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An Essay Towards a New Theory of Vision
by George Berkeley
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An Essay Towards a New Theory of Vision

by

George Berkeley (1685-1753)



CONTENTS

Sect.

1 Design 2 Distance of itself invisible 3 Remote distance perceived rather by experience than by sense 4 Near distance thought to be perceived by the ANGLE of the OPTIC AXES 5 Difference between this and the former manner of perceiving distance 6 Also by diverging rays 7 This depends not on experience 8 These the common accounts, but not satisfactory 9 Some IDEAS perceived by the mediation of others 10 No IDEA which is not itself perceived, can be the means of perceiving another 11 Distance perceived by means of some other IDEA 12 Those lines and angles mentioned in optics, are not themselves perceived 13 Hence the mind does not perceive distance by lines and angles 14 Also because they have no real existence 15 And because they are insufficient to explain the phenomena 16 The IDEAS that suggest distance are, 1st, the sensation arising from the turn of the eyes 17 Betwixt which and distance there is no necessary connection 18 Scarce room for mistake in this matter 19 No regard had to the angle of the OPTIC AXES 20 Judgment of distance made with both eyes, the result of EXPERIENCE 21 2ndly, Confusedness of appearance 22 This the occasion of those judgments attributed to diverging rays 23 Objection answered 24 What deceives the writers of optics in this matter 25 The cause why one IDEA may suggest another 26 This applied to confusion and distance 27 Thirrdly, the straining of the eye 28 The occasions which suggest distance have in their own nature no relation to it 29 A difficult case proposed by Dr. Barrow as repugnant to all the known theories 30 This case contradicts a received principle in catoptrics 31 It is shown to agree with the principles we have laid down 32 This phenomenon illustrated 33 It confirms the truth of the principle whereby it is explained 34 Vision when distinct, and when confused 35 The different effects of parallel diverging and converging rays 36 How converging and diverging rays come to suggest the same distance 37 A person extreme purblind would judge aright in the forementioned case 38 Lines and angles, why useful in optics 39 The not understanding this, a cause of mistake 40 A query proposed, by Mr. Molyneux in his DIOPTRICS, considered 41 One born blind would not at first have any IDEA of distance by sight 42 This not agreeable to the common principles 43 The proper objects of sight, not without the mind, nor the images of any thing without the mind 44 This more fully explained 45 In what sense we must be understood to see distance and external things 46 Distance, and things placed at a distance, not otherwise perceived by the eye than by the ear 47 The IDEAS of sight more apt to be confounded with the IDEAS of touch than those of hearing are 48 How this comes to pass 49 Strictly speaking, we never see and feel the same thing 50 Objects of SIGHT twofold, mediate and immediate 51 These hard to separate in our thoughts 52 The received accounts of our perceiving magnitude by sight, false 53 Magnitude perceived as immediately as distance 54 Two kinds of sensible extension, neither of which is infinitely divisible 55 The tangible magnitude of an OBJECT steady, the visible not 56 By what means tangible magnitude is perceived by sight 57 This further enlarged on 58 No necessary connection between confusion or faintness of appearance, and small or great magnitude 59 The tangible magnitude of an OBJECT more heeded than the visible, and why 60 An instance of this 61 Men do not measure by visible feet or inches 62 No necessary connection between visible and tangible extension 63 Greater visible magnitude might signify lesser tangible magnitude 64 The judgments we make of magnitude depend altogether on experience 65 Distance and magnitude seen as shame or anger 66 But we are prone to think otherwise, and why 67 The moon seems greater in the horizon than in the meridian 68 The cause of this phenomenon assigned 69 The horizontal moon, why greater at one time than another. 70 The account we have given proved to be true 71 And confirmed by the moon's appearing greater in a mist 72 Objection answered 73 The way wherein faintness suggests greater magnitude illustrated 74 Appearance of the horizontal moon, why thought difficult to explain 75 Attempts towards the solution of it made by several, but in vain 76 The opinion of Dr. Wallis 77 It is shown to be unsatisfactory 78 How lines and angles may be of use in computing apparent magnitudes 79 One born blind, being made to see, what judgment he would make of magnitude 80 The MINIMUM VISIBLE the same to all creatures 81 Objection answered 82 The eye at all times perceives the same number of visible points 83 Two imperfections in the VISIVE FACULTY 84 Answering to which, we may conceive two perfections 85 In neither of these two ways do microscopes improve the sight 86 The case of microscopical eyes, considered 87 The sight, admirably adapted to the ends of seeing 88 Difficulty concerning erect vision 89 The common way of explaining it 90 The same shown to be false 91 Not distinguishing between IDEAS of sight and touch, cause of mistake in this matter 92 The case of one born blind, proper to be considered 93 Such a one might by touch attain to have IDEAS of UPPER and LOWER 94 Which modes of situation he would attribute only to things tangible 95 He would not at first sight think anything he saw, high or low, erect or inverted 96 This illustrated by an example 97 By what means he would come to denominate visible OBJECTS, high or low, etc. 98 Why he should think those OBJECTS highest, which are painted on the lowest part of his eye, and VICE VERSA 99 How he would perceive by sight, the situation of external objects 100 Our propension to think the contrary, no argument against what has been said 101 Objection 102 Answer 103 An object could not be known at first sight by the colour 104 Nor by the magnitude thereof 105 Nor by the figure 106 In the first act of vision, no tangible thing would be suggested by sight 107 Difficulty proposed concerning number 108 Number of things visible, would not at first sight suggest the like number of things tangible 109 Number the creature of the mind 110 One born blind would not at first sight number visible things as others do 111 The situation of any object determined with respect only to objects of the same sense 112 No distance, great or small, between a visible and tangible thing 113 The not observing this, cause of difficulty in erect vision 114 Which otherwise includes nothing unaccountable 115 What is meant by the picture being inverted 116 Cause of mistake in this matter 117 Images in the eye, not pictures of external objects 118 In what sense they are pictures 119 In this affair we must carefully distinguish between ideas of sight and touch 120 Difficult to explain by words the true Theory of Vision 121 The question, whether there is any IDEA common to sight and touch, stated 122 Abstract extension inquired into 123 It is incomprehensible 124 Abstract extension not the OBJECT of geometry 125 The general IDEA of a triangle, considered 126 Vacuum, or pure space, not common to sight and touch 127 There is no idea, or kind of idea, common to both senses 128 First argument in proof hereof 129 Second argument 130 Visible figure and extension, not distinct IDEAS from colour 131 Third argument 132 Confirmation drawn from Mr. Molyneux's problem of a sphere and a cube, published by Mr. Locke 133 Which is falsely solved, if the common supposition be true 134 More might be said in proof of our tenet, but this suffices 135 Further reflection on the foregoing problem 136 The same thing doth not affect both sight and touch 137 The same idea of motion not common to sight and touch 138 The way wherein we apprehend motion by sight, easily collected from what hath been said 139 QU. How visible and tangible IDEAS came to have the same name if not of the same kind 140 This accounted for without supposing them of the same kind 141 OBJ. That a tangible square is liker to a visible square than to a visible circle 142 ANS. That a visible square is fitter than a visible circle, to represent a tangible square 143 But it doth not hence follow, that a visible square is like a tangible square 144 Why we are more apt to confound visible with tangible IDEAS, than other signs with the things signified 145 Several other reasons hereof, assigned 146 Reluctancy in rejecting any opinion, no argument of its truth 147 Proper objects of vision the language of nature 148 In it there is much admirable, and deserving our attention 149 Question proposed, concerning the object of geometry 150 At first view we are apt to think visible extension the object of geometry 151 Visible extension shown not to be the object of geometry 152 Words may as well be thought the object of geometry, as visible extension 153 It is proposed to inquire, what progress an intelligence that could see, but not feel, might make in geometry 154 He cannot understand those parts which relate to solids, and their surfaces, and lines generated by their section 155 Nor even the elements of plane geometry 156 The proper objects of sight incapable of being managed as geometrical figures 157 The opinion of those who hold plane figures to be the immediate objects of sight, considered 158 Planes no more the immediate objects of sight, than solids 159 Difficult to enter precisely into the thoughts of the above-mentioned intelligence 160 The object of geometry, its not being sufficiently understood, cause of difficulty, and useless labour in that science



AN ESSAY TOWARDS A NEW THEORY OF VISION

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.'

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 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. The eye the nearer it is placed to the point B in the foregoing 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 anyone 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 greater 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. But in order co a more full explication of this point, and to show 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.



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 show us the difference between confused and faint vision. Confused vision is when the rays proceedings from each distinct point of the OBJECT are not accurately recollected 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, 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 connected 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 take notice of a query relating thereto, proposed by the ingenious Mr. Molyneux, is his TREATISE OF DIOPTRICS,[Par. I. Prop. 31, Sect. 9.] where speaking of this difficulty, 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 doarine 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 9th 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.

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 provided by sight to be at any distance, or without the mind, is (VID. sect. 28) entirely the effect of experience, which one in those circumstances could not yet have attained to.

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. 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 doth 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.

44. But for a fuller explication of this point, and to show that the immediate objects of sight are not so much as the ideas or resemblances of things placed at a distance, it is requisite that we look nearer into the matter and carefully observe what is meant in common discourse, when one says that which he sees is at a distance from him. Suppose, for example, that looking at the moon I should say it were fifty or sixty semidiameters of the earth distant from me. Let us see what moon this is spoken of: it is plain it cannot be the visible moon, or anything like the visible moon, or that which I see, which is only a round, luminous plane of about thirty visible points in diameter. For in case I am carried from the place where I stand directly towards the moon, it is manifest the object varies, still as I go on; and by the time that I am advanced fifty or sixty semidiameters of the earth, I shall be so far from being near a small, round, luminous flat that I shall perceive nothing like it; this object having long since disappeared, and if I would recover it, it must be by going back to the earth from whence I set out. Again, suppose I perceive by sight the faint and obscure idea of something which I doubt whether it be a man, or a tree, or a tower, but judge it to be at the distance of about a mile. It is plain I cannot mean that what I see is a mile off, or that it is the image or likeness of anything which is a mile off, since that every step I take towards it the appearance alters, and from being obscure, small, and faint, grows clear, large, and vigorous. And when I come to the mile's end, that which I saw first is quite lost, neither do I find anything in the likeness of it.

45. In these and the like instances the truth of the matter stands thus: having of a long time experienced certain ideas, perceivable by touch, as distance, tangible figure, and solidity, to have been connected with certain ideas of sight, I do upon perceiving these ideas of sight forthwith conclude what tangible ideas are, by the wonted ordinary course of Nature like to follow. Looking at an object I perceive a certain visible figure and colour, with some degree of faintness and other circumstances, which from what I have formerly observed, determine me to think that if I advance forward so many paces or miles, I shall be affected with such and such ideas of touch: so that in truth and strictness of speech I neither see distance itself, nor anything that I take to be at a distance. I say, neither distance nor things placed at a distance are themselves, or their ideas, truly perceived by sight. This I am persuaded of, as to what concerns myself: and I believe whoever will look narrowly into his own thoughts and examine what he means by saying he sees this or that thing at a distance, will agree with me that what he sees only suggests to his understanding that after having passed a certain distance, to be measured by the motion of his body, which is perceivable by touch, he shall come to perceive such and such tangible ideas which have been usually connected with such and such visible ideas. But that one might be deceived by these suggestions of sense, and that there is no necessary connexion between visible and tangible ideas suggested by them, we need go no farther than the next looking-glass or pictures to be convinced. Note that when I speak of tangible ideas, I take the word idea for any the immediate object of sense or understanding, in which large signification it is commonly used by the moderns.

46. From what we have shown it is a manifest consequence that the ideas of space, outness, and things placed at a distance are not, strictly speaking, the object of sight; they are not otherwise perceived by the eye than by the ear. Sitting in my study I hear a coach drive along the street; I look through the casement and see it; I walk out and enter into it; thus, common speech would incline one to think I heard, saw, and touched the same thing, to wit, the coach. It is nevertheless certain, the ideas intromitted by each sense are widely different and distinct from each other; but having been observed constantly to go together, they are spoken of as one and the same thing. By the variation of the noise I perceive the different distances of the coach, and know that it approaches before I look out. Thus by the ear I perceive distance, just after the same manner as I do by the eye.

47. I do not nevertheless say I hear distance in like manner as I say that I see it, the ideas perceived by hearing not being so apt to be confounded with the ideas of touch as those of sight are. So likewise a man is easily convinced that bodies and external things are not properly the object of hearing; but only sounds, by the mediation whereof the idea of this or that body or distance is suggested to his thoughts. But then one is with more difficulty brought to discern the difference there is betwixt the ideas of sight and touch: though it be certain a man no more sees and feels the same thing than he hears and feels the same thing.

48. One reason of which seems to be this. It is thought a great absurdity to imagine that one and the same thing should have any more than one extension, and one figure. But the extension and figure of a body, being let into the mind two ways, and that indifferently either by sight or touch, it seems to follow that we see the same extension and the same figure which we feel.

49. But if we take a close and accurate view of things, it must be acknowledged that we never see and feel one and the same object. That which is seen is one thing, and that which is felt is another. If the visible figure and extension be not the same with the tangible figure and extension, we are not to infer that one and the same thing has divers extensions. The true consequence is that the objects of sight and touch are two distinct things. It may perhaps require some thought rightly to conceive this distinction. And the difficulty seems not a little increased, because the combination of visible ideas hath constantly the same name as the combination of tangible ideas wherewith it is connected: which doth of necessity arise from the use and end of language.

50. In order therefore to treat accurately and unconfusedly of vision, we must bear in mind that there are two sorts of objects apprehended by the eye, the one primarily and immediately, the other secondarily and by intervention of the former. Those of the first sort neither are, nor appear to be, without the mind, or at any distance off; they may indeed grow greater or smaller, more confused, or more clear, or more faint, but they do not, cannot approach or recede from us. Whenever we say an object is at a distance, whenever we say it draws near, or goes farther off, we must always mean it of the latter sort, which properly belong to the touch, and are not so truly perceived as suggested by the eye in like manner as thoughts by the ear.

51. No sooner do we hear the words of a familiar language pronounced in our ears, but the ideas corresponding thereto present themselves to our minds: in the very same instant the sound and the meaning enter the understanding: so closely are they united that it is not in our power to keep out the one, except we exclude the other also. We even act in all respects as if we heard the very thoughts themselves. So likewise the secondary objects, or those which are only suggested by sight, do often more strongly affect us, and are more regarded than the proper objects of that sense; along with which they enter into the mind, and with which they have a far more strict connexion, than ideas have with words. Hence it is we find it so difficult to discriminate between the immediate and mediate objects of sight, and are so prone to attribute to the former what belongs only to the latter. They are, as it were, most closely twisted, blended, and incorporated together. And the prejudice is confirmed and riveted in our thoughts by a long tract of time, by the use of language, and want of reflexion. However, I believe anyone that shall attentively consider what we have already said, and shall say, upon this subject before we have done (especially if he pursue it in his own thoughts) may be able to deliver himself from that prejudice. Sure I am it is worth some attention, to whoever would understand the true nature of vision.

52. I have now done with distance, and proceed to show how it is that we perceive by sight the magnitude of objects. It is the opinion of some that we do it by angles, or by angles in conjunction with distance: but neither angles nor distance being perceivable by sight, and the things we see being in truth at no distance from us, it follows that as we have shown lines and angles not to be the medium the mind makes use of in apprehending the apparent place, so neither are they the medium whereby it apprehends the apparent magnitude of objects.

53. It is well known that the same extension at a near distance shall subtend a greater angle, and at a farther distance a lesser angle. And by this principle (we are told) the mind estimates the magnitude of an object, comparing the angle under which it is seen with its distance, and thence inferring the magnitude thereof. What inclines men to this mistake (beside the humour of making one see by geometry) is that the same perceptions or ideas which suggest distance do also suggest magnitude. But if we examine it we shall find they suggest the latter as immediately as the former. I say, they do not first suggest distance, and then leave it to the judgment to use that as a medium whereby to collect the magnitude; but they have as close and immediate a connexion with the magnitude as with the distance; and suggest magnitude as independently of distance as they do distance independently of magnitude. All which will be evident to whoever considers what hath been already said, and what follows.

54. It hath been shown there are two sorts of objects apprehended by sight; each whereof hath its distinct magnitude, or extension. The one, properly tangible, i.e. to be perceived and measured by touch, and not immediately falling under the sense of seeing: the other, properly and immediately visible, by mediation of which the former is brought in view. Each of these magnitudes are greater or lesser, according as they contain in them more or fewer points, they being made up of points or minimums. For, whatever may be said of extension in abstract, it is certain sensible extension is not infinitely divisible. There is a MINIMUM TANGIBILE and a MINIMUM VISIBILE, beyond which sense cannot perceive. This everyone's experience will inform him.

55. The magnitude of the object which exists without the mind, and is at a distance, continues always invariably the same: but the visible object still changing as you approach to, or recede from, the tangible object, it hath no fixed and determinate greatness. Whenever, therefore, we speak of the magnitude of anything, for instance a tree or a house, we must mean the tangible magnitude, otherwise there can be nothing steady and free from ambiguity spoken of it. But though the tangible and visible magnitude in truth belong to two distinct objects: I shall nevertheless (especially since those objects are called by the same name, and are observed to coexist), to avoid tediousness and singularity of speech, sometimes speak of them as belonging to one and the same thing.

56. Now in order to discover by what means the magnitude of tangible objects is perceived by sight. I need only reflect on what passes in my own mind, and observe what those things be which introduce the ideas of greater or lesser into my thoughts, when I look on any object. And these I find to be, FIRST, the magnitude or extension of the visible object, which being immediately perceived by sight, is connected with that other which is tangible and placed at a distance. SECONDLY, the confusion or distinctness. And thirdly, the vigorousness or faintness of the aforesaid visible appearance. CETERIS PARIBUS, by how much the greater or lesser the visible object is, by so much the greater or lesser do I conclude the tangible object to be. But, be the idea immediately perceived by sight never so large, yet if it be withal confused, I judge the magnitude of the thing to be but small. If it be distinct and clear, I judge it greater. And if it be faint, I apprehend it to be yet greater. What is here meant by confusion and faintness hath been explained in sect. 35.

57. Moreover the judgments we make of greatness do, in like manner as those of distance, depend on the disposition of the eye, also on the figure, number, and situation of objects and other circumstances that have been observed to attend great or small tangible magnitudes. Thus, for instance, the very same quantity of visible extension, which in the figure of a tower doth suggest the idea of great magnitude, shall in the figure of a man suggest the idea of much smaller magnitude. That this is owing to the experience we have had of the usual bigness of a tower and a man no one, I suppose, need be told.

58. It is also evident that confusion or faintness have no more a necessary connexion with little or great magnitude than they have with little or great distance. As they suggest the latter, so they suggest the former to our minds. And by consequence, if it were not for experience, we should no more judge a faint or confused appearance to be connected with great or little magnitude, than we should that it was connected with great or little distance.

59. Nor will it be found that great or small visible magnitude hath any necessary relation to great or small tangible magnitude: so that the one may certainly be inferred from the other. But before we come to the proof of this, it is fit we consider the difference there is betwixt the extension and figure which is the proper object of touch, and that other which is termed visible; and how the former is principally, though not immediately taken notice of, when we look at any object. This has been before mentioned, but we shall here inquire into the cause thereof. We regard the objects that environ us in proportion as they are adapted to benefit or injure our own bodies, and thereby produce in our minds the sensation of pleasure or pain. Now bodies operating on our organs, by an immediate application, and the hurt or advantage arising therefrom, depending altogether on the tangible, and not at all on the visible, qualities of any object: this is a plain reason why those should be regarded by us much more than these: and for this end the visive sense seems to have been bestowed on animals, to wit, that by the perception of visible ideas (which in themselves are not capable of affecting or any wise altering the frame of their bodies) they may be able to foresee (from the experience they have had what tangible ideas are connected with such and such visible ideas) and damage or benefit which is like to ensue, upon the application of their own bodies to this or that body which is at a distance. Which foresight, how necessary it is to the preservation of an animal, everyone's experience can inform him. Hence it is that when we look at an object, the tangible figure and extension thereof are principally attended to; whilst there is small heed taken of the visible figure and magnitude, which, though more immediately perceived, do less concern us, and are not fitted to produce any alteration in our bodies.

60. That the matter of fact is true will be evident to anyone who considers that a man placed at ten foot distance is thought as great as if he were placed at a distance only of five foot: which is true not with relation to the visible, but tangible greatness of the object: the visible magnitude being far greater at one station: than it is at the other.

61. Inches, feet, etc., are settled stated lengths whereby we measure objects and estimate their magnitude: we say, for example, an object appears to be six inches or six foot long. Now, that this cannot be meant of visible inches, etc., is evident, because a visible inch is itself no constant, determinate magnitude, and cannot therefore serve to mark out and determine the magnitude of any other thing. Take an inch marked upon a ruler: view it, successively, at the distance of half a foot, a foot, a foot and a half, etc., from the eye: at each of which, and at all the intermediate distances, the inch shall have a different visible extension, i.e. there shall be more or fewer points discerned in it. Now I ask which of all these various extensions is that stated, determinate one that is agreed on for a common measure of other magnitudes? No reason can be assigned why we should pitch on one more than another: and except there be some invariable, determinate extension fixed on to be marked to the word inch, it is plain it can be used to little purpose; and to say a thing contains this or that number of inches shall imply no more than that it is extended, without bringing any particular idea of that extension into the mind. Farther, an inch and a foot, from different distances, shall both exhibit the same visible magnitude, and yet at the same time you shall say that one seems several times greater than the other. From all which it is manifest that the judgments we make of the magnitude of objects by sight are altogether in reference to their tangible extension. Whenever we say an object is great, or small, of this or that determinate measure, I say it must be meant of the tangible, and not the visible extension, which, though immediately perceived, is nevertheless little taken notice of.

62. Now, that there is no necessary connexion between these two distinct extensions is evident from hence: because our eyes might have been framed in such a manner as to be able to see nothing but what were less than the MINIMUM TANGIBILE. In which case it is not impossible we might have perceived all the immediate objects of sight, the very same that we do now: but unto those visible appearances there would not be connected those different tangible magnitudes that are now. Which shows the judgments we make of the magnitude of things placed at a distance from the various greatness of the immediate objects of sight do not arise from any essential or necessary but only a customary tie, which has been observed between them.

63. Moreover, it is not only certain that any idea of sight might not have been connected with this or that idea of touch, which we now observe to accompany it: but also that the greater visible magnitudes might have been connected with, and introduced into our minds lesser tangible magnitudes and the lesser visible magnitudes greater tangible magnitudes. Nay, that it actually is so we have daily experience; that object which makes a strong and large appearance, not seeming near so great as another, the visible magnitude whereof is much less, but more faint, and the appearance upper, or which is the same thing painted lower on the RETINA, which faintness and situation suggest both greater magnitude and greater distance.

64. From which, and from sect. 57 and 58, it is manifest that as we do not perceive the magnitudes of objects immediately by sight, so neither do we perceive them by the mediation of anything which has a necessary connexion with them. Those ideas that now suggest unto us the various magnitudes of external objects before we touch them, might possibly have suggested no such thing: or they might have signified them in a direct contrary manner: so that the very same ideas, on the perception whereof we judge an object to be small, might as well have served to make us conclude it great. Those ideas being in their own nature equally fitted to bring into our minds the idea of small or great, or no size at all of outward objects; just as the words of any language are in their own nature indifferent to signify this or that thing or nothing at all.

65. As we see distance, so we see magnitude. And we see both in the same way that we see shame or anger in the looks of a man. Those passions are themselves invisible, they are nevertheless let in by the eye along with colours and alterations of countenance, which are the immediate object of vision: and which signify them for no other reason than barely because they have been observed to accompany them. Without which experience we should no more have taken blushing for a sign of shame than of gladness.

66. We are nevertheless exceeding prone to imagine those things which are perceived only by the mediation of others to be themselves the immediate objects of sight; or, at least, to have in their own nature a fitness to be suggested by them, before ever they had been experienced to coexist with them. From which prejudice everyone, perhaps, will not find it easy to emancipate himself, by any [but] the clearest convictions of reason. And there are some grounds to think that if there was one only invariable and universal languages in the world, and that men were born with the faculty of speaking it, it would be the opinion of many that the ideas of other men's minds were properly perceived by the ear, or had at least a necessary and inseparable tie with the sounds that were affixed to them. All which seems to arise from want of a due application of our discerning faculty, thereby to discriminate between the ideas that are in our understandings, and consider them apart from each other; which would preserve us from confounding those that are different, and make us see what ideas do, and what do not include or imply this or that other idea.

67. There is a celebrated phenomenon, the solution whereof I shall attempt to give by the principles that have been laid down, in reference to the manner wherein we apprehend by sight the magnitude of objects. The apparent magnitude of the moon when placed in the horizon is much greater than when it is in the meridian, though the angle under which the diameter of the moon is seen be not observed greater in the former case than in the latter: and the horizontal moon doth not constantly appear of the same bigness, but at some times seemeth far greater than at others.

68. Now in order to explain the reason of the moon's appearing greater than ordinary in the horizon, it must be observed that the particles which compose our atmosphere intercept the rays of light proceeding from any object to the eye; and by how much the greater is the portion of atmosphere interjacent between the object and the eye, by so much the more are the rays intercepted; and by consequence the appearance of the object rendered more faint, every object appearing more vigorous or more faint in proportion as it sendeth more or fewer rays into the eye. Now between the eye and the moon, when situated in the horizon, there lies a far greater quantity of atmosphere than there does when the moon is in the meridian. Whence it comes to pass that the appearance of the horizontal moon is fainter, and therefore by sect. 56 it should be thought bigger in that situation than in the meridian, or in any other elevation above the horizon.

69. Farther, the air being variously impregnated, sometimes more and sometimes less, with vapours and exhalations fitted to retund and intercept the rays of light, it follows that the appearance of the horizontal moon hath not always an equal faintness, and by consequence that luminary, though in the very same situation, is at one time judged greater than at another.

70. That we have here given the true account of the phenomena of the horizontal moon will, I suppose, be farther evident to anyone from the following considerations. FIRST, it is plain that which in this case suggests the idea of greater magnitude must be something which is itself perceived; for that which is unperceived cannot suggest to our perception any other thing. SECONDLY, it must be something that does not constantly remain the same, but is subject to some change or variation, since the appearance of the horizontal moon varies, being at one time greater than at another. And yet, THIRDLY, it cannot be the visible figure or magnitude, since that remains the same, or is rather lesser, by how much the moon is nearer to the horizon. It remains therefore that the true cause is that affection or alteration of the visible appearance which proceeds from the greater paucity of rays arriving at the eye, and which I term FAINTNESS: since this answers all the forementioned conditions, and I am not conscious of any other perception that doth.

71. Add to this that in misty weather it is a common observation that the appearance of the horizontal moon is far larger than usual, which greatly conspires with and strengthens our opinion. Neither would it prove in the least irreconcilable with what we have said, if the horizontal moon should chance sometimes to seem enlarged beyond its usual extent, even in more serene weather. For we must not only have regard to the mist which happens to be in the place where we stand; we ought also to take into our thoughts the whole sum of vapours and exhalations which lie betwixt the eye and the moon: all which cooperating to render the appearance of the moon more faint, and thereby increase its magnitude, it may chance to appear greater than it usually does, even in the horizontal position, at a time when, though there be no extraordinary fog or haziness, just in the place where we stand, yet the air between the eye and the moon, taken all together, may be loaded with a greater quantity of interspersed vapours and exhalations than at other times.

72. It may be objected that in consequence of our principles the interposition of a body in some degree opaque, which may intercept a great part of the rays of light, should render the appearance of the moon in the meridian as large as when it is viewed in the horizon. To which I answer, it is not faintness anyhow applied that suggests greater magnitude, there being no necessary but only an experimental connexion between those two things. It follows that the faintness which enlarges the appearance must be applied in such sort, and with such circumstances, as have been observed to attend the vision of great magnitudes. When from a distance we behold great objects, the particles of the intermediate air and vapours, which are themselves unperceivable, do interrupt the rays of light, and thereby render the appearance less strong and vivid: now, faintness of appearance caused in this sort hath been experienced to coexist with great magnitude. But when it is caused by the interposition of an opaque sensible body, this circumstance alters the case, so that a faint appearance this way caused doth not suggest greater magnitude, because it hath not been experienced to coexist with it.

73. Faintness, as well as all other ideas or perceptions which suggest magnitude or distance, doth it in the same way that words suggest the notions to which they are annexed. Now, it is known a word pronounced with certain circumstances, or in a certain context with other words, hath not always the same import and signification that it hath when pronounced in some other circumstances or different context of words. The very same visible appearance as to faintness and all other respects, if placed on high, shall not suggest the same magnitude that it would if it were seen at an equal distance on a level with the eye. The reason whereof is that we are rarely accustomed to view objects at a great height; our concerns lie among things situated rather before than above us, and accordingly our eyes are not placed on the top of our heads, but in such a position as is most convenient for us to see distant objects standing in our way. And this situation of them being a circumstance which usually attends the vision of distant objects, we may from hence account for (what is commonly observed) an object's appearing of different magnitude, even with respect to its horizontal extension, on the top of a steeple, for example, an hundred feet high to one standing below, from what it would if placed at an hundred feet distance on a level with his eye. For it hath been shown that the judgment we make on the magnitude of a thing depends not on the visible appearance alone, but also on divers other circumstances, any one of which being omitted or varied may suffice to make some alteration in our judgment. Hence, the circumstances of viewing a distant object in such a situation as is usual, and suits with the ordinary posture of the head and eyes being omitted, and instead thereof a different situation of the object, which requires a different posture of the head taking place, it is not to be wondered at if the magnitude be judged different: but it will be demanded why an high object should constantly appear less than an equidistant low object of the same dimensions, for so it is observed to be: it may indeed be granted that the variation of some circumstances may vary the judgment made on the magnitude of high objects, which we are less used to look at: but it does not hence appear why they should be judged less rather than greater? I answer that in case the magnitude of distant objects was suggested by the extent of their visible appearance alone, and thought proportional thereto, it is certain they would then be judged much less than now they seem to be (VIDE sect. 79). But several circumstances concurring to form the judgment we make on the magnitude of distant objects, by means of which they appear far larger than others, whose visible appearance hath an equal or even greater extension; it follows that upon the change or omission of any of those circumstances which are wont to attend the vision of distant objects, and so come to influence the judgments made on their magnitude, they shall proportionably appear less than otherwise they would. For any of those things that caused an object to be thought greater than in proportion to its visible extension being either omitted or applied without the usual circumstances, the judgment depends more entirely on the visible extension, and consequently the object must be judged less. Thus in the present case the situation of the thing seen being different from what it usually is in those objects we have occasion to view, and whose magnitude we observe, it follows that the very same object, being an hundred feet high, should seem less than if it was an hundred feet off on (or nearly on) a level with the eye. What has been here set forth seems to me to have no small share in contributing to magnify the appearance of the horizontal moon, and deserves not to be passed over in the explication of it.

74. If we attentively consider the phenomenon before us, we shall find the not discerning between the mediate and immediate objects of sight to be the chief cause of the difficulty that occurs in the explication of it. The magnitude of the visible moon, or that which is the proper and immediate object of vision, is not greater when the moon is in the horizon than when it is in the meridian. How comes it, therefore, to seem greater in one situation than the other? What is it can put this cheat on the understanding? It has no other perception of the moon than what it gets by sight: and that which is seen is of the same extent, I say, the visible appearance hath the same, or rather a less, magnitude when the moon is viewed in the horizontal than when in the meridional position: and yet it is esteemed greater in the former than in the latter. Herein consists the difficulty, which doth vanish and admit of a most easy solution, if we consider that as the visible moon is not greater in the horizon than in the meridian, so neither is it thought to be so. It hath been already shown that in any act of vision the visible object absolutely, or in itself, is little taken notice of, the mind still carrying its view from that to some tangible ideas which have been observed to be connected with it, and by that means come to be suggested by it. So that when a thing is said to appear great or small, or whatever estimate be made of the magnitude of any thing, this is meant not of the visible but of the tangible object. This duly considered, it will be no hard matter to reconcile the seeming contradiction there is, that the moon should appear of a different bigness, the visible magnitude thereof remaining still the same. For by sect. 56 the very same visible extension, with a different faintness, shall suggest a different tangible extension. When therefore the horizontal moon is said to appear greater than the meridional moon, this must be understood not of a greater visible extension, but a of greater tangible or real extension, which by reason of the more than ordinary faintness of the visible appearance, is suggested to the mind along with it.

75. Many attempts have been made by learned men to account for this appearance. Gassendus, Descartes, Hobbes, and several others have employed their thoughts on that subject; but how fruitless and unsatisfactory their endeavours have been is sufficiently shown in THE TRANSACTIONS,[Phil. Trans. Num. 187. p. 314] where you may see their several opinions at large set forth and confuted, not without some surprize at the gross blunders that ingenious men have been forced into by endeavouring to reconcile this appearance with the ordinary Principles of optics. Since the writing of which there hath been published in the TRANSACTIONS [Numb. 187. P. 323] another paper relating to the same affair by the celebrated Dr. Wallis, wherein he attempts to account for that phenomenon which, though it seems not to contain anything new or different from what had been said before by others, I shall nevertheless consider in this place.

76. His opinion, in short, is this; we judge not of the magnitude of an object by the visual angle alone, but by the visual angle in conjunction with the distance. Hence, though the angle remain the same, or even become less, yet if withal the distance seem to have been increased, the object shall appear greater. Now, one way whereby we estimate the distance of anything is by the number and extent of the intermediate objects: when therefore the moon is seen in the horizon, the variety of fields, houses, etc., together with the large prospect of the wide extended land or sea that lies between the eye and the utmost limb of the horizon, suggest unto the mind the idea of greater distance, and consequently magnify the appearance. And this, according to Dr. Wallis, is the true account of the extraordinary largeness attributed by the mind to the horizontal moon at a time when the angle subtended by its diameter is not one jot greater than it used to be.

77. With reference to this opinion, not to repeat what hath been already said concerning distance, I shall only observe, FIRST, that if the prospect of interjacent objects be that which suggests the idea of farther distance, and this idea of farther distance be the cause that brings into the mind the idea of greater magnitude, it should hence follow that if one looked at the horizontal moon from behind a wall, it would appear no bigger than ordinary. For in that case the wall interposing cuts off all that prospect of sea and land, etc. which might otherwise increase the apparent distance, and thereby the apparent magnitude of the moon. Nor will it suffice to say the memory doth even then suggest all that extent of land, etc., which lies within the horizon; which suggestion occasions a sudden judgment of sense that the moon is farther off and larger than usual. For ask any man who, from such a station beholding the horizontal moon, shall think her greater than usual, whether he hath at that time in his mind any idea of the intermediate objects, or long tract of land that lies between his eye and the extreme edge of the horizon? And whether it be that idea which is the cause of his making the aforementioned judgment? He will, I suppose, reply in the negative, and declare the horizontal moon shall appear greater than the meridional, though he never thinks of all or any of those things that lie between him and it. SECONDLY, it seems impossible by this hypothesis to account for the moon's appearing in the very same situation at one time greater than at another; which nevertheless has been shown to be very agreeable to the principles we have laid down, and receives a most easy and natural explication from them. For the further clearing' up of this point it is to be observed that what we immediately and properly see are only lights and colours in sundry situations and shades and degrees of faintness and clearness, confusion and distinctness. All which visible objects are only in the mind, nor do they suggest ought external, whether distance or magnitude, otherwise than by habitual connexion as words do things. We are also to remark that, beside the straining of the eyes, and beside the vivid and faint, the distinct and confused appearances (which, bearing some proportion to lines and angles, have been substituted instead of them in the foregoing part of this treatise), there are other means which suggest both distance and magnitude; particularly the situation of visible points of objects, as upper or lower; the one suggesting a farther distance and greater magnitude, the other a nearer distance and lesser magnitude: all which is an effect only of custom and experience; there being really nothing intermediate in the line of distance between the uppermost and lowermost, which are both equidistant, or rather at no distance from the eye, as there is also nothing in upper or lower, which by necessary connexion should suggest greater or lesser magnitude. Now, as these customary, experimental means of suggesting distance do likewise suggest magnitude, so they suggest the one as immediately as the other. I say they do not (VIDE sect. 53) first suggest distance, and then leave the mind from thence to infer or compute magnitude, jut suggest magnitude as immediately and directly as they suggest distance.

78. This phenomenon of the horizontal moon is a clear instance of the insufficiency of lines and angles for explaining the way wherein the mind perceives and estimates the magnitude of outward objects. There is nevertheless a use of computation by them in order to determine the apparent magnitude of things, so far as they have a connexion with, and are proportional to, those other ideas or perceptions which are the true and immediate occasions that suggest to the mind the apparent magnitude of things. But this in general may, I think, be observed concerning mathematical computation in optics: that it can never be very precise and exact since the judgments we make of the magnitude of external things do often depend on several circumstances, which are not proportionable to, or capable of being defined by, lines and angles.

79. From what has been said we may safely deduce this consequence; to wit, that a man born blind and made to see would, at first opening of his eyes, make a very different judgment of the magnitude of objects intromitted by them from what others do. He would not consider the ideas of sight with reference to, or as having any connexion with, the ideas of touch: his view of them being entirely terminated within themselves, he can no otherwise judge them great or small than as they contain a greater or lesser number of visible points. Now, it being certain that any visible point can cover or exclude from view only one other visible point, it follows that whatever object intercepts the view of another hath an equal number of visible points with it; and consequently they shall both be thought by him to have the same magnitude. Hence it is evident one in those circumstances would judge his thumb, with which he might hide a tower or hinder its being seen, equal to that tower, or his hand, the interposition whereof might conceal experimental means the firmament from his view, equal to the firmament: how great an inequality soever there may in our apprehensions seem to be betwixt those two things, because of the customary and close connexion that has grown up in our minds between the objects of sight and touch; whereby the very different and distinct ideas of those two senses are so blended and confounded together as to be mistaken for one and the same thing; out of which prejudice we cannot easily extricate ourselves.

80. For the better explaining the nature of vision, and setting the manner wherein we perceive magnitudes in a due light, I shall proceed to make some observations concerning matters relating thereto, whereof the want of reflexion, and duly separating between tangible and visible ideas, is apt to create in us mistaken and confused notions. And FIRST, I shall observe that the MINIMUM VISIBILE is exactly equal in all beings whatsoever that are endowed with the visive faculty. No exquisite formation of the eye, no peculiar sharpness of sight, can make it less in one creature than in another; for it not being distinguishable into parts, nor in any wise a consisting of them, it must necessarily be the same to all. For suppose it otherwise, and that the MINIMUM VISIBILE of a mite, for instance, be less than the MINIMUM VISIBILE of a man: the latter therefore may by detraction of some part be made equal to the former: it doth therefore consist of parts, which is inconsistent with the notion of a MINIMUM VISIBILE or point.

81. It will perhaps be objected that the MINIMUM VISIBILE of a man doth really and in itself contain parts whereby it surpasses that of a mite, though they are not perceivable by the man. To which I answer, the MINIMUM VISIBILE having (in like manner as all other the proper and immediate objects of sight) been shown not to have any existence without the mind of him who sees it, it follows there cannot be any pan of it that is not actually perceived, and therefore visible. Now for any object to contain distinct visible parts, and at the same time to be a MINIMUM VISIBILE, is a manifest contradiction.

82. Of these visible points we see at all times an equal number. It is every whit as great when our view is contracted and bounded by near objects as when it is extended to larger and remoter. For it being impossible that one MINIMUM VISIBILE should obscure or keep out of sight mote than one other, it is a plain consequence that when my view is on all sides bounded by the walls of my study see just as many visible points as I could, in case that by the removal of the study-walls and all other obstructions, I had a full prospect of the circumjacent fields, mountains, sea, and open firmament: for so long as I am shut up within the walls, by their interposition every point of the external objects is covered from my view: but each point that is seen being able to cover or exclude from sight one only other corresponding point, it follows that whilst my sight is confined to those narrow walls I see as many points, or MINIMA VISIBILIA, as I should were those walls away, by looking on all the external objects whose prospect is intercepted by them. Whenever therefore we are said to have a greater prospect at one time than another, this must be understood with relation, not to the proper and immediate, but the secondary and mediate objects of vision, which, as hath been shown, properly belong to the touch.

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