“Hæc sunt, quæ circa partem opticæ præcipue mathematicam dicenda mihi suggessit meditatio. Circa reliquas (quæ φυσικώτεραι sunt, adeoque sæpiuscule pro certis principiis plausibiles conjecturas venditare necessum habent) nihil fere quicquam admodum verisimile succurrit, [pg 136]a pervulgatis (ab iis, inquam, quæ Keplerus, Scheinerus[315], Cartesius, et post illos alii tradiderunt) alienum aut diversum. Atqui tacere malo, quam toties oblatam cramben reponere. Proinde receptui cano; nee ita tamen ut prorsus discedam, anteaquam improbam quandam difficultatem (pro sinceritate quam et vobis et veritati debeo minime dissimulandam) in medium protulero, quæ doctrinæ nostræ, hactenus inculcatæ, se objicit adversam, ab ea saltem nullam admittit solutionem. Illa, breviter, talis est. Lenti vel speculo cavo EBF exponatur punctum visibile A, ita distans, ut radii ex A manantes ex inflectione versus axem AB cogantur. Sitque radiationis limes (seu puncti A imago, qualem supra passim statuimus) punctum Z. Inter hoc autem et inflectentis verticem Buspiam positus concipiatur oculus. Quæri jam potest, ubi loci debeat punctum A apparere? Retrorsum ad punctum Z videri non fert natura (cum omnis impressio sensum afficiens proveniat a partibus A) ac experientia reclamat. Nostris autem e placitis consequi videtur, ipsum ad partes anticas apparens, ab intervallo longissime dissito (quod et maximum sensibile quodvis intervallum quodammodo exsuperet), apparere. Cum enim quo radiis minus divergentibus attingitur objectum, eo (seclusis utique prænotionibus et præjudiciis) longius abesse sentiatur; et quod parallelos ad oculum radios projicit, remotissime positum æstimetur: exigere ratio videtur, ut quod convergentibus radiis apprehenditur, adhuc magis, si fieri posset, quoad apparentiam elongetur. Quin et circa casum hunc generatim inquiri possit, quidnam omnino sit, quod apparentem puncti A locum determinet, faciatque quod constanti ratione nunc propius, nunc remotius appareat? Cui itidem dubio nihil quicquam ex hactenus dictorum analogia responderi posse videtur, nisi [pg 137]debere punctum A perpetuo longissime semotum videri. Verum experientia secus attestatur, illud pro diversa oculi inter puncta B, Z, positione varie distans, nunquam fere (si unquam) longinquius ipso A libere spectato, subinde vero multo propinquius adparere; quinimo, quo oculum appellentes radii magis convergunt, eo speciem objecti propius accedere. Nempe, si puncto B admoveatur oculus, suo (ad lentem) fere nativo in loco conspicitur punctum A (vel æque distans, ad speculum); ad O reductus oculus ejusce speciem appropinquantem cernit; ad P adhuc vicinius ipsum existimat; ac ita sensim, donec alicubi tandem, velut ad Q, constituto oculo, objectum summe propinquum apparens in meram confusionem incipiat evanescere. Quæ sane cuncta rationibus atque decretis nostris repugnare videntur, aut cum iis saltem parum amice conspirant. Neque nostram tantum sententiam pulsat hoc experimentum, at ex æquo cæteras quas norim omnes: veterem imprimis ac vulgatam, nostræ præ reliquis affinem, ita convellere videtur, ut ejus vi coactus doctissimus A. Tacquetus isti principio (cui pene soli totam inædificaverat Catoptricam suam) ceu infido ac inconstanti renunciarit, adeoque suam ipse doctrinam labefactarit? id tamen, opinor, minime facturus, si rem totam inspexissit penitius, atque difficultatis fundum attigissit. Apud me vero non ita pollet hæc, nec eousque præpollebit ulla difficultas, ut ab iis quæ manifeste rationi consentanea video, discedam; præsertim quum, ut his accidit, ejusmodi difficultas in singularis cujuspiam casus disparitate fundetur. Nimirum in præsente casu peculiare quiddam, naturæ subtilitati involutum, delitescit, ægre fortassis, nisi perfectius explorato videndi modo, detegendum. Circa quod nil, fateor, hactenus excogitare potui, quod adblandiretur animo meo, nedum plane satisfaceret. Vobis itaque nodum hunc, utinam feliciore conatu, resolvendum committo.”
In English as follows:
“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 [pg 138]different from what has been already said by Kepler, Scheinerus, Des Cartes, &c. 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 obliges 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 axis AB. 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 shews that it doth 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 [pg 139]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 almost 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 does 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 by 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 [pg 140]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[316] 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[317]. The eye, the nearer it is placed to the point B in the above 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 any one 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 [pg 141] 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 greatest 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[318]. But, in order to a more full explication of this point, and to shew 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.
