flame is being whisked about the eye, each vessel in a flickering, though in a forcible, mien keeps its own image, as it were, stamped upon the sentients nearest it—just where it falls retinally when we look against the sky with the naked eye. If the flame has waved about before one eye for a little while, and we close this organ also, a brilliant, glancing, exquisitely complete copy of the vessels will vibrate before us for a few moments; even if the protected eye be suffered to view a surface too faintly illuminated to impart strong images of the vessels to that eye, or to extinguish acute impressions upon the nervous substance of the other, the said vessels will actively

disport on that surface. In fine, this phenomenon, I infer, is due to the circumstance that those sentients which lie directly under the vessels are usually less exposed to lucid stimulation than others, and that therefore when light is made to flow over the retina in a uniformly diffused fashion, they are in a state to become comparatively much excited. Thus whilst the whole retina, by the process we subject it to, is affected by luminous impression, the sentients underneath the vessels are pre-eminently so.

Save these two, not a glimpse can I catch of extra vascular spectres. The former has no existence with the divergent pencils we began with (27), or rather, when we use the candle, standing in lieu of those produced by divergent pencils, and may be seen in the very face of the flame if we look right into it whilst it oscillates near the eye. The latter accompanies experiments by all the pencils, and might be regarded as an example of the sort of supernumerary phantom we are in quest of, if there be such a one, when the sentient surface was spread immediately upon a whole plexus of vessels; so that it might be difficult to say, hence only, whether that expansion were the inmost or outmost of the spherical stratification. Yet when we balance the intrinsic consistency of the explanation proffered by H. Müller, with retinal anatomy, and the fact that this is borne out by entoptical phenomena in placing the vessels at various retinal depths, whereas no membrane, or any continuous surface contiguous to them all, overlays them, there seems to be little or no reason for attaching weight to this phenomenon, if found standing alone in ambiguous significance, in a sense contrary to the concurrent import of those remaining, if they shall be discovered to have such concord. Lastly, the other case imagined, of two shadows from the same radiant, would give birth to two pictures of the vascular plexus, so competing in size that they would breach one another, which does not appear to happen.

Being led, then, per viam exclusionis, to regard the vascular phantom as an immediate projection upon the sentient points, the question remains whether, somehow, the image of the foramen may not be simply a shadow similarly projected. H. Müller's suggestion seems worthy of acceptance, and is to the following effect:

33. We do not see in waving the candle round the eye a uniformly dark circular area, nor a complete circle at all, at any one instant, though we may elicit the whole circle in the course of one revolution of the flame round the optic axis. At any one moment we see a crescent, whose convexity looks to be towards the flame itself, and is really towards the flame's retinal image, this crescent approaching half-moon shape as the image advances towards the foramen centrale, and having a parallax like the vessels have, though of less amount. It is, therefore, the image of the crest of the wall of the central pit of the retina. On the outer side of the crescent there may be remarked a bright beam, which Helmholtz supposes to be reflected from the upper surface of the fovea, but which I rather regard as reflected, as in the case of the vessels, from the brim of the pit. I find that with a=40°, B=4° for the crescent, when for the same value of a, the vessel crossing the foramen, which presents the most parallax, gives B=8°. From which it results that the brim of the pit is 0.0036, or of an inch, and the vessel 0.0738, or of an inch, from the sentient surface.

From many entoptical trials, H. Müller estimates the interval between the "percipient layer" of the retina and the vessels at 0.17, 0.19 to 0.21, 0.22, 0.25 to 0.29, 0.29 to 0.32 millimetres. In the case of three other observers, 0·19, 0.26, 0.36 millimetres; and these numbers harmonize very well with those I have obtained. Then, from anatomical measurements, he determines that the bacillar layer of the retina in the region of the yellow spot is from 0.2 to 0.3 millimetres behind the vessels, and from the elements of this layer pointing as normals to the retina and collateral reasons, he concludes that they are the percipients.

Chary as we may be in trusting to absolute calculations from such observations as we can make, for the resolution of so principal a question as the primary seat of vision, yet it can hardly be gainsayed that a comparative scrutiny of all the phenomena fairly entitles us to decide that there is a certain anterior placing of the vessels and margin of the fovea with respect to the sentient surface, which appears to point with a high probability to the site assigned.

APPENDIX.

Visual Sentients.

34. Having expended our means of analysis by aid of entoptical, parallax, and allied helps, when we arrive at the seat of the sentients themselves, we must now resort to other expedients in order to get some acquaintance with their differential structure, as affecting the use of sight, and with any troubles of vision that may arise from the working of the machinery of the eyeball. Such knowledge is requisite to protect us against any error that might else creep into entoptical research proper, from a posterior source, as also may lead us directly to a more fundamental idea of the mode in which light stimulates the sentients. I shall proceed as systematically as I can under the altered circumstances.

If the extremity of the finger or nail be laid upon the sclerotic immediately, or through the lid, even never so lightly, in the nearest attainable regions to the most sensible parts of the retina, we shall elicit a quasi-luminous areola of the contour of the applied surface, though the surface itself seems lit up but in a very meagre degree, or not at all—that is, unless the applied surface be very small, when the brightness of the areola will so encroach upon the included area as to make it difficult to say whether it pales away entirely at the surface itself or not. Thus the resulting image of the surface stimulates the shadows of opaque bodies embedded in the retina, with their reflective borders. This marginal effect must, as Young remarks,* be due to the flexure undergone by the retina along that line. He says greater flexure along the contour than upon the applied

surface, but I would wish to make the distinction that, though it is obvious that such a flexure as crowds together the internal elements of the retina produces a sensation of light, yet the experiment seems to yield no evidence that the bare pressure upon its outer surface, or the gathering of its elements closer to one another in the act of depression, has any consequence of a similar kind. Hence, we might infer that it is only the inner surface of the sentient layer which is sensible, or if the cones rather than the rods are sentients, that the rays of light affect them by impinging upon their sides. And if this be the arrangement, that each little sentient surface should be veiled from pressure in a little pit, we might perceive why the most employed portion of the sentient expansion should be walled in at the bottom of an abrupt fovea.

However, the characteristic colour of this and other phenomena from pressure is white, with a tendency towards the less refrangible colours. As if all sorts of lucid vibrations were engendered by mechanical stimulus, with some tendency towards those of slowest waves. The nervous impression in the instance before us is but transitory, but severe compression of the globe produces spectra of diversified orbital structures; and may be made to endure, seemingly along the lines chiefly where flexure such as above has been suffered, quite as long as the spectral image of the noonday sun has ever been known to last.

Not only is the retinal response to objective light injured or annihilated, according to the intensity of these spectra, but we find our vision impaired, or, except for strongly illuminated objects, obliterated by the sole existence of such retinal flexure, as occasions a marginal quasi-light, even though this does not suffice for leaving a discernible spectrum behind it.

35. When we turn in the dark the eyeballs sharply, or even mildly, a couple of white circular rings, brighter at one margin than the other, each enclosing a paler area with a central dark spot, flash forth, the diameter subtending an angle of several degrees. They are angularly apart from each other, and from the spectrum of a bright disc planted at the foramen centrale, and enjoy lateral angular play in strict conformity with the received opinion that they originate at the base of the optic nerve. The phenomenon is plainly the result of flexure of the retina where the nerve runs into it, as the eye is

* Philosophical Transactions. 1798.

pulled round in its socket until it drags upon the nerve. And it is to be noted that it is again where the inner retinal elements are squeezed laterally that the phenomenon is

disclosed.

36. In connexion with these facts, it may be convenient to notice an opinion universally adopted by physiologists, from Purkinje to the latest student of the accidents of vision, that the vascular figure, at least for the chief vessels, is rendered visible to us by the motion of the blood in the vessels, and may be thus made more so by pressing upon the contents of the eye through the anterior surface. I have finally convinced myself that all this is but an illusion, though one so deceptive that very much caution is required in trying to unmask it. It is astonishing how little light is necessary to display to us the vascular figure by the rays reflected from the coats of the vessels, especially of the white arteries, as if when the eye receives a very small quantity of light the increase effected where the reflected beams fall is of great moment in producing sensation. And if we carefully darken the eyes the spectral condition of the retina, which is impressed with the images of the vessels (see 32), just like the spectrum of a candle-flame, oscillates a considerable interval before it utterly departs; but if we shut ourselves in a room from which all light is excluded for a half-hour or more the last remnant of the spectrum vanishes, and then it is in vain to attempt to trace the course of a central retinal vessel. Nor can we do so by pressure upon the ball of the eye. The path of the vessels observed on opening an eye, after being compressed, against the sky, is nothing more than a momentary vision of their shadows by a retina impressed with mechanical spectra. This negative fact again seems to intimate that the retina only shows us quasi-lights when it is creased on its inner side, or at any rate only when squeezed upon hard enough in a radial direction, to yield a similar mechanical effect, in forcing together laterally, by flattening, the internal elements.

37. Yet, even in the darkest place, after any time we discover that false sensations of light forbid us to realize the fact of the total absence of light, because lights reach us in transient whitish or reddish spots, as if from some percussing body, seizing upon any region from the horizon to the zenith; one or more lucid clouds, if I may so speak, more or less apart, arising in any instant and dissolving in the next. Should we yawn we aggravate the appearances very singularly-that is, we squeeze the retina by forcibly compressing the eye behind the orbital muscle.

Having watched these lucid phantoms against a feebly illuminated ceiling of a room, we soon learn to distinguish them against a cloudless noonday sky, and to ascertain that they are always present.

Now, to the duplicate sclerotic coat of the conjoint globes twelve muscles are attached, eight before and four behind the equator, their inserent spaces so distributed as, when projected into our visual vault, to leave but little of it unrepresented by them. Thus it becomes a puzzling task to extricate from one another quasi-luminous phenomena brought to the general stock by individual orbital muscles. But, after the experience we have had of the instantaneous respondence of the sentients to the slightest tonch of the sclerotic, and to a gentle pull of the optic nerve, we should anticipate that the direct strain of these potent instruments upon the tunics would be attended with vivid phosphorescence, as tending to draw them or the retina conically outwards, and thus to bend the inner ends of the sentients together; and a vigilant survey satisfies me that muscular action imparts the greater quantity, if not the whole, of the involuntary phantoms we are contemplating. We see frequent false lucidities after sleep, when the recreated sentients are aroused by the most trifling shock, and these indefatigable muscles are apt to jerk at the ball discordantly; and habitually the balls roll in their sockets to give room to the blood impelled at each pulsation to equally traverse their substance, or for the disposal of the fluids of the conjunctiva. Still, whilst the will does not interfere with these movements, the eyeballs are nearly kept suspended by the muscles, so as to be enabled to preserve their globular form, and are wheeled round smoothly, with so slight resistance to the traction of any muscles, that but exceedingly weak impressions are made upon the sentients. Nevertheless, if the will overrule this mutual consent of the muscles, the result is far otherwise; and if they be made to contract in vehement antagonism to one another, striking events accrue. Then dragging