Secondly, an OBJECT placed at a certain distance from the eye, to which the breadth of the PUPIL bears a considerable proportion, being made to approach, is seen more confusedly: and the nearer it is brought the more confused appearance it makes. And this being found constantly to be so, there ariseth in the mind an habitual CONNECTION between the several degrees of confusion and distance; the greater confusion still implying the lesser distance, and the lesser confusion the greater distance of the OBJECT.
This confused appearance of the OBJECT doth therefore seem to be the MEDIUM whereby the mind judgeth of distance in those cases wherein the most approved writers of optics will have it judge by the different divergency with which the rays flowing from the radiating point fall on the PUPIL. No man, I believe, will pretend to see or feel those imaginary angles that the rays are supposed to form according to their various inclinations on his eye. But he cannot choose seeing whether the OBJECT appear more or less confused. It is therefore a manifest consequence from what bath been demonstrated, that instead of the greater or lesser divergency of the rays, the mind makes use of the greater or lesser confusedness of the appearance, thereby to determine the apparent place of an OBJECT.
Nor doth it avail to say there is not any necessary connection between confused VISION and distance, great or small. For I ask any man what necessary connection he sees between the redness of a blush and shame? And yet no sooner shall he behold that colour to arise in the face of another, but it brings into his and the IDEA of that passion which hath been observed to accompany it.
What seems to have misled the writers of optics in this matter is that they imagine men judge of distance as they do of a conclusion in mathematics, betwixt which and the premises it is indeed absolutely requisite there be an apparent, necessary connection: but it is far otherwise in the sudden judgments men make of distance. We are not to think that brutes and children, or even grown reasonable men, whenever they perceive an OBJECT to approach, or depart from them, do it by virtue of GEOMETRY and DEMONSTRATION.
That one IDEA may suggest another to the mind it will suffice that they have been observed to go together, without any demonstration of the necessity of their coexistence, or without so much as knowing what it is that makes them so to coexist. Of this there are innumerable instances of which no one can be ignorant.
Thus, greater confusion having been constantly attended with nearer distance, no sooner is the former IDEA perceived, but it suggests the latter to our thoughts. And if it had been the ordinary course of Nature that the farther off an OBJECT were placed, the more confused it should appear, it is certain the very same perception that now makes us think an OBJECT approaches would then have made us to imagine it went farther off. That perception, abstracting from CUSTOM and EXPERIENCE, being equally fitted to produce the IDEA of great distance, or small distance, or no distance at all.
Thirdly, an OBJECT being placed at the distance above specified, and brought nearer to the eye, we may nevertheless prevent, at least for some time, the appearances growing more confused, by straining the eye. In which case that sensation supplies the place of confused VISION in aiding the mind to judge of the distance of the OBJECT; it being esteemed so much the nearer by how much the effort or straining of the eye in order to distinct VISION is greater.
I have here set down those sensations or IDEAS that seem to be the constant and general occasions of introducing into the mind the different IDEAS of near distance. It is true in most cases that divers other circumstances contribute to frame our IDEA of distance, to wit, the particular number, size, kind, etc., of the things seen. Concerning which, as well as all other the forementioned occasions which suggest distance, I shall only observe they have none of them, in their own nature, any relation or connection with it: nor is it possible they should ever signify the various degrees thereof, otherwise than as by EXPERIENCE they have been found to be connected with them.
I shall proceed upon these principles to account for a phenomenon which has hitherto strangely puzzled the writers of optics, and is so far from being accounted for by any of their THEORIES OF VISION that it is, by their own confession, plainly repugnant to them; and of consequence, if nothing else could be objected, were alone sufficient to bring their credit in question. The whole difficulty I shall lay before you in the words of the learned Dr. Barrow, with which he concludes his optic lectures:—
'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, Descartes, and others. 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 obligeth 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 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.'
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 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.