plication of these maxims to the above-mentioned problem, all perfons, before M. Bouguer, made ufe of the real distance instead of the apparent one: by which only the mind can form its judgment. It is manifeft, that, if any circumftances contribute to make the dittance appear otherwife than it is in reality, the apparent magnitude of the object will be affected by it; for the fame reafon, that, if the magnitude be mifipprehended, the idea of the diftance will vary. 494. M. BOUGUER obferves, that very great distances, and thofe that are confiderably lefs than they, make nearly the fame impreffion upon the eye. We, therefore, always imagine great distances to be lefs than they are; and for this reafon the ground plan of a long vifta always appears to rife. The vifual rays come in a determinate direction; but as we imagine them to terminate fooner than they do, we neceffarily conceive that the place from which they iffue is elevated. Every large plane, therefore, as AB,(p/ 257,15.6.) viewed by an eye at O, will feem to lie in fuch a direction as Ab; and confequently lines, in order to appear truly parallel on the plane Ab,must be drawn fo as that they would appear parallel on the plane Ab, and be from thence projected to the plane AB. 495. M. BOUGUER thows feveral geometrical methods of determining this inclination; and fays, that by thefe means he has often found it to be 4 or 5, though fometimes only 2° or 240. The determination of this angle, he obferves, is variable; depending upon the manner in which the ground is illuminated and the intenfity of the light. The colour of the foil is alfo not without its influBut what is very remarkable, yet may be depended upon, is, that if we look towards a rifing ground, the difference between the apparent ground plan and the true one will be much more confiderable, fo that they will fometimes make an angle of 25 or 30°. Of this he had made frequent obfervations. Mountains, he fays, begin to be inacceffible when their fides make an angle from 35 to 37° with the horizon, as then it is not poffible to climb them but by means of ftones or fhrubs, to ferve as fteps to fix the feet on. In thefe cafes, both he and his companions always agreed, that the apparent inclination of the fide of the mountain was 60° or 70°. ence. 496. Thefe deceptions are reprefented in Plate CCLVI, fig. 18, in which, when the ground plan AM, or AN, is much inclined, the apparent ground-plan Am, or An, makes a very large angle with it. On the contrary, if the ground dips below the level, the inclination of the apparent to the true ground-plan diminishes, till, at a certain degree of the flope, it becomes nothing at all; the two plans AP and Ap being the fame, fo that parallel lines drawn upon them would always appear fo. If the inclination below the horizon is carried beyond the fituation AP, the error will increafe; and what is very remarkable, it will be on the contrary fide; the apparent plan Ar being always below the true plan AR, fo that if a perfon would draw upon the plan AR lines that fhall appear parallel to the eye, they must be drawn converging, and not diverging, as is ufual on the level ground; because they must be the projections of two lines imagined to be parallel, on the plan Ar, which is more inclined to the horizon than AR. The fere. marks are applicable to different planes expofed to the eye at the fame time. For if BH, (PI. CCLVII, fig. 7.) be the front of a building, at the distance of AB from the eye, it will be reduced in appearance to the diftance Ab; and the front of the building will be bh, rather inclined towards the fpectator, uplefs the distance be inconfiderable. 497. After many more obfervations upon this fubject, M. Bouguer adds, that when a man ftands upon a level plane, it does not seem to rife fenfibly but at fome diftance from him. The apparent plane, therefore, has a curvature in it, at that diftance, the form of which is not very eafy to determine; fo that a man standing upon a level plane, of vall extent, will imagine that he ftands in the centre of a bafon. This is alfo, in fome measure, the cafe with a perfon standing upon the level of the fea. 498. He obferves, that there is no difficulty in drawing lines according to these rules, fo as to have any given effect upon the eye, except when fome parts of the profpect are very near the fpectator, and others very diftant from him; because, in this cafe, regard muft he had to the conical or conoidal figure of a furface. A right line paffing at a small distance from the obferver, and below the level of his eye, in that cafe almost always appears fenfibly curved at a certain diftance from the eye; and almost all figures in this cafe are fubject to fome complicated optical alteration to which the rules of perfpective have not as yet been extended. If a circle be drawn near our feet, and within that part of the ground which appears level to us, it will always appear to be a circle, and at a very confiderable diftance it will appear an ellipfe; but between thefe two fituations, it will not appear to be either the one or the other, but will be like one of thofe ovals of Defcartes which is more curved on one of its fides than the other. On these principles a parterre, which appears diftorted when it is feen in a low fituation, appears perfectly regular when it is viewed from a balcony or any other eminence. Still, however, the apparent irregularity takes place at a greater diftance, while the part that is near the fpectator is exempt from it. If AB, (PI. CCLIV. fig. 12.) be the ground plane, and Aa be a perpendicular, under the eye, the higher it is fituated, at O, to the greater diftance will T, the place at which the plane begins to have an apparent afcent along Tb, be removed. 499. All the varieties that can occur with respect to the VISIBLE MOTION of objects, are thus fuccinctly fummed up by Dr PORTERFIELD, under 11 heads:-1. An object moving very swiftly is not feen, unlefs it be very luminous. Thus a cannonball is not feen if it is viewed tranfverfely: but if it be viewed according to the line it defcribes, it may be feen, because its picture continues long on the fame place of the retina; which, therefore, receives a more fenfible imprefiion from the object. 2. A live coal fwung briskly round in a circle ap pears a continued circle of fire, because the impreffions made on the retina by light, being of a vibrating, and confequently of a lasting nature, do not prefently perifh, but continue till the coal per forms its whole circuit, and returns again to its former place. 3. If two objects, unequally diftant from from the eye, move with equal velocity, the more remote one will appear the flower; or, if their celerities be proportional to their diftances, they will appear equally fwift. 4. If two objects, unequally diftant from the eye, move with unequal velocitics in the fame direction, their apparent velocities are in a ratio compounded of the direct ratio of their true velocities, and the reciprocal one of their distances from the eye. 5. A visible object moving with any velocity appears to be at reft, if the space defcribed in the interval of one fecond be imperceptible at the distance of the eye. Hence a near object moving very flowly, as the index of a clock, or a remote one very fwiftly, as a planet, feems to be at reft. 6. An object moving with any degree of velocity will appear at reft, if the space it runs over in a fecond of time be to its diftance from the eye as 1 to 1400. 7. The eye proceeding ftraight from one place to another, a lateral object, not too far off, whether on the right or left, will feem to move the contrary way. 8. The eye proceeding ftraight from one place to another, and being fenfible of its motion, diftant objects will feem to move the fame way, and with the fame velocity. Thus, to a perfon running eaftwards, the moon on his right hand appears to move the fame way, and with equal fwiftnefs; for, by reafon of its diftance, its image continues fixed upon the fame place of the retina; from whence we imagine that the object moves along with the eye. 9. If the cye and the object move both the fame way, only the eye much fwifter than the object, the laft will appear to go back wards. 10. If two or more objects move with the fame velocity, and a third remain at reft, the moveable ones will appear fixed, and the quiefcent in motion the contrary way. Thus clouds moving very fwiftly, their parts feem to preferve their fituation, and the moon to move the contrary way. 11. If the eye be moved with great velocity, lateral objects at reft appear to move the contrary way. Thus to a perfon fitting in a coach, and riding brifkly through a wood, the trees feem to retire the contrary way; and to people in a fhip, &c. the fhores feem to recede. 500. At the conclufion of these observations, the Doctor endeavours to explain another, phenomenon of motion, which, though very common and well known, had not been explained in a fatisfactory manner. If a perfon turns fwiftly round, all objects about will feem to move round in a circle the contrary way; and this deception continues, not only while the perfon himself moves round, but for fome time after he cenfes to move, when the eye, as well as the objects, is at abfolute reft. The reason why objects appear to move round the contrary way, when the eye turns round, is not fo difficult to explain; for though, proper ly fpeaking, motica is not feen, as not being in itfelf the immediate object of fight; yet by the fight we eafily know when the image changes its place on the retina, and thence conclude that either the object, the eye, or both, are moved. But by the fight alone we can never determine how far this motion belongs to the object, to the eye, or to both. If we imagine the eye at rcft, we afcribe the whole motion to the object, though it be truly treft. If we imagine the object at relt, we afcribe the whole motion to the eye, though it beTongs entirely to the object; and when the eye is in motion, though we are fenfible of its motion, yet, if we do not imagine that it moves fo fwiftly as it really does, we afcribe only a part of the motion to the eye, and the reft of it we afcribe to the object, though it be truly at reft. This laft, he fays, happens in the prefent cafe, when the eye turns round; for though we are fenfible of the motion of the eye, yet we do not apprehend that it moves fo faft as it really docs; and therefore the bodies about appear to move the contrary way, as is agreeable to experience. But the great difficulty ftill remains, viz. Why, after the eye ceafes to move, objects fhould, for fome time, ftill appear to continue in motion, though their pictures on the retina be truly at reft, and do not at all change their place. This, he imagined, proceeds from a mistake we are in with refpect to the eye, which, though it be abfolutely at reft, we nevertheleis conceive as moving the contrary way to that in which it moved before; from which mistake, with refpect to the motion of the eye, the objects at reft will appear to move the fame way which the eye is imagined to move; and, confequently, will feem to continue their motion for fome time after the eye is at reft. 501. This is ingenious, but perhaps not juft. An account of this matter, which feems more fatisfactory, has been given to the public by Dr WELLS. "Some of the older writers upon optics (fays he) imagined the vifive spirits to be contained in the head, as water is in a veffel; which, therefore, when once put in motion by the rotation of our bodies, muft continue in it for fome time after this has ceafed; and to this real circular movement of the vifive fpirits, while the body is at reft, they attributed the apparent motions of objects in giddinefs. DECHALES faw the weaknefs of this hypothefis; and conjectured, that the phenomenon might be owing to a real movement of the eyes; but produced no fact in proof of his opinion. Dr PORTERFIELD, on the contrary, fuppofed the difficulty of explaining it to confift in showing, why objects at reft appear in motion to an eye which is alfo at reft. The folution he offered of this representation of the phenomenon, is not only extremely ingenious, but is, I believe, the only probable one which can be given. It does not apply, however, to the fact which truly exifts; for the eye is not at reft, as he imagined. The laft authe, I know of who has touched upon this subjet is Dr DARWIN. His words are," When any one turns round rapidly on one foot till he be comes dizzy, and falls upon the ground, the spectra of the ambient objects continue to present themfelves in rotation, or appear to librate, and he feems to behold them for fome time inmotion." I do not pretend to understand his opinion fully; but if fuch an apparent motion of the furrounding objects depends in any way upon their spectra, or illufive reprefentations, occafioned by their former impreffions upon the retina, no fimilar motion would be observed, were we to turn ourselves round with our eyes fhut, and not to open them till we became giddy. But whoever will make the experiment, will find, that objects about him appear to be equally in motion, when he has beFff2 come come giddy by turning himself round, whether this has been done with his eyes open or fhut. I fhall now propofe my own opinion upon this fubject: 507. "If the eye be at reft, we judge an object to be in motion, when its picture falls in fucceeding times upon different parts of the retina; and if the eye be in motion, we judge an object to be at reft, as long as the change in the place of its picture upon the retina holds a certain correfpondence with the change of the eye's pofition. Let us now fuppofe the eye to be in motion, while, from fome diforder in the fyftem of fenation, we are either without those feelings which indicate the various pofitions of the eye, or are not able to attend to them. In such a state of things an object at reft muft appear to be in motion, fince it fends in fucceeding times its picture to different parts of the retina. And this feems to be what happens in giddinefs." Dr WELLS then relates the particulars of a cafe of giddinefs, which happened to himself, and produced feveral optical deceptions; from which he infers, that "all thefe phenomena demonftrate, that there was a real motion in my eyes at the time I imagined them to be at reft; for the apparent fituation of the spot, with respect to the paper, could not poffibly have been altered, without a real change of the pofition of thefe organs. To have this proved, I defired a perfon to urn quickly round, till he became very giddy; then to stop himfelf, and look stedfaftiy at me. He did fo, and I could plainly fee, that although he thought his eyes were fixed, they were in reality moving in their fockets, firft toward one fide and then toward the other." 503. M. LE CAT well explains a remarkable deception, by which a perfon fhall imagine an object to be on the oppofite fide of a board, when it is not fo, and alfo inverted and magnified. It is illuf trated by fig. 8. pl. CCLVII. in which D reprefents the eye, and CB a large black board, pierced with afmall hole. E is a large white board, placed beyond it, and firongly illuminated; and d a pin, or other fmall object, held betwixt the eye and the first board, In thefe circumftances, the pin hall be imagined to be at F, on the other fide of the board, where it will appear inverted and magniFed, because what is in fact perceived, is the thadow of the pin upon the retina; and the light that is topped by the upper part of the pin coming from the lower part of the enlightened board, and that which is ftopped by the lower part coming from the upper part of the board, the fhadow muft neceffarily be inverted with respect to the object. 504. There is a curious phenomenon relating to wifion, which fome have afcribed to the inflection of light, but which Mr MELVILLE explains in a very different and very simple manner. When any opaque body is held at the diftance of 3 or 4 inches from the eye, fo that a part of fome more distant Justinas object, fuch as the window, or the Hame of a candle, may be feen by rays paffing near its edge, if another opaque body, nearer to the eye, be brought acrols from the oppofite fide, the edge of the fit body will feem to fwell outwards and meet the latter; and in doing fo will intercept a portion of the luminous object that was feen before. This appearance he explains in the following manner; Let AB(fig. 9. pl. CCLVII.) reprefent the luminous object to which the fight is directed, CD the more diftant opaque body, GH the nearer, and EF the diameter of the pupil. Join ED, FD, EG, FG, and produce them till they meet AB in K, N. M, and L. It is plain that the parts AN, MB, of the luminous object cannot be feen. But taking any point a between N and K, and drawing a Dd, fince the portion F of the pupil is filled with light flowing from that point, it must be vifible. Any point b, between a and K, must fill ƒF, a greater portion of the pupil, and therefore muf appear brighter. Again, any point, between b and K, muft appear brighter than h, because it fills a greater portion g F with light. The point K itfelf, and every other point in the pace KL, muft appear very luminous, fince they fend entire pencils of rays EKF, ELF, to the eye; and the vifible brightness of every point from L towards M, muft decrease gradually, as from K to N; that is, the spaces KN, LM, will appear as dim fhadowy borders, or fringes, adjacent to the edges of the opaque bodies. When the edge G is brought to touch the right line KF, the penumbras unite; and as foon as it reaches NDF, the above phenonenon begins; for it cannot pass that right line without meeting fome line a D d, drawn from a point between Ñ and K, and, by intercepting all the rays that fall upon the pupil, render it invifible. In advancing gradually to the line KDE, it will meet other lines b Df,Dg, &c. and therefore render the points b, c, &c. from N to K fucceffively invifible; and therefore the edge of the fixed opaque body CD muft feem to swell outwards, and cover the whole fpice NK; while GH, by its motion, covers MK. When GH is placed at a greater diftance from the eye, CD continuing fixed, the space OP to be paffed over in order to intercept NK is lefs; and therefore, with an equal motion of GH, the apparent fwelling of CD muft be quicker; which is found true by experience. If ML reprefent a luminous object, and REFO any plane expofed to its light, the space FQ will be entirely fhaded from the rays, and the ipace FE will be occupied by a penumbra, gradually darker, from E to F. Let now GH continue fixed, and CD move parallel to the plane EF; and as foon as it pafles the line LF, it is evident that the fhadow QF will feem to fwell outwards; and when CD reaches ME, fo as to cover with its fhadow the fpace RE, QF, by its extenfion, will cover PE. This holds true likewife by experiment. IV. Of the CONCAVE FIGURE of the SKY. 505. THIS apparent concavity is only an optical deception founded on the incapacity of our organs of vifion to take in very large diftances. Dr SMITH in his Complete Syftem of Optics, hath demonftrated, that, if the turface of the earth was perfectly plane, the diftance of the vifible horizon from the eye would fearce exceed the distance of 5cco times the height of the eye above the ground, fuppofing the height of the eye between 5 and 6 feet: beyond this diftance all objects would appear in the vifible horizon. For, let OP (fig. 13. pl. CCLIV.) be the height of the eye above the line PA drawn upon the ground; and if an object AB, equal in height to PO, be removed to a diftance PA equal to 5000 times that height, it will hardly be |