tient surface of the retina by the plane of the paper, in which the optic axis falls, and c to be the lenticular centre of the eye. Let A B and A'B' be equal chords of the circle cutting each other in E. Draw CD perpendicular to A B, and join by straight lines c with A, A', B, B', and E, producing C E to meet the circumference A' BA in F. Then EFCF-CE. But CE= = = = = CD = And CD C B COS B CD, whilst BCD ACB (ACF+BCF) (A CA' + BCB). Again, ECD BCD-BCF (ACA B C B'). Moreover CB, very nearly =CF. Hence, if A CA'a, BC BB, EF=d, and the optical radius =r, the equation first given becomes B) } cos (a-B) (3) Acquiescing implicitly for the present in the hypothesis that the vessels are in front of the sentient surface, if a be the retinal place at a given instant of the image of a candle-flame, which is being waved laterally before the eye to keep the vessels in sight, and E the place of some vessel; then B, found by joining AE by a straight line, and producing it to meet the surface, marks the point by which E will be seen. Then, should we carry the candle round to the opposite side of the eye, so that the shadow of E, whose position is supposed unknown, deviates equally, twice, in one plane, that in which the optical centre of the eye and the two resting points of the flame lie, then B' will mark the sentient place of the second shadow. Then, if we observe the whole angle a between the two resting points of the flame, and the angle, B, between the pair of shadows, we can determine the distance, D, of the vessel from the sentient surface. For example, let a = = 96°, B = 4°, r=3 of an inch (8), then d of an inch, as is easily found by aid of a table of natural cosines. Thus, in ordinary language, when we hold the flame below the eye, the capillary patch at the punctum aureum will appear above any objective point upon which we gaze directly, revolving round it with a notable parallax as the flame encompasses the optic axis, receding from the point should the flame approach the axis, and vice versû; the shadows of all the other vessels appearing in accordance with the plan of finding their places, as above expounded. So that it is indisputable that the shadowy figures of the vessels are projected by rays which diverge by reflection at the site of the image of the flame in the back of the eye. With other conditions the same, the parallax is greater for a vessel more removed from the sentients. The principles of 4 and 10 apply here generally, the divergent pencil falling upon the vessels from very obliquely situated points, yielding much deviation of the shadow from its perpendicular retinal projection; the screen thus, too, becoming further separated from the object as the radiating image of the flame approaches it. So, as the candle travels about, do we see any two vessels which decussate one over the other, glide across each other from a consequent difference in parallax. Also the relations between the positions of the radiant points, the body and the screen (with an allow ance for its obliquity), and the size of the shadow (3) hold good here also, whence the broad shadows afforded by a vessel when in the vicinity of the image of the flame. Were we, in figure 5, to join a and A' by a straight line, and draw a tangent at F, and produce A, B and A', B' to meet it, we should obtain a figure similar to so much of figure 1 as has reference to two divergent pencils (4), and we might use the equation given in connexion with it for finding the distance of E from the tangent, and thus at no great labour, as we know the size of the eye, to get d. B 29. Yet, again, let A B (Fig. 6) and A' в be two equal chords of the outer of two concentric circles, in the plane of the paper, in which the geometrical and optic centres of the eye are assumed to lie, and cutting the inner in E' and E respectively; c the eye's optical centre; and C D perpendicular to A' B. Draw the straight lines C A, CA, C F, CF' and C B. Then, as for fig. 5— Or, using the same notation for the angles, and for E F, as for fig. 5, but calling c E, r, instead of c F, we have If E E' indicate a section of the sentient surface, and F B F' a section of some tunic without it, and light radiating from the image of the flame A, were to cause the point в in the tunic to be seen by being there reflected, E is the point by which we should behold it, and BC F the parallax. If the image of the flame rest at A', similarly, BC F' will be the parallax. 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 B, 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 im* If a 40°, and 64°, equation (3) gives d=0.0037 of an inch, equation (4) gives d=0.0033 of an inch. possible, 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 B A', 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 BA', which cuts the three sentient circles in e', e", e"", indicating the parallaxes F C F', FC 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 B at another place—we may simply by writing for ẞ in equation (3) 2 find d, the distance of either sentient 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). 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. t. 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 repassing (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 were 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 ana |