quently that ray which is moft turned round upon b, or which is most refracted, will make an angle with ya that will be nearer to a right one, than that ray makes with it which is leaft turned round upon b, or which is leaft refracted. Therefore that ray which is most refracted will make a greater angle with the incident ray than that which is leaft refracted. 463. But fince the emerging rays, as they are differently refrangible, make different angles with the fame incident ray y, the refraction which they fuffer at emerfion will feparate them from one another. The angle y r m, which the most refrangible or violet rays make with the incident ones, is found by calculation to be 54° 7'; and the angle y so, which the leaft refrangible or red rays make with the incident ones, is found to be 30° 57': the angles which the rays or the intermediate colours, indigo, blue green, yellow, and orange, make with the incident rays, are intermediate angles between 54° 7′ and 50° 57'. 464. XII. "If a line is fuppofed to be drawn from the centre of the fun through the eye of the fpectator; the angle which, after two refractions and two reflections, any effectual ray makes with the incident ray, will be equal to the angle which it makes with that line." 465. If y w (Pl. CCLVII. fig. 4.) is an incident ray, bo an effectual ray, and qn a line drawn from the centre of the fun through o the eye of the spectator; the angle y so, which the effectual ray makes with the incident ray, is equal to s o n, the angle which the fame effectual ray makes with the line qn. For y avand qn, confidered as drawn from the centre of the fun, are parallel; bo cróffes them, and confequently makes the alternate angles so, son, equal to one another. Eucl. B. 1. Pr. 29. 466. XIII." When the fun fhines upon the drops of rain as they are falling, the rays that come from thefe drops to the eye of a fpectator, after two reflections and two refractions, produce the fecondary rainbow." 467. The fecondary rainbow is the outermoft; CHD, fig. 3. When the fun fhines upon a drop of rain H; and the rays HO, which emerge at H fo as to be effectual, make an angle HOP of 54° 7' with LOP a line drawn from the fun through the eye of the ipectator; the fame effectual rays will make likewife an angle of 54° 7′ with the incident rays S, and the rays which emerge at this angle are violet ones, by what was observed above. Therefore, if the ipectator's eye is at O, none but violet rays will enter it: for as all the other rays make a lefs angle with OP, they will fall above the spectator's cye. In like manner, if the effectual rays that emerge from the drop G make an angle of 54° 57' with the line OP, they will likewife make the fame angle with the incident rays S; and confequently, from the drop G to the fpectator's eye at O, no rays will come but red ones; for all the other rays, making a greater angle with the line OP, will fall below the eye at O. For the fame reafon, the rays emerging from the intermediate drops between H and G, and coming to the spectator's eye at O, will emerge at intermediate angles, and therefore will have the intermediate colours. Thus, if there are feven drops from H to G inclufively, their colours will be violet, indigo, blue, green, yellow, orange, and red. This coloured line is the breadth of the fecondary rainbow. 468. Now, if HOP was to turn round upon the line OP, like a pair of compaffes upon one of the legs OP with the opening HOP, it is plain from the fuppofition, that, in fuch a revolution of the drop H, the angle HOP would be the fame, and confequently the emerging rays would make the fame angle with the incident ones. But in fuch a revolution the drop would defcribe a circle of which P would be the centre, and CNHRD an arc. Confequently, fince, when the drop is at N, or at R, or anywhere elfe in that arc, the emerging rays make the fame angle with the incident ones, as when the drop is at H, the colour of the drop will be the fame to an eye placed at O, whether the drop is at N, or at H, or at R, or anywhere elfe in that arc. Now, though the drop does not thus turn round as it falls, and does not pass through the feveral parts of this arc, yet, fince there are drops of rain falling everywhere at the fame time, when one drop is at H, there will be another at R, another at N, and others in all parts of the arc; and thefe drops will all of them be violet-coloured, for the fame reason that the drop H would have been of this colour if it had been in any of thofe places. In like manner, as the drop G is red when it is at G, it would likewife be red in any part of the arc CWGQD; and fo will any other drop, when, as it is falling, it comes to any part of that arc. Thus, as the fun shines upon the rain whilft it falls, there will be two arcs produced, a violet coloured one CNHRD, and a red one CWGQD; and for the fame reafons the intermediate space between these two arcs will be filled up with arcs of the intermediate colours. All these arcs together make up the fecondary rainbow. 469. XIV. "The colours of the secondary rainbow are fainter than thofe of the primary rain. bow; and are ranged in the contrary order." 470. The primary rainbow is produced by fuch rays as have been only once reflected; the fecondary rainbow is produced by fuch rays as have been twice reflected. But at every reflection some rays pafs out of the drop of rain without being reflected; fo that the oftener the rays are reflected the fewer of them are left. Therefore the colours of the fecondary bow are produced by fewer rays, and confequently will be fainter, than the colours of the primary bow. In the primary bow, reckoning from the outfide of it, the colours are ranged in this order; red, orange, yellow, green, blue, indigo, violet. In the fecondary bow, reckoning from the outfide, the colours are violet, indigo, blue, green, yellow, orange, red. So that the red, which is the outermoft or highest colour in the primary bow, is the innermoft or lowest co. lour in the fecondary one. 471. Now the violet rays, when they emerge fo as to be effectual after one reflection, make a less angle with the incident rays than the red ones; confequently the violet rays make a leis angle with the lines OP (Pl. CCLVII, fig. 3.) than the red ones. But, in the primary rainbow, the rays are only only once reflected, and the angle which the ef. fectual rays make with OP is the distance of the coloured drop from P the centre of the bow. Therefore the violet drops, or violet arc, in the primary bow, will be nearer to the centre of the bow than the red drops or red arc; that is, the innermost colour in the primary bow will be violet, and the outermoft colour will be red. And, for the fame reason, through the whole primary bow, every colour will be nearer to the centre P, as the rays of that colour are more refrangible. But the violet rays, when they emerge fo as to be effectual after two reflections, make a greater angle with the incident rays than the red ones; con. fequently the violet rays will make a greater angle with the line OP than the red ones. But in the fecondary rainbow the rays are twice reflected, and the angle which effectual rays make with OP is the distance of the coloured drop from P the centre of the bow. Therefore the violet drops or violet arc in the fecondary bow will be farther from the centre of the bow than the red drops or red arc; that is, the outermoft colour in the fecondary bow will be violet, and the innermoft colour will be red. And, for the fame reason, through the whole fecondary bow, every colour will be further from the centre P, as the rays of that colour are more refrangible. $ 2. Of HALOES, PARHELIA, &c. 472. Under the articles HALO and PARHELION will be found a pretty full account of the different hypothefes concerning these phenomena, and likewife of the method by which these hypotheses are fupported, from the known laws of refraction and reflection; to which therefore we refer, to avoid repetition. 3. Of the APPARENT PLACE, DISTANCE, MAGNITUDE, and MOTION of OBJECTS. 473. PHILOSOPHERS in general had taken for granted, that the place to which the eye refers any visible object seen by reflection or refraction, is that in which the visual ray meets a perpendicular from the object upon the reflecting or refracting plane. But this method of judging of the place of objects was called in question by Dr BARROW, who contended that the arguments brought in favour of the opinion were not conclufive. Thefe arguments are, that the images of objects appear straight in a plane mirror, but curved in a convex or concave one: that a straight thread, when partly immerfed perpendicularly in water, does not appear crooked as when it is obliquely plunged into the fluid; but that which is within the water feems to be a continuation of that which is without. With respect to the reflected image, however, of a perpendicular right line from a convex or concave mirror, he says, that it is not easy for the eye to diftinguish the curve that it really makes; and that, if the appearance of a perpendicular thread, part of which is plunged in water, be closely attended to, it will not favour the common bypothefis. If the thread is of any fhining metal, as filver, and viewed obliquely, the image of the part immerfed will appear to detach itfeif fenfibly from that part which is without the water, fo that it cannot be true that every object appears to be in the fame place where the refracted ray meets the perpendicular; and the fame obfervation, he thinks, may be extended to the case of reflection. The Dr fays, we refer every point of an object to the place from which the pencils of light, that give us the image of it, iffe, or from which they would have iflued if no reflecting or refracting substance intervened. Purfuing this principle, he proceeds to investigate the place in which the rays iffuing from each of the points of an object, and which reach the eye after one reflection or refraction, meet; and he found, that if the refracting furface was plane, and the refraction was made from a denfer medium into a rarer, thofe rays would always meet in a place between the eye and a perpendicular to the point of incidence. If a convex mirror be used, the cafe will be the fame; but if the mirror be plane, the rays will meet in the perpendicular, and beyond it if it be concave. He alfo determined, according to these principles, what form the image of a right line will take, when it is prefented in different manners to a spherical mirror, or when it is feen through a refracting medium. 474. Probable as Dr BARROW thought the maxim which he endeavoured to establish concern. ing the fuppofed place of visible objects, he mentions an objection to it, and acknowledges that he was not able to give a fatisfactory solution of it. It is this: Let an object be placed beyond the focus of a convex lens; and if the eye be close to the lens, it will appear confufed, but very near to its true place. If the eye be a little withdrawn, the confufion will increafe, and the object will feem to come nearer; and when the eye is very near the focus, the confusion will be exceedingly great, and the object will feem to be close to the eye. But in this experiment the eye receives no rays but those that are converging; and the point from which they iffue is so far from being nearer than the object, that it is beyond it; notwithftanding which, the object is conceived to be much nearer than it is, though no very diftinct idea ean be formed of its precife diftance. It may be ob ferved, that in reality, the rays falling upon the eye in this cafe in a manner quite different from that in which they fall upon it in other circumftances, we can form no judgment about the place from which they iffue. This fubject was afterwards taken up by Berkeley, Smith, Montucla, and others. 475. M. DE LA HIRE made feveral valuable obfervations concerning the diftance of visible objects, and various other phenomena of vifion, which are well worth notice. He also took par ticular pains to ascertain the manner in which the eye conforms itfelf to the view of objects placed at different diftances. He enumerates five circumftances, which affift us in judging of the distance of objects, namely, their apparent magnitude, the ftrength of the colouring, the direction of the two eyes, the parallax of the objects, and the diftin&tnefs of their small parts. Painters, he says, can only take advantage of the two first mentioned circumftances, and therefore pictures can never perfectly deceive the eye; but in the decorations of theatres, they make ufe of them all. The fize of objects, and the ftrength of their colouring, are diminished in proportion to the diftance at which they are intended to appear. Parts of the fame object which are to appear at different diftances, as columns in an order of architecture, are drawn upon different planes, a little removed from one another, that the two eyes may be obliged to change their direction, to diftinguifh the parts of the nearer plane from those of the more remote. The fmall diftance of the planes ferves to make a small parallax, by changing the pofition of the eye; and as we do not preferve a diftinct idea of the quantity of parallax, correfponding to the different diftances of objects, it is fufficient that we perceive there is a parallax, to be convinced that thefe planes are diftant from one another, without determining what that diftance is; and as to the last circumstance, viz. the diftin&tnefs of the fmall parts of objects, it is of no use in discovering the deception, on account of the falfe light that is thrown upon thefe deco rations. 476. To thefe obfervations concerning deceptions of fight, we fhall add a fimilar one of M. LE CAT, who took notice that the reafon why we imagine objects to be larger when they are feen through a mift, is the dimnefs or obfcurity with which they are then feen; this circumftance being affociated with the idea of great diftance. This he fays is confirmed by our being furprised to find upon approaching fuch objects, that they are fo much nearer to us, as well as so much smaller, than we had imagined. 477. M. DE LA HIRE mentions one cafe which is of difficult folution. It is when a candle, in a dark place, and fituated beyond the limits of diftinct vifion, is viewed through a very narrow chink in a card; in which cafe a confiderable number of candles, fometimes fo many as fix, will be feen along the chink. This appearance he afcribes to ímall irregularities in the furface of the humours of the eye, the effect of which is not fenfible when rays are admitted into the eye through the whole extent of the pupil, and confequently one principal image effaces a number of fmall ones; whereas, in this case, each of them is formed feparately, and no one of them is fo confiderable as to prevent the others from being perceived at the fame time. plain the cause of thofe dark spots which feem to float before the eyes, especially those of old peo ple. They are moft vifible when the eyes are turned towards an uniformly white object, as the fnow in the open fields. If they be fixed when the eye is fo, this philofopher supposed that they were occafioned by extravafated blood upon the retina. But he thought that the moveable spots were occafioned by opaque matter floating in the aqueous humour of the eye. He thought the vitreous humour was not fufficiently limpid for this purpose. 480. By the following calculation, M. De la Hire gives us an idea of the extreme fenfibility of the optic nerves. One may see very easily, at the diftance of 4000 toifes, the fail of a wind-mill, 6 feet in diameter; and the eye being fuppofed to be an inch in diameter, the picture of this fail, at the bottom of the eye, will be one eight thoufandth of an inch, which is less than the 666th part of a line, and is about the 66th part of a common hair, on the 8th part of a fingle thread of filk. So fmall, therefore, muft one of the fibres of the optic nerve be, which he says is almost inconceivable, fince each of these fibres is a tube that contains fpirits. If birds perceive distant objects as well as men, which he thinks very probable, he obferves that the fibres of their optic nerves must be much finer than ours. 481. Dr BERKELEY, bishop of Cloyne, in his Effay towards a New Theory of Vifion, observes, that the circle formed upon the retina, by the rays which do not come to a focus, produce the fame confufion in the eye, whether they crofs one another before they reach the retina, or tend to do it afterwards; and therefore that the judgment concerning distance will be the fame in both cafes, without any regard to the place from which the rays originally issued; fo that in this cafe, as, by receding from the lens, the confufion which al ways accompanies the nearness of an object increafes, the mind will judge that the object comes nearer. But, fays Dr SMITH, if this be true, the object ought always to appear at a lefs distance from the eye than that at which objects are seen diftinctly, which is not the cafe; and to explain 478. There are few perfons, M. De la Hire ob- this appearance, as well as every other in which ferves, who have both their eyes perfectly equal, a judgment is formed concerning diftance, he not only with refpect to the limits of diftinct vi- maintains, that we judge of it by the apparent fion, but also with respect to the colour with magnitude of objects only, or chiefly; fo that, which objects appear tinged when they are viewed fince the image grows larger as we recede from by them, especially if one of the eyes has been ex- the lens through which it is viewed, we conceive pofed to the impreffion of a ftrong light. To the objects to come nearer. He also endeavours compare them together in this refpect, he directs to fhow, that in all cafes in which glaffes are used, us to take two thin cards, and to make in each of we judge of diftance by the fame fimple rule; them a round hole of or of a line in diameter, from which he concludes univerfally, that the apand, applying one of them to each of the eyes, to parent distance of an object seen in a glass is to look through the holes on a white paper, equally its apparent difiance feen by the naked eye, as illuminated; when a circle of the paper will ap- the apparent magnitude to the naked eye is to its pear to each of the eyes, and, placing the cards apparent magnitude in the glass. properly, thefe two circles may be made to touch one another, and thereby the appearance of the fame object to each of the eyes may be compared to the greatest advantage. To make this experiment with the greatest exactnefs, it is neceffary, he fays, that the eyes be kept fhut fome time before the cards be applied to them. 479. M. DE LA HIRE first endeavoured to ex 482. But that we do not judge of distance merely by the angle under which objects are seen, is an obfervation as old as ALHAZEN, who mentions feveral inftances, in which, though the angles under which objects appear to be different, the magnitudes are univerfally and inftantaneoufly deemed not to be fo. And Mr ROBINS clearly fhows the hypothefis of Dr Smith to be contrary to to fact in the most common and fimple cafes. In microfcopes, he fays, it is impoffible that the eye fhould judge the object to be nearer than the diftance at which it has viewed the object itself, in proportion to the degree of magnifying. For when the microscope magnifies much, this rule would place the image at a diftance, of which the fight cannot poffibly form any opinion, as be. ing an interval from the eye at which no object can be feen. In general, he believes, that whoever looks at an object through a convex glafs, and then at the object itself without the glafs, will find it to appear nearer in the latter cafe, though it be magnified in the glafs; and in the fame trial with the concave glafs, though by the glass the object be diminished, it will appear nearer through the glafs than without it. But the moft convincing proof, that the apparent diftance of the image is not determined by its apparent magnitude, is the following experiment: If a double convex glafs be held upright before fome luminous object, as a candle, there will be seen two images, one erect, and the other inverted. The firft is made fimply by reflection from the neareft furface, the fecond by reflection from the farther furface, the rays undergoing a refraction from the firft furface both before and after the reflection. If this glafs has not too short a focal distance when it is held near the object, the inverted image will appear larger than the other, and alfo nearer; but if the glafs be carried off from the object, though the eye remain as near to it as before, the inverted image will diminish so much fafter than the other, that, at length, it will appear very much less than it, but ftill nearer. Here, fays Mr Robins, two images of the fame object are feen under one view, and their apparent diftances immediately compared; and here, it is evident, that those diftances have no neceffary connection with the apparent magnitude. He also fhows how this experiment may be made ftill more convincing, by fticking a piece of paper on the middle of the lens and viewing it through a fhort tube. 483. M. BOUGUER adopts the general maxim of Dr BARROW, in fuppofing that we refer objects to the place from which the pencils of rays feemingly converge at their entrance into the pupil. But when rays iffue from below the furface of a veffel of water or any other refracting medium, 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 refracting medium; and another, of thofe that fall upon the furface with the fame degree of obliquity, entering the eye laterally with refpect to one another. Some times, he fays, one of thefe images is attended to by the mind, and fometimes the other, and different images may be obferved by different perfons. An object plunged in water, affords an example, he fays, of this duplicity of images. If BAb (Plate CCLVII, fig. 5.) be part of the surface of water, and the object be at O, there will be two images of it in two different places; one at G, on the cauftiç by refraction, and the other at E, in the perpendicular AO, which is as much a cauftic as the other line. The former image is visible by the rays ODM, Odm, which are one higher than the other, in their progrefs to the eye; whereas the image at E is made by the rays ODM, Oef, which enter the eye laterally. This, fays he, may ferve to explain the difficulty of F. Tacquet, Barrow, Smith, and many other authors, and which Newton himself confidered as a very difficult problem, though it might not be abfolutely infoluble. 484. G. W. KRAFT has ably supported the opinion of Dr Barrow, that the place of any point, feen by reflection from the furface of any medium, is that in which rays iffuing from it, infinitely near to one another, would meet; and confidering the case of a diftant object viewed in a concave mir. ror, by an eye very near to it, when the image, according to Euclid and other writers, would be between the eye and the object, and the rule of Dr Barrow cannot be applied; he fays that in this cafe the fpeculum may be confidered as a plane, the effect being the same, only the image is more obfcure. 485. Dr PORTERFIELD gives a diftinct and comprehenfive view of the natural methods of judging concerning the diftance of objects. The confor mation of the eye, he fays, can be of no ufe to us with refpect to objects that are placed without the limits of diftinct vifion. As the object, however, does then appear more or lefs confused, according as it is more or lefs removed from those limits, this confufion affifts the mind in judging of the diftance of the object; it being always ef teemed fo much the nearer, or the farther off, by how much the confufion is lefs or greater. But this confufion hath its limits alfo, beyond which it can never extend; for when an object is placed at a certain diftance from the eye, to which the breadth of the pupil bears no fenfible proportion, the rays of light that come from a point in the object, and pass the pupil, are fo little diverging, that they may be confidered as parallel. For a picture on the retina will not be fenfibly more confused, though the object be removed to a much greater diftance. The moft univerfal, and the most fure means of judging of the distance of objects is, he fays, the angle made by the optic axis. For our two eyes are like two different ftations, by the affiftance of which distances are taken: and this is the reason why thofe perfons who are blind of one eye fo frequently mifs their mark in pouring liquor into a glafs, fnuffing a candle, and fuch other actions, as require that the diftance be exactly diftinguished. To prove the usefulness of this method of judging of the distance of objects, he directs to fufpend a ring in a thread, fo that its fide may be towards us, and the hole in it to the right and left hand; and taking a small rod, crooked at the end, retire from the ring 2 or 3 paces, and having with one hand covered one of our eyes, to endeavour with the other to pafs the crooked end of the rod through the ring. This, fays he, appears very easy; and yet, upon trial, perhaps we shall not fucceed once in 100 times, especially if we move the rod a little quickly. The ufe of this fecond method of judging of diftances De Chales limited to 120 feet; beyond which, he says, we are not fenfible of any difference in the angle of the optic axis. 486. A 3d method of judging of the diftance of objects, confifts in their apparent magnitudes, on which fo much refs was laid by Dr SMITH. From this change in the magnitude of the image upon the retina, we eafily judge of the diftance of objects, as often as we are otherwife acquainted with the magnitude of the objects themselves; but as often as we are ignorant of the real magnitude of bodies, we can never, fron. their apparent magnitude, form any judgment of their diftance. From this we may fee why we are fo fre. quently deceived in our eftimates of diftance, by any extraordinary magnitudes of objects feen at the end of it; as, in travelling towards a large city, or a castle, or a cathedral church, or a mountain larger than ordinary, we fancy them to be nearer than we find them to be. This alfo is the reason why animals, and all small objects, seen in valleys, contiguous to large mountains, appear exceedingly fmall, because both appear nearer to us than they really are. 487. Dr JURIN clearly accounts for our imagining objects, when feen from a high building, to be smaller than they are, and smaller than we fancy them to be when we view them at the fame distance on level ground. It is, fays he, becaufe we have no diftinct idea of distance in that direc. tion, and therefore judge of things by their pictures upon the eye only: but custom will enable us to judge rightly even in this cafe. Let a boy, fays he, who has never been upon any high building, go to the top of the monument, and look down into the street; the objects feen there, as men and horfes, will appear fo fmall as greatly to furprise him. For this reafon, ftatues placed upon very high buildings ought to be made of a larger fize than those which are feen at a nearer distance; because all perfons, except architects, are apt to imagine the height of fuch buildings to be much lefs than it really is. 488. The 4th method by which Dr PORTERFIELD fays that we judge of the distance of objects, is the force with which their colour strikes our eyes. For if we be affured that two objects are of a fimilar and like colour, and that one appears more bright and lively than the other, we judge, that the brighter object is the nearer of the two. 489..The 5th method confifts in the different appearance of the small parts of objects. When these parts appear diftinct, we judge that the object is near; but when they appear confufed, or when they do not appear at all, we judge that it is at a greater diftance. For the image of any object, or part of an object, diminishes as the diftance of it increases. 490. The 6th and laft method by which we judge of the diftance of objects is, that the eye does not reprefent to our mind one object alone, but at the fame time all thofe that are placed betwixt us and the principal object, whose distance we are confidering; and the more this distance is divided into feparate and diftinct parts, the greater it appears to be. For this reafon, diftances upon uneven furfaces appear lefs than upon a plane: for the inequalities of the furfaces, fuch as hills, and holes, and rivers, that lie low and out of fight, either do not appear, or hinder the parts that lie behind them from appearing; and fo the whole VOL. XVI. PART II. apparent diftance is diminified by the parts tha do not appear in it. This is the reafon that the banks of a river appear contiguous to a diftant eye, when the river is low and not feen. For the fame reafon a large lake, or an arm of the fear fuch as the Frith of Forth, appears to be much narrower, than an equal extent of level ground, diverfified with houses, fields, plantations, &c. 491. Dr PORTERFIELD wery well explains feve ral fallacies in vifion depending upon our mifta king the distances of objects. Of this kind, he fays, is the appearance of parallel lines, and long viftas confifting of parallel rows of trees; for they feem to converge more and more as they are far« ther extended from the eye. The reafon of this, he says, is because the apparent magnitudes of their perpendicular intervals are perpetually dimi nifhing, while, at the fame time, we miftake their diftance. Hence we may fee why, when two pa rallel rows of trees ftand upon an afcent, whereby the more remote parts appear farther off than they really are; becaufe the line that measures the length of the viftas now appears under a greater angle than when it was horizontal; the trees, in fuch a cafe, will feem to converge lefs, and fome times, inftead of converging, they will be though to diverge. For the fame reason that a long vista appears to converge more and more the farther it is extended from the eye, the remoter parts of a horizontal walk or a long floor will appear to afcend gradually; and objects placed upon it, the more remote they are the higher they will appear, till the laft be feen on a level with the eye; whereas the ceiling of a long gallery appears to defcend towards a horizontal line, drawn from the eye of the fpectator. For this reafon, alfo, the surface of the fea, feen from an eminence, seems to rife higher and higher the farther we look; and the upper parts of high buildings feem to ftoop, or incline forwards over the eye below, because they feem to approach towards a vertical line proceed ing from the fpectator's eye. 492. Our author alfo fhows the reason why a windmill, feen from a great distance, is fonetimes imagined to move the contrary way from what it really does, by our taking the near end of the fail for the more remote. The uncertainty we fometimes find in the courfe of the motion of a branch of lighted candles, turned round at a dif. tance, is owing, he says, to the fame caufe; as alfo our fometimes miftaking a convex for a concave furface, more especially in viewing feals and impreffions with a convex glafs or a double microfcope; and laftly, that, upon coming in a dark night into a street, in which there is but one row of lamps, we often mistake the fide of the street they are on. 493. Much more light was thrown upon this curious fubject by M. BOUGUER. The proper method of drawing the appearance of two rows of trees, that fhall appear parallel to the eye, is a problem which has exercited the ingenuity of feveral philofophers and mathematicians. That the apparent magnitudes of objects decreases with the angle under which they are feen, has been acknowledged; as well as, that it is only by cuftom and experience, that we learn to form a judgment both of magnitudes and diftances. But in the apFff plication |