An Essay Towards a New Theory of Vision | Page 7

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
AxAB. 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 shows
that it does 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 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 doth 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 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.'
30. The ancient and received principle, which Dr. Barrow here
mentions as the main foundation of Tacquet's 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