VISIBLE. 



the refrafting plane. That this is the cafe whli rcfpeft to 

 plane mirrors is uiiiverfally acknowledged ; and foine expe- 

 riments with mirrors of other forms feem to favour the fame 

 conclufion, and thereby afford peafon for extending the ana- 

 logy to all cafes of vifion. If a right line be held perpendi- 

 cularly over a convex or concave mirror, its image feems to 

 make one line with it. The fame is the cafe with a right line 

 held perpendicularly within water ; for the part which is 

 within the water feems to be a continuation of tliat wliich is 

 without, at leaft when it is viewed with no more than com- 

 mon attention, and in fome pofitions. But Dr. Barrow 

 called in queftion this method of judging of the place of 

 an objeft, and thereby opened a new field of enquiry and 

 debate in tliis branch of fcience. This, with other optical 

 inveftigations, he publirtied in his Optical Leftures, firft. 

 printed in 1674. Having, as he imagined, refuted the com- 

 mon hypothefis concerning the place of vifible objefts, he 

 fubftitutcs another rule, by which, he fays, our judgments 

 are aftually directed in this cafe. According to him, we 

 refer every point of an objeft to tlie place from which the 

 pencils of light, tliat give us the image of it, iflae, or from 

 which they would have iffued, if no refledting or refrafting 

 fubftance intervened. Purfuing this principle, Dr. Barrow 

 proceeded to inveftigate the place, in which the rays, iffuing 

 from each of the points of an objcft, and which reach the 

 eye after one refledlion or refraftion, meet ; and he found, 

 that if the refrafting fiirface was plane, and the refraftion 

 was made from a denfer medium into a rarer, thofe rays 

 ■would always meet in a place between the eye and a per- 

 pendicular to the point of incidence. 



If a convex mirror be ufed, the cafe will be the fame ; 

 but if the mirror be plane, the rays will meet in tlie perpen- 

 dicular, and beyond it if it be concave. He alfo determined, 

 according to thefe principles, what [form the image of a 

 right hne will take when it is prcfented in different manners 

 to a fpherical mirror, or when it is feen through a refrafting 

 medium. 



Dr. Barrow, however, mentions an objeftion againft the 

 maxim which lie endeavoured to eftablifli, concerning the 

 fuppofed place of vifible objefts, and candidly owns that he 

 ■was not able to give a fatisfaftory folution of it. The ob- 

 jeAion i o this ; let an objeiS be placed beyond the focus of a 

 convex lens, and if the eye be clofe to the lens, it will ap- 

 pear confufed, but very near to its true place. If the eye 

 he a little withdrawn, the confufion will increafe, and the 

 objeft will feem to come nearer ; and when the eye is very 

 near the focus, the confufion will be exceedingly great, and 

 the objeft will feem to be clofe to the eye. But in this ex- 

 periment the eye receives no rays but thofe that are con- 

 verging ; and the point from which they iffue is fo far from 

 being nearer than the objeft, that it is beyond it ; notwith- 

 ftanding which, the objett is conceived to be much ncai-er 

 than it is, though no very difiinft idea can be formed of its 

 precife diftance. 



The firft perfon who took much notice of Dr. Barrow's 

 hypothefis, and the difficulty attending it, was Dr. Berke- 

 ley, who, in his Effay on a New Theory of Vifion, p. 50, 

 obferves, that the circle formed upon the retina by the rays 

 which do not come to a focus, produces the fame confufion in 

 the eye, whether they crofs one another before they reach 

 the retina, or tend to it afterwards : and therefore, that the 

 judgment concerning diflanccs will be the fame in bath the 

 cafcs^ without any regard to the place from which the rays 

 origihally iffued ; fo that in this cafe, as, by receding from 

 the lens, the confufion, which always accompanies the near- 

 nefs of an objeft, increafes, the mind will judge that the 

 object comes nearer. See j4pparent Distance. 



Vol. XXXVII. 



M. Bouguer, an iugenious writer on Optics, in his 

 Traite d'Optique, p. 104, adopts the general maxim of 

 Dr. Barrow, in fuppofing that we refer objefts to the place 

 from wliich the pencils of rays feemingly converge at their 

 entrance into the pupil. But when rays iffue fuom below 

 the furface of a veffel of water, or any other refrafting me- 

 dium, he finds that there are always two different places 

 of this feeming convergence : one of them of the rays that 

 iffue from it in the fame vertical circle, and, therefore, fall 

 with different degrees of obliquity upon the furface of the 

 refrafting medium, and another of thofe that fall upon the 

 furface with the fame degree of obhquity, entering the eye 

 laterally with refpeft to one another. Sometimes, he fays, 

 one of thefe images is attended to by the mind, and fome- 

 times the other ; and different images may be obferved by dif- 

 ferent perfons. An objeft, plunged into water, affords an 

 example, he fays, of this duplicity of images. 



G. W. Krafft has ably fupported the opinion of Dr. Bar- 

 row, that the place of any point feen by reficftion from 

 the furface of any medium, is that in which rays ifluing 

 from it, infinitely near to one another, would meet ; and 

 confidering the cafe of a diftant objeft, viewed in a concave 

 mirror by an eye very near to it, when the image, according 

 to Euchd and other writers, would be between the eye and 

 the objeft, and the rule of Dr. Barrow cannot be applied ; 

 he fays, that in this cafe, the fpeculum may be confidered as 

 a plane, the elfeft being the fame, only that the image it 

 more obfcure. Com. Petropol. vol. xii. p. 252. 256. See 

 Piiedley's Hift. of Light, &c. p. 89. 688, &c. 



From the principle above illullrated, feveral remarkable 

 phenomena of vifion are accounted for : as, 



1. That if the diftance between two vifible objefts be an 

 angle that is infenfible, the diftant bodies will .appear as if 

 contiguous : whence a continuous body being the refult of 

 feveral contiguous ones ; if the dift.ances between feveral 

 vifibles fubtend infenfible angles, they will appear one con- 

 tinuous body ; which gives a pretty iUuftration of the notion 

 of a continuum. 



Hence parallel lines, and long villas, confifting of paral- 

 lel rows of trees, feem to converge more and more, the 

 farther they are extended from the eye ; becaufe the apparent 

 magnitudes of their perpendicular intervals are perpetually 

 diminifhing, while, at the fame time, we miftake their dif- 

 tance. When two parallel rows of trees ftand upon an afcent, 

 the more remote parts appear farther off than they really 

 are, becaufe the line that meafures the length of the viftas 

 now appears under a greater angle than when it was hori- 

 zontal ; the trees, in fucii a cafe, feeming to converge lefs, 

 and fometimes, inftead of converging, feeming to diverge. 

 See Par.^llellism of Rows of Trees. 



The proper method of drawing the appearance of two 

 rows of trees that fhall appear parallel to the eye, is a 

 problem that has cxercifed the ingenuity of feveral philo- 

 lophers and mathematicians. That the apparent magni- 

 tude of objefts decreafes with the angle under ■which 

 they are feen, has always been acknowledged : and it is 

 alfo acknowledged, that wc learn to form a judgment both 

 of magnitudes and diftances only by cuilom and experience ; 

 but in the application of lliefe maxims to the above men- 

 tioned problem, all perfons, before M. Bouguer, made life 

 of the real diftance inllead of the apparent one, by which 

 only the mind can form its judgment. And it is maniftll, 

 that if any circumftances contribute to make the diflaiicc 

 appear otherwife than it is in reality, the apparent magni- 

 tude of the objeft will he affefted by it, for the fame reafon, 

 that if the magnitude be mifapprthendcd, the idea of the 

 diftance will vary. For want of atlcndiog to 'his dif- 

 L 1 tinftion, 



