ton concerning the different refrangibility of the rays of light, he had no idea but that they were all affected in the same proportion by every medium, so that the refrangibility of the extreme rays might be determined if that of the mean ones was given. From this it would follow, as Mr. Dollond observes, that equal and contrary refractions must not only destroy each other, but that the divergency of the colours from one refraction would likewise be corrected by the other, and that there could be no possibility of producing any such thing as refraction which would not be affected by the different refrangibility of light; or, in other words, that however a ray of light might be refracted backwards and forwards by different mediums, as water, glass, &c., provided it was so done that the emergent ray should be parallel to the incident one, it would ever after be white; and consequently, if it should come out inclined to the incident, it would diverge, and ever after be coloured; and from this it was natural to infer that all spherical object-glasses of telescopes must be equally affected by the different refrangibility of light, in proportion to their apertures, of whatever materials they may be formed. of his optics could not answer his description of it. He found that when light passed out of air through several contiguous refracting mediums, as through water and glass, and thence again into air, whether the refracting surfaces be parallel or inclined to one another, that light, as often as by contrary refractions it is so corrected as to emerge in lines parallel to those in which it was incident, continued ever after to be white; but, if the emergent rays were inclined to the incident, the whiteness of the emergent light would by degrees, in passing on from the place of emergence, become tinged at its edges with colours. This he tried by refracting light with prisms of glass, placed within a prismatic vessel of water. By theorems deduced from this experiment, he inferred that the refraction of rays of every sort, made out of any medium into air, may be known by having the refraction of the rays of any one sort; and also that the refraction out of one medium into another may be found as often as we can ascertain the refractions out of them both into any third medium. This paper of M. Klingenstierna being communicated to Mr. Dollond by M. Mallet induced him to determined him to have recourse to experiment. He therefore cemented together two plates of glass parallel at their edges, so as to form a prismatic vessel when stopped at the ends or bases; and, the edge being turned downwards, he placed in it a glass prism, with one of its edges upwards, and filled up the vacancy with clear water; so that the refraction of the prism was contrived to be contrary to that of the water, in order that a ray of light transmitted through both these refracting mediums might be affected by the difference only between the two refractions. As he found the water to refract more or less than the glass prism, he diminished or increased the angle between the glass plates till he found the two contrary refractions to be equal, which he discovered by viewing an object through this double prism. For, when it appeared neither raised nor depressed, he was satisfied that the refractions were equal, and that the emergent rays were parallel to the incident. For this reason Sir Isaac Newton and other philo-entertain doubts concerning Newton's report, and sophers had despaired of bringing refracti .g telescopes to any great degree of perfection, without making them of an immoderate and very inconvenient length. They therefore applied themselves chiefly to the improvement of the reflecting telescope; and the business of refraction was dropped till about the year 1747, when M. Euler, improving upon a hint of Sir Isaac Newton's, formed a scheme of making object-glasses of two materials of different refractive powers, hoping that by this difference the refractions would balance one another, and thereby prevent the dispersion of the rays that is occasioned by the difference of refrangibility. These object-glasses were composed of two lenses of glass with water between them. The memoir of M. Euler excited the attention of Mr. Dollond. He carefully went over all M. Euler's calculations, substituting for his hypothetical laws of refraction those which had been actually ascertained by the experiments of Newton, and found that, after this necessary substitution, it followed from M. Euler's own principles that there could be no union of the foci of all kinds of colours but in a lens infinitely large. M. Euler did not attempt to controvert the experiments of Newton; but he said that they were not contrary to his hypothesis but in so small a degree as might be neglected; and asserted that, if they were admitted in all their extent, it would be impossible to correct the difference of refrangibility occasioned by the transmission of the rays from one medium into another of different density-a correction which he thought was very possible, since he supposed it to be actually effected in the structure of the eye, which in his opinion was made to consist of different mediums for that very purpose. To this kind of reasoning Mr. Dollond made no reply but by appealing to the experiments of Newton, and the great circumspection with which it was known that he conducted all his enquiries. Now, according to the prevailing opinion, he observes, the object should have appeared through this double prism in its natural colour; for, if the difference of refrangibility had been in all respects equal in the two equal refractions, they would have rectified each other. But this experiment fully proved the fallacy of the received opinion by showing the divergency of the light by the glass prism to be almost double of that by the water; for the image of the object, though not at all refracted, had yet as many prismatic colours as if it had been seen through a glass wedge only whose refracting angle was nearly thirty degrees. This experiment was identical with that by Sir Isaac Newton, above mentioned, notwithstanding the result was so remarkably different; but Mr. Dollond states that he used all possible precaution and care in his process, and he kept his apparatus by him, that he might evince the truth of what he wrote whenever he should be required to do it. The paper of M. Euler was particularly noticed by He plainly saw, however, that if the refracting M. Klingenstierna, of Sweden, who paid a consi- angle of the water vessel could have admitted of a derable degree of attention to the subject, and dis-sufficient increase the divergency of the coloured rays covered that, from Newton's own principles, the would have been greatly diminished or entirely rectiresult of the eighth experiment of the second book fied, and that there would have been a very great refraction without colour, as he had already pro- | fraction of each wedge with these different angles, he duced a great discolouring without refraction; but the inconveniency of so large an angle as that of the prismatic vessel must have been to bring the light to an equal divergency with that of the glass prism, whose angle was about 60°, made it necessary to try some experiments of the same kind with smaller angles. Accordingly, he got a wedge of plate glass, the angle of which was only 9°, and using it under the same circumstances he increased the angle of the water wedge in which it was placed till the divergency of the light by the water was equal to that by the glass; that is, till the image of the object, though considerably refracted by the excess of the refraction of the water, appeared nevertheless quite free from any colours proceeding from the different refrangibility of the light and, as near as he could then measure, the refraction by the water was about three-fourths of that by the glass. He acknowledges, indeed, that he was not very exact in taking the measures, because his business was not at that time to determine the exact proportions so much as to show that the divergency of the colours by different substances was by no means in proportion to the refractions, and that there was a possibility of refraction without any divergency of the light at all. : As these experiments clearly proved that different substances made the light to diverge very differently in proportion to their general refractive power, Mr. Dollond began to suspect that such variety might possibly be found in different kinds of glass, especially as experience had already shown that some of the kinds made much better object-glasses in the usual way than others; and, as no satisfactory cause had been assigned for such difference, he thought there was great reason to presume that it might be owing to the different divergency of the light in the same refractions. His next business therefore was to grind wedges of different kinds of glass and apply them together, so that the refractions might be made in contrary directions, in order to discover, as in the above-mentioned experiments, whether the refraction and the divergency of the colours would disappear together. found that of the white glass to be to that of the crown-glass nearly as two to three, and this proportion held very nearly in all small angles : so that any two wedges made in this proportion and applied together, so as to refract in a contrary direction, would refract the light without any dispersion of the rays. In a letter to M. Klingenstierna, quoted by M. Clairaut, Mr. Dollond says that the sine of incidence in crown-glass is to that of its general refraction as I to 1.53, and in flint-glass as 1 to 1.583. To apply this knowledge to practice, Mr. Dollond went to work upon the object-glasses of telescopes, not doubting but that, upon the same principles on which a refracted colourless ray was produced by prisms, it might be done by lenses also made of similar materials; and he succeeded by considering that, in order to make two spherical glasses that should refract the light in contrary directions, the one must be concave and the other convex and as the rays are to converge to a real focus the excess of refraction must evidently be in the convex lens. Also, as the convex glass is to refract the most, it appeared from his experiments that it must be made of crownglass, and the concave of the white Bint-glass. Further, as the refractions of spherical glasses are in an inverse ratio of their focal distances, it follows that the focal distances of the two glasses should be inversely as the ratios of the refractions of the wedges; for, being thus proportioned, every ray of light that passes through this combined glass, at whatever distance it may pass from its axis, will constantly be refracted by the difference between two contrary refractions in the proportion required, and therefore the different refrangibility of the light will be entirely removed. Notwithstanding our author had these clear grounds in theory and experiment to go upon, he found that he had many difficulties to struggle with when he came to reduce them into actual practice; but, with great patience and address, he at length got into a ready method of making telescopes upon these admirable principles. His principal difficulties arose from the following circumstances:-In the first place, the focal distances, as well as particular surfaces, must be very He discovered a difference in the refractive qualities accurately proportioned to the densities or refracting of different kinds of glass with respect to the di- powers of the glasses, which are very apt to vary in vergency of colours. The yellow or straw-coloured the same sort of glass made at different times. foreign sort commonly called Venice glass, and the Secondly, the centres of the two glasses must be English crown-glass, proved to be very nearly alike in placed truly in the common axis of the telescope, that respect, though, in general, the crown-glass otherwise the desired effect will be in a great measure seemed to make the light diverge the less of the two. destroyed. At length, after numerous trials, he was The common English plate-glass made the light able to construct refracting telescopes with such diverge more, and the white crystal, or English flint-apertures and magnifying powers, under limited glass, most of all. lengths, as, in the opinion of the best judges, far exceeded any thing that had been produced before, representing objects with great distinctness and in their true colours. It was objected to Mr. Dollond's discovery that the small dispersion of the rays in crown-glass is only apparent, owing to the opacity of that kind of glass, which does not transmit the fainter-coloured rays in a sufficient quantity; but this objection was particularly considered and answered by M. Beguelin. It was now his business to examine the particular qualities of every kind of glass that he could procure, and he soon found the crown-glass and the white flintglass to be the best. He therefore ground one wedge of white flint of about twenty-five degrees, and another of crown-glass of about twenty-nine degrees, which refracted very nearly alike, but their power of making the colours diverge was very different. He then ground several others of crown-glass to different angles till he got one which was equal, with respect As Mr. Dollond did not explain the methods which to the divergency of the light, to that in the white he took in the choice of different spheres proper flint-glass; for, when they were put together so as to to destroy the effect of the different refrangibility refract in contrary directions, the refracted light was of the rays of light, and gave no hint that he himself entirely free from colours. Then, measuring the re-had any rule to direct his workmen in it, and as the calculation of the dispersion of the rays in so complicated an affair is very delicate, M. Clairaut, who had paid a good deal of attention to this subject, from the beginning of the controversy, endeavoured to make out a complete theory of it. quantities, which these calculators professedly did, in order to make their algebraical expressions more commodious, their conclusions were not sufficiently exact. But what he found to be of the most consequence was the want of an exact method of measuring the refractive and dispersing powers of the different kinds of glass; and for want of this the greatest precision in calculation was entirely useless. These considerations induced this gentleman to take another view of this subject; but still he could not reconcile the actual effect of Mr. Dollond's telescopes with his own conclusions: so that he imagined either that he had not the true refraction and dis "Without some assistance of this kind it is impossible," says this author, "to construct telescopes of equal goodness with those of Mr. Dollond, except by a servile imitation of his; which, however, on many accounts, would be very unlikely to answer. Besides, Mr. Dollond only gave his proportions in general, and pretty near the truth; whereas the greatest possible precision is necessary. Also the best of Mr. Dollond's early telescopes were far short of the Newtonian ones; whereas it might be ex-persion of the two kinds of glass given him, or else pected that they should exceed them if the foci of all the coloured rays could be as perfectly united after refraction through glass as after reflection from a mirror, since there is more light lost in the latter case than in the former." With a view therefore to assist the artist, he endeavoured to ascertain the refractive power of different kinds of glass, and also their property of separating the rays of light by the following exact methods. He made use of two prisms placed close to one another, as Mr. Dollond had done: but, instead of looking through them, he placed them in a darkened room; and when the image of the sun, transmitted through them, was perfectly white, he concluded that the different refrangibility of the rays was corrected. In order to ascertain with more ease the true angles that prisms ought to have to destroy the effect of the difference of refrangibility, he constructed one which had one of its surfaces cylindrical, with several degrees of amplitude. By this means, without changing his prisms, he had the choice of an infinity of angles, among which, by examining the point of the curve surface which, receiving the solar ray, gave a white image, he could easily find the true one. He also ascertained the proportion in which different kinds of glass separated the rays of light, by measuring with proper precautions the oblong image of the sun, made by transmitting a beam of light through them. In making these experiments he discovered an easy method of convincing any person of the greater refractive power of English flint-glass above the common French glass, both with respect to the mean refraction and the different refrangibility of the colours; for having taken two prisms of these two kinds of glass, but equal in all other respects, and placed them so that they received at the same time two rays of the sun, with the same degree of incidence, he saw that, of the two images, that which was produced by the English flint-glass was a little higher up on the wall than the other, and longer by more than one half. Notwithstanding Messrs. Clairaut and d'Alembert seemed to have exhausted the business of calculation on the subject of Mr. Dollond's telescopes, no use could be made of their labours by foreign artists. For still the telescopes made in England according to no exact rule, as foreigners supposed, were greatly superior to any that could be made elsewhere, though under the immediate direction of those able calculators. For this M. Beguelin assigned several reasons. Among others, he thought that their geometrical theorems were too general, and their calculations too complicated for the use of workmen. He also thought that in consequence of neglecting small that the aberration which still remained after his calculations must have been destroyed by some irregularity in the surfaces of the lenses. M. Euler, who first gave occasion to this enquiry, which terminated so happily for the advancement of science, being persuaded both by his reasoning and calculations, that Mr. Dollond had discovered no new principle in optics, and yet not being able to controvert the universal testimony in favour of the goodness of his telescopes, concluded that this extraordinary effect was owing, in part, to the crown glass not transmitting all the red light, which would otherwise have come to a different focus, and have distorted the image; but principally to his happening to hit on a just curvature of his glass, which he did not doubt would have produced the same effect if his lenses had all been made of the same kind of glass. In another place he states that the goodness of Mr. Dollond's telescope might be owing to the eye-glass. "If my theory," says he, "be true, this disagreeable consequence follows, that Mr. Dollond's object-glasses cannot be exempt from the dispersion of colours: yet a regard to so respectable a testimony embarrasses me extremely, it being as difficult to question such express authority as to abandon a theory which appears to me perfectly well founded, and to embrace an opinion which is as contrary to all the established laws of nature as it is strange and seemingly absurd." While M. Euler was employed upon this subject, he informs us that he received a letter from M. Zeiher, in which he gave him a particular account of the success of his experiments on the composition of glass, and stated that, having mixed minium ard sand in different proportions, the result of the mean refraction and the dispersion of the rays varied according to the following table. Proportion of mi- I. II. III. VI. Mean refraction glass. Dispersion of the rays in comparison of crown-glass. 3:1 2028 : 1000 4800 : 1000 2 1 1830 1000 3550 We shall conclude the history of the discoveries concerning refraction with some account of the refraction of the atmosphere. Tables of this kind were calculated by Mr. Lambert, with a view to correct the inaccuracies of geometrical observations of the altitude of mountains. The observations of Mr. Lambert, however, go upon the supposition that the refractive | flection of light from the atmosphere which prevented power of the atmosphere is invariable. But this is by total darkness after the sun set. He was also of no means the case; and therefore his rules must be opinion that rainbows, halos, and mock suns, were considered as true for the mean state of the air only. all occasioned by the reflection of the sun-beams in A most remarkable variety in the refractive power different circumstances, by which an imperfect image of the atmosphere was observed by Dr. Nettleton, of his body was produced, the colour only being exnear Halifax in Yorkshire, which demonstrates how hibited, and not his proper figure. The image, he little we can depend upon the calculated heights of says, is not single, as in a mirror; for each drop of mountains, when the observations are made with an rain is too small to reflect a visible image, but the instrument, and the refractive power of the air is to conjunction of all the images is visible. be allowed for. Being desirous to learn, by observation, how far the mercury would descend in the barometer at any given elevation (for which there is the best opportunity in that hilly country), he proposed to take the height of some of their highest hills; but, when he attempted it, he found his observations so much disturbed by refraction that he could come to no certain conclusions. Having measured one hill of a considerable height, in a clear day, and observed the mercury at the bottom and at the top, he found according to to that estimate that about ninety feet or more were required to make the mercury fallth of an inch; but afterwards repeating the experiment on a cloudy day, when the air was rather hazy, he found the small angles so much increased by refraction as to make the hill very much higher than before. He afterwards made a series of observations at his own house, by pointing a quadrant to the tops of some neighbouring hills, and observed that they would appear higher in the morning before sunrise, and also late in the evening, than at noon in a clear day, by several minutes. In one case the elevations of the same hill differed more than thirty minutes. From this he infers that observations made on very high hills, especially when viewed at a distance, and under small angles, as they generally are, are generally uncertain, and not much to be depended upon. Without enquiring any further into the nature of light or vision, the ancient geometricians contented themselves with deducing a system of optics from the two observations mentioned above, viz. the rectilinear progress of light and the equality of the angles of incidence and reflection. The treatise on optics which has been ascribed to Euclid is devoted to determining the apparent size and figure of objects, from the angle under which they appear, or which the extremities of them subtend 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 so imperfect, and so inaccurately drawn up, that it is not generally thought to be the production of that great geometrician. It appears from a circumstance in the history of Socrates that the effects of burning glasses had also been observed by the ancients; and it is probable that the Romans had a method of lighting their sacred fire by means of a concave speculum. The burning power of concave mirrors is taken notice of by Euclid; and, if we give credit to what some ancient historians are said to have written concerning the exploits of Archimedes, we shall be induced to think that he made great use of this principle, in constructing some very powerful burning mirrors. It is allowed, however, that this eminent geometrician did write a treatise on the subject of burning mirrors, though it be not now extant, We may now proceed to examine the progress made in our knowledge of reflected light. However much the ancients might have been mistaken with B. Porta supposes that the burning mirrors of the regard to the nature of light, we find that they were ancients were of metal, in the form of a section of a acquainted with two very important observations parabola. It follows, from the properties of this concerning it; viz. that light is propagated in right curve, that all the rays which fall upon it parallel to lines, and that the angle of incidence is equal to the its axis will meet in the same point at the focus. angle of reflection. Who it was that made these Consequently, if a portion of the parabola be cut off, important observations is not known. But im- it will make a convenient burning mirror. In some portant as they are, and the foundation of a great drawings of this instrument the portion of the part of even the present system of optics, it is possi-parabola is so small as to look like a ring. With an ble that, if he were known, he might not be allowed to instrument of this kind it is thought that the ancients have any great share of merit, at least for the former produced the most intense heat. Some have also of them; the fact is so very obvious, and so easily thought that this was the form of the mirror with ascertained. As to the latter, that the angle of inci- | which Archimedes burnt the Roman fleet. dence is equal to the angle of reflection, it was probably All this time, however, the nature of reflection was first discovered by observing a ray of the sun reflected very far from being understood. Even Lord Bacon, from the surface of water, or some other polished who made much greater advances in natural philosobody; or from observing the images of objects re-phy than his predecessors, and who pointed out the flected by such surfaces. If philosophers attended true method of improving it, was so far deceived with to this phenomenon at all, they could not but take notice, that, if the ray fell nearly perpendicular upon such a surface, it was reflected near the perpendicular; and if it fell obliquely it was reflected obliquely: and if they thought of applying any kind of measures to these angles, however coarse and imperfect, they could not but see that there was sufficient reason to assert their equality. At the same time they could not but know that the incident and reflected rays were both from the same plane. Aristotle stated his conviction that it was the re regard to the nature of reflection and refraction that he supposed it possible to see the image reflected from a looking-glass, without seeing the glass itself; and to illustrate this phenomenon he quotes a story 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 glasses while he walked upon the ground. B. Porta says that this effect may be produced by a plane mirror only; and that an ingenious person may succeed in it: but his more particular descrip |