change in the difperfion. After many trials, he obtained a kind of glafs greatly fuperior to the flint glafs of Mr Dollond, with refpect to the conftruction of telescopes; fince it occafioned three times as great a difperfion of the rays as the common glass, at the fame time that the mean refac. tion was only as 1'61 to 1. M. Euler alfo gives inftructions how to find both the mean and extreme refractive power of different kinds of glafs; and advises to make use of prifms with very large refracting angles, not less than 70o. 53. Notwithstanding it evidently appeared, that Mr Dollond had made a real difcovery of fomething not comprehended in the optical principles of Sir Ifaac Newton, it did not appear fo to Mr MURDOCH. Upon this occafion, he interpofed in the defence of Sir Ifaac Newton; maintaining, that Mr Dollond's pofitions, which he fays, he knows not by what mishap have been deemed paradoxes in Sir Ifaac's theory of light, are really the necessary confequences of it. But, admitting all that he advances in this part of his defence, Newton must have made ufe of a prism with a much smaller refracting angle than, from his own account of his experiments, we have any reafon to believe that he ever did make ufe of. The fact probably was, that Sir Ifaac deceived himself in this cafe, by attending to what he imagined to be the clear confequences of his other experiments. In reality, it is no reflection upon Sir Ifaac Newton, who did fo much, to say that he was miftaken in this particular cafe, and that he did not make the discovery that Mr Dollond did; though Mr Dollond, and all who contributed to this difcovery, have no fmall merit in venturing to queftion the authority of so great a man. 54. Mr DOLLOND, however, was not the only optician who had the merit of making this difcovery; it had also been made and applied by Mr CHEST of Cheft-hall. He had obferved that prifms of flint glass gave larger spectrums than prifms of water, when the mean refraction was the fame in both, i. e. when the deviation of the refracted ray from the direction of the incident was the fame. He tried prifms of other glafs, and found fimilar differences; and he employed the discovery in the fame manner, and made achromatic experiments fome time before Dollond. There is, however, no evidence that Dollond ftole the idea from Mr Cheft, or that they had not both claims to the discovery. 55. Still the beft refracting telescopes, conftruct. ed on the principles of Mr Dollond, are defective, on account of that colour which, by the aberration of the rays, they give to objects viewed through them, unless the object glafs be of fmall diameter. This defect, men of genius and fcience have laboured to remove, fome by one contrivance and fome by another. F. BosCOVICH, to whom every branch of optics is much indebted, has, in his attempts for this purpose, difplayed much ingenuity; but the philofopher whofe exertions have been crowned with most fuccefs, and who has perhaps made the most important discovery in this branch of science fince the era of Newton, is Dr ROBERT BLAIR, regius profeffor of aftronomy in the college of Edinburgh. 56. By a judicious fet of experiments ably con ducted, Dr BLAIR has proved, that the quality of difperfing the rays in a greater degree than crown glafs, is not confined to a few mediums, but is poffeffed by a great variety of fluids, and by fome of these in a moft extraordinary degree. He has shown, that although the greater refrangibility of the violet rays than of the red rays, when light paffes from any medium whatever into a vacuum, may be confidered as a law of nature; yet in the paffages of light from one medium into another, it depends entirely on the qualities of the mediums which of these rays fhall be the moft refrangible, or whether there fhall be any difference in their refrangibility. To correct the aberration arifing from difference of refrangibility among the rays of light, he inftituted a fet of experiments, in the conducting of which he detected a very fingular and important quality in the muriatic acid. In all the difperfive mediums hitherto examined, the green rays, which are the mean refrangible in crown glafs, were found among the lefs refrangible; but in the muriatic acid, thefe fame rays were found by him to make a part of the more refrangible. This difcovery led to complete fuccefs in removing the great defect of op. tical inftruments, viz. that diffipation of ABERRATION of the rays which arifes from their une. qual refrangibility, and has hitherto rendered it impoffible to converge all of them to one point, either by fingle or oppofitę, refractions. A fluid, in which the particles of marine acid and metalline particles hold a due proportion, at the fame time that it feparates the extreme rays of the fpectrum much more than crown glass, refracts all the orders of the rays in the fame proportion that glafs does: and hence rays of all colours, made to diverge by the refraction of the glass, may either be rendered parallel by a fubfequent refrac tion made in the confine of the glass and this fluid; or by weakening the refractive density of the fluid, the refraction which takes place in the confine of it; and glass may be rendered as regular as reflection, without the leaft colour whatever. The Doctor has a telescope, not exceeding 15 inches in length, with a compound object-glafs of this kind, which equals in all respects, if it does not surpass, the best of Dollond's 42 inches long. Of this object-glafs a figure will be found in the 3d volume of the Tranfa&ions of the Koyal Society of Edinburgh; to which we refer our readers for a full and perfpicuous account of the experiments which led to this discovery, as well as of the important purposes to which it may be applied. 57. We conclude the hiftory of the discoveries concerning refraction with fome account of the refractions of the atmosphere. Tables of this have been calculated by Mr LAMBERT, to correct the inaccuracies of geometrical obfervations of the altitudes of mountains. The obfervations of Mr Lambert, however, go upon the fuppofition that the refractive power of the atmosphere is invariable: But this is by no means the cafe; and therefore his rules must be confidered as true for the mean state of the air only. 58. A most remarkable variety in the refractive power of the atmosphere was observed by Dr NETTLETON, near Halifax in Yorkshire, which demonftrates how little we can depend upon the calculated of the second magnitude they may, therefore, pro bably not exceed 100. Now the apparent increase and diminution of the light, which we observe in the twinkling of the ftars, feems to be repeated at not very unequal intervals, perhaps about 4 or 5 times in a fecond. He therefore fuppofed, that the inequalities which naturally arife from the chance of the rays coming fometimes a little denfer, and fometimes a little rarer, in fo fmall a num ber of them as muft fall upon the eye in the 4th or 5th part of a fecond, may be fufficient to ac count for this appearance. M. BOUGUER found, that a difference in the light of objects of one part in 66 was fufficiently diftinguishable. calculated heights of mountains, when the obfervations are made with an inftrument, and the refractive power of the air is to be allowed for. Being defirous to learn, by obfervation, how far the mercury would defcend in the barometer at any given elevation (for which there is the beft opportunity in that hilly country), he propofed to take the height of fome of their higheft hills; but when he attempted it, he found his obfervation disturbed by refraction, that he could come to no certainty. Having measured one hill of a confiderable height, in a clear day, and obferved the mercury at the bottom and the top, he found, according to that eftimation, that about 90 feet or more were required to make the mercury fall one roth of an inch; but afterwards, repeating the experiment in a cloudy day, when the air was rather grofs and hazy, he found the fmall angles fo much increased by refraction as to make the hill much higher than before. He afterwards frequently made obfervations at his own houfe, by pointing a quadrant to the tops of fome neighbour ing hills, and obferved that they would appear higher in the morning before sunrise, and alfo late in the evening, than at noon in a clear day, by feveral minutes. In one cafe the elevation of the Lame hill differed more than 30 minutes. From this he infers that obfervations made on very high hills, especially when viewed at a distance, and, under fmall angles, as they generally are, are uncertain and not much to be depended upon. 59. M. EULER confidered with great accuracy the refractive power of the atmosphere, as affected by different degrees of heat and elafticity; in which he shows, that its refractive power to a confiderable distance from the zenith, is fufficiently near the proportion of the tangent of that distance, and that the law of refraction follows the direct ratio of the height of the barometer, and the inverse ratio of the difference marked by the thermometer; but when stars are in the horizon, the changes are in a ratio fomewhat greater than this, more especially on account of the variation in the heat. 60. The CAUSE of the TWINKLING of the STARS is now generally acknowledged to be the unequal refraction of light, in confequence of inequalities and undulations in the atmosphere. Mr MICHELL fuppofes that the arrival of fewer or more rays at one time, especially from the fmaller or the more remote fixed ftars, may make nch an unequal impreffion upon the eye, as may, at least, have fome fhare in producing this effect; ince it may be supposed, that even a fingle particle of light is fufficient to make a fenfible impreffion upon the organs of fight; fo that very few particles arriving at the eye in a fecond of time, perhaps no more than 3 or 4, may be fufficient to make an object conftantly vifible. For though the impreffion may be confidered as momentary, yet the perception occafioned by it is of fome duration. Hence, he fays, it is not improbable that the number of the particles of light which enter the eye in a fecond of time, even from Sirius himself (the light of which does not exceed that of the fmalleft vifible fixed ftar, in a greater proportion than that of about 1000 to 1), may not exceed 3000 or 4000, and from ftars VOL. XVI. PART I. 61. It will perhaps, he fays, be objected, that the rays coming from Sirius, are too numerous, to admit of a fufficient inequality arifing from the common effect of chance, fo frequently as would be neceffary to produce this effect, whatever might happen with refpect to the fmaller ftars; but he obferves, that, till we know what ine quality is necessary to produce this effect, we can only guefs at it one way or the other. Since thefe obfervations were published, Mr Michell has entertained fome fufpicion, that the unequal den fity of light does not contribute to this effect in fo great a degree as he had imagined, especially in confequence of obferving that even Venus does fometimes twinkle. This he once obferved her to do remarkably when fhe was about 60° high, though Jupiter, which was then about 16° high, and was fenfibly lefs luminous, did not twinkle at all. If, notwithstanding the great number of rays which, no doubt, come to the eye from fuch a furface as this planet prefents, its appearance be liable to be affected in this manner, it must be owing to fuch undulations in the atmosphere, as will probably render the effect of every other caufe altogether infenfible. The conjecture, however, has fo much probability in it, that it well deserved to be recited. 62. M. MUSCHENBROEK fufpects that the twinkling of the stars arifes from fome affection of the eye, as well as the ftate of the atmosphere. For he fays, that in Holland, when the weather is frofty, and the fky very clear, the ftars twinkle móft manifeftly to the naked eye, though not in telefcopes; and fince he does pot fuppofe that there is any great exhalation, or dancing of the vapour at that time, he queftions whether the vivacity of the light affecting the eye may not be concerned in the phenomenon. But he might very easily have fatisfied himself with refpect to this, by looking at the stars near the zenith, when the light traverfes but a small part of the atmosphere; for he would not have perceived them to twinkle near fo much as they do near the horizon, when much more of their light is intercepted by the atmosphere. 63. Some aftronomers have lately endeavoured to explain the twinkling of the fixed stars by the extreme minutenefs of their apparent diameter; fo that they fuppofe the fight of them is intercep ted by every mote that floats in the air. But Mr MICHELL obferves, that no object can hide a ftar from us, that is not large enough to exceed the apparent diameter of the ftar, by the diameter of the pupil of the eye: fo that if a ftar was a mathematical point, the interpofing object muft still be equal Tt in in fize to the pupil of the eye: nay, it must be large enough to hide the ftar from both eyes at the fame time. 64. Besides a variation in the quantity of light, a momentary change of colour has likewife been obferved in fome of the fixed ftars. Mr MELVILLE fays, that when one looks ftedfaftly at Sirius, or any bright star not much elevated above the horizon, its colour feems not to be conftantly white, but appears tinctured at every twinkling with red and blue. This obfervation Mr Melville puts among his queries, with refpect to which he could not entirely fatisfy himfelf; and he obferves, that the feparation of colours by the refractive power of the atmosphere is, probably, too fmall to be perceived. But the fuppofition of Mr Michell above mentioned will pretty well account for this circumftance. For the red and blue rays being much fewer than thofe of the intermediate colours, and therefore much more liable to inequalities, from the common effect of chance, a finall excefs or defect in either of them will make a very fenfible difference in the colour of the stars. SECT. III. DISCOVERIES concerning the REFLEC TION of LIGHT. 65. However much the ancients might have been mistaken with regard to the nature of light, we find that they were acquainted with two very important obfervations concerning it; viz. that light is propagated in right lines, and that the angle of incidence is equal to the angle of reflection. Who firft made thefe important obfervations is not known. But, indeed, important as they are, and the foundation of a great part of even the prefent fyftem of optics, the merit of the former discovery is the lefs, that the fact is obvious, and eafily afcertained. As to the latter, that the angle of incidence is equal to the angle of reflection, it was probably first discovered by observing a ray of the fun reflected from the surface of water, or fome other polifhed body; or from obferving the images of objects reflected by fuch furfaces. 66. ARISTOTLE was fenfible that it is the reflection of light from the atmosphere which prevents total darkness after the fun fets, and in places where he doth not fhine in the day time. He was also of opinion, that rainbows, haloes, and mock funs, were all occafioned by the reflection of the fun-beams in' different circumstances, by which an imperfect image of his body was produced, the colour only being exhibited, and not his proper figure. The image, he fays, is not fingle, as in a mirror; for each drop of rain is too small to reflect a viilble image, but the conjunction of all the images is vifible. 67. Without inquiring any farther into the nature of light or vifion, the ancient geometricians contented themselves with deducing a fyftem of optics from the two obfervations mentioned above. The treatife of optics afcribed to EUCLID is employed about determining the apparent fize and figure of objects, from the angle under which they appor, or which the extremities of them fubtend at the eye, and the apparent place of the image of an object reflected from a polished mirror; which he fixes at the place where the reflected ray meets a perpendicular to the mirror drawn through the object. But this work is fo inaccurately drawn up, that it is not generally believed to be Euclid's. 68. It appears from a circumftancce in the hiftory of SOCRATES, that the effects of BURNINGGLASSES had also been obferved by the ancients; and it is probable that the Romans had a method of lighting their facred fire by means of a concave fpeculum. It feems indeed to have been known pretty early, that there is an increase of heat in the place where the rays of light meet, when they are reflected from a concave mirror. The burning power of concave mirrors is taken notice of by Euclid in the ad hock of the treatife above mentioned. If we credit what fome ancient hiftorians have written concerning the exploits of ARCHIMEDES, we fhall be induced to think that he made great ufe of this principle, in conftruct ing fome very powerful burning mirrors. It is al lowed, that this eminent geometrician did write a treatife on the subject of burning mirrors, though it be not now extant; having perished with moft of his other works and inventions in the deftruc tion of Syracufe. 69. J. B. PORTA supposes that the burning mirrors of the ancients were of metal, in the form of a fection of a parabola. It follows from the properties of this curve, that all the rays which fall upon it, parallel to its axis, will meet in the fame point at the focus. Confequently, if the vertes of the parabola be cut off, as in Fig. 1. Plate CCXLIX, it will make a convenient burning mirror. In fome drawings of this inftrument the fruftrum is fo fmall, as to look like a ring. With an inftrument of this kind, it is thought, that the Romans lighted their facred fire. Some have alfo thought that this was the form of the mirror with which Archimedes burnt the Roman fleet, or by applying a smaller parabolic mirror for this purpofe, as is reprefented fig. 2. 70. All this time, however, the nature of reflection was very far from being understood. Even lord BACON, who made much greater advances in natural philofophy than his predeceffors, and who pointed out the true method of improving it, was fo far deceived with regard to the nature of reflection and refraction, that he supposed it poffible to fee the image reflected from a look. ing-glafs, without feeing the glafs itself; and to this purpose he quotes a ftory of friar Bacon, who is reported to have apparently walked in the air between two steeples, and which was thought to have been effected by reflection from glaffes while he walked upon the ground. 71. The whole business of feeing images in the air may be traced up to Vitellio; and what he faid upon the fubject feems to have paffed from writer to writer, with confiderable additions to the time of lord Bacon. What Vitellio endea vours to fhow is, that it is poflible, by means of a cylindrical convex fpeculum, to fee the images of objects in the air, out of the fpeculum, when the objects themselves cannot be seen. But, if his defcription of the apparatus requifite for this expe riment be attended to, it will be feen that the eye was to be directed towards the speculum, which was placed within a room, while both the object and the spectator were without it. But if he himself did make any trial with the apparatus that |