mihi suggessit meditatio. Circa reliquas (quæ φυσικώτεραι sunt,
adeoque sæpiuscule pro certis principiis plausibiles conjecturas
venditare necessum habent) nihil fere quicquam admodum verisimile
succurrit, a pervulgatis (ab iis, inquam, quæ Keplerus,
Scheinerus(315), Cartesius, et post illos alii tradiderunt)
alienum aut diversum. Atqui tacere malo, quam toties oblatam
cramben reponere. Proinde receptui cano; nee ita tamen ut prorsus
discedam, anteaquam improbam quandam difficultatem (pro
sinceritate quam et vobis et veritati debeo minime dissimulandam)
in medium protulero, quæ doctrinæ nostræ, hactenus inculcatæ, se
objicit adversam, ab ea saltem nullam admittit solutionem. Illa,
breviter, talis est. Lenti vel speculo cavo _EBF_ exponatur
punctum visibile _A_, ita distans, ut radii ex _A_ manantes ex
inflectione versus axem _AB_ cogantur. Sitque radiationis limes
(seu puncti _A_ imago, qualem supra passim statuimus) punctum _Z_.
Inter hoc autem et inflectentis verticem _B_ uspiam positus
concipiatur oculus. Quæri jam potest, ubi loci debeat punctum _A_
apparere? Retrorsum ad punctum _Z_ videri non fert natura (cum
omnis impressio sensum afficiens proveniat a partibus _A_) ac
experientia reclamat. Nostris autem e placitis consequi videtur,
ipsum ad partes anticas apparens, ab intervallo longissime dissito
(quod et maximum sensibile quodvis intervallum quodammodo
exsuperet), apparere. Cum enim quo radiis minus divergentibus
attingitur objectum, eo (seclusis utique prænotionibus et
præjudiciis) longius abesse sentiatur; et quod parallelos ad
oculum radios projicit, remotissime positum æstimetur: exigere
ratio videtur, ut quod convergentibus radiis apprehenditur, adhuc
magis, si fieri posset, quoad apparentiam elongetur. Quin et circa
casum hunc generatim inquiri possit, quidnam omnino sit, quod
apparentem puncti _A_ locum determinet, faciatque quod constanti
ratione nunc propius, nunc remotius appareat? Cui itidem dubio
nihil quicquam ex hactenus dictorum analogia responderi posse
videtur, nisi debere punctum _A_ perpetuo longissime semotum
videri. Verum experientia secus attestatur, illud pro diversa
oculi inter puncta _B_, _Z_, positione varie distans, nunquam fere
(si unquam) longinquius ipso _A_ libere spectato, subinde vero
multo propinquius adparere; quinimo, quo oculum appellentes radii
magis convergunt, eo speciem objecti propius accedere. Nempe, si
puncto _B_ admoveatur oculus, suo (ad lentem) fere nativo in loco
conspicitur punctum _A_ (vel æque distans, ad speculum); ad _O_
reductus oculus ejusce speciem appropinquantem cernit; ad _P_
adhuc vicinius ipsum existimat; ac ita sensim, donec alicubi
tandem, velut ad _Q_, constituto oculo, objectum summe propinquum
apparens in meram confusionem incipiat evanescere. Quæ sane cuncta
rationibus atque decretis nostris repugnare videntur, aut cum iis
saltem parum amice conspirant. Neque nostram tantum sententiam
pulsat hoc experimentum, at ex æquo cæteras quas norim omnes:
veterem imprimis ac vulgatam, nostræ præ reliquis affinem, ita
convellere videtur, ut ejus vi coactus doctissimus A. Tacquetus
isti principio (cui pene soli totam inædificaverat _Catoptricam_
suam) ceu infido ac inconstanti renunciarit, adeoque suam ipse
doctrinam labefactarit? id tamen, opinor, minime facturus, si rem
totam inspexissit penitius, atque difficultatis fundum attigissit.
Apud me vero non ita pollet hæc, nec eousque præpollebit ulla
difficultas, ut ab iis quæ manifeste rationi consentanea video,
discedam; præsertim quum, ut his accidit, ejusmodi difficultas in
singularis cujuspiam casus disparitate fundetur. Nimirum in
præsente casu peculiare quiddam, naturæ subtilitati involutum,
delitescit, ægre fortassis, nisi perfectius explorato videndi
modo, detegendum. Circa quod nil, fateor, hactenus excogitare
potui, quod adblandiretur animo meo, nedum plane satisfaceret.
Vobis itaque nodum hunc, utinam feliciore conatu, resolvendum
committo.”
_In English as follows_:
“I have here delivered what my thoughts have suggested to me
concerning that part of optics which is more properly
mathematical. As for the other parts of that science (which, being
rather physical, do consequently abound with plausible conjectures
instead of certain principles), there has in them scarce anything
occurred to my observation different from what has been already
said by Kepler, Scheinerus, Des Cartes, &c. And methinks I had
better say nothing at all than repeat that which has been so often
said by others. I think it therefore high time to take my leave of
this subject. But, before I quit it for good and all, the fair and
ingenuous dealing that I owe both to you and to truth obliges me
to acquaint you with a certain untoward difficulty, which seems
directly opposite to the doctrine I have been hitherto
inculcating, at least admits of no solution from it. In short it
is this. Before the double convex glass or concave speculum _EBF_,
let the point _A_ be placed at such a distance that the rays
proceeding from _A_, after refraction or reflection, be brought to
unite somewhere in the axis _AB_. And suppose the point of union
(i.e. the image of the point _A_, as hath been already set forth)
to be _Z_; between which and _B_, the vertex of the glass or
speculum, conceive the eye to be anywhere placed. The question now
is, where the point _A_ ought to appear. Experience shews that it
doth not appear behind at the point _Z_; and it were contrary to
nature that it should; since all the impression which affects the
sense comes from towards _A_. But, from our tenets it should seem
to follow that it would appear before the eye at a vast distance
off, so great as should in some sort surpass all sensible
distance. For since, if we exclude all anticipations and
prejudices, every object appears by so much the farther off by how
much the rays it sends to the eye are less diverging; and that
object is thought to be most remote from which parallel rays
proceed unto the eye; reason would make one think that object
should appear at yet a greater distance which is seen by
converging rays. Moreover, it may in general be asked concerning
this case, what it is that determines the apparent place of the
point _A_, and maketh it to appear after a constant manner,
sometimes nearer, at other times farther off? To which doubt I see
nothing that can be answered agreeable to the principles we have
laid down, except only that the point _A_ ought always to appear
extremely remote. But, on the contrary, we are assured by
experience, that the point _A_ appears variously distant,
according to the different situations of the eye between the
points _B_ and _Z_. And that it doth almost never (if at all) seem
farther off than it would if it were beheld by the naked eye; but,
on the contrary, it doth sometimes appear much nearer. Nay, it is
even certain that by how much the rays falling on the eye do more
converge, by so much the nearer does the object seem to approach.
For, the eye being placed close to the point _B_, the object _A_
appears nearly in its own natural place, if the point _B_ is taken
in the glass, or at the same distance, if in the speculum. The eye
being brought back to _O_, the object seems to draw near; and,
being come to _P_, it beholds it still nearer: and so on by little
and little, till at length the eye being placed somewhere, suppose
at _Q_, the object appearing extremely near begins to vanish into
mere confusion. All which doth seem repugnant to our principles;
at least, not rightly to agree with them. Nor is our tenet alone
struck at by this experiment, but likewise all others that ever
came to my knowledge are every whit as much endangered by it. The
ancient one especially (which is most commonly received, and comes
nearest to mine) seems to be so effectually overthrown thereby
that the most learned Tacquet has been forced to reject that
principle, as false and uncertain, on which alone he had built
almost his whole _Catoptrics_, and consequently, by taking away
the foundation, hath himself pulled down the superstructure he had
raised on it. Which, nevertheless, I do not believe he would have
done, had he but considered the whole matter more thoroughly, and
examined the difficulty to the bottom. But as for me, neither this
nor any other difficulty shall have so great an influence on me,
as to make me renounce that which I know to be manifestly
agreeable to reason. Especially when, as it here falls out, the
difficulty is founded in the peculiar nature of a certain odd and
particular case. For, in the present case something peculiar lies
hid, which, being involved in the subtilty of nature, will perhaps
hardly be discovered till such time as the manner of vision is
more perfectly made known. Concerning which, I must own I have
hitherto been able to find out nothing that has the least show of
probability, not to mention certainty. I shall therefore leave
this knot to be untied by you, wishing you may have better success
in it than I have had.”
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30. The ancient and received principle, which Dr. Barrow here mentions as
the main foundation of Tacquet’s(316) _Catoptrics_, is, that every
“visible point seen by reflection from a speculum shall appear placed at
the intersection of the reflected ray and the perpendicular of incidence.”
Which intersection in the present case happening to be behind the eye, it
greatly shakes the authority of that principle whereon the aforementioned
author proceeds throughout his whole _Catoptrics_, in determining the
apparent place of objects seen by reflection from any kind of speculum.
31. Let us now see how this phenomenon agrees with our tenets(317). The
eye, the nearer it is placed to the point _B_ in the above figures, the
more distinct is the appearance of the object: but, as it recedes to _O_,
the appearance grows more confused; and at _P_ it sees the object yet more
confused; and so on, till the eye, being brought back to _Z_, sees the
object in the greatest confusion of all. Wherefore, by sect. 21, the
object should seem to approach the eye gradually, as it recedes from the
point _B_; that is, at _O_ it should (in consequence of the principle I
have laid down in the aforesaid section) seem nearer than it did at _B_,
and at _P_ nearer than at _O_, and at _Q_ nearer than at _P_, and so on,
till it quite vanishes at _Z_. Which is the very matter of fact, as any
one that pleases may easily satisfy himself by experiment.
32. This case is much the same as if we should suppose an Englishman to
meet a foreigner who used the same words with the English, but in a direct
contrary signification. The Englishman would not fail to make a wrong
judgment of the ideas annexed to those sounds, in the mind of him that
used them. Just so in the present case, the object speaks (if I may so
say) with words that the eye is well acquainted with, that is, confusions
of appearance; but, whereas heretofore the greatest confusions were always
wont to signify nearer distances, they have in this case a direct contrary
signification, being connected with the greater distances. Whence it
follows that the eye must unavoidably be mistaken, since it will take the
confusions in the sense it has been used to, which is directly opposed to
the true.
33. This phenomenon, as it entirely subverts the opinion of those who will
have us judge of distance by lines and angles, on which supposition it is
altogether inexplicable, so it seems to me no small confirmation of the
truth of that principle whereby it is explained(318). But, in order to a
more full explication of this point, and to shew how far the hypothesis of
the mind’s judging by the various divergency of rays may be of use in
determining the apparent place of an object, it will be necessary to
premise some few things, which are already well known to those who have
any skill in Dioptrics.
34. _First_, Any radiating point is then distinctly seen when the rays
proceeding from it are, by the refractive power of the crystalline,
accurately reunited in the retina or fund of the eye. But if they are
reunited either before they arrive at the retina, or after they have
passed it, then there is confused vision.
[Illustration]
Figure 1
[Illustration]
Figure 2
[Illustration]
Figure 3
35. _Secondly_, Suppose, in the adjacent figures, _NP_ represent an eye
duly framed, and retaining its natural figure. In fig. 1 the rays falling
nearly parallel on the eye, are, by the crystalline _AB_, refracted, so as
their focus, or point of union _F_, falls exactly on the retina. But, if
the rays fall sensibly diverging on the eye, as in fig. 2, then their
focus falls beyond the retina; or, if the rays are made to converge by the
lens _QS_, before they come at the eye, as in fig. 3, their focus _F_ will
fall before the retina. In which two last cases it is evident, from the
foregoing section, that the appearance of the point _Z_ is confused. And,
by how much the greater is the convergency or divergency of the rays
falling on the pupil, by so much the farther will the point of their
reunion be from the retina, either before or behind it, and consequently
the point _Z_ will appear by so much the more confused. And this, by the
bye, may shew us the difference between confused and faint vision.
Confused vision is, when the rays proceeding from each distinct point of
the object are not accurately re-collected in one corresponding point on
the retina, but take up some space thereon—so that rays from different
points become mixed and confused together. This is opposed to a distinct
vision, and attends near objects. Faint vision is when, by reason of the
distance of the object, or grossness of the interjacent medium, few rays
arrive from the object to the eye. This is opposed to vigorous or clear
vision, and attends remote objects. But to return.
36. The eye, or (to speak truly) the mind, perceiving only the confusion
itself, without ever considering the cause from which it proceeds, doth
constantly annex the same degree of distance to the same degree of
confusion. Whether that confusion be occasioned by converging or by
diverging rays it matters not. Whence it follows that the eye, viewing the
object _Z_ through the glass _QS_ (which by refraction causeth the rays
_ZQ_, _ZS_, &c. to converge), should judge it to be at such a nearness, at
which, if it were placed, it would radiate on the eye, with rays diverging
to that degree as would produce the same confusion which is now produced
by converging rays, i.e. would cover a portion of the retina equal to
_DC._ (Vid. fig. 3, _sup._) But then this must be understood (to use Dr.
Barrow’s phrase) “seclusis prænotionibus et præjudiciis,” in case we
abstract from all other circumstances of vision, such as the figure, size,
faintness, &c. of the visible objects—all which do ordinarily concur to
form our idea of distance, the mind having, by frequent experience,
observed their several sorts or degrees to be connected with various
distances.
37. It plainly follows from what has been said, that a person perfectly
purblind (i.e. that could not see an object distinctly but when placed
close to his eye) would not make the same wrong judgment that others do in
the forementioned case. For, to him, greater confusions constantly
suggesting greater distances, he must, as he recedes from the glass, and
the object grows more confused, judge it to be at a farther distance;
contrary to what they do who have had the perception of the objects
growing more confused connected with the idea of approach.
38. Hence also it doth appear, there may be good use of computation, by
lines and angles, in optics(319); not that the mind judges of distance
immediately by them, but because it judges by somewhat which is connected
with them, and to the determination whereof they may be subservient. Thus,
the mind judging of the distance of an object by the confusedness of its
appearance, and this confusedness being greater or lesser to the naked
eye, according as the object is seen by rays more or less diverging, it
follows that a man may make use of the divergency of the rays, in
computing the apparent distance, though not for its own sake, yet on
account of the confusion with which it is connected. But so it is, the
confusion itself is entirely neglected by mathematicians, as having no
necessary relation with distance, such as the greater or lesser angles of
divergency are conceived to have. And these (especially for that they fall
under mathematical computation) are alone regarded, in determining the
apparent places of objects, as though they were the sole and immediate
cause of the judgments the mind makes of distance. Whereas, in truth, they
should not at all be regarded in themselves, or any otherwise than as they
are supposed to be the cause of confused vision.
39. The not considering of this has been a fundamental and perplexing
oversight. For proof whereof, we need go no farther than the case before
us. It having been observed that the most diverging rays brought into the
mind the idea of nearest distance, and that still as the divergency
decreased the distance increased, and it being thought the connexion
between the various degrees of divergency and distance was immediate—this
naturally leads one to conclude, from an ill-grounded analogy, that
converging rays shall make an object appear at an immense distance, and
that, as the convergency increases, the distance (if it were possible)
should do so likewise. That this was the cause of Dr. Barrow’s mistake is
evident from his own words which we have quoted. Whereas had the learned
Doctor observed that diverging and converging rays, how opposite soever
they may seem, do nevertheless agree in producing the same effect, to wit,
confusedness of vision, greater degrees whereof are produced
indifferently, either as the divergency or convergency of the rays
increaseth; and that it is by this effect, which is the same in both, that
either the divergency or convergency is perceived by the eye—I say, had he
but considered this, it is certain he would have made a quite contrary
judgment, and rightly concluded that those rays which fall on the eye with
greater degrees of convergency should make the object from whence they
proceed appear by so much the nearer. But it is plain it was impossible
for any man to attain to a right notion of this matter so long as he had
regard only to lines and angles, and did not apprehend the true nature of
vision, and how far it was of mathematical consideration.
40. Before we dismiss this subject, it is fit we take notice of a query
relating thereto, proposed by the ingenious Mr. Molyneux, in his _Treatise
of Dioptrics_ (par. i. prop. 31. sect. 9), where, speaking of the
difficulty we have been explaining, he has these words: “And so he (i.e.
Dr. Barrow) leaves this difficulty to the solution of others, which I
(after so great an example) shall do likewise; but with the resolution of
the same admirable author, of not quitting the evident doctrine which we
have before laid down, for determining the _locus objecti_, on account of
being pressed by one difficulty, which seems inexplicable till a more
intimate knowledge of the visive faculty be obtained by mortals. In the
meantime I propose it to the consideration of the ingenious, whether the
_locus apparens_ of an object placed as in this ninth section be not as
much before the eye as the distinct base is behind the eye?” To which
query we may venture to answer in the negative. For, in the present case,
the rule for determining the distance of the distinct base, or respective
focus from the glass is this: _As the difference between the distance of
the object and focus is to the focus or focal length, so the distance of
the object from the glass is to the distance of the respective focus or
distinct base from the glass._ (Molyneux, _Dioptr._, par. i. prop. 5.) Let
us now suppose the object to be placed at the distance of the focal
length, and one-half of the focal length from the glass, and the eye close
to the glass. Hence it will follow, by the rule, that the distance of the
distinct base behind the eye is double the true distance of the object
before the eye. If, therefore, Mr. Molyneux’s conjecture held good, it
would follow that the eye should see the object twice as far off as it
really is; and in other cases at three or four times its due distance, or
more. But this manifestly contradicts experience, the object never
appearing, at farthest, beyond its due distance. Whatever, therefore, is
built on this supposition (vid. corol. i. prop. 57. ibid.) comes to the
ground along with it.
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41. From what hath been premised, it is a manifest consequence, that a man
born blind, being made to see, would at first have no idea of distance by
sight: the sun and stars, the remotest objects as well as the nearer,
would all seem to be in his eye, or rather in his mind. The objects
intromitted by sight would seem to him (as in truth they are) no other
than a new set of thoughts or sensations, each whereof is as near to him
as the perceptions of pain or pleasure, or the most inward passions of his
soul. For, our judging objects perceived by sight to be at any distance,
or without the mind, is (vid. sect, xxviii.) entirely the effect of
experience; which one in those circumstances could not yet have attained
to(320).
42. It is indeed otherwise upon the common supposition—that men judge of
distance by the angle of the optic axes, just as one in the dark, or a
blind man by the angle comprehended by two sticks, one whereof he held in
each hand(321). For, if this were true, it would follow that one blind
from his birth, being made to see, should stand in need of no new
experience, in order to perceive distance by sight. But that this is false
has, I think, been sufficiently demonstrated.
43. And perhaps, upon a strict inquiry, we shall not find that even those
who from their birth have grown up in a continued habit of seeing are
irrecoverably prejudiced on the other side, to wit, in thinking what they
see to be at a distance from them. For, at this time it seems agreed on
all hands, by those who have had any thoughts of that matter, that
colours, which are the proper and immediate object of sight, are not
without the mind.—But then, it will be said, by sight we have also the
ideas of extension, and figure, and motion; all which may well be thought
without and at some distance from the mind, though colour should not. In
answer to this, I appeal to any man’s experience, whether the visible
extension of any object do not appear as near to him as the colour of that
object; nay, whether they do not both seem to be in the very same place.
Is not the extension we see coloured, and is it possible for us, so much
as in thought, to separate and abstract colour from extension? Now, where
the extension is, there surely is the figure, and there the motion too. I
speak of those which are perceived by sight(322).