In the first place, it is objected, that in the beginning of the Essay I argue either against all use of lines and angles in optics, and then what I say is false; or against those writers only who will have it that we can perceive by sense the optic axes, angles, &c., and then it is insignificant, this being an absurdity which no one ever held. To which I answer that I argue only against those who are of opinion that we perceive the distance of objects by lines and angles, or, as they term it, by a kind of innate geometry. And, to shew that this is not fighting with my own shadow, I shall here set down a passage from the celebrated Des Cartes[460]:—
“Distantiam præterea discimus, per mutuam quandam conspirationem oculorum. Ut enim cæcus noster duo bacilla tenens, A E et C E, de quorum longitudine incertus, solumque intervallum manuum A et C, cum magnitudine [pg 208] angulorum A C E, et C A E exploratum habens, inde, ut ex Geometria quadam omnibus innata, scire potest ubi sit punctum E. Sic quum nostri oculi R S T et r s t ambo, vertuntur ad X, magnitudo lineæ S s, et angulorum X S s et X s S, certos nos reddunt ubi sit punctum X. Et idem opera alterutrius possumus indagare, loco illum movendo, ut si versus X illum semper dirigentes, prime sistamus in puncto S, et statim post in puncto s, hoc sufficiet ut magnitudo lineæ S s, et duorum angulorum X S s et X s S nostræ imaginationi simul occurrant, et distantiam puncti X nos edoceant: idque per actionem mentis, quæ licet simplex judicium esse videatur, ratiocinationem tamen quandam involutam habet, similem illi, qua Geometræ per duas stationes diversas, loca inaccessa dimetiuntur.”
I might amass together citations from several authors to the same purpose, but, this being so clear in the point, and from an author of so great note, I shall not trouble the reader with any more. What I have said on this head was not for the sake of rinding fault with other men; but, because I judged it necessary to demonstrate in the first place that we neither see distance immediately, nor yet perceive it by the mediation of anything that hath (as lines and angles) a necessary connexion with it. For on the demonstration of this point the whole theory depends[461].
Secondly, it is objected, that the explication I give of the appearance of the horizontal moon (which may also be [pg 209] applied to the sun) is the same that Gassendus had given before. I answer, there is indeed mention made of the grossness of the atmosphere in both; but then the methods wherein it is applied to solve the phenomenon are widely different, as will be evident to whoever shall compare what I have said on this subject with the following words of Gassendus:—
“Heinc dici posse videtur: solem humilem oculo spectatum ideo apparere majorem, quam dum altius egreditur, quia dum vicinus est horizonti prolixa est series vaporum, atque adeo corpusculorum quæ solis radios ita retundunt, ut oculus minus conniveat, et pupilla quasi umbrefacta longe magis amplificetur, quam dum sole multum elato rari vapores intercipiuntur, solque ipse ita splendescit, ut pupilla in ipsum spectans contractissima efficiatur. Nempe ex hoc esse videtur, cur visibilis species ex sole procedens, et per pupillam amplificatam intromissa in retinam, ampliorem in illa sedem occupet, majoremque proinde creet solis apparentiam, quam dum per contractam pupillam eodem intromissa contendit.” Vid. Epist. 1. De Apparente Magnitudine Solis Humilis et Sublimis, p. 6. This solution of Gassendus proceeds on a false principle, to wit, that the pupil's being enlarged augments the species or image on the fund of the eye.
Thirdly, against what is said in Sect. 80, it is objected, that the same thing which is so small as scarce to be discerned by a man, may appear like a mountain to some small insect; from which it follows that the minimum visibile is not equal in respect of all creatures[462]. I answer, if this objection be sounded to the bottom, it will be found to mean no more than that the same particle of matter which is marked to a man by one minimum visibile, exhibits to an insect a great number of minima visibilia. But this does not prove that one minimum visibile of the insect is not equal to one minimum visibile of the man. The not distinguishing between the mediate and immediate objects of sight is, I suspect, a cause of misapprehension in this matter.
Some other misinterpretations and difficulties have been [pg 210] made, but, in the points they refer to, I have endeavoured to be so very plain that I know not how to express myself more clearly. All I shall add is, that if they who are pleased to criticise on my Essay would but read the whole over with some attention, they might be the better able to comprehend my meaning, and consequently to judge of my mistakes.