1. My design is to show the manner wherein we perceive by sight the distance, magnitude, and situation of OBJECTS. Also to consider the difference there is betwixt the IDEAS of sight and touch, and whether there be any IDEA common to both senses.

2. It is, I think, agreed by all that DISTANCE, of itself and immediately, cannot be seen. For DISTANCE being a Line directed end-wise to the eye, it projects only one point in the fund of the eye, which point remains invariably the same, whether the distance be longer or shorter.

3. I find it also acknowledged that the estimate we make of the distance of OBJECTS considerably remote is rather an act of judgment grounded on EXPERIENCE than of SENSE. For example, when I perceive a great number of intermediate OBJECTS, such as houses, fields, rivers, and the like, which I have experienced to take up a considerable space, I thence form a judgment or conclusion that the OBJECT I see beyond them is at a great distance. Again, when an OBJECT appears faint and small, which at a near distance I have experienced to make a vigorous and large appearance, I instantly conclude it to be far off: And this, it is evident, is the result of EXPERIENCE; without which, from the faintness and littleness I should not have inferred anything concerning the distance of OBJECTS.

4. But when an OBJECT is placed at so near a distance as that the interval between the eyes bears any sensible proportion to it, the opinion of speculative men is that the two OPTIC AXES (the fancy that we see only with one eye at once being exploded) concurring at the OBJECT do there make an ANGLE, by means of which, according as it is greater or lesser, the OBJECT is perceived to be nearer or farther off.

5. Betwixt which and the foregoing manner of estimating distance there is this remarkable difference: that whereas there was no apparent, necessary connection between small distance and a large and strong appearance, or between great distance and a little and faint appearance, there appears a very necessary connection between an obtuse angle and near distance, and an acute angle and farther distance. It does not in the least depend upon experience, but may be evidently known by anyone before he had experienced it, that the nearer the concurrence of the OPTIC AXES, the greater the ANGLE, and the remoter their concurrence is, the lesser will be the ANGLE comprehended by them.

6. There is another way mentioned by optic writers, whereby they will have us judge of those distances, in respect of which the breadth of the PUPIL hath any sensible bigness: And that is the greater or lesser divergency of the rays, which issuing from the visible point do fall on the PUPIL, that point being judged nearest which is seen by most diverging rays, and that remoter which is seen by less diverging rays: and so on, the apparent distance still increasing, as the divergency of the rays decreases, till at length it becomes infinite, when the rays that fall on the PUPIL are to sense parallel. And after this manner it is said we perceive distance when we look only with one eye.

7. In this case also it is plain we are not beholding to experience: it being a certain, necessary truth that the nearer the direct rays falling on the eye approach to a PARALLELISM, the farther off is the point of their intersection, or the visible point from whence they flow.

8. I have here set down the common, current accounts that are given of our perceiving near distances by sight, which, though they are unquestionably received for true by MATHEMATICIANS, and accordingly made use of by them in determining the apparent places of OBJECTS, do, nevertheless seem to me very unsatisfactory: and that for these following reasons:—

9. FIRST, It is evident that when the mind perceives any IDEA, not immediately and of itself, it must be by the means of some other IDEA. Thus, for instance, the passions which are in the mind of another are of themselves to me invisible. I may nevertheless perceive them by sight, though not immediately, yet by means of the colours they produce in the countenance. We often see shame or fear in the looks of a man, by perceiving the changes of his countenance to red or pale.

10. Moreover it is evident that no IDEA which is not itself perceived can be the means of perceiving any other IDEA. If I do not perceive the redness or paleness of a man's face themselves, it is impossible I should perceive by them the passions which are in his mind.

11. Now from sect. 2 it is plain that distance is in its own nature imperceptible, and yet it is perceived by sight. It remains, therefore, that it be brought into view by means of some other IDEA that is itself immediately perceived in the act of VISION.

12. But those LINES and ANGLES, by means whereof some MATHEMATICIANS pretend to explain the perception of distance, are themselves not at all perceived, nor are they in truth ever thought of by those unskilful in optics. I appeal to anyone's experience whether upon sight of an OBJECT he computes its distance by the bigness of the ANGLE made by the meeting of the two OPTIC AXES? Or whether he ever thinks of the greater or lesser divergency of the rays, which arrive from any point to his PUPIL? Everyone is himself the best judge of what he perceives, and what not. In vain shall all the MATHEMATICIANS in the world tell me, that I perceive certain LINES and ANGLES which introduce into my mind the various IDEAS of DISTANCE, so long as I myself am conscious of no such thing.

13. Since, therefore, those ANGLES and LINES are not themselves perceived by sight, it follows from sect. 10 that the mind doth not by them judge of the distance of OBJECTS.

14. Secondly, the truth of this assertion will be yet farther evident to anyone that considers those LINES and ANGLES have no real existence in nature, being only an HYPOTHESIS framed by the MATHEMATICIANS, and by them introduced into OPTICS, that they might treat of that science in a GEOMETRICAL way.

15. The third and last reason I shall give for rejecting that doctrine is, that though we should grant the real existence of those OPTIC ANGLES, etc., and that it was possible for the mind to perceive them, yet these principles would not be found sufficient to explain the PHENOMENA of DISTANCE, as shall be shown hereafter.

16. Now, it being already shown that distance is suggested to the mind by the mediation of some other IDEA which is itself perceived in the act of seeing, it remains that we inquire what IDEAS or SENSATIONS there be that attend VISION, unto which we may suppose the IDEAS of distance are connected, and by which they are introduced into the mind. And FIRST, it is certain by experience that when we look at a near OBJECT with both eyes, according as it approaches or recedes from us, we alter the disposition of our eyes, by lessening or widening the interval between the PUPILS. This disposition or turn of the eyes is attended with a sensation, which seems to me to be that which in this case brings the IDEA of greater or lesser distance into the mind.

17. Not that there is any natural or necessary connection between the sensation we perceive by the turn of the eyes and greater or lesser distance, but because the mind has by constant EXPERIENCE found the different sensations corresponding to the different dispositions of the eyes to be attended each with a different degree of distance in the OBJECT: there has grown an habitual or customary connection between those two sorts of IDEAS, so that the mind no sooner perceives the sensation arising from the different turn it gives the eyes, In order to bring the PUPILS nearer or farther asunder, but it withal perceives the different IDEA of distance which was wont to be connected with that sensation; just as upon hearing a certain sound, the IDEA is immediately suggested to the understanding which custom had united with it.

18 Nor do I see how I can easily be mistaken in this matter. I know evidently that distance is not perceived of itself. That by consequence it must be perceived by means of some other IDEA which is immediately perceived, and varies with the different degrees of distance. I know also that the sensation arising from the turn of the eyes is of itself immediately perceived, and various degrees thereof are connected with different distances, which never fail to accompany them into my mind, when I view an OBJECT distinctly with both eyes, whose distance is so small that in respect of it the interval between the eyes has any considerable magnitude.

19. I know it is a received opinion that by altering the disposition of the eyes the mind perceives whether the angle of the OPTIC AXES is made greater or lesser. And that accordingly by a kind of NATURAL GEOMETRY it judges the point of their intersection to be nearer or farther off. But that this is not true I am convinced by my own experience, since I am not conscious that I make any such use of the perception I have by the turn of my eyes. And for me to make those judgments, and draw those conclusions from it, without knowing that I do so, seems altogether incomprehensible.

20. From all which it follows that the judgment we make of the distance of an OBJECT, viewed with both eyes, is entirely the RESULT OF EXPERIENCE. If we had not constantly found certain sensations arising from the various disposition of the eyes, attended with certain degrees of distance, we should never make those sudden judgments from them concerning the distance of OBJECTS; no more than we would pretend to judge a man's thoughts by his pronouncing words we had never heard before.

21. 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.

22. 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.

23 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.

24. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. 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.'