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<div style='text-align:center'>*** START OF THE PROJECT GUTENBERG EBOOK 79069 ***</div>


<div class="transnote">
<p><b><a id="Transcribers_notes"></a>Transcriber’s notes</b>:</p>

<p>This e-book comprises the text of a lecture delivered on November
27, 1800 and subsequently published in the <i>Philosophical Transactions
of the Royal Society</i>, Issue 91 (1801), pp. 23–88</p>

<p>It retains the original page numbering and includes 57 Figures that
are grouped together in seven Plates near the end of the lecture text.
Cross references to the figures have been hyperlinked to the relevant
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possible. Footnotes have been numbered consecutively and moved to the
end. They are hyperlinked in both directions. The text contains
sections of complex mathematics and some unfamiliar symbols.</p>

<p>New original cover art included with this eBook is granted to the
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<p class="tac fs130 ls01em">The Philosophical Transactions of the Royal Society</p>

<p class="surtitle">The Bakerian Lecture:</p>
<p><span class="pagenum" id="Page_23">23</span></p>

<h1>
On the Mechanism of the Eye
</h1>

<p class="tac ws02em fs120">by Thomas Young M.D.  F.R.S.</p>

<p class="tac mtb1em">Read November 27, 1800.</p>


<p class="mt2em ti0">I. In the year 1793, I had the honour of laying before the
Royal Society, some observations on the faculty by which the
eye accommodates itself to the perception of objects at different
distances.‍&#x2060;<a id="FNanchor_1_1" href="#Footnote_1_1" class="fnanchor">1</a> The opinion which I then entertained, although it
had never been placed exactly in the same light, was neither so
new, nor so much forgotten, as was supposed by myself, and
by most of those with whom I had any intercourse on the subject.
Mr. <span class="smcap">Hunter</span>, who had long before formed a similar opinion,
was still less aware of having been anticipated in it, and
was engaged, at the time of his death, in an investigation of the
facts relative to it;‍&#x2060;<a id="FNanchor_2_2" href="#Footnote_2_2" class="fnanchor">2</a> an investigation for which, as far as
physiology was concerned, he was undoubtedly well qualified.
Mr. <span class="smcap">Home</span>, with the assistance of Mr. <span class="smcap">Ramsden</span>, whose recent
loss this Society cannot but lament, continued the inquiry
which Mr. <span class="smcap">Hunter</span> had begun; and the results of his experiments
appeared very satisfactorily to confute the hypothesis of
the muscularity of the crystalline lens.‍&#x2060;<a id="FNanchor_3_3" href="#Footnote_3_3" class="fnanchor">3</a> I therefore thought
it incumbent on me, to take the earliest opportunity of testifying
my persuasion of the justice of Mr. <span class="smcap">Home</span>’s conclusions,
which I accordingly mentioned in a Dissertation published at
<span class="pagenum" id="Page_24">24</span>Gottingen in 1796,‍&#x2060;<a id="FNanchor_4_4" href="#Footnote_4_4" class="fnanchor">4</a> and also in an Essay presented last year
to this Society.‍&#x2060;<a id="FNanchor_5_5" href="#Footnote_5_5" class="fnanchor">5</a> About three months ago, I was induced to
resume the subject, by perusing Dr. <span class="smcap">Porterfield</span>’s paper on
the internal motions of the eye;‍&#x2060;<a id="FNanchor_6_6" href="#Footnote_6_6" class="fnanchor">6</a> and I have very unexpectedly
made some observations, which I think I may venture to say,
appear to be finally conclusive in favour of my former opinion,
as far as that opinion attributed to the lens a power of changing
its figure. At the same time, I must remark, that every person
who has been engaged in experiments of this nature, will
be aware of the extreme delicacy and precaution requisite, both
in conducting them, and in drawing inferences from them; and
will also readily allow, that no apology is necessary for the
fallacies which have misled many others, as well as myself, in
the application of those experiments to optical and physiological
determinations.</p>


<p class="mt2em ti0">II. Besides the inquiry respecting the accommodation of the
eye to different distances, I shall have occasion to notice some
other particulars relative to its functions; and I shall begin
with a general consideration of the sense of vision. I shall
then enumerate some dioptrical propositions subservient to my
purposes, and describe an instrument for readily ascertaining
the focal distance of the eye. On these foundations, I shall
investigate the dimensions and refractive powers of the human
eye in its quiescent state; and the form and magnitude of the
picture which is delineated on the retina, I shall next inquire,
how great are the changes which the eye admits, and what
degree of alteration in its proportions will be necessary for
these changes, on the various suppositions that are principally
<span class="pagenum" id="Page_25">25</span>deserving of comparison. I shall proceed to relate a variety of
experiments which appear to be the most proper to decide on
the truth of each of these suppositions, and to examine such
arguments as have been brought forwards, against the opinion
which I shall endeavour to maintain; and I shall conclude with
some anatomical illustrations of the capacity of the organs
of various classes of animals, for the functions attributed to
them.</p>


<p class="mt2em ti0">III. Of all the external senses, the eye is generally supposed
to be by far the best understood; yet so complicated and so
diversified are its powers, that many of them have been hitherto
uninvestigated; and on others, much laborious research has been
spent in vain. It cannot indeed be denied, that we are capable
of explaining the use and operation of its different parts, in a
far more satisfactory and interesting manner than those of the
ear, which is the only organ that can be strictly compared with
it; since, in smelling, tasting, and feeling, the objects to be examined
come almost unprepared into immediate contact with
the extremities of the nerves; and the only difficulty is, in conceiving
the nature of the effect produced by them, and its communication
to the sensorium. But the eye and the ear are
merely preparatory organs, calculated for transmitting the impressions
of light and sound to the retina, and to the termination
of the soft auditory nerve. In the eye, light is conveyed to
the retina, without any change of the nature of its propagation:
in the ear, it is very probable, that instead of the successive motion
of different parts of the same elastic medium, the small bones
transmit the vibrations of sound, as passive inelastic hard bodies,
obeying the motions of the air in their whole extent at the same
instant. In the eye, we judge very precisely of the direction of
<span class="pagenum" id="Page_26">26</span>light, from the part of the retina on which it impinges: in the
ear, we have no other criterion than the slight difference of motion
in the small bones, according to the part of the tympanum on
which the sound, concentrated by different reflections, first
strikes; hence, the idea of direction is necessarily very indistinct,
and there is no reason to suppose, that different parts of the
auditory nerve are exclusively affected by sounds in different
directions. Each sensitive point of the retina is capable of receiving
distinct impressions, as well of the colour as of the
strength of light; but it is not absolutely certain, that every
part of the auditory nerve is capable of receiving the impression
of each of the much greater diversity of tones that we can distinguish;
although it is extremely probable, that all the different
parts of the surface exposed to the fluid of the vestibule, are
more or less affected by every sound, but in different degrees
and succession, according to the direction and quality of the
vibration. Whether or no, strictly speaking, we can hear two
sounds, or see two objects, in the same instant, cannot easily be
determined; but it is sufficient, that we can do both, without the
intervention of any interval of time perceptible to the mind;
and indeed we could form no idea of magnitude, without a comparative,
and therefore nearly cotemporary perception of two
or more parts of the same object. The extent of the field of
perfect vision for each position of the eye, is certainly not very
great; but it will appear hereafter, that its refractive powers are
calculated to take in a moderately distinct view of a whole
hemisphere: the sense of hearing is equally perfect in almost
every direction.</p>

<p><span class="pagenum" id="Page_27">27</span></p>


<p class="mt2em ti0">IV. DIOPTRICAL PROPOSITIONS.</p>

<p class="tac mtb1em"><i>Proposition</i> I. <i>Phenomenon</i>.</p>

<p>In all refractions, the ratio of the sine of the angle of
incidence to the sine of the angle of refraction is constant.
(<span class="smcap">Newton</span>’s Opt. I. Ax. 5. <span class="smcap">Smith</span>’s Opt. 13. <span class="smcap">Wood</span>’s Opt. 24.)</p>

<p><i>Scholium</i> 1. We shall call it the ratio of <i>m</i> to <i>m</i> ⫧ 1, and
<i>m</i> ⫧ 1, <i>n</i>. In refractions out of air into water, <i>m</i> = 4 and <i>n</i>
= 3, very nearly; out of air into glass, the ratio is nearly that
of 3 to 2.</p>

<p><i>Scholium</i> 2. According to <span class="smcap">Barrow</span>, (<i>Lect. Opt</i>. ii 4.) <span class="smcap">Huygens</span>,
<span class="smcap">Euler</span>, (<i>Conject. phys. circa prop, soni et luminis. Opusc. t. ii.</i>)
and the opinion which I lately submitted to the Royal Society,
(Phil. Trans. for 1800. p. 128,) the velocity of light is the greater
the rarer the medium: according to <span class="smcap">Newton</span>, (Schol. Prop.
96. l. i. Princip. Prop. 10. p. 3. l. ii. Opt.) and the doctrine
more generally received, the reverse. On both suppositions, it
is always the same in the same medium, and varies in the ratio
of the sines of the angles. This circumstance is of use in facilitating
the computation of some very complicated refractions.</p>

<p class="tac mtb1em"><i>Proposition</i> II. <i>Phenomenon</i>.</p>

<p>If between two refracting mediums, a third medium, terminated
by parallel surfaces, be interposed, the whole refraction
will remain unchanged. (<span class="smcap">Newton</span>’s Opt. l. i. p. 2. Prop. 3.
<span class="smcap">Smith</span>, r. 399. <span class="smcap">Wood</span>, 105.)</p>

<p><i>Corollary</i>. Hence, when the refractions out of two mediums
into a third are given, the refraction at the common surface of
these mediums may be thus found. Let the refractions given
<span class="pagenum" id="Page_28">28</span>be as <i>m</i>: <i>n</i>, and as <i>m</i>′: <i>n</i>′; then the ratio sought will be that of
<i>m n</i>′: <i>m</i>′ <i>n</i>. For instance, let the three mediums be glass, water,
and air; then <i>m</i> = 3, <i>n</i> = 2, <i>m</i>′ = 4, <i>n</i>′ = 3, <i>m n</i>′ = 9, and
<i>m</i>′ <i>n</i> = 8. If the ratios be 4: 3, and 13: 14, we have <i>m&nbsp;n</i>′: <i>m</i>′ <i>n</i>
:: 39: 56; and, dividing by 56—39, we obtain 2.3 and 3.3
for <i>m</i> and <i>m</i> + 1, in Schol. 1, Prop. I.</p>

<p class="tac mtb1em"><i>Proposition</i> III. <i>Problem</i>. (Plate II. <a href="#Pl.II">Fig. 1</a>.)</p>

<p>At the vertex of a given triangle (CBA), to place a given refracting
surface (B), so that the incident and refracted rays may
coincide with the sides of the triangle (AB and BC.)</p>

<p>Let the sides be called <i>d</i> and <i>e</i>; then in the base take, next to
<i>d</i> (or AB), a portion (AE) equal to \(\dfrac{nd}{nd+me}\), or (AD =) \(\dfrac{md}{md+ne}\);
draw a line (EB, or DB) to the vertex, and the surface must be
perpendicular to this line, whenever the problem is physically
possible. When \(e\) becomes infinite, and parallel to the base, take
\(\dfrac{nd}{m}\) or \(\dfrac{md}{n}\) next to \(d\), for the intersection of the radius of curvature.</p>

<p class="tac mtb1em"><i>Proposition</i> IV. <i>Theorem</i>. (<a href="#Pl.II">Fig. 2</a>.)</p>

<p>In oblique refractions at spherical surfaces, the line (AI, KL,)
joining the conjugate foci (A, I; K, L;) passes through the point
(G), where a perpendicular from the centre (H) falls on the
line (EF), bisecting the chords (BC, BD,) cut off from the incident
and refracted rays.</p>

<p>Corollary 1. Let <i>t</i> and <i>u</i> be the cosines of incidence and refraction,
the radius being 1, and <i>d</i> and <i>e</i> the respective distances
of the foci of incident and refracted rays; then \(e=\dfrac{mduu}{mdu-ndt-ntt}\)</p>

<p><i>Corollary</i> 2. For a plane surface, \(e=\dfrac{mduu}{-ntt}\).</p>

<p><span class="pagenum" id="Page_29">29</span></p>

<p><i>Corollary</i> 3. For parallel rays, \(d=\infty\), and \(e=\dfrac{muu}{mu-nt}\).</p>

<p><i>Scholium</i> 1. It may be observed, that the caustic by refraction
stops short at its cusp, not geometrically, but physically, the
total reflection interfering.</p>

<p><i>Corollary</i> 4. Call \(\dfrac{muu}{mu-nt}\), <i>b</i> and \(\dfrac{ntt}{mu-nt}\), <i>c</i>;
then \(e=\dfrac{bd}{d-c}\),
and \(e-b=\dfrac{bc}{d-c}\); or, in words, the rectangle contained by the
focal lengths of parallel rays, passing and repassing any surface
in the same lines, is equal to the rectangle contained by the
differences between these lengths and the distances of any conjugate
foci.</p>

<p><i>Corollary</i> 5. For perpendicular rays, \(e=\dfrac{md}{d-n}=m+\dfrac{mn}{d-n}\);
or, if the radius be \(a,e=\dfrac{mad}{d-na}\); and if <i>d</i> and <i>e</i> be given to find
the radius, \(a=\dfrac{de}{md+ne}\).</p>

<p><i>Corollary</i> 6. For rays perpendicular and parallel, <i>e</i>&nbsp;=&nbsp;<i>m</i>, or
<i>e</i>&nbsp;=&nbsp;<i>m&nbsp;a</i>.</p>

<p><i>Corollary</i> 7. For a double convex lens, neglecting the thickness,
call the first radius <i>g</i>, the second <i>h</i>, and \(e=\dfrac{ndgh}{dg+dh-ngh}\).
Hence \(n=\dfrac{de}{d+e}\cdot \dfrac{g+h}{gh}\).  and,
for parallel rays, \(e=\dfrac{ngh}{g+h}\), and
\(n=e\cdot \dfrac{g+h}{gh}\). If \(g=h=a, e=\dfrac{nad}{2d-na}\); and for parallel rays \(e=\dfrac{na}{2}\):
calling this principal focal length <i>b</i>, \(e=\dfrac{bd}{d-b}\), as in
Cor. 4; whence we have the joint focus of two lenses; also,
\(b=\dfrac{de}{d+e}\).</p>

<p><i>Corollary</i> 8. In a sphere, \(e=ma\cdot \dfrac{d+a}{2d-(m-2)a}\), for the distance
from the centre, and \(b=\dfrac{ma}{2}\).</p>

<p><span class="pagenum" id="Page_30">30</span></p>

<p><i>Scholium</i> 2. In all these cases, if the rays converge, <i>d</i> must
be negative. For instance, to find the joint focus of two convex,
or concave lenses, the expression becomes, \(e=\dfrac{bd}{b+d}\).</p>

<p><i>Corollary</i> 9. In Cor. 3, the divisor becomes ultimately constant;
and, when the inclination is smalls the focus varies as <i>u&nbsp;u</i>.</p>

<p><i>Corollary</i> 10. For parallel rays falling obliquely on a double
convex, or double concave lens, of inconsiderable thickness, the
radius being 1, \(e=\dfrac{ntu}{2(mu-nt)}\); which varies ultimately as the
product of the cosines, or as \(\dfrac{m+n}{nn}t+t^{2}\).</p>

<p><i>Scholium</i> 3. In the double convex lens, the thickness diminishes
the effect of the obliquity near the axis; in the double
concave, it increases it.</p>

<p><i>Scholium</i> 4. No spherical surface, excepting one particular
case, (<span class="smcap">Wood</span>, 155,) can collect an oblique pencil of rays, even
to a physical point. The oblique rays which we have hitherto
considered, are only such as lie in that section of the pencil
which is made by a plane passing through the centre and the
radiant point. They continue in this plane, notwithstanding the
refraction, and therefore will not meet the rays of the collateral
sections, till they arrive at the axis. The remark was made by
Sir <span class="smcap">Isaac Newton</span>, and extended by Dr. <span class="smcap">Smith</span>, (<span class="smcap">Smith</span> r.
493, 494:) it appears, however, to have been too little noticed.
(<span class="smcap">Wood</span>, 362.) The geometrical focus thus becomes a line, a
circle, an oval, or other figure, according to the form of the
pencil, the nature of the surface, and the place of the plane receiving
the image. Some of the varieties of the focal image of
a cylindrical pencil obliquely refracted are shown in Plate VI.
<a href="#Pl.VI">Fig. 28</a>.</p>

<p><span class="pagenum" id="Page_31">31</span></p>

<p><i>Corollary</i> 11. Hence the line joining the remoter conjugate
foci, will always pass through the centre. The distance
of the remoter focus of parallel rays will be expressed by
\(f=\dfrac{m}{mu-nt}\); and the least circle of aberration will be at the
distance \(\dfrac{1+u^{2}-2u^{4}}{(1+uu)\cdot (mu-nt)}\) dividing the length of aberration in
the ratio of the distance of its limits from the surface. In the
case of Cor. 10. \(f=\dfrac{n}{2(mu-nt)}\).</p>

<p>Corollary 12. This proposition extends also to reflected rays;
and, in that case, the line from the centre passes through the
point of incidence.</p>

<p class="tac mtb1em"><i>Proposition</i> V. <i>Problem</i>.</p>

<p>To find the place and magnitude of the image of a small
object, after refraction at any number of spherical surfaces.</p>

<p><i>Construction</i>. (Plate II. <a href="#Pl.II">Fig. 3</a>.) From any point (B) in the
object (AB), draw lines to (C), the centre of the first surface,
and to (D), the focus of parallel rays coming in a contrary
direction: from the intersection of the second line (BD) with
the tangent (EF) at the vertex, draw a line (EH) parallel to
the axis, and it will cut the first line (BC) in (H), the first
image of the point (B). Proceed with this image as a new object,
and repeat the operation for each surface, and the last point
will be in the image required. For calculation, find the place
of the image by Cor. 5. Prop. IV. and its magnitude will be to
that of the object, as their respective distances from the centre.</p>

<p><i>Corollary</i>. If a confused image be received on any given
plane, its magnitude will be determined by the line drawn from
the preceding image through the centre of the last surface.</p>

<p><span class="pagenum" id="Page_32">32</span></p>

<p class="tac mtb1em"><i>Proposition</i> VI. <i>Problem</i>.</p>

<p>To determine the law by which the refraction at a spherical
surface must vary, so as to collect parallel rays to a perfect
focus.</p>

<p><i>Solution</i>. Let <i>v</i> be the versed sine to the radius 1; then, at
each point without the axis, <i>n</i> remaining the same, <i>m</i> must
become \(\sqrt{mm±2nv}\); and all the rays will be collected in
the principal focus.</p>

<p><i>Corollary</i>. The same law will serve for a double convex lens,
in the case of equidistant conjugate foci, substituting <i>n</i> for <i>m</i>.</p>

<p class="tac mtb1em"><i>Proposition</i> VII. <i>Problem</i>.</p>

<p>To find the principal focus of a sphere, or lens, of which the
internal parts are more dense than the external.</p>

<p><i>Solution</i>. In order that the focal distance may be finite, the
density of a finite portion about the centre must be equable:
call the radius of this portion \(\dfrac{1}{l}\), that of the sphere being unity;
let the whole refraction out of the surrounding medium into this
central part, be as <i>m</i> to <i>n</i>; take \(r=\dfrac{\log l}{\log m- \log n}\), and let the density
be supposed to vary every where inversely as the power \(\dfrac{1}{r}\)
of the distance from the centre: then the principal focal distance
from the centre will be \(\dfrac{r-1}{2}\cdot \dfrac{m}{nl-m}\). When <i>r</i>&nbsp;=&nbsp;1, it becomes
\(\dfrac{1}{2(\text{H.L}.m-\text{H.L}.n)}\). For a lens, deduct one fourth of the difference
between its axis and the diameter of the sphere of which its
surfaces are portions.</p>

<p><i>Corollary</i>. If the density be supposed to vary suddenly at the
surface, <i>m</i> must express the difference of the refractions at the
<span class="pagenum" id="Page_33">33</span>centre and at the surface; and the focal distance, thus determined,
must be diminished according to the refraction at the surface.</p>

<p class="tac mtb1em"><i>Proposition</i> VIII. <i>Problem</i>.</p>

<p>To find the nearer focus of parallel rays falling obliquely on
a sphere of variable density.</p>

<p><i>Solution</i>. Let <i>r</i> be as in the last proposition, <i>s</i> the sine of incidence,
<i>t</i> the cosine, and <i>e</i> the distance of the focus from the
point of emersion. Then \(e=\dfrac{w-t}{2-tw}\), <i>w</i> being \(=\dfrac{2}{(r-1)s^{\frac{r+1}{r-1}\cdot }}\)
\((a\text{A}+b\text{B}+c\text{C}+...)+2a\text{A}+6b\text{B}s^{2}+10c\text{C}s^{4}+...\)
where \(a=\dfrac{r}{r+1}\), \(b=\dfrac{r}{3r-1}\), \(c=\dfrac{r}{5r-3}\), \(\text{A}=1, \text{B}=\frac{1}{2}\text{A}, \text{C}=\frac{3}{4}\text{B}, \text{D}=\frac{5}{6}\text{C}\). But, when <i>s</i> is large, the latter part of the series converges
somewhat slowly. The former part might be abridged
if it were necessary: but, since the focus in this case is always
very imperfect, it is of the less consequence to provide an easy
calculation.</p>

<p><i>General Scholium</i>. The two first propositions relate to well
known phenomena; the third can hardly be new; the fourth
approaches the nearest to <span class="smcap">Maclaurin</span>’s construction, but is far
more simple and convenient; the fifth and sixth have no difficulty;
but the two last require a long demonstration. The one
is abridged by a property of logarithms; the other is derived from
the laws of centripetal forces, on the supposition of velocities
directly as the refractive densities, correcting the series for the
place of the apsis, and making the sine of incidence variable,
to determine the fluxion of the angle of deviation.</p>

<p class="mt2em ti0">V. Dr. <span class="smcap">Porterfield</span> has employed an experiment, first
made by <span class="smcap">Scheiner</span>, to the determination of the focal distance
<span class="pagenum" id="Page_34">34</span>of the eye; and has described, under the name of an optometer,
a very excellent instrument, founded on the principle of the
phenomenon.‍&#x2060;<a id="FNanchor_7_7" href="#Footnote_7_7" class="fnanchor">7</a> But the apparatus is capable of considerable
improvement; and I shall beg leave to describe an optometer,
simple in its construction, and equally convenient and accurate
in its application.</p>

<p>Let an obstacle be interposed between a radiant point (R,
Plate II. <a href="#Pl.II">Fig. 4</a>,) and any refracting surface, or lens (CD),
and let this obstacle be perforated at two points (A and B) only.
Let the refracted rays be intercepted by a plane, so as to form
an image on it. Then it is evident, that when this plane (EF)
passes through the focus of refracted rays, the image formed
on it will be a single point. But, if the plane be advanced forwards
(to GH), or removed backwards (to IK), the small
pencils passing through the perforations, will no longer meet
in a single point, but will fall on two distinct spots of the plane
(G,&nbsp;H; I,&nbsp;K;) and, in either case, form a double image of the
object.</p>

<p>Let us now add two more radiating points, (S and T, <a href="#Pl.II">Fig. 5</a>,)
the one nearer to the lens than the first point, the other more
remote; and, when the plane which receives the images passes
through the focus of rays coming from the first point, the images
of the second and third points must both be double (<i>s&nbsp;s</i>, <i>t&nbsp;t</i>;)
since the plane (EF) is without the focal distance of rays
coming from the furthest point, and within that of rays coming
from the nearest. Upon this principle. Dr. <span class="smcap">Porterfield</span>’s
optometer was founded.</p>

<p>But, if the three points be supposed to be joined by a line,
and this line to be somewhat inclined to the axis of the lens,
<span class="pagenum" id="Page_35">35</span>each point of the line, except the first point (R, <a href="#Pl.II">Fig. 6</a>,) will
have a double image; and each pair of images, being contiguous
to those of the neighbouring radiant points, will form with them
two continued lines, and the images being more widely separated
as the point which they represent is further from the first
radiant point, the lines (<i>s&nbsp;t</i>, <i>s&nbsp;t</i>,) will converge on each side
towards (<i>r</i>) the image of this point, and there will intersect
each other.</p>

<p>The same happens when we look at any object through two
pin holes, within the limits of the pupil. If the object be at the
point of perfect vision, the image on the retina will be single:
but, in every other case, the image being double, we shall appear
to see a double object: and, if we look at a line pointed nearly
to the eye, it will appear as two lines, crossing each other in the
point of perfect vision. For this purpose, the holes may be
converted into slits, which render the images nearly as distinct,
at the same time that they admit more light. The number may
be increased from two to four, or more, whenever particular
investigations render it necessary.</p>

<p>The optometer may be made of a slip of card-paper, or of
ivory, about eight inches in length, and one in breadth, divided
longitudinally by a black line, which must not be too strong.
The end of the card must be cut as is shown in Plate III. <a href="#Pl.III">Fig. 7</a>,
in order that it may be turned up, and fixed in an inclined
position by means of the shoulder: or a detached piece, nearly
of this form, may be applied to the optometer, as it is here engraved.
A hole about half an inch square must be made in this
part; and the sides so cut as to receive a slider of thick paper,
with slits of different sizes, from a fortieth to a tenth of an inch
in breadth, divided by spaces somewhat broader; so that each
observer may choose that which best suits the aperture of his pupil.
<span class="pagenum" id="Page_36">36</span>In order to adapt the instrument to the use of presbyopic eyes,
the other end must be furnished with a lens of four inches focal
length; and a scale must be made near the line on each side
of it, divided from one end into inches, and from the other according
to the table here calculated from Cor. 7. Prop. IV, by
means of which, not only diverging, but also parallel and converging
rays from the lens are referred to their virtual focus.
The instrument is easily applicable to the purpose of ascertaining
the focal length of spectacles required for myopic or
presbyopic eyes. Mr. <span class="smcap">Cary</span> has been so good as to furnish
me with the numbers and focal lengths of the glasses commonly
made; and I have calculated the distances at which those
numbers must be placed on the scale of the optometer, so that
a presbyopic eye may be enabled to see at eight inches distance,
by using the glasses of the focal length placed opposite to the
nearest crossing of the lines; and a myopic eye with parallel
rays, by using the glasses indicated by the number that stands
opposite their furthest crossing. To facilitate the observation,
I have also placed these numbers opposite that point which
will be the nearest crossing to myopic eyes; but this, upon the
arbitrary supposition of an equal capability of change of focus
in every eye, which I must confess is often far from the truth.
It cannot be expected, that every person, on the first trial,
will fix precisely upon that power which best suits the defect
of his sight. Few can bring their eyes at pleasure to the state
of full action, or of perfect relaxation; and a power two or
three degrees lower than that which is thus ascertained, will be
found sufficient for ordinary purposes. I have also added to the
second table, such numbers as will point out the spectacles
necessary for a presbyopic eye, to see at twelve and at eighteen
inches respectively: the middle series will perhaps be the most
<span class="pagenum" id="Page_37">37</span>proper for placing the numbers on the scale. The optometer
should be applied to each eye; and, at the time of observing, the
opposite eye should not be shut, but the instrument should be
screened from its view. The place of intersection may be accurately
ascertained, by means of an index sliding along the scale.
The optometer is represented in Plate III. <a href="#Pl.III">Fig. 8 and 9</a>; and
the manner in which the lines appear, in <a href="#Pl.III">Fig. 10.</a></p>

<p class="tac pt1"><i>Table</i> I. <i>For extending the scale by a lens of 4 inches focus:</i></p>

<div class="center">
<table id="table1">
<tr class="bt">
<td>
 4
</td>
<td>
2.00
</td>
<td>
11
</td>
<td>
2.93
</td>
<td>
 30
</td>
<td>
3.52
</td>
<td>
 200
</td>
<td>
3.92
</td>
<td>
-35
</td>
<td>
4.51
</td>
<td>
-12 
</td>
<td>
6.00
</td>
</tr>
<tr>
<td>
 5
</td>
<td>
2.22
</td>
<td>
12
</td>
<td>
3.00
</td>
<td>
 40
</td>
<td>
3.64
</td>
<td>
∞
</td>
<td>
4.00
</td>
<td>
-30
</td>
<td>
4.62
</td>
<td>
-11 
</td>
<td>
6.29
</td>
</tr>
<tr>
<td>
 6
</td>
<td>
2.40
</td>
<td>
13
</td>
<td>
3.06
</td>
<td>
 50
</td>
<td>
3.70
</td>
<td>
-200
</td>
<td>
4.08
</td>
<td>
-25
</td>
<td>
4.76
</td>
<td>
-10 
</td>
<td>
6.67
</td>
</tr>
<tr>
<td>
 7
</td>
<td>
2.55
</td>
<td>
14
</td>
<td>
3.11
</td>
<td>
 60
</td>
<td>
3.75
</td>
<td>
-100
</td>
<td>
4.17
</td>
<td>
-20
</td>
<td>
5.00
</td>
<td>
-9.5
</td>
<td>
6.90
</td>
</tr>
<tr>
<td>
 8
</td>
<td>
2.67
</td>
<td>
15
</td>
<td>
3.16
</td>
<td>
 70
</td>
<td>
3.78
</td>
<td>
-50 
</td>
<td>
4.35
</td>
<td>
-15
</td>
<td>
5.45
</td>
<td>
-9.0
</td>
<td>
7.20
</td>
</tr>
<tr>
<td>
 9
</td>
<td>
2.77
</td>
<td>
20
</td>
<td>
3.33
</td>
<td>
 80
</td>
<td>
3.81
</td>
<td>
-45 
</td>
<td>
4.39
</td>
<td>
-14
</td>
<td>
5.60
</td>
<td>
-8.5
</td>
<td>
7.56
</td>
</tr>
<tr class="bb">
<td>
10
</td>
<td>
2.86
</td>
<td>
25
</td>
<td>
3.45
</td>
<td>
100
</td>
<td>
3.85
</td>
<td>
-40 
</td>
<td>
4.44
</td>
<td>
-13
</td>
<td>
5.78
</td>
<td>
-8.0
</td>
<td>
8.00
</td>
</tr>
</table>
</div>

<p class="tac pt1"><i>Table</i> II. <i>For placing the numbers indicating the focal length of
convex glasses.</i></p>

<div class="center">
<table id="table2">
<thead>
<tr>
<th>
Foc.
</th>
<th>
VIII.
</th>
<th>
XII.
</th>
<th>
XVIII.
</th>
<th>
Foc.
</th>
<th>
VIII.
</th>
<th>
XII.
</th>
<th>
XVIII.
</th>
<th>
Foc.
</th>
<th>
VIII.
</th>
<th>
XII.
</th>
<th>
XVIII.
</th>
</tr>
</thead>
<tr>
<td>
 0
</td>
<td>
 8.00
</td>
<td>
12.00
</td>
<td>
18.00
</td>
<td>
20
</td>
<td>
13.33
</td>
<td>
  30.00
</td>
<td>
180.00
</td>
<td>
8  
</td>
<td>
∞
</td>
<td>
-24.00
</td>
<td>
-14.40
</td>
</tr>
<tr>
<td>
40
</td>
<td>
10.00
</td>
<td>
17.14
</td>
<td>
32.73
</td>
<td>
18
</td>
<td>
14.40
</td>
<td>
  36.00
</td>
<td>
∞
</td>
<td>
7  
</td>
<td>
-56.00
</td>
<td>
-16.80
</td>
<td>
-11.45
</td>
</tr>
<tr>
<td>
36
</td>
<td>
10.28
</td>
<td>
18.00
</td>
<td>
36.00
</td>
<td>
16
</td>
<td>
16.00
</td>
<td>
  48.00
</td>
<td>
-144.00
</td>
<td>
6  
</td>
<td>
-24.00
</td>
<td>
-12.00
</td>
<td>
- 9.00
</td>
</tr>
<tr>
<td>
30
</td>
<td>
10.91
</td>
<td>
20.00
</td>
<td>
45.00
</td>
<td>
14
</td>
<td>
18.67
</td>
<td>
  84.00
</td>
<td>
- 63.00
</td>
<td>
5  
</td>
<td>
-13.33
</td>
<td>
- 8.57
</td>
<td>
- 5.92
</td>
</tr>
<tr>
<td>
28
</td>
<td>
11.20
</td>
<td>
21.00
</td>
<td>
50.40
</td>
<td>
12
</td>
<td>
24.00
</td>
<td>
∞
</td>
<td>
- 36.00
</td>
<td>
4.5
</td>
<td>
-10.29
</td>
<td>
- 7.20
</td>
<td>
- 6.00
</td>
</tr>
<tr>
<td>
26
</td>
<td>
11.56
</td>
<td>
22.29
</td>
<td>
58.50
</td>
<td>
11
</td>
<td>
29.33
</td>
<td>
-132.00
</td>
<td>
- 28.29
</td>
<td>
4.0
</td>
<td>
- 8.00
</td>
<td>
- 6.00
</td>
<td>
- 5.14
</td>
</tr>
<tr>
<td>
24
</td>
<td>
12.00
</td>
<td>
24.00
</td>
<td>
72.00
</td>
<td>
10
</td>
<td>
40.00
</td>
<td>
- 60.00
</td>
<td>
- 22.50
</td>
<td>
3.5
</td>
<td>
- 6.22
</td>
<td>
- 4.94
</td>
<td>
- 4.34
</td>
</tr>
<tr class="bb">
<td>
22
</td>
<td>
12.77
</td>
<td>
20.40
</td>
<td>
99.00
</td>
<td>
 9
</td>
<td>
72.00
</td>
<td>
- 36.00
</td>
<td>
- 18.00
</td>
<td>
3.0
</td>
<td>
- 4.80
</td>
<td>
- 4.00
</td>
<td>
- 3.6 
</td>
</tr>
</table>
</div>


<p class="tac pt1"><i>Table</i> III. <i>For concave glasses.</i></p>

<div class="center">
<table id="table3">
<thead>
<tr>
<th>
Number.
</th>
<th>
Focus and<br>furthest<br>place.
</th>
<th>
Nearest<br>place.
</th>
<th>
Number.
</th>
<th>
Focus and<br>furthest<br>place.
</th>
<th>
Nearest<br>place.
</th>
<th>
Number.
</th>
<th>
Focus and<br>furthest<br>place.
</th>
<th>
Nearest<br>place.
</th>
</tr>
</thead>
<tr>
<td>
0
</td>
<td>

</td>
<td>
4.00
</td>
<td>
 7
</td>
<td>
8  
</td>
<td>
2.67
</td>
<td>
14
</td>
<td>
3.00
</td>
<td>
1.71
</td>
</tr>
<tr>
<td>
1
</td>
<td>
24
</td>
<td>
3.43
</td>
<td>
 8
</td>
<td>
7  
</td>
<td>
2.54
</td>
<td>
15
</td>
<td>
2.75
</td>
<td>
1.63
</td>
</tr>
<tr>
<td>
2
</td>
<td>
18
</td>
<td>
3.27
</td>
<td>
 9
</td>
<td>
6  
</td>
<td>
2.40
</td>
<td>
16
</td>
<td>
2.50
</td>
<td>
1.54
</td>
</tr>
<tr>
<td>
3
</td>
<td>
16
</td>
<td>
3.20
</td>
<td>
10
</td>
<td>
5  
</td>
<td>
2.22
</td>
<td>
17
</td>
<td>
2.25
</td>
<td>
1.44
</td>
</tr>
<tr>
<td>
4
</td>
<td>
12
</td>
<td>
3.00
</td>
<td>
11
</td>
<td>
4.5
</td>
<td>
2.12
</td>
<td>
18
</td>
<td>
2.00
</td>
<td>
1.33
</td>
</tr>
<tr>
<td>
5
</td>
<td>
10
</td>
<td>
2.86
</td>
<td>
12
</td>
<td>
4.0
</td>
<td>
2.00
</td>
<td>
19
</td>
<td>
1.75
</td>
<td>
1.22
</td>
</tr>
<tr class="bb">
<td>
6
</td>
<td>
 9
</td>
<td>
2.77
</td>
<td>
13
</td>
<td>
3.5
</td>
<td>
1.87
</td>
<td>
20
</td>
<td>
1.50
</td>
<td>
1.02
</td>
</tr>
</table>
</div>


<p><span class="pagenum" id="Page_38">38</span></p>
<p class="mt2em ti0">VI. Being convinced of the advantage of making every
observation with as little assistance as possible, I have endeavoured
to confine most of my experiments to my own eyes;
and I shall, in general, ground my calculations on the supposition
of an eye nearly similar to my own. I shall therefore
first endeavour to ascertain all its dimensions, and all its
faculties.</p>

<p>For measuring the diameters, I fix a small key on each point
of a pair of compasses; and I can venture to bring the rings
into immediate contact with the sclerotica. The transverse
diameter is externally 98 hundredths of an inch.</p>

<p>To find the axis, I turn the eye as much inwards as possible,
and press one of the keys close to the sclerotica, at the external
angle, till it arrives at the spot where the spectrum formed
by its pressure coincides with the direction of the visual axis, and,
looking in a glass, I bring the other key to the cornea. The
optical axis of the eye, making allowance of three hundredths
for the coats, is thus found to be 91 hundredths of an inch, from
the external surface of the cornea to the retina. With an eye
less prominent, this method might not have succeeded.</p>

<p>The vertical diameter, or rather chord, of the cornea, is 45
hundredths: its versed sine 11 hundredths. To ascertain the
versed sine, I looked with the right eye at the image of the
left, in a small speculum held close to the nose, while the left
eye was so averted that the margin of the cornea appeared as a
straight line, and compared the projection of the cornea with
the image of a cancellated scale held in a proper direction behind
the left eye, and close to the left temple. The horizontal
chord of the cornea is nearly 49 hundredths.</p>

<p>Hence the radius of the cornea is 31 hundredths. It may
<span class="pagenum" id="Page_39">39</span>be thought that I assign too great a convexity to the cornea;
but I have corrected it by a number of concurrent observations,
which will be enumerated hereafter.</p>

<p>The eye being directed towards its image, the projection of
the margin of the sclerotica is 22 hundredths from the margin
of the cornea, towards the external angle, and 27 towards the
internal angle of the eye: so that the cornea has an eccentricity
of one fortieth of an inch, with respect to the section of
the eye perpendicular to the visual axis.</p>

<p>The aperture of the pupil varies from 27 to 13 hundredths;
at least this is its apparent size, which must be somewhat diminished,
on account of the magnifying power of the cornea,
perhaps to 25 and 12. When dilated, it is nearly as eccentric
as the cornea; but, when most contracted, its centre coincides
with the reflection of an image from an object held immediately
before the eye; and this image very nearly with the centre of
the whole apparent margin of the sclerotica: so that the cornea
is perpendicularly intersected by the visual axis.</p>

<p>My eye, in a state of relaxation, collects to a focus on the
retina, those rays which diverge vertically from an object at the
distance of ten inches from the cornea, and the rays which
diverge horizontally from an object at seven inches distance.
For, if I hold the plane of the optometer vertically, the images
of the line appear to cross at ten inches; if horizontally, at seven.
The difference is expressed by a focal length of 23 inches. I
have never experienced any inconvenience from this imperfection,
nor did I ever discover it till I made these experiments;
and I believe I can examine minute objects with as much accuracy
as most of those whose eyes are differently formed. On
mentioning it to Mr. <span class="smcap">Cary</span>, he informed me, that he had
<span class="pagenum" id="Page_40">40</span>frequently taken notice of a similar circumstance; that many
persons were obliged to hold a concave glass obliquely, in order
to see with distinctness, counterbalancing, by the inclination of
the glass, the too great refractive power of the eye in the direction
of that inclination, (Cor. 10. Prop. IV.) and finding but
little assistance from spectacles of the same focal length. The
difference is not in the cornea, for it exists when the effect of
the cornea is removed by a method to be described hereafter.
The cause is, without doubt, the obliquity of the uvea, and of
the crystalline lens, which is nearly parallel to it, with respect
to the visual axis: this obliquity will appear, from the dimensions
already given, to be about 10 degrees. Without entering
into a very accurate calculation, the difference observed is found
(by the same corollary) to require an inclination of about 13
degrees; and the remaining three degrees may easily be added,
by the greater obliquity of the posterior surface of the crystalline
opposite the pupil. There would be no difficulty in fixing the
glasses of spectacles, or the concave eye-glass of a telescope, in
such a position as to remedy the defect.</p>

<p>In order to ascertain the focal distance of the lens, we must
assign its probable distance from the cornea. Now the versed
sine of the cornea being 11 hundredths, and the uvea being
nearly flat, the anterior surface of the lens must probably be
somewhat behind the chord of the cornea; but by a very inconsiderable
distance, for the uvea has the substance of a thin membrane,
and the lens approaches very near to it: we will therefore
call this distance 12 hundredths. The axis and proportions
of the lens must be estimated by comparison with anatomical
observations; since they affect, in a small degree, the determination
of its focal distance. M. <span class="smcap">Petit</span> found the axis
<span class="pagenum" id="Page_41">41</span>almost always about two lines, or 18 hundredths of an inch.
The radius of the anterior surface was in the greatest number
3 lines, but oftener more than less. We will suppose mine
to be \(3\frac{1}{4}\), or nearly \(\frac{1}{10}\) of an inch. The radius of the
posterior surface was most frequently \(2\frac{1}{2}\) lines, or \(\frac{2}{9}\) of an
inch.‍&#x2060;<a id="FNanchor_8_8" href="#Footnote_8_8" class="fnanchor">8</a> The
optical centre will be therefore \(\left( \frac{18\times 30}{30+22}= \right)\) about
one-tenth of an inch from the anterior surface: hence we have
22 hundredths, for the distance of the centre from the cornea.
Now, taking 10 inches as the distance of the radiant point, the
focus of the cornea will be 115 hundredths behind the centre
of the lens. (Cor. 5. Prop. IV.) But the actual joint focus is
(91&nbsp;—&nbsp;22&nbsp;=) 69 behind the centre: hence, disregarding the
thickness of the lens, its principal focal distance is 173 hundredths.
(Cor. 7. Prop. IV.) For its refractive power in the
eye, we have (by Cor. 7. Prop. IV.) <i>n</i>&nbsp;=&nbsp;13.5, and <i>m</i>&nbsp;=&nbsp;14.5.
Calculating upon this refractive power, with the consideration
of the thickness also, we find that it requires a correction,
and comes near to the ratio of 14 to 13 for the sines. It
is well known that the refractive powers of the humours are
equal to that of water; and, that the thickness of the cornea is
too equable to produce any effect on the focal distance.</p>

<p>For determining the refractive power of the crystalline lens
by a direct experiment, I made use of a method suggested to
me by Dr. <span class="smcap">Wollaston</span>. I found the refractive power of the
centre of the recent human crystalline to that of water, as 21
to 20. The difference of this ratio from the ratio of 14 to 13,
ascertained from calculation, is probably owing to two circumstances.
The first is, that the substance of the lens being in
some degree soluble in water, a portion of the aqueous fluid
<span class="pagenum" id="Page_42">42</span>within its capsule penetrates after death, so as somewhat to
lessen the density. When dry, the refractive power is little inferior
to that of crown glass. The second circumstance is, the
unequal density of the lens. The ratio of 14 to 13 is founded
on the supposition of an equable density: but, the central part
being the most dense, the whole acts as a lens of smaller dimensions;
and it may be found by Prop. VII. that if the central
portion of a sphere be supposed of uniform density, refracting
as 21 to 20, to the distance of one half of the radius, and
the density of the external parts to decrease gradually, and at
the surface to become equal to that of the surrounding medium,
the sphere thus constituted, will be equal in focal length to a
uniform sphere of the same size, with a refraction of 16 to 15
nearly. And the effect will be nearly the same, if the central
portion be supposed to be smaller than this, but the density
to be somewhat greater at the surface than that of the surrounding
medium, or to vary more rapidly externally than internally.
On the whole, it is probable that the refractive
power of the centre of the human crystalline, in its living state,
is to that of water nearly as 18 to 17; that the water imbibed
after death, reduces it to the ratio of 21 to 20; but that, on
account of the unequable density of the lens, its effect in the
eye is equivalent to a refraction of 14 to 13 for its whole size.
Dr. <span class="smcap">Wollaston</span> has ascertained the refraction out of air, into
the centre of the recent crystalline of oxen and sheep, to be
nearly as 143 to 100; into the centre of the crystalline of fish,
and into the dried crystalline of sheep, as 152 to 100. Hence,
the refraction of the crystalline of oxen in water, should be
as 15 to 14: but the human crystalline, when recent, is decidedly
less refractive.</p>

<p><span class="pagenum" id="Page_43">43</span></p>

<p>These considerations will explain the inconsistency of different
observations on the refractive power of the crystalline;
and, in particular, how the refraction which I formerly calculated,
from measuring the focal length of the lens,‍&#x2060;<a id="FNanchor_9_9" href="#Footnote_9_9" class="fnanchor">9</a> is so much
greater than that which is determined by other means. But,
for direct experiments, Dr. <span class="smcap">Wollaston</span>’s method is exceedingly
accurate.</p>

<p>When I look at a minute lucid point, such as the image of
a candle in a small concave speculum, it appears as a radiated
star, as a cross, or as an unequal line, and never as a perfect
point, unless I apply a concave lens inclined at a proper angle,
to correct the unequal refraction of my eye. If I bring the
point very near, it spreads into a surface nearly circular, and
almost equably illuminated, except some faint lines, nearly in a
radiating direction. For this purpose, the best image is a candle,
or a small speculum, viewed through a minute lens at some
little distance, or seen by reflection in a larger lens. If any
pressure has been applied to the eye, such as that of the finger
keeping it shut, the sight is often confused for a short time after
the removal of the finger, and the image is in this case spotty
or curdled. The radiating lines are probably occasioned by
some slight inequalities in the surface of the lens, which is very
superficially furrowed in the direction of its fibres: the curdled
appearance will be explained hereafter. When the point is further
removed, the image becomes evidently oval, the vertical
diameter being longest, and the lines a little more distinct than
before, the light being strongest in the neighbourhood of the
centre; but immediately at the centre there is a darker spot,
owing to such a slight depression at the vertex as is often
<span class="pagenum" id="Page_44">44</span>observable in examining the lens after death. The situation of
the rays is constant, though not regular; the most conspicuous
are seven or eight in number; sometimes about twenty fainter
ones may be counted. Removing the point a little further, the
image becomes a short vertical line; the rays that diverged horizontally
being perfectly collected, while the vertical rays are
still separate. In the next stage, which is the most perfect
focus, the line spreads in the middle, and approaches nearly to
a square, with projecting angles, but is marked with some
darker lines towards the diagonals. The square then flattens
into a rhombus, and the rhombus into a horizontal line unequally
bright. At every greater distance, the line lengthens,
and acquires also breadth, by radiations shooting out from it, but
does not become a uniform surface, the central part remaining
always considerably brightest, in consequence of the same flattening
of the vertex which before made it fainter. Some of
these figures bear a considerable analogy to the images derived
from the refraction of oblique rays, (Schol. 4. Prop. IV.) and
still more strongly resemble a combination of two of them in
opposite directions; so as to leave no doubt, but that both surfaces
of the lens are oblique to the visual axis, and co-operate
in distorting the focal point. This may also be verified, by
observing the image delineated by a common glass lens, when
inclined to the incident rays. (See Plate VI. <a href="#Pl.IV">Fig. 28—40</a>.)</p>

<p>The visual axis being fixed in any direction, I can at the
same time see a luminous object placed laterally at a considerable
distance from it; but in various directions the angle
is very different. Upwards it extends to 50 degrees, inwards
to 60, downwards to 70, and outwards to 90 degrees. These
internal limits of the field of view nearly correspond with
<span class="pagenum" id="Page_45">45</span>the external limits formed by the different parts of the face,
when the eye is directed forwards and somewhat downwards,
which is its most natural position; although the internal limits
are a little more extensive than the external; and both are well
calculated for enabling us to perceive the most readily, such
objects as are the most likely to concern us. Dr. <span class="smcap">Wollaston</span>’s
eye has a larger field of view, both vertically and horizontally,
but nearly in the same proportions, except that it extends further
upwards. It is well known, that the retina advances further
forwards towards the internal angle of the eye, than towards
the external angle; but upwards and downwards its extent is
nearly equal, and is indeed every way greater than the limits of
the field of view, even if allowance is made for the refraction
of the cornea only. The sensible portion seems to coincide
more nearly with the painted choroid of quadrupeds: but the
whole extent of perfect vision is little more than 10 degrees; or,
more strictly speaking, the imperfection begins within a degree
or two of the visual axis, and at the distance of 5 or 6 degrees
becomes nearly stationary, until, at a still greater distance, vision
is wholly extinguished. The imperfection is partly owing to
the unavoidable aberration of oblique rays, but principally to
the insensibility of the retina: for, if the image of the sun
itself be received on a part of the retina remote from the axis,
the impression will not be sufficiently strong to form a permanent
spectrum, although an object of very moderate brightness
will produce this effect when directly viewed. It would probably
have been inconsistent with the economy of nature, to bestow a
larger share of sensibility on the retina. The optic nerve is at
present very large; and the delicacy of the organ renders it,
even at present, very susceptible of injury from slight irritation.
<span class="pagenum" id="Page_46">46</span>and very liable to inflammatory affections; and, in order to
make the sight so perfect as it is, it was necessary to confine that
perfection within narrow limits. The motion of the eye has a
range of about 55 degrees in every direction; so that the field
of perfect vision, in succession, is by this motion extended to
110 degrees.</p>

<p>But the whole of the retina is of such a form as to receive
the most perfect image, on every part of its surface, that the
state of each refracted pencil will admit; and the varying density
of the crystalline renders that state more capable of delineating
such a picture, than any other imaginable contrivance could
have done. To illustrate this, I have constructed a diagram,
representing the successive images of a distant object filling the
whole extent of view, as they would be formed by the successive
refractions of the different surfaces. Taking the scale of
my own eye, I am obliged to substitute, for a series of objects
at any indefinitely great distance, a circle of 10 inches radius;
and it is most convenient to consider only those rays which pass
through the anterior vertex of the lens; since the actual centre
of each pencil must be in the ray which passes through the
centre of the pupil, and the short distance of the vertex of the
lens from this point, will always tend to correct the unequal
refraction of oblique rays. The first curve (Plate IV. <a href="#Pl.IV">Fig. 16</a>.)
is the image formed by the furthest intersection of rays refracted
at the cornea; the second, the image formed by the nearest intersection;
the distance between these, shows the degree of confusion
in the image; and the third curve, its brightest part. Such
must be the form of the image which the cornea tends to delineate
in an eye deprived of the crystalline lens; nor can any
external remedy properly correct the imperfection of lateral
<span class="pagenum" id="Page_47">47</span>vision. The next three curves show the images formed after
the refraction at the anterior surface of the lens, distinguished in
the same manner; and the three following, the result of all the
successive refractions. The tenth curve is a repetition of the
ninth, with a slight correction near the axis, at F, where, from
the breadth of the pupil, some perpendicular rays must fall. By
comparing this with the eleventh, which is the form of the retina,
it will appear that nothing more is wanting for their perfect
coincidence, than a moderate diminution of density in the lateral
parts of the lens. If the law, by which this density varies, were
more accurately ascertained, its effect on the image might be
calculated from the eighth proposition; but the operations would
be somewhat laborious: probably the image, thus corrected,
would approach very nearly to the form of the twelfth curve.</p>

<p>To find the place of the entrance of the optic nerve, I fix
two candles at ten inches distance, retire sixteen feet, and direct
my eye to a point four feet to the right or left of the middle of
the space between them: they are then lost in a confused spot
of light; but any inclination of the eye brings one or the other
of them into the field of view. In <span class="smcap">Bernoulli</span>’s eye, a greater
deviation was required for the direction of the axis;‍&#x2060;<a id="FNanchor_10_10" href="#Footnote_10_10" class="fnanchor">10</a> and the
obscured part appeared to be of greater extent. From the
experiment here related, the distance of the centre of the optic
nerve from the visual axis is found (by Prop. V.) to be 16 hundredths
of an inch; and the diameter of the most insensible part
of the retina, one-thirtieth of an inch. In order to ascertain the
distance of the optic nerve from the point opposite to the pupil,
I took the sclerotica of the human eye, divided it into segments,
from the centre of the cornea towards the optic nerve, and extended
it on a plane. I then measured the longest and shortest
<span class="pagenum" id="Page_48">48</span>distances from the cornea to the perforation made by the nerve,
and their difference was exactly one-fifth of an inch. To this
we must add a fiftieth, on account of the eccentricity of the
pupil in the uvea, which in the eye that I measured was not
great, and the distance of the centre of the nerve from the
point opposite the pupil will be 11 hundredths. Hence it appears,
that the visual axis is five hundredths, or one-twentieth of
an inch, further from the optic nerve than the point opposite the
pupil. It is possible that this distance may be different in different
eyes: in mine, the obliquity of the lens, and the eccentricity
of the pupil with respect to it, will tend to throw a direct
ray upon it, without much inclination of the whole eye; and it
is not improbable, that the eye is also turned slightly outwards,
if looking at any object before it, although the inclination is
too small to be subjected to measurement.</p>

<p>It must also be observed, that it is very difficult to ascertain
the proportions of the eye so exactly as to determine, with certainty,
the size of an image on the retina; the situation, curvature,
and constitution of the lens, make so material a difference
in the result, that there may possibly be an error of almost one-
tenth of the whole. In order, therefore, to obtain some confirmation
from experiment, I placed two candles at a small distance
from each other, turned the eye inwards, and applied the
ring of a key so as to produce a spectrum, of which the edge
coincided with the inner candle; then, fixing my eye on the outward
one, I found that the spectrum advanced over two-sevenths
of the distance between them. Hence, the same portion of the
retina that subtended an angle of seven parts at the centre of
motion of the eye, subtended an angle of five at the supposed
intersection of the principal rays; (Plate III. <a href="#Pl.III">Fig. 11</a>.) and the
<span class="pagenum" id="Page_49">49</span>distance of this intersection from the retina was 637 thousandths.
This nearly corresponds with the former calculation; nor can
the distance of the centre of the optic nerve from the point of
most perfect vision be, on any supposition, much less than that
which is here assigned. And, in the eyes of quadrupeds, the
most strongly painted part of the choroid is further from the
nerve than the real axis of the eye.</p>

<p>I have endeavoured to express in four figures, the form of
every part of my eye, as nearly as I have been able to ascertain
it; the first (Pl. V. <a href="#Pl.V">Fig. 17</a>.) is a vertical section; the second
(Fig. 18.) a horizontal section; the third and fourth are front
views, in different states of the pupil. (<a href="#Pl.V">Fig. 19 and 20</a>.)</p>

<p>Considering how little inconvenience is experienced from so
material an inequality in the refraction of the lens as I have
described, we have no reason to expect a very accurate provision
for correcting the aberration of the lateral rays. But, as far as
can be ascertained by the optometer, the aberration arising from
figure is completely corrected; since four or more images of the
same line appear to meet exactly in the same point, which they
would not do if the lateral rays were materially more refracted
than the rays near the axis. The figure of the surfaces is sometimes,
and perhaps always, more or less hyperbolical‍&#x2060;<a id="FNanchor_11_11" href="#Footnote_11_11" class="fnanchor">11</a> or elliptical:
in the interior laminæ indeed, the solid angle of the
margin is somewhat rounded off; but the weaker refractive
power of the external parts, must greatly tend to correct the
aberration arising from the too great curvature towards the
margin of the disc. Had the refractive power been uniform, it
might have collected the lateral rays of a direct pencil nearly as
well; but it would have been less adapted to oblique pencils of
<span class="pagenum" id="Page_50">50</span>rays; and the eye must also have been encumbered with a mass
of much greater density than is now required, even for the
central parts: and, if the whole lens had been smaller, it would
also have admitted too little light. It is possible too, that Mr.
<span class="smcap">Ramsden</span>’s observation,‍&#x2060;<a id="FNanchor_12_12" href="#Footnote_12_12" class="fnanchor">12</a> on the advantage of having no reflecting
surface, may be well-founded: but it has not been demonstrated,
that less light is lost in passing through a medium
of variable density, than in a sudden transition from one part of
that medium to another; nor are we yet sufficiently acquainted
with the cause of this reflection, to be enabled to reason satisfactorily
on the subject. But, neither this gradation, nor any other
provision, has the effect of rendering the eye perfectly achromatic.
Dr. <span class="smcap">Jurin</span> had remarked this, long ago,‍&#x2060;<a id="FNanchor_13_13" href="#Footnote_13_13" class="fnanchor">13</a> from observing
the colour bordering the image of an object seen indistinctly.
Dr. <span class="smcap">Wollaston</span> pointed out to me on the optometer, the red
and blue appearance of the opposite internal angles of the crossing
lines; and mentioned, at the same time, a very elegant experiment
for proving the dispersive power of the eye. He looks
through a prism at a small lucid point, which of course becomes
a linear spectrum. But the eye cannot so adapt itself as to make
the whole spectrum appear a line; for, if the focus be adapted
to collect the red rays to a point, the blue will be too much refracted,
and expand into a surface; and the reverse will happen
if the eye be adapted to the blue rays; so that, in either case, the
line will be seen as a triangular space. The observation is confirmed,
by placing a small concave speculum in different parts
of a prismatic spectrum, and ascertaining the utmost distances
at which the eye can collect the rays of different colours to a
focus. By these means I find, that the red rays, from a point at
<span class="pagenum" id="Page_51">51</span>12 inches distance, are as much refracted as white or yellow
light at 11. The difference is equal to the refraction of a lens
132 inches in focus. But the aberration of the red rays in a
lens of crown glass, of equal mean refractive power with the
eye, would be equivalent to the effect of a lens 44 inches in
focus. If, therefore, we can depend upon this calculation, the
dispersive power of the eye collectively, is one-third of the dispersive
power of crown glass, at an equal angle of deviation. 1
cannot observe much aberration in the violet rays. This may
be, in part, owing to their faintness; but yet I think their aberration
must be less than that of the red rays. I believe it was
Mr. <span class="smcap">Ramsden</span>’s opinion, that since the separation of coloured
rays is only observed where there is a sudden change of density,
such a body as the lens, of a density gradually varying, would
have no effect whatever in separating the rays of different colours.
If this hypothesis should appear to be well-founded, we must
attribute the whole dispersion to the aqueous humour; and its
dispersive power will be half that of crown glass, at the same
deviation. But we have an instance, in the atmosphere, of a
very gradual change of density; and yet Mr. <span class="smcap">Gilpin</span> informs
me, that the stars, when near the horizon, appear very evidently
coloured. At a more favourable season of the year, it would
not be difficult to ascertain, by means of the optometer, the
dispersive power of the eye, and of its different parts, with greater
accuracy than by the experiment here related. Had the dispersive
power of the whole eye been equal to that of flint glass,
the distances of perfect vision would have varied from 12 inches
to 7 for different rays, in the same state of the mean refractive
powers.</p>


<p class="mt2em ti0">VII. The faculty of accommodating the eye to various
<span class="pagenum" id="Page_52">52</span>distances, appears to exist in very different degrees in different
individuals. The shortest distance of perfect vision in my eye,
is 26 tenths of an inch for horizontal, and 29 for vertical rays.
This power is equivalent to the addition of a lens of 4 inches
focus. Dr. <span class="smcap">Wollaston</span> can see at 7 inches, and with converging
rays; the difference answering to 6 inches focal length. Mr.
<span class="smcap">Abernethy</span> has perfect vision from 3 inches to 30, or a power
equal to that of a lens 3-1/3 inches in focus. A young lady of my
acquaintance can see at 2 inches and at 4; the difference being
equivalent to 4 inches focus. A middle aged lady at 3 and at 4;
the power of accommodation being only equal to the effect of a
lens of 12 inches focus. In general, I have reason to think, that
the faculty diminishes in some degree, as persons advance in life;
but some also of a middle age appear to possess it in a very small
degree. I shall take the range of my own eye, as being probably
about the medium, and inquire what changes will be necessary
in order to produce it; whether we suppose the radius of the
cornea to be diminished, or the distance of the lens from the
retina to be increased, or these two causes to act conjointly, or
the figure of the lens itself to undergo an alteration.</p>

<p>1. We have calculated, that when the eye is in a state of
relaxation, the refraction of the cornea is such as to collect
rays diverging from a point ten inches distant, to a focus at
the distance of 13-2/3 tenths. In order that it may bring to the
same focus, rays diverging from a point distant 29 tenths, we
find (by Cor. 5, Prop. IV.) that its radius must be diminished
from 31 to 25 hundredths, or very nearly in the ratio of five
to four.</p>

<p>2. Supposing the change from perfect vision at ten inches to
29 tenths, to be effected by a removal of the retina to a greater
<span class="pagenum" id="Page_53">53</span>distance from the lens, this will require, (by the same Corollary,)
an elongation of 135 thousandths, or more than one-seventh
of the diameter of the eye. In Mr. <span class="smcap">Abernethy</span>’s eye, an
elongation of 17 hundredths, or more than one-sixth, is requisite.</p>

<p>3. If the radius of the cornea be diminished one-sixteenth,
or to 29 hundredths, the eye must at the same time be elongated
97 thousandths, or about one-ninth of its diameter.</p>

<p>4. Supposing the crystalline lens to change its form; if it
became a sphere, its diameter would be 28 hundredths, and, its
anterior surface retaining its situation, the eye would have perfect
vision at the distance of an inch and a half. (Cor. 5 and
8, Prop. IV.) This is more than double the actual change.
But it is impossible to determine precisely how great an alteration
of form is necessary, without ascertaining the nature of the
curves into which its surfaces may be changed. If it were
always a spheroid more or less oblate, the focal length of each
surface would vary inversely as the square of the axis: but, if
the surfaces became, from spherical, portions of hyperbolic
conoids, or of oblong spheroids, or changed from more obtuse
to more acute figures of this kind, the focal length would vary
more rapidly. Disregarding the elongation of the axis, and
supposing the curvature of each surface to be changed proportionally,
the radius of the anterior must become about 24, and
that of the posterior 17 hundredths.</p>


<p class="mt2em ti0">VIII. I shall now proceed to inquire, which of these changes
takes place in nature; and I shall begin with a relation of experiments
made in order to ascertain the curvature of the cornea
in all circumstances.</p>

<p>The method described in Mr. <span class="smcap">Home</span>’s Croonian Lecture for
<span class="pagenum" id="Page_54">54</span>1795,‍&#x2060;<a id="FNanchor_14_14" href="#Footnote_14_14" class="fnanchor">14</a> appears to be far preferable to the apparatus of the
preceding year:‍&#x2060;<a id="FNanchor_15_15" href="#Footnote_15_15" class="fnanchor">15</a> for a difference in the distance of two images
seen in the cornea, would be far greater, and more conspicuous,
than a change of its prominency, and far less liable to be
disturbed by accidental causes. It is nearly, and perhaps
totally impossible to change the focus of the eye, without some
motion of its axis. The eyes sympathize perfectly with each
other; and the change of focus is almost inseparable from a
change of the relative situation of the optic axes; so much, that
if I direct both my eyes at an object beyond their furthest focus,
I cannot avoid bringing that focus a little nearer: while one
axis moves, it is not easy to keep the other perfectly at rest;
and it is not impossible, that a change in the proportions of some
eyes, may render a slight alteration of the position of the axis
absolutely necessary. These considerations may partly explain
the trifling difference in the place of the cornea that was observed
in 1794. It appears that the experiments of 1795 were
made with considerable accuracy, and no doubt with excellent
instruments; and their failing to ascertain the existence of any
change, induced Mr. <span class="smcap">Home</span> and Mr. <span class="smcap">Ramsden</span> to abandon,
in great measure, the opinion which suggested them, and to
suppose, that a change of the cornea produces only one-third of
the effect. Dr. <span class="smcap">Olbers</span> of Bremen, who in the year 1780
published a most elaborate dissertation on the internal changes
of the eye,‍&#x2060;<a id="FNanchor_16_16" href="#Footnote_16_16" class="fnanchor">16</a> which he lately presented to the Royal Society,
had been equally unsuccessful in his attempts to measure this
change of the cornea, at the same time that his opinion was in
favour of its existence.</p>

<p><span class="pagenum" id="Page_55">55</span></p>

<p>Room was however still left for a repetition of the experiments;
and I began with an apparatus nearly resembling that
which Mr. <span class="smcap">Home</span> has described. I had an excellent achromatic
microscope, made by Mr. <span class="smcap">Ramsden</span> for my friend Mr. <span class="smcap">John
Ellis</span>, of five inches focal length, magnifying about 20 times.
To this I adapted a cancellated micrometer, in the focus of the
eye not employed in looking through the microscope: it was
a large card, divided by horizontal and vertical lines into
fortieths of an inch. When the image in the microscope was compared
with this scale, care was taken to place the head so that
the relative motion of the images on the micrometer, caused by
the unsteadiness of the optic axis, should always be in the direction
of the horizontal lines, and that there could be no error,
from this motion, in the dimensions of the image taken vertically.
I placed two candles so as to exhibit images in a vertical
position in the eye of Mr. <span class="smcap">König</span>, who had the goodness to
assist me; and, having brought them into the field of the microscope,
where they occupied 35 of the small divisions, I
desired him to fix his eye on objects at different distances in the
same direction: but I could not perceive the least variation in the
distance of the images.</p>

<p>Finding a considerable difficulty in a proper adjustment of
the microscope, and being able to depend on my naked eye in
measuring distances, without an error of one 500th of an inch, I
determined to make a similar experiment without any magnifying
power. I constructed a divided eye-glass of two portions of
a lens, so small, that they passed between two images reflected
from my own eye; and, looking in a glass, I brought the apparent
places of the images to coincide, and then made the
change requisite for viewing nearer objects: but the images still
<span class="pagenum" id="Page_56">56</span>coincided. Neither could I observe any change in the images
reflected from the other eye, where they could be viewed with
greater convenience, as they did not interfere with the eye-
glass. But, not being at that time aware of the perfect sympathy
of the eyes, I thought it most certain to confine my observation
to the one with which I saw. I must remark that, by a
little habit, I have acquired a very ready command over the
accommodation of my eye, so as to be able to view an object
with attention, without adjusting my eye to its distance.</p>

<p>I also stretched two threads, a little inclined to each other,
across a ring, and divided them by spots of ink into equal
spaces. I then fixed the ring, applied my eye close behind it,
and placed two candles in proper situations before me, and a
third on one side, to illuminate the threads. Then, setting a
small looking-glass, first at four inches distance, and next at
two, I looked at the images reflected in it, and observed at
what part of the threads they exactly reached across in each
case; and with the same result as before.</p>

<p>I next fixed the cancellated micrometer at a proper distance,
illuminated it strongly, and viewed it through a pin-hole, by
which means it became distinct in every state of the eye; and,
looking with the other eye into a small glass, I compared the
image with the micrometer, in the manner already described.
I then changed the focal distance of the eye, so that the lucid
points appeared to spread into surfaces, from being too remote
for perfect vision; and I noted on the scale, the distance of their
centres; but that distance was invariable.</p>

<p>Lastly, I drew a diagonal scale, with a diamond, on a looking-
glass, (Plate III. <a href="#Pl.III">Fig. 12</a>.) and brought the images into contact
with the lines of the scale. Then, since the image of the
<span class="pagenum" id="Page_57">57</span>eye occupies on the surface of a glass half its real dimensions,
at whatever distance it is viewed, its true size is always double
the measure thus obtained. I illuminated the glass strongly,
and made a perforation in a narrow slip of black card, which I
held between the images; and was thus enabled to compare
them with the scale, although their apparent distance was double
that of the scale. I viewed them in all states of the eye;
but I could perceive no variation in the interval between them.</p>

<p>The sufficiency of these methods may be thus demonstrated.
Make a pressure along the edge of the upper eyelid with any small
cylinder, for instance a pencil, and the optometer will show that
the focus of horizontal rays is a little elongated, while that of
vertical rays is shortened; an effect which can only be owing to a
change of curvature in the cornea. Not only the apparatus here
described, but even the eye unassisted, will be capable of discovering
a considerable change in the images reflected from the cornea,
although the change be much smaller than that which is requisite
for the accommodation of the eye to different distances.
On the whole, I cannot hesitate to conclude, that if the radius
of the cornea were diminished but one-twentieth, the change
would be very readily perceptible by some of the experiments
related; and the whole alteration of the eye requires one-fifth.</p>

<p>But a much more accurate and decisive experiment remains. I
take out of a small botanical microscope, a double convex lens, of
eight-tenths radius and focal distance, fixed in a socket one-fifth
of an inch in depth; securing its edges with wax, I drop into it a
little water, nearly cold, till it is three-fourths full, and then apply
it to my eye, so that the cornea enters halfway into the socket,
and is every where in contact with the water. (Plate III. <a href="#Pl.III">Fig. 13</a>.)
My eye immediately becomes presbyopic, and the refractive
<span class="pagenum" id="Page_58">58</span>power of the lens, which is reduced by the water to a focal
length of about 16 tenths, (Cor. 5. Prop. IV.) is not sufficient
to supply the place of the cornea, rendered inefficacious by the
intervention of the water; but the addition of another lens, of
five inches and a half focus, restores my eye to its natural state,
and somewhat more. I then apply the optometer, and I find
the same inequality in the horizontal and vertical refractions as
without the water; and I have, in both directions, a power of
accommodation equivalent to a focal length of four inches, as
before. At first sight indeed, the accommodation appears to
be somewhat less, and only able to bring the eye from the state
fitted for parallel rays to a focus at five inches distance; and
this made me once imagine, that the cornea might have some
slight effect in the natural state; but, considering that the artificial
cornea was about a tenth of an inch before the place of
the natural cornea, I calculated the effect of this difference, and
found it exactly sufficient to account for the diminution of the
range of vision. I cannot ascertain the distance of the glass
lens from the cornea to the hundredth of an inch; but the error
cannot be much greater, and it may be on either side.</p>

<p>After this, it is almost necessary to apologize for having
stated the former experiments; but, in so delicate a subject, we
cannot have too great a variety of concurring evidence.</p>


<p class="mt2em ti0">IX. Having satisfied myself that the cornea is not concerned
in the accommodation of the eye, my next object was to inquire
if any alteration in the length of its axis could be discovered;
for this appeared to be the only possible alternative: and, considering
that such a change must amount to one-seventh of the
diameter of the eye, I flattered myself with the expectation of
submitting it to measurement. Now, if the axis of the eye
<span class="pagenum" id="Page_59">59</span>were elongated one-seventh, its transverse diameter must be
diminished one-fourteenth, and the semi-diameter would be
shortened a thirtieth of an inch.</p>

<p>I therefore placed two candles so that when the eye was
turned inwards, and directed towards its own image in a glass,
the light reflected from one of the candles by the sclerotica
appeared upon its external margin, so as to define it distinctly
by a bright line; and the image of the other candle was seen in
the centre of the cornea. I then applied the double eye-glass,
and the scale of the looking-glass, in the manner already described;
but neither of them indicated any diminution of the
distance, when the focal length of the eye was changed.</p>

<p>Another test, and a much more delicate one, was the application
of the ring of a key at the external angle, when the eye
was turned as much inwards as possible, and confined at the
same time by a strong oval iron ring, pressed against it at the
internal angle. The key was forced in as far as the sensibility
of the integuments would admit, and was wedged, by a moderate
pressure, between the eye and the bone. In this situation,
the phantom caused by the pressure extended within the field
of perfect vision, and was very accurately defined; nor did it,
as I formerly imagined, by any means prevent a distinct perception
of the objects actually seen in that direction; and a straight
line coming within the field of this oval phantom, appeared
somewhat inflected towards its centre; (Plate III. <a href="#Pl.III">Fig. 14</a>.)
a distortion easily understood by considering the effect of the
pressure on the form of the retina. Supposing now, the distance
between the key and the iron ring to have been, as it
really was, invariable, the elongation of the eye must have been
either totally or very nearly prevented; and, instead of an
<span class="pagenum" id="Page_60">60</span>increase of the length of the eye’s axis, the oval spot caused
by the pressure would have spread over a space at least ten
times as large as the most sensible part of the retina. But no
such circumstance took place: the power of accommodation
was as extensive as ever; and there was no perceptible change,
either in the size or in the figure of the oval spot.</p>

<p>Again, since the rays which pass through the centre of the
pupil, or rather the anterior vertex of the lens, may, as already
observed, be considered as delineating the image; and, since
the divergence of these rays with respect to each other, is but
little affected by the refraction of the lens, they may still be
said to diverge from the centre of the pupil; and the image of
a given object on the retina must be very considerably enlarged,
by the removal of the retina to a greater distance from
the pupil and lens. (Cor. Prop. V‍&#x2060;<a id="FNanchor_17_17" href="#Footnote_17_17" class="fnanchor">17</a>&#x2060;.) To ascertain the real
magnitude of the image with accuracy, is not so easy as it at
first sight appears; but, besides the experiment last related,
which might be employed as an argument to this purpose, there
are two other methods of estimating it. The first is too hazardous
to be of much use; but, with proper precautions, it may be
attempted. I fix my eye on a brass circle placed in the rays of
the sun, and, after some time, remove it to the cancellated micrometer;
then, changing the focus of my eye, while the micrometer
remains at a given distance, I endeavour to discover
whether there is any difference in the apparent magnitude of the
spectrum on the scale; but I can discern none. I have not insisted
on the attempt; especially as I have not been able to make the
<span class="pagenum" id="Page_61">61</span>spectrum distinct enough without inconvenience; and no light
is sufficiently strong to cause a permanent impression on any
part of the retina remote from the visual axis. I therefore had
recourse to another experiment, I placed two candles so as
exactly to answer to the extent of the termination of the optic
nerve, and, marking accurately the point to which my eye was
directed, I made the utmost change in its focal length; expecting
that, if there were any elongation of the axis, the external
candle would appear to recede outwards upon the visible space.
(Plate III. <a href="#Pl.III">Fig. 15</a>.) But this did not happen; the apparent place
of the obscure part was precisely the same as before. I will
not undertake to say, that I could have observed a very minute
difference either way: but I am persuaded, that I should have
discovered an alteration of less than a tenth part of the whole.</p>

<p>It may be inquired if no change in the magnitude of the
image is to be expected on any other supposition; and it will
appear to be possible, that the changes of curvature may be so
adapted, that the magnitude of the confused image may remain
perfectly constant. Indeed, to calculate from the dimensions
which we have hitherto used, it would be expected that the
image should be diminished about one-sixtieth, by the utmost
increase of the convexity of the lens. But the whole depends
on the situation of the refracting surfaces, and the respective
increase of their curvature, which, on account of the variable
density of the lens, can scarcely be estimated with sufficient
accuracy. Had the pupil been placed before the cornea, the
magnitude of the image must, on any supposition, have been
very variable: at present, this inconvenience is avoided by the
situation of the pupil; so that we have here an additional
instance of the perfection of this admirable organ.</p>

<p><span class="pagenum" id="Page_62">62</span></p>

<p>From the experiments related, it appears to be highly improbable
that any material change in the length of the axis
actually takes place; and it is almost impossible to conceive by
what power such a change could be effected. The straight
muscles, with the adipose substance lying under them, would
certainly, when acting independently of the socket, tend to
flatten the eye: for, since their contraction would necessarily
lessen the circumference or superficies of the mass that they
contain, and round off all its prominences, their attachment
about the nerve and the anterior part of the eye must therefore
be brought nearer together. (Plate V. <a href="#Pl.V">Fig. 21, 22</a>.) Dr.
<span class="smcap">Olbers</span> compares the muscles and the eye to a cone, of which
the sides are protruded, and would by contraction be brought
into a straight line. But this would require a force to preserve
the cornea as a fixed point, at a given distance from the origin
of the muscles; a force which certainly does not exist. In the
natural situation of the visual axis, the orbit being conical, the
eye might be somewhat lengthened, although irregularly, by
being forced further into it; but, when turned towards either
side, the same action would rather shorten its axis; nor is there
any thing about the human eye that could supply its place.
In quadrupeds, the oblique muscles are wider than in man;
and in many situations might assist in the effect. Indeed a
portion of the orbicular muscle of the globe is attached so near
to the nerve, that it might also co-operate in the action: and I
have no reason to doubt the accuracy of Dr. <span class="smcap">Olbers</span>, who
states, that he effected a considerable elongation, by tying threads
to the muscles, in the eyes of hogs and of calves; yet he does
not say in what position the axis was fixed; and the flaccidity
of the eye after death might render such a change very easy as
<span class="pagenum" id="Page_63">63</span>would be impossible in a living eye. Dr. <span class="smcap">Olbers</span> also mentions
an observation of Professor <span class="smcap">Wrisberg</span>, on the eye of a man
whom he believed to be destitute of the power of accommodation
in his life-time, and whom he found, after death, to have
wanted one or more of the muscles: but this want of accommodation
was not at all accurately ascertained. I measured, in
the human eye, the distance of the attachment of the inferior
oblique muscle from the insertion of the nerve: it was one-fifth
of an inch; and from the centre of vision not a tenth of an
inch; so that, although the oblique muscles do in some positions
nearly form a part of a great circle round the eye, their action
would be more fitted to flatten than to elongate it. We have
therefore reason to agree with <span class="smcap">Winslow</span>, in attributing to them
the office of helping to support the eye on that side where the
bones are most deficient: they seem also well calculated to
prevent its being drawn too much backwards by the action of
the straight muscles. And, even if there were no difficulty in
supposing the muscles to elongate the eye in every position, yet
at least some small difference would be expected in the extent
of the change, when the eye is in different situations, at an
interval of more than a right angle from each other; but the
optometer shews that there is none.</p>

<p>Dr. <span class="smcap">Hosack</span> alleges that he was able, by making a pressure
on the eye, to accommodate it to a nearer object:‍&#x2060;<a id="FNanchor_18_18" href="#Footnote_18_18" class="fnanchor">18</a> it does not
appear that he made use of very accurate means of ascertaining
the fact; but, if such an effect took place, the cause must have
been an inflection of the cornea.</p>

<p>It is unnecessary to dwell on the opinion which supposes a
joint operation, of changes in the curvature of the cornea and
<span class="pagenum" id="Page_64">64</span>in the length of the axis. This opinion had derived very great
respectability, from the most ingenious and elegant manner in
which Dr. <span class="smcap">Olbers</span> had treated it, and from being the last result
of the investigation of Mr. <span class="smcap">Home</span> and Mr. <span class="smcap">Ramsden</span>. But
either of the series of experiments which have been related,
appears to be sufficient to confute it.</p>


<p class="mt2em ti0">X. It now remains to inquire into the pretensions of the
crystalline lens to the power of altering the focal length of the
eye. The grand objection to the efficacy of a change of figure
in the lens, was derived from the experiments in which those
who have been deprived of it have appeared to possess the
faculty of accommodation.</p>

<p>My friend Mr. <span class="smcap">Ware</span>, convinced as he was of the neatness
and accuracy of the experiments related in the Croonian Lecture
for 1795, yet could not still help imagining, from the obvious
advantage all his patients found, after the extraction
of the lens, in using two kinds of spectacles, that there must,
in such cases, be a deficiency in that faculty. This circumstance,
combined with a consideration of the directions very judiciously
given by Dr. <span class="smcap">Porterfield</span>, for ascertaining the point in question,
first made me wish to repeat the experiments upon various
individuals, and with the instrument which I have above described
as an improvement of Dr. <span class="smcap">Porterfield</span>’s optometer:
and I must here acknowledge my great obligation to Mr.
<span class="smcap">Ware</span>, for the readiness and liberality with which he introduced
me to such of his numerous patients as he thought most
likely to furnish a satisfactory determination. 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
<span class="pagenum" id="Page_65">65</span>actual focal distance is totally unchangeable. This will appear
from a selection of the most decisive observations.</p>

<p>1. Mr. R. can read at four inches and at six only, with the
same glass. He saw the double lines meeting at three inches,
and always at the same point; but the cornea was somewhat
irregularly prominent, and his vision not very distinct; nor had
I, at the time I saw him, a convenient apparatus.</p>

<p>I afterwards provided a small optometer, with a lens of less
than two inches focus, adding a series of letters, not in alphabetical
order, and projected into such a form as to be most legible
at a small inclination. The excess of the magnifying power
had the advantage of making the lines more divergent, and
their crossing more conspicuous; and the letters served for
more readily naming the distance of the intersection, and, at
the same time, for judging of the extent of the power of distinguishing
objects too near or too remote for perfect vision.
(Plate V. <a href="#Pl.V">Fig. 23</a>.)</p>

<p>2. Mr. J. had not an eye very proper for the experiment;
but he appeared to distinguish the letters at \(2\frac{1}{2}\) inches, and
at less than an inch. This at first persuaded me, that he
must have a power of changing the focal distance: but I afterwards
recollected that he had withdrawn his eye considerably,
to look at the nearer letters, and had also partly closed his
eyelids, no doubt contracting at the same time the aperture of
the pupil; an action which, even in a perfect eye, always accompanies
the change of focus. The slider was not applied.</p>

<p>3. Miss H. a young lady of about twenty, had a very narrow
pupil, and I had not an opportunity of trying the small optometer:
but, when she once saw an object double through the
slits, no exertion could make it appear single at the same distance.
<span class="pagenum" id="Page_66">66</span>She used for distant objects a glass of \(4\frac{1}{2}\) inches focus;
with this she could read as far off as 12 inches, and as near as
five: for nearer objects she added another of equal focus, and
could then read at 7 inches, and at \(2\frac{1}{2}\).</p>

<p>4. <span class="smcap">Hanson</span>, a carpenter, aged 63, had a cataract extracted
a few years since from one eye: the pupil was clear and large,
and he saw well to work with a lens of \(2\frac{3}{8}\) inches focus; and
could read at 8 and at 15 inches, but most conveniently at 11.
With the same glass, the lines of the optometer appeared always
to meet at 11 inches; but he could not perceive that they
crossed, the line being too strong, and the intersection too distant.
The experiment was afterwards repeated with the small
optometer: he read the letters from 2 to 3 inches; but the
intersection was always at \(2\frac{1}{2}\) inches. He now fully understood
the circumstances that were to be noticed, and saw the crossing
with perfect distinctness: at one time, he said it was a tenth of
an inch nearer; but I observed that he had removed his eye
two or three tenths from the glass, a circumstance which
accounted for this small difference.</p>

<p>5. Notwithstanding <span class="smcap">Hanson</span>’s age, I consider him as a very
fair subject for the experiment. But a still more unexceptionable
eye was that of Mrs. <span class="smcap">Maberly</span>. She is about 30, and had
the crystalline of both eyes extracted a few years since, but
sees best with her right. She walks without glasses; and, with
the assistance of a lens of about four inches focus, can read
and work with ease. She could distinguish the letters of the
small optometer from an inch to \(2\frac{1}{2}\) inches; but the intersection
was invariably at the same point, about 19 tenths of an inch
distant. A portion of the capsule is stretched across the pupil,
and causes her to see remote objects double, when without her
<span class="pagenum" id="Page_67">67</span>glasses; nor can she, by any exertion, bring the two images
nearer together, although the exertion makes them more distinct,
no doubt by contracting the pupil. The experiment with
the optometer was conducted, in the presence of Mr. <span class="smcap">Ware</span>,
with patience and perseverance; nor was any opinion given to
make her report partial.</p>

<p>Considering the difficulty of finding an eye perfectly suitable
for the experiments, these proofs may be deemed tolerably
satisfactory. But, since one positive argument will counterbalance
many negative ones, provided it be equally grounded
on fact, it becomes necessary to inquire into the competency of
the evidence employed to ascertain the power of accommodation
attributed, in the Croonian Lecture for 1794, to the eye of
<span class="smcap">Benjamin Clerk</span>. And it appears, that the distinction long
since very properly made by Dr. <span class="smcap">Jurin</span>, between distinct vision
and perfect vision, will readily explain away the whole of that
evidence.</p>

<p>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 unchanged. And it is
remarkable, that in those experiments, when the comparison
with the perfect eye was made, the aperture of the imperfect
eye only was very considerably reduced. <span class="smcap">Benjamin Clerk</span>,
with an aperture of \(\frac{3}{40}\) of an inch, could read with the same
glass at \(1\frac{7}{8}\) inch, and at 7 inches.‍&#x2060;<a id="FNanchor_19_19" href="#Footnote_19_19" class="fnanchor">19</a> With an equal aperture, I
can read at \(1\frac{1}{2}\) inch and at 30 inches: and I can retain the state
of perfect relaxation, and read with the same aperture at \(2\frac{1}{4}\)
inches; and this is as great a difference as was observed in
<span class="pagenum" id="Page_68">68</span><span class="smcap">Benjamin Clerk</span>’s eye. It is also a fact of no small importance,
that Sir <span class="smcap">Henry Englefield</span> was much astonished, as
well as the other observers, at the accuracy with which the
man’s eye was adjusted to the same distance, in the repeated
trials that were made with it.‍&#x2060;<a id="FNanchor_20_20" href="#Footnote_20_20" class="fnanchor">20</a> This circumstance alone makes
it highly probable, that its perfect vision was confined within
very narrow limits.</p>

<p>Hitherto I have endeavoured to shew the inconveniences
attending other suppositions, and to remove the objections to
the opinion of an internal change of the figure of the lens.
I shall now state two experiments, which, in the first place, come
very near to a mathematical demonstration of the existence of
such a change, and, in the second, explain in great measure its
origin, and the manner in which it is effected.</p>

<p>I have already described the appearances of the imperfect
image of a minute point at different distances from the eye, in
a state of relaxation. For the present purpose, I will only
repeat, that if the point is beyond the furthest focal distance of
the eye, it assumes that appearance which is generally described
by the name of a star, the central part being considerably the
brightest. (Plate VI. F<a href="#Pl.VI">ig. 36—39</a>.) But, when the focal distance
of the eye is shortened, the imperfect image is of course
enlarged; and, besides this necessary consequence, the light is
also very differently distributed; the central part becomes faint,
and the margin strongly illuminated, so as to have almost
the appearance of an oval ring. (<a href="#Pl.VI">Fig. 41</a>.) If I apply the
slider of the optometer, the shadows of the slits, while the eye
is relaxed, are perfectly straight, dividing the oval either way
into parallel segments: (<a href="#Pl.VI">Fig. 42, 44</a>.) but, when the accommodation<span class="pagenum" id="Page_69">69</span>
takes place, they immediately become curved, and the
more so the further they are from the centre of the image, to
which their concavity is directed. (<a href="#Pl.VI">Fig. 43, 45</a>.) If the point
be brought much within the focal distance, the change of the
eye will increase the illumination of the centre, at the expense
of the margin. The same appearances are equally observable,
when the effect of the cornea is removed by immersion in water;
and the only imaginable way of accounting for the diversity, is
to suppose the central parts of the lens to acquire a greater
degree of curvature than the marginal parts. If the refraction
of the lens remained the same, it is absolutely impossible that
any change of the distance of the retina should produce a curvature
in those shadows, which, in the relaxed state of the eye,
are found to be in all parts straight; and, that neither the form
nor the relative situation of the cornea is concerned, appears
from the application of water already mentioned.</p>

<p>The truth of this explanation is fully confirmed by the optometer.
When I look through four narrow slits, without exertion,
the lines always appear to meet in one point: but, when I
make the intersection approach me, the two outer lines meet
considerably beyond the inner ones, and the two lines of the
same side cross each other at a still greater distance. (Plate V.
<a href="#Pl.V">Fig. 24</a>.)</p>

<p>The experiment will not succeed with every eye; nor can it
be expected that such an imperfection should be universal: but
one case is sufficient to establish the argument, even if no other
were found. I do not however doubt, that in those who have a
large pupil, the aberration may be very frequently observable.
In Dr. <span class="smcap">Wollaston</span>’s eye, the diversity of appearance is imperceptible;
but Mr. <span class="smcap">König</span> described the intersections exactly as
<span class="pagenum" id="Page_70">70</span>they appear to me, although he had received no hint of what I
had observed. The lateral refraction is the most easily ascertained,
by substituting for the slits a tapering piece of card, so
as to cover all the central parts of the pupil, and thus determining
the nearest crossing of the shadows transmitted through
the marginal parts only. When the furthest intersection was at
38, I could bring it to 22 parts with two narrow slits; but with
the tapered card only to 29. From these data we may determine
pretty nearly, into what form the lens must be changed,
supposing both the surfaces to undergo proportional alterations
of curvature, and taking for granted the dimensions already
laid down: for, from the lateral aberration thus given, we may
find (by Prop. III.) the subtangents at about one-tenth of an
inch from the axis; and the radius of curvature at each vertex,
is already determined to be about 21 and 15 hundredths of an
inch. Hence the anterior surface must be a portion of a hyperboloid,
of which the greater axis is about 50; and the posterior
surface will be nearly parabolical. In this manner the change
will be effected, without any diminution of the transverse diameter
of the lens. The elongation of its axis will not exceed
the fiftieth of an inch; and, on the supposition with which we
set out, the protrusion will be chiefly at the posterior vertex.
The form of the lens thus changed will be nearly that of Plate V.
<a href="#Pl.V">Fig. 26</a>; the relaxed state being nearly as represented in Fig. 25.
Should, however, the rigidity of the internal parts, or any other
considerations, render it convenient to suppose the anterior surface
more changed, it would still have room, without interfering
with the uvea; or it might even force the uvea a little forwards,
without any visible alteration of the external appearance of
the eye.</p>

<p><span class="pagenum" id="Page_71">71</span></p>

<p>From this investigation of the change of the figure of the
lens, it appears that the action which I formerly attributed to
the external coats, cannot afford an explanation of the phenomenon.
The necessary effect of such an action would be, to
produce a figure approaching to that of an oblate spheroid;
and, to say nothing of the inconvenience attending a diminution
of the diameter of the lens, the lateral refraction would
be much more increased than the central; nor would the
slight change of density, at an equal distance from the axis,
be at all equivalent to the increase of curvature: we must
therefore suppose some different mode of action in the power
producing the change. Now, whether we call the lens a
muscle or not, it seems demonstrable, that such a change of
figure takes place as can be produced by no external cause;
and we may at least illustrate it by a comparison with the
usual action of muscular fibres. A muscle never contracts,
without at the same time swelling laterally, and it is of no
consequence which of the effects we consider as primary. I
was induced, by an occasional opacity, to give the name of
membranous tendons to the radiations from the centre of the
lens; but, on a more accurate examination, nothing really analogous
to tendon can be discovered. And, if it were supposed
that the parts next the axis were throughout of a tendinous, and
therefore unchangeable nature, the contraction must be principally
effected by the lateral parts of the fibres; so that the coats
would become thicker towards the margin, by their contraction,
while the general alteration of form would require them to be
thinner; and there would be a contrariety in the actions of the
various parts. But, if we compare the central parts of each
surface to the belly of the muscle, there is no difficulty in
<span class="pagenum" id="Page_72">72</span>conceiving their thickness to be immediately increased, and to
produce an immediate elongation of the axis, and an increase
of the central curvature; while the lateral parts co-operate
more or less, according to their distance from the centre, and
in different individuals in somewhat different proportions. On
this supposition, we have no longer any difficulty in attributing
a power of change to the crystalline of fishes. M. <span class="smcap">Petit</span>, in a
great number of observations, uniformly found the lens of
fishes more or less flattened: but, even if it were not, a slight
extension of the lateral part of the superficial fibres would allow
those softer coats to become thicker at each vertex, and to form
the whole lens into a spheroid somewhat oblong; and here, the
lens being the only agent in refraction, a less alteration than in
other animals would be sufficient. It is also worthy of inquiry,
whether the state of contraction may not immediately add to
the refractive power. According to the old experiment, by
which Dr. <span class="smcap">Goddard</span> attempted to show that muscles become
more dense as they contract, such an effect might naturally
be expected. That experiment is, however, very indecisive, and
the opinion is indeed generally exploded, but perhaps too hastily;
and whoever shall ascertain the existence or non-existence
of such a condensation, will render essential service to physiology
in general.</p>

<p>Dr. <span class="smcap">Pemberton</span>, in the year 1719, first systematically discussed
the opinion of the muscularity of the crystalline lens.‍&#x2060;<a id="FNanchor_21_21" href="#Footnote_21_21" class="fnanchor">21</a>
He referred to <span class="smcap">Leeuwenhoek</span>’s microscopical observations;
but he so overwhelmed his subject with intricate calculations,
that few have attempted to develope it: and he grounded the
<span class="pagenum" id="Page_73">73</span>whole on an experiment borrowed from <span class="smcap">Barrow</span>, which with
me has totally failed; and I cannot but agree with Dr. <span class="smcap">Olbers</span>
in the remark, that it is easier to confute him than to understand
him. He argued for a partial change of the figure of the lens;
and perhaps the opinion was more just than the reasons adduced
for its support. <span class="smcap">Lobe′</span>, or rather <span class="smcap">Albinus</span>,‍&#x2060;<a id="FNanchor_22_22" href="#Footnote_22_22" class="fnanchor">22</a> decidedly favours
a similar theory; and suggests the analogy of the lens to the
muscular parts of pellucid animals, in which even the best
microscopes can discover no fibres. <span class="smcap">Camper</span> also mentions
the hypothesis with considerable approbation.‍&#x2060;<a id="FNanchor_23_23" href="#Footnote_23_23" class="fnanchor">23</a> Professor <span class="smcap">Reil</span>
published, in 1793, a Dissertation on the Structure of the Lens;
and, in a subsequent paper, annexed to the translation of my
former Essay in Professor <span class="smcap">Gren</span>’s Journal,‍&#x2060;<a id="FNanchor_24_24" href="#Footnote_24_24" class="fnanchor">24</a> he discussed the
question of its muscularity. I regret that I have not now an
opportunity of referring to this publication; but I do not recollect
that Professor <span class="smcap">Reil</span>’s objections are different from those
which I have already noticed.</p>

<p>Considering the sympathy of the crystalline lens with the
uvea, and the delicate nature of the change of its figure, there
is little reason to expect that any artificial stimulus would be
more successful in exciting a contractive action in the lens, than
it has hitherto been in the uvea; much less would that contraction
be visible without art. Soon after Mr. <span class="smcap">Hunter</span>’s death, I
pursued the experiment which he had suggested, for ascertaining
how far such a contraction might be observable. My apparatus
(Plate V. <a href="#Pl.V">Fig. 27</a>.) was executed by Mr. <span class="smcap">Jones</span>. It
consisted of a wooden vessel blacked within, which was to be
<span class="pagenum" id="Page_74">74</span>filled with cool, and then with warmer water: a plane speculum
was placed under it; a perforation in the bottom was filled with
a plate of glass; proper rings were fixed for the reception of
the lens, or of the whole eye, and also wires for transmitting
electricity: above these, a piece of ground and painted glass,
for receiving the image, was supported by a bracket, which
moved by a pivot, in connection with a scale divided into fiftieths
of an inch. With this apparatus I made some experiments,
assisted by Mr. <span class="smcap">Wilkinson</span>, whose residence was near
a slaughter-house: but we could obtain, by this method, no
satisfactory evidence of the change; nor was our expectation
much disappointed. I understand also, that another member
of this Society was equally unsuccessful, in attempting to produce
a conspicuous change in the lens by electricity.</p>


<p class="mt2em ti0">XI. In man and in the most common quadrupeds, the structure
of the lens is nearly similar. The number of radiations is of
little consequence; but I find that in the human crystalline there
are ten on each side, (Plate VI. <a href="#Pl.VI">Fig. 46</a>.) not three, as I once,
from a hasty observation, concluded.‍&#x2060;<a id="FNanchor_25_25" href="#Footnote_25_25" class="fnanchor">25</a> Those who find any
difficulty in discovering the fibres, must have a sight very ill
adapted to microscopical researches, I have laboured with the
most obstinate perseverance to trace nerves into the lens, and
I have sometimes imagined that I had succeeded; but I cannot
positively go further than to state my full conviction of their
existence, and of the precipitancy of those who have absolutely
denied it. The long nerves, which are very conspicuous between
the choroid and sclerotic coats, divide each into two,
three, or more branches, at the spot where the ciliary zone
begins, and seem indeed to furnish the choroid with some fine
<span class="pagenum" id="Page_75">75</span>filaments at the same place. The branches often re-unite, with
a slight protuberance, that scarcely deserves the name of a
ganglion: here they are tied down, and mixed with the hard
whitish-brown membrane that covers the compact spongy substance,
in which the vessels of the ciliary processes anastomose
and subdivide. (Plate VI. <a href="#Pl.VI">Fig. 47</a>.) The quantity of the
nerves which proceeds to the iris, appears to be considerably
smaller than that which arrives at the place of division: hence
there can be little doubt that the division is calculated to supply
the lens with some minute branches; and it is not improbable,
from the appearance of the parts, that some fibres may pass to
the cornea; although it might more naturally be expected, that
the tunica conjunctiva would be supplied from without. But
the subdivisions which probably pass to the lens, enter immediately
into a mixture of ligamentous substance and of a tough
brownish membrane; and I have not hitherto been able to
develope them. Perhaps animals may be found in which this
substance is of a different nature; and I do not despair that,
with the assistance of injections, for more readily distinguishing
the blood vessels, it may still be possible to trace them in
quadrupeds. Our inability to discover them, is scarcely an
argument against their existence: they must naturally be delicate
and transparent; and we have an instance, in the cornea,
of considerable sensibility, where no nerve has yet been traced.
The capsule adheres to the ciliary substance, and the lens to
the capsule, principally in two or three points; but I confess, I
have not been able to observe that these points are exactly
opposite to the trunks of nerves; so that, probably, the adhesion
is chiefly caused by those vessels which are sometimes seen
passing to the capsule in injected eyes. We may, however,
<span class="pagenum" id="Page_76">76</span>discover ramifications from some of these points, upon and
within the substance of the lens, (Plate VI. <a href="#Pl.VI">Fig. 48</a>.) generally
following a direction near to that of the fibres, and sometimes
proceeding from a point opposite to one of the radiating lines of
the same surface. But the principal vessels of the lens appear
to be derived from the central artery, by two or three branches
at some little distance from the posterior vertex; which I
conceive to be the cause of the frequent adhesion of a portion
of a cataract to the capsule, about this point: they follow
nearly the course of the radiations, and then of the fibres;
but there is often a superficial subdivision of one of the radii,
at the spot where one of them enters. The vessels coming
from the choroid appear principally to supply a substance,
hitherto unobserved, which fills up the marginal part of the
capsule of the crystalline, in the form of a thin zone, and
makes a slight elevation, visible even through the capsule.
(<a href="#Pl.VI">Fig. 49—51</a>.) It consists of coarser fibres than the lens, but
in a direction nearly similar; they are often intermixed with
small globules. In some animals, the margin of the zone is
crenated, especially behind, where it is shorter: this is observable
in the partridge; and, in the same bird, the whole surface
of the lens is seen to be covered with points, or rather
globules, arranged in regular lines, (Plate VII. <a href="#Pl.VII">Fig. 52</a>.) so as
to have somewhat the appearance of a honeycomb, but towards
the vertex less uniformly disposed. This regularity is a sufficient
proof that there could be no optical deception in the appearance;
although it requires a good microscope to discover it distinctly:
but the zone may be easily peeled off under water,
and hardened in spirits. Its use is uncertain; but it may possibly
secrete the liquid of the crystalline; and it as much deserves the
<span class="pagenum" id="Page_77">77</span>name of a gland, as the greater part of the substances usually
so denominated. In peeling it off, I have very distinctly observed
ramifications, which were passing through it into the lens;
(Plate VI. <a href="#Pl.VI">Fig. 50</a>.) and indeed it is not at all difficult to
detect the vessels connecting the margin of the lens with its
capsule; and it is surprising that M. <span class="smcap">Petit</span> should have
doubted of their existence. I have not yet clearly discerned
this crystalline gland in the human eye; but I infer the existence
of something similar to the globules, from the spotted appearance
of the image of a lucid point already mentioned; for which
I can no otherwise account, than by attributing it to a derangement
of these particles, produced by the external force, and
to an unequal impression made by them on the surface of
the lens.</p>

<p>In birds and in fishes, the fibres of the crystalline radiate
equally, becoming finer as they approach the vertex, till they
are lost in a uniform substance, of the same degree of firmness,
which appears to be perforated in the centre by a blood vessel.
(Plate VII. <a href="#Pl.VII">Fig. 53</a>.) In quadrupeds, the fibres at their angular
meeting are certainly not continued, as <span class="smcap">Leeuwenhoek</span> imagined,
across the line of division; but there does not appear to be any
dissimilar substance interposed between them, except that very
minute trunks of vessels often mark that line. But, since the
whole mass of the lens, as far as it is moveable, is probably
endued with a power of changing its figure, there is no need
of any strength of union, or place of attachment, for the fibres,
since the motion meets with little or no resistance. Every
common muscle, as soon as its contraction ceases, returns to
its natural form, even without the assistance of an antagonist;
and the lens itself, when taken out of the eye, in its capsule.
<span class="pagenum" id="Page_78">78</span>has elasticity enough to reassume its proper figure, on the
removal of a force that has compressed it. The capsule is
highly elastic; and, since it is laterally fixed to the ciliary zone,
it must co-operate in restoring the lens to its flattest form. If
it be inquired, why the lens is not capable of becoming less
convex, as well as more so, it may be answered, that the lateral
parts have probably little contractive power; and, if they had
more, they would have no room to increase the size of the disc,
which they must do, in order to shorten the axis; and the parts
about the axis have no fibres so arranged as to shorten it by
their own contraction.</p>

<p>I consider myself as being partly repaid for the labour lost in
search of the nerves of the lens, by having acquired a more
accurate conception of the nature and situation of the ciliary
substance. It had already been observed, that in the hare and
in the wolf, the ciliary processes are not attached to the capsule
of the lens; and if by the ciliary processes we understand
those filaments which are seen detached after tearing
away the capsule, and consist of ramifying vessels, the observation
is equally true of the common quadrupeds, and I will
venture to say, of the human eye.‍&#x2060;<a id="FNanchor_26_26" href="#Footnote_26_26" class="fnanchor">26</a> Perhaps this remark
has been made by others, but the circumstance is not generally
understood. It is so difficult to obtain a distinct view of
these bodies, undisturbed, that I am partly indebted to accident,
for having been undeceived respecting them: but, having once
made the observation, I have learnt to show it in an unquestionable
manner. I remove the posterior hemisphere of the
sclerotica, or somewhat more, and also as much as possible of
the vitreous humour, introduce the point of a pair of scissors
<span class="pagenum" id="Page_79">79</span>into the capsule, turn out the lens, and cut off the greater
part of the posterior portion of the capsule, and of the rest
of the vitreous humour. I next dissect the choroid and uvea
from the sclerotica; and, dividing the anterior part of the capsule
into segments from its centre, I turn them back upon the
ciliary zone. The ciliary processes then appear, covered with
their pigment, and perfectly distinct both from the capsule and
from the uvea; (Plate VII. <a href="#Pl.VII">Fig. 54</a>.) and the surface of the
capsule is seen shining, and evidently natural, close to the base
of these substances. I do not deny that the separation between
the uvea and the processes, extends somewhat further back
than the separation between the processes and the capsule; but
the difference is inconsiderable, and, in the calf, does not amount
to above half the length of the detached part. The appearance
of the processes is wholly irreconcileable with muscularity; and
their being considered as muscles attached to the capsule, is
therefore doubly inadmissible. Their lateral union with the
capsule, commences at the base of their posterior smooth surface,
and is continued nearly to the point where they are more
intimately united with the termination of the uvea; so that,
however this portion of the base of the processes were disposed
to contract, it would be much too short to produce any sensible
effect. What their use may be, cannot easily be determined:
if it were necessary to have any peculiar organs for secretion,
we might call them glands, for the percolation of the aqueous
humour; but there is no reason to think them requisite for this
purpose.</p>

<p>The marsupium nigrum of birds, and the horse-shoe-like
appearance of the choroid of fishes, are two substances which
have sometimes, with equal injustice, been termed muscular.
All the apparent fibres of the marsupium nigrum are, as
<span class="pagenum" id="Page_80">80</span><span class="smcap">Haller</span> had very truly asserted, merely duplicatures of a
membrane, which, when its ends are cut off, may easily be
unfolded under the microscope, with the assistance of a fine hair
pencil, so as to leave no longer any suspicion of a muscular
texture. The experiment related by Mr. <span class="smcap">Home</span>,‍&#x2060;<a id="FNanchor_27_27" href="#Footnote_27_27" class="fnanchor">27</a> can scarcely
be deemed a very strong argument for attributing to this substance
a faculty which its appearance so little authorises us to
expect in it. The red substance in the choroid of fishes,
(Plate VII. <a href="#Pl.VII">Fig. 55</a>.) is more capable of deceiving the observer;
its colour gives it some little pretension, and I began to examine
it with a prepossession in favour of its muscular nature. But,
when we recollect the general colour of the muscles of fishes,
the consideration of its redness will no longer have any
weight. Stripped of the membrane which loosely covers its
internal surface, (<a href="#Pl.VII">Fig. 56</a>.) it seems to have transverse divisions,
somewhat resembling those of muscles, and to terminate
in a manner somewhat similar; (<a href="#Pl.VII">Fig. 57</a>.) but, when
viewed in a microscope, the transverse divisions appear to be
cracks, and the whole mass is evidently of a uniform texture,
without the least fibrous appearance; and, if a particle of any
kind of muscle is compared with it, the contrast becomes very
striking. Besides, it is fixed down, throughout its extent, to
the posterior lamina of the choroid, and has no attachment
capable of directing its effect; to say nothing of the difficulty
of conceiving what that effect could be. Its use must remain,
in common with that of many other parts of the animal frame,
entirely concealed from our curiosity.</p>

<p>The bony scales of the eyes of birds, which were long ago
described in the Philosophical Transactions by Mr. <span class="smcap">Ranby</span>,‍&#x2060;<a id="FNanchor_28_28" href="#Footnote_28_28" class="fnanchor">28</a>
<span class="pagenum" id="Page_81">81</span>and by Mr. <span class="smcap">Warren</span>‍&#x2060;<a id="FNanchor_29_29" href="#Footnote_29_29" class="fnanchor">29</a>&#x2060;,
    afterwards in two excellent Memoirs of
M. <span class="smcap">Petit</span> on the eye of the turkey and of the owl,‍&#x2060;<a id="FNanchor_30_30" href="#Footnote_30_30" class="fnanchor">30</a> and lately
by Mr. <span class="smcap">Pierce Smith</span>,‍&#x2060;<a id="FNanchor_31_31" href="#Footnote_31_31" class="fnanchor">31</a>
    and Mr, <span class="smcap">Home</span>,‍&#x2060;<a id="FNanchor_32_32" href="#Footnote_32_32" class="fnanchor">32</a> can, on any supposition,
have but little concern in the accommodation of the eye
to different distances: they rather seem to be necessary for the
protection of that organ, large and prominent as it is, and unsupported
by any strength in the orbit, against the various accidents
to which the mode of life and rapid motion of those animals
must expose it; and they are much less liable to fracture
than an entire bony ring of the same thickness would have been.
The marsupium nigrum appears to be intended to assist in
giving strength to the eye, to prevent any change in the
place of the lens by external force: it is so situated as to intercept
but little light, and that little is principally what would
have fallen on the insertion of the optic nerve; and it seems to
be too firmly tied to the lens, even to admit any considerable
elongation of the axis of the eye, although it certainly would
not impede a protrusion of the cornea.</p>

<p>With respect to the eyes of insects, an observation of <span class="smcap">Poupart</span>
deserves to be repeated here. He remarks, that the eye
of the libellula is hollow; that it communicates with an air-vessel placed longitudinally in the trunk of the body; and that
it is capable of being inflated from this cavity: he supposes that
the insect is provided with this apparatus, in order for the
accommodation of its eye to the perception of objects at different
distances.‍&#x2060;<a id="FNanchor_33_33" href="#Footnote_33_33" class="fnanchor">33</a> I have not yet had an opportunity of examining
<span class="pagenum" id="Page_82">82</span>the eye of the libellula; but there is no difficulty in supposing
that the means of producing the change of the refractive powers
of the eye, may be, in different classes of animals, as diversified
as their habits, and the general conformation of their
organs.</p>

<p>I beg leave to correct here an observation in my former paper,
relative to the faint lateral radiations, which I supposed to proceed
from the margin of the iris.‍&#x2060;<a id="FNanchor_34_34" href="#Footnote_34_34" class="fnanchor">34</a> I find, on further examination,
that they are occasioned by reflections from the eyelashes.</p>


<p class="mt2em ti0">XII. I shall now finally recapitulate the principal objects and
results of the investigation which I have taken the liberty of
detailing so fully to the Royal Society. First, the determination
of the refractive power of a variable medium, and its application
to the constitution of the crystalline lens. Secondly, the construction
of an instrument for ascertaining, upon inspection, the
exact focal distance of every eye, and the remedy for its imperfections.
Thirdly, to show the accurate adjustment of every
part of the eye, for seeing with distinctness the greatest possible
extent of objects at the same instant. Fourthly, to measure
the collective dispersion of coloured rays in the eye. Fifthly,
by immerging the eye in water, to demonstrate that its accommodation
does not depend on any change in the curvature of
the cornea. Sixthly, by confining the eye at the extremities
of its axis, to prove that no material alteration of its length can
take place. Seventhly, to examine what inference can be drawn
from the experiments hitherto made on persons deprived of the
lens; to pursue the inquiry, on the principles suggested by Dr.
<span class="smcap">Porterfield</span>; and to confirm his opinion of the utter inability
<span class="pagenum" id="Page_83">83</span>of such persons to change the refractive state of the organ.
Eighthly, to deduce, from the aberration of the lateral rays,
a decisive argument in favour of a change in the figure of the
crystalline; to ascertain, from the quantity of this aberration,
the form into which the lens appears to be thrown in my own
eye, and the mode by which the change must be produced in
that of every other person. And I flatter myself, that I shall
not be deemed too precipitate, in denominating this series of
experiments satisfactorily demonstrative.</p>


<hr class="chap x-ebookmaker-drop">
<div class="chapter">
  <h2 class="nobreak" id="CORRECTIONS">
    CORRECTIONS.
  </h2>
</div>



<p><a href="#Page_28">Page 28</a>, line ii. Prop. III. <i>after e, insert</i> the base being unity.</p>

<p><a href="#Page_30">Page 30</a>, line 8, Cor. 10. <i>for n t u, read n t t</i>; line 9, <i>for</i> product &amp;c., <i>read</i> square
of the cosine of incidence.</p>

<p><a href="#Page_31">Page 31</a>, line 5, Cor. 11. <i>for</i> \(1+u^{2}-2u^{4}\), <i>read</i> \(2 m u\).</p>

<p><a href="#Page_31">Page 31</a>. Prop. V. Cor. See the note in p. 60.</p>

<p><a href="#Page_33">Page 33</a>. Prop. VIII. By a mistake of a sign, the eighth proposition is rendered
erroneous; no use having been made of that proposition, it has been inserted without
proper revision. It ought to stand thus, with its demonstration:</p>

<p><span class="smcap">Proposition</span> VIII. <span class="smcap">Problem</span>.</p>

<p>To find the path of a ray of light falling obliquely on a sphere, of a refractive
density varying as any power of the distance from the centre.</p>

<p>The refractive density, in the sense of these propositions, varies as the ratio of the
sines, and as the velocity of light in the medium. (Schol. 2. Prop. I.) Let the velocity
at the distance \(x\) be \(x^{-\dfrac{1}{r}}\); then, considering the refractive force as a species of
attraction, we have, in Prop. 41. l. 1. Princip. \(\sqrt{\text{ABFD}}=x^{-\dfrac{1}{r}}\), \(Q=s\), the sine
of incidence, the radius being unity, \(\text{Z}=s x^{-1}\),
\(\text{D}c=\dfrac{s}{2xx\sqrt{x^{-\dfrac{2}{r}}-s^{2}x^{-2}}}\)
\(=\dfrac{1}{2}sx^{\dfrac{1}{r}-2}\)·\(\left(1-s^{2}x^{\dfrac{2}{r}-2}\right)^{-\dfrac{1}{2}}\),
and the fluxion of the area described by the radius
\(=-\dfrac{1}{2}s x^{\dfrac{1}{r}-2}ẋ\)·\(\left( 1-s^{2}x^{\dfrac{2}{r}-2} \right)^{-\dfrac{1}{2}}\).
Let the sine of the inclination to the radius
<span class="pagenum" id="Page_84">84</span>at each point be called <i>y</i>; then \(y = s x^{\dfrac{1}{r}-1}\),
\(ẏ = \dfrac{1-r}{r}s x^{\dfrac{1}{r}-2}ẋ\), and the fluxion
of the area = \(\dfrac{r}{2r-2}ẏ\cdot\)\(\left( 1-yy \right)^{-\dfrac{1}{2}}\), of which the fluent is
\(\dfrac{r}{2r-2}\text{Y}\), y being the sine of the arc Y; and the angle corresponding is
\(\dfrac{r}{r-1}\text{Y}\). The value of that angle being
found for any two values of <i>x</i> or <i>y</i>, the difference is the intervening angle described
by the radius. This angle is therefore always to the difference of the inclinations as
\(r\) to \(r-1\), and the deviation is to that difference as \(1\) to \(r-1\).</p>
<p>Corollary. Hence, in the passage to the apsis, and the return to the surface, the
deviation is always proportionate to the arc cut off by the incident ray produced:
therefore such a sphere could never collect parallel rays to any focus, the lateral density
being too small towards the surface.</p>

<p><a href="#Page_33">Page 33</a>, line 20, <i>for</i> but the two last &amp;c. <i>read</i> the seventh may either be deduced
from the eighth, or may be demonstrated independently of it.</p>

<p><a href="#Page_42">Page 42</a>, line 18, <i>after</i> internally, <i>insert</i> Or, if a lens of equal mean dimensions,
and equal focal length, with the crystalline, be supposed to consist of two
segments of the external portion of such a sphere, the refractive density at the centre
of this lens must be as 18 to 17.</p>

<p><a href="#Page_47">Page 47</a>, line 12, <i>for</i> calculated &amp;c. <i>read</i> estimated by means of the eighth
proposition; and probably.</p>

<p><a href="#Page_53">Page 53</a>, line 24, <i>for</i> 24, <i>read</i> 21; line 25, <i>for</i> 17, <i>read</i> 15.</p>

<p><a href="#Page_61">Page 61</a>, line 21, <i>for</i> sixtieth, <i>read</i> fortieth..</p>

<p><span class="pagenum"><a id="Page_85"></a>85</span></p>


<hr class="chap x-ebookmaker-drop">
<div class="chapter">
  <h2 class="nobreak" id="EXPLANATION_OF_THE_FIGURES">
    EXPLANATION OF THE FIGURES.
  </h2>
</div>

<div class="explain">
<figure class="figcenter illowe39_3750" id="Pl.II">
  <figcaption>
    <p>Plate II</p>
  </figcaption>
  <img class="w100" src="images/072.jpg" alt="">
</figure>

<p>Plate II. Fig. 1. See <a href="#Page_28">Page 28</a>. Prop. III.</p>

<p>Fig. 2. See Page 28. Prop. IV.</p>

<p>Fig. 3. See <a href="#Page_31">Page 31</a>. Prop. V.</p>

<p>Fig. 4—6. Relating to the optometer. See <a href="#Page_34">Page 34</a>.</p>

<figure class="figcenter illowe39_3750" id="Pl.III">
  <figcaption>
    <p>Plate III</p>
  </figcaption>
  <img class="w100" src="images/076.jpg" alt="">
</figure>

<p> Plate III. Fig. 7. The form of the ends of the optometer,
when made of card. The apertures in the shoulders are for
holding a lens: the square ends turn under, and are fastened
together.</p>

<p>Fig. 8. The scale of the optometer. The middle line is
divided, from the lower end, into inches. The next column
shows the number of a concave lens requisite for a short-
sighted eye; by looking through the slider and observing the
number opposite to which the intersection appears when most
remote. By observing the place of apparent intersection when
nearest, the number requisite will be found in the other column,
provided that the eye have the average power of accommodation.
At the other end, the middle line is graduated for extending
the scale of inches by means of a lens four inches in
focus; the negative numbers implying that such rays as proceed
from them are made to converge towards a point on the
other side of the lens. The other column shows the focal length
of convex glasses required by those eyes to which the intersection
appears, when nearest, opposite the respective places of
the numbers.</p>

<p>Fig. 9. A side view of the optometer, half its size.</p>

<p>Fig. 10. The appearance of the lines through the slider.</p>

<p>Fig. 11. Method of measuring the magnitude of an image
on the retina. See <a href="#Page_48">Page 48</a>.</p>

<p><span class="pagenum" id="Page_86">86</span></p>

<p>Fig. 12. Diagonal scale drawn on a looking-glass.</p>

<p>Fig. 13. The method of applying a lens with water to the
cornea.</p>

<p>Fig. 14. The appearance of a spectrum occasioned by pressure;
and the inflection of straight lines seen within the limits
of the spectrum.</p>

<p>Fig. 15. An illustration of the enlargement of the image,
which would be the consequence of an elongation of the eye:
the images of the candles which, in one instance, fall on
the insertion of the nerve, falling, in the other instance, beyond
it.</p>

<figure class="figcenter illowe39_3750" id="Pl.IV">
  <figcaption>
    <p>Plate IV</p>
  </figcaption>
  <img class="w100" src="images/080.jpg" alt="">
</figure>

<p>Plate IV. Fig. 16. The successive forms of the image of a
large distant object, as it would be delineated by each refractive
surface in the eye; to show how that form at last coincides with
the retina. E&nbsp;G is the distance between the foci of horizontal
and vertical rays in my eye.</p>

<figure class="figcenter illowe39_3750" id="Pl.V">
  <figcaption>
    <p>Plate V</p>
  </figcaption>
  <img class="w100" src="images/084.jpg" alt="">
</figure>

<p>Plate V. Fig. 17. Vertical section of my right eye, seen from
without; twice the natural size.</p>

<p>Fig. 18. Horizontal section, seen from above.</p>

<p>Fig. 19. Front view of my left eye when the pupil is contracted;
of the natural size.</p>

<p>Fig. 20. The same view when the pupil is dilated.</p>

<p>Fig. 21. Outline of the eye and its straight muscles when
at rest.</p>

<p>Fig. 22. Change of figure which would be the consequence
of the action of those muscles upon the eye, and upon the
adipose substance behind it.</p>

<p>Fig. 23. Scale of the small optometer.</p>

<p>Fig. 24. Appearance of four images of a line seen by my eye
when its focus is shortest.</p>

<p><span class="pagenum" id="Page_87">87</span></p>

<p>Fig. 25. Outline of the lens when relaxed; from a comparison
of M. <span class="smcap">Petit</span>’s measures with the phenomena of my own
eye, and on the supposition that it is found in a relaxed state
after death.</p>

<p>Fig. 26. Outline of the lens sufficiently changed to produce
the shortest focal distance.</p>

<p>Fig. 27. Apparatus for ascertaining the focal length of the
lens in water.</p>

<figure class="figcenter illowe39_3750" id="Pl.VI">
  <figcaption>
    <p>Plate VI</p>
  </figcaption>
  <img class="w100" src="images/088.jpg" alt="">
</figure>

<p>Plate VI. Fig. 28. Various forms of the image depicted by a
cylindrical pencil of rays obliquely refracted by a spherical surface,
when received on planes at distances progressively greater.</p>

<p>Fig. 29. Image of a minute lucid object held very near to
my eye.</p>

<p>Fig. 30. The same appearance when the eye has been
rubbed.</p>

<p>Fig. 31—37. Different forms of the image of a lucid point
at greater and greater distances; the most perfect focus being
like Fig. 33, but much smaller.</p>

<p>Fig. 38. Image of a very remote point seen by my right eye.</p>

<p>Fig. 39. Image of a remote point seen by my left eye; being
more obtuse at one end, probably from a less obliquity of the
posterior surface of the crystalline lens.</p>

<p>Fig. 40. Combination of two figures similar to the fifth
variety of Fig. 28; to imitate Fig. 38.</p>

<p>Fig. 41. Appearance of a distant lucid point when the eye is
adapted to a very near object.</p>

<p>Fig. 42, 44. Shadow of parallel wires in the image of a
distant point, when the eye is relaxed.</p>

<p>Fig. 43, 45. The same shadows rendered curved by a
change in the figure of the crystalline lens.</p>

<p><span class="pagenum" id="Page_88">88</span></p>

<p>Fig. 46. The order of the fibres of the human crystalline.</p>

<p>Fig. 47. The division of the nerves at the ciliary zone; the
sclerotica being removed. One of the nerves of the uvea is
seen passing forwards and subdividing. From the calf.</p>

<p>Fig. 48. Ramifications from the margin of the crystalline
lens.</p>

<p>Fig. 49. The zone of the crystalline faintly seen through the
capsule.</p>

<p>Fig. 50. The zone raised from its situation, with the ramifications
passing through it into the lens.</p>

<p>Fig. 51. The zone of the crystalline detached.</p>

<figure class="figcenter illowe36_2500" id="Pl.VII">
  <figcaption>
    <p>Plate VII</p>
  </figcaption>
  <img class="w100" src="images/092.jpg" alt="">
</figure>

<p>Plate VII. Fig. 52. The crenated zone, and the globules
regularly arranged on the crystalline of the partridge.</p>

<p>Fig. 53. The order of the fibres in the lens of birds and
fishes.</p>

<p>Fig. 54. The segments of the capsule of the crystalline
turned back, to show the detached ciliary processes. From
the calf.</p>

<p>Fig. 55. Part of the choroid of the cod-fish, with its red
substance. The central artery hangs loose from the insertion
of the nerve.</p>

<p>Fig. 56. The membrane covering this substance internally,
raised by the blow-pipe.</p>

<p>Fig. 57. The appearance of the red substance, after the
removal of the membrane.</p>
</div>

<h3>FOOTNOTES:</h3>
<div class="footnotes">

<div class="footnote"><p><a id="Footnote_1_1" href="#FNanchor_1_1" class="label">1</a>
Phil. Trans. for 1793, p. 169.</p></div>

<div class="footnote"><p><a id="Footnote_2_2" href="#FNanchor_2_2" class="label">2</a>
Phil. Trans. for 1794, p. 21.</p></div>

<div class="footnote"><p><a id="Footnote_3_3" href="#FNanchor_3_3" class="label">3</a>
Phil. Trans. for 1795, p. 1.</p></div>

<div class="footnote"><p><a id="Footnote_4_4" href="#FNanchor_4_4" class="label">4</a>
De Corporis humani Viribus conservatricibus, p. 68.</p></div>

<div class="footnote"><p><a id="Footnote_5_5" href="#FNanchor_5_5" class="label">5</a>
Phil. Trans. for 1800, p. 146.</p></div>

<div class="footnote"><p><a id="Footnote_6_6" href="#FNanchor_6_6" class="label">6</a>
Edinb. Med. Essays, Vol. IV. p. 124.</p></div>

<div class="footnote"><p><a id="Footnote_7_7" href="#FNanchor_7_7" class="label">7</a>
Edinb. Med. Ess. Vol. IV. p. 185.</p></div>

<div class="footnote"><p><a id="Footnote_8_8" href="#FNanchor_8_8" class="label">8</a>
Mem. de I’Acad. de Paris, 1730. p. 6. Ed. Amst.</p></div>

<div class="footnote"><p><a id="Footnote_9_9" href="#FNanchor_9_9" class="label">9</a>
Phil. Trans, for 1793. p. 174.</p></div>

<div class="footnote"><p><a id="Footnote_10_10" href="#FNanchor_10_10" class="label">10</a>
Comm. Petrop. I. p. 314.</p></div>

<div class="footnote"><p><a id="Footnote_11_11" href="#FNanchor_11_11" class="label">11</a>
<span class="smcap">Petit</span> Mem. del’Acad. 1725, p. 20.</p></div>

<div class="footnote"><p><a id="Footnote_12_12" href="#FNanchor_12_12" class="label">12</a>
Phil.Trans. for 1795, p. 2.</p></div>

<div class="footnote"><p><a id="Footnote_13_13" href="#FNanchor_13_13" class="label">13</a>
<span class="smcap">Smith</span>, e. 96.</p></div>

<div class="footnote"><p><a id="Footnote_14_14" href="#FNanchor_14_14" class="label">14</a>
Phil. Trans, for 1796, p. 2.</p></div>

<div class="footnote"><p><a id="Footnote_15_15" href="#FNanchor_15_15" class="label">15</a>
Phil. Trans, for 1795, p. 13.</p></div>

<div class="footnote"><p><a id="Footnote_16_16" href="#FNanchor_16_16" class="label">16</a>
De Oculi Mutationibus internis. Gotting. 1780. 4°.</p></div>

<div class="footnote"><p><a id="Footnote_17_17" href="#FNanchor_17_17" class="label">17</a>
This Corollary should stand thus. “If a confused image be received on any
given plane, it will be necessary, in order to determine its magnitude, to advert to the
aperture admitting the rays. If the aperture be supposed to be infinitely small, it may
be considered as a radiant point, in order to find the direction of the emergent rays.”</p></div>

<div class="footnote"><p><a id="Footnote_18_18" href="#FNanchor_18_18" class="label">18</a>
Phil. Trans, for 1794. p. 212.</p></div>

<div class="footnote"><p><a id="Footnote_19_19" href="#FNanchor_19_19" class="label">19</a>
Phil. Trans, for 1795. p. 9.</p></div>

<div class="footnote"><p><a id="Footnote_20_20" href="#FNanchor_20_20" class="label">20</a>
Phil. Trans, for 1795. p. 8.</p></div>

<div class="footnote"><p><a id="Footnote_21_21" href="#FNanchor_21_21" class="label">21</a>
De Facultate Oculi qua ad diversas Rerum distantias se accommodat. L. B. 1719.
Ap. Hall. Disp. Anat. IV. p. 301.</p></div>

<div class="footnote"><p><a id="Footnote_22_22" href="#FNanchor_22_22" class="label">22</a>
De quibusdam Oculi Partibus, L. B. 1746. Ap. Hall. Disp. Anat. IV. p. 301.</p></div>

<div class="footnote"><p><a id="Footnote_23_23" href="#FNanchor_23_23" class="label">23</a>
De Oculo Humano. L. B. 1742. Ap. Hall. Disp. Anat. VII. 2. p. 108, 109.</p></div>

<div class="footnote"><p><a id="Footnote_24_24" href="#FNanchor_24_24" class="label">24</a>
1794. p. 352, 354.</p></div>

<div class="footnote"><p><a id="Footnote_25_25" href="#FNanchor_25_25" class="label">25</a>
De Corp. Hum. Vir. Cons, p. 68.</p></div>

<div class="footnote"><p><a id="Footnote_26_26" href="#FNanchor_26_26" class="label">26</a>
Vid. Hall. Physiol. V. p. 432. et <span class="smcap">Duverney</span>, ibi citat.</p></div>

<div class="footnote"><p><a id="Footnote_27_27" href="#FNanchor_27_27" class="label">27</a>
Phil. Trans, for 1796. p. 18.</p></div>

<div class="footnote"><p><a id="Footnote_28_28" href="#FNanchor_28_28" class="label">28</a>
Phil. Trans. Vol. XXXIII. p. 223. Abr. Vol. VII. p. 435.</p></div>

<div class="footnote"><p><a id="Footnote_29_29" href="#FNanchor_29_29" class="label">29</a>
Phil. Trans. Vol. XXXIV. p. 113. Abr. Vol. VII. p. 437.</p></div>

<div class="footnote"><p><a id="Footnote_30_30" href="#FNanchor_30_30" class="label">30</a>
Mem. del’Acad. 1735. p. 163. 1736, p. 166. Ed. Amst.</p></div>

<div class="footnote"><p><a id="Footnote_31_31" href="#FNanchor_31_31" class="label">31</a>
Phil. Trans. for 1795. p. 263.</p></div>

<div class="footnote"><p><a id="Footnote_32_32" href="#FNanchor_32_32" class="label">32</a>
Phil. Trans. for 1796. p. 14.</p></div>

<div class="footnote"><p><a id="Footnote_33_33" href="#FNanchor_33_33" class="label">33</a>
Phil. Trans. Vol. XXII. p. 673. Abr. II. p. 762.</p></div>

<div class="footnote"><p><a id="Footnote_34_34" href="#FNanchor_34_34" class="label">34</a>
Phil. Trans. for 1793. p. 178.</p></div>
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<div style='text-align:center'>*** END OF THE PROJECT GUTENBERG EBOOK 79069 ***</div>
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