An Essay Towards a New Theory of Vision | Page 9

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, etc., 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 supra). But then this must be understood (to
use Dr. Barrow's phrase) SECLUSIS PRAENOTIONIBUS ET
PRAEJUDICIIS, in case we abstract from all other circumstances of
vision, such as the figure, size, faintness, etc. 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 conneted with various distances.
37 It plainly follows from what hath 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; not that the mind judgeth of distance
immediately by them, but because it judgeth 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 and 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