of 1', 8"; fo is the fine of any other incidence, to the fine of its angle of refraction; and fo is radius, or 1000000, to 999736; which, therefore, is the proportion between the fine of incidence in vacuo and the fine of refraction from thence into common air. It appears, by thefe experiments, that the refractive power of the air is proportionable to its denfity. And fince the denfity of the atmosphere is as its weight directly, and its heat inverfely, the ratio of its denfity, at any given time, may be had by comparing the heights of the barometer and thermometer; and thence he concludes that this will alfo be the ratio of the refraction of the air. But Dr SMITH obferves, that, before we can depend upon the accuracy of this conclufion, we ought to examine whether heat and cold alone may not alter the refractive power of air, while its denfity continues the fame. This, he fays, may be tried, by heating the condenfed or rarefied air, shut up in the prifm, juft before it is fixed to the telescope, and by obferving whether the hair in its focus will continue to cover the fame mark all the while that the air is cooling. 25. The French academicians, being informed of the refult of the above-mentioned experiment, employed M. DELISLE the younger to repeat their former experiment with more care; and he prefently found, that their operators had never made any vacuum at all, there being chinks in their inftrument, through which the air had infinuated itself. He therefore annexed a gage to his inftrument, by which means he was fure of his vacuum; and then the refult of the experiment was the fame with that in England. The refraction was always in proportion to the denfity of the air, excepting when the mercury was very low, and confequently the air very rare, in which cafe the whole quantity being very fmail, he could not perceive much difference in them. Comparing, however, the refractive power of the atmof phere obferved at Paris with the refult of his experiment, he found, that the best vacuum he could make was far fhort of that of the etherial regions above the atmosphere. 26. Dr Hooks first fuggefted the thought of making allowance for the effect of the refraction of light, in paffing from the higher and varer, to the lower and denfer regions of the atmosphere, in the computed height of mountains. To this he afcribes the different opinions of authors concerning the height of feveral very high hills. He could not account for the appearance of the Peak of Teneriffe, and feveral very high mountains, at fo great a diftance as that at which they are actually feen, but upon the fuppofition of the curvature of the vifual ray, that is made by its paffing obliquely through a medium of fuch different denfity, from the top of them to the eye, very far diftant in the horizon. Ail calculations of the height of mountains that are made upon the fuppolition that the rays of light come from the tops of them, to our eyes, in ftraight lines, muft, he fays, be very erroneous. Dr Hooke gives a very good account of the TWINKLING OF THE STARS; afcribing it to the irregular and unequal refraction of the rays of light, which is also the reafon why the limbs of the fun, moon, and planets ap pear to wave or dance. And that there is fuch an unequal diftribution of the parts of the atmofphere, he fays, is manifeft from the different degrees of heat and cold in the air. This, he says, will be evident by looking upon diftant objects, over a piece of hot glafs, which cannot be fuppofed to throw out any kind of exhalation from itfelf, as well as through afcending steams of water. 27. About this time GRIMALDI first observed that the coloured image of the fun refracted through a prifm is always oblong, and that colours proceed from refraction. The way in which he firft difcovered this, was by Vitellio's experiment above mentioned, in which a piece of white paper placed at the bottom of a glafs vetfel filled with water, and expofed to the light of the fun, appears coloured. However, he obferved, that in cafe the two furfaces of the refracting me dium were exactly parallel to each other, no colours were produced. But of the true caufe of thofe colours, viz. the different refrangibility of the rays of light, he had not the least suspicion. 28. This difcovery was referved for Sir ISAAC NEWTON, and occured to him in 1666. At that time he was bufied in grinding optic glaffes, and procured a triangular glafs prifm to fatisfy himfelf concerning the phenomena of colours. While he amused himself with this, the oblong figure of the coloured fpectrum firft ftruck him. He was furprifed at the great difproportion betwixt its length and breadth; the former being about five times the measure of the latter. He could hardly think that any difference in the thickness of the glafs, or in the compofition of it, could have fuch an influence on the light. However, without concluding any thing à priori, he proceeded to examine the effects of these circumftances, and tried what would be the confequence of transmitting the light through parts of the glafs that were of different thickneffes, or through holes in the window-fhutter of different fizes; or by fetting the prifm on the outfide of the fhutter, that the light might pafs through it, and be refracted before it was terminated by the hole. He then fufpected that thefe colours might arife from the light being dilated by fome unevenness in the glass, or fome other accidental irregularity; and to try this, he took another prifm, like the former, and placed it in fuch a manner as that the light paffing through them both might be refracted contrarywife, and fo be returned by the latter into the fame courfe from which it had been diverted by the former. In this manner he thought that the regular effects of the firft prifm would be destroyed by the 2d; but that the irregular ones would be augmented by the multiplicity of refractions. The event was, that the light, which by the first prism was diffused into an oblong form, was by the ad reduced into a circular one, with as much regularity as if it had not paffed through either of them. 29. At last, after various experiments and conjectures, he hit upon what he calls the experimentum crucis, and which completed this great difCovery. He took two boards, and placed one of them clofe behind the prifm at the windows, fo that the light might país through a fmall hole made in it for the purpose, and fall on the other S$ 2 board, board, which he placed at the diftance of about 12 feet; having firft made a small hole in it also, for fome of that incident light to pass through. He then placed another prism behind the 2d board, fo that the light which was tranfmitted through both the boards might pafs through that alfo, and be again refracted before it arrived at the wall. This done, he took the firft prifm in his hand, and turned it about its axis, fo much as to make the several parts of the image caft on the fecond board fucceffively to pass through the hole in it, that he might obferve to what places on the wall the ad prifm would refract them; and he faw, by the change of thofe places, that the light tending to that end of the image towards which the refraction of the first prifm was made, did, in the ad prifm, fuffer a refraction confidera. bly greater than the light which tended to the other end. The true caufe, therefore, of the length of the image was discovered to be no other, than that light is not fimilar or homogeneal; but that it confifts of rays, fome of which are more refrangible than others: fo that, without any difference in their incidence on the fame medium, fome of them fhall be more refracted than others; and therefore, that, according to their particular degrees of refrangibility, they will be tranfmitted through the p.ifm to different parts of the oppofite wall. 30. Since it appears from thefe experiments, that different rays of light have different degrees of refrangibility, it neceffarily follows, that the rules laid down by preceding philofophers concerning the refractive power of water, glass, &c. muft be limited to the middle kind of ray. Sir Ifaac, however, proves that the fine of the incidence of every kind of light, considered apart, is to its fine of refraction in a given ratio. This he deduces, both by experiment, and alfo geometrically, from the fuppofition that bodies refract the light by acting upon its rays in lines perpendicular to their furfaces. 31. The most important difcovery with regard to refraction, fince the time of Sir Ifaac Newton, is that of Mr DOLLOND, who found out a method of curing the faults of refracting telescopes arifing from the different refrangibility of the rays, and which had been generally thought impoffible to be removed. Notwithstanding the great difcovery of Sir Ifaac Newton concerning the different refrangibility of the rays of light, he had no idea but that they were all affected in the fame proportion by every medium, fo 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 muft not only detroy each other, but that the divergency of the colours from one refraction would likewife be corrected by the other, and that there could be no poffibility of producing any fuch 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 fo done that the emergent ray should be parallel to the incident one, it would ever after be white; and con fequently, if it fhould 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-glaffes of telescopes must be equally affected by the different refrangibility of light, in proportion to their apertures, of whatever materials they may be formed. 32. For this reafon, Sir Ifaac Newton, and all other philofophers and opticians, had despaired of bringing refracting 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 bufinefs of refraction was dropped till about 1747, when M. EULER, improving upon a hint of Sir Ifaac Newton's, formed a fcheme of making object-glaffes of two materials, of different refractive powers; hoping, that by this difference, the refractions would balance one another, and thereby prevent the difperfion of the rays that is occafioned by the difference of refrangibility. Thefe object-glaffes were composed of two lenfes of glafs, with water between them. This memoir of M. Euler excited the attention of Mr Dollond. He carefully went over all M. Euler's calcula tions, fubftituting for his hypothetical laws of refraction thofe which had been actually ascertained by the experiments of Newton; and found, that, after this neceffary fubftitution, 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. 33. M. EULER did not mean to controvert the experiments of Newton: but he faid, that they were not contrary to his hypothefis, but in fo fmall a degree as might be neglected; and afferted, that, if they were admitted in all their extent, it would be impoffible to correct the difference of refrangibility occafioned by the tranfmiffion of the rays from one medium into another of different denfity; a correction which he thought was very poffible, fince he fuppofed it to be actually effected in the ftructure of the eyes, which, in his opinion, was made to confift 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 circumfpection with which it was known that he conducted all his inquiries. In this state of the controverfy, the friends of M. CLAIRAUT engaged him to attend to it; and it appeared to him, that, fince the experiments of Newton cited by Mr Dollond could not be questioned, the speculations of M. Euler were more ingenious than useful. 34. The fame paper of M. Euler was alfo particularly noticed by M. KLINGENSTIERNA of Sweden, who gave a confiderable degree of attention to the fubject, and difcovered, that, from Newton's own principles, the refult of the 8th experiment of the 2d book of his Optics could not anfwer his defcription of it. He found, he fays, that when light goes out of air through several contiguous refracting mediums, as through water and glafs, and thence goes out again into air, whether the refracting furfaces be parallel or inclined to one another, that light, as often as by contrary contrary refractions it is fo corrected as to emerge in lines parallel to those in which it was incident, continues ever after to be white; but if the emergent rays be inclined to the incident, the whitenefs of the emerging light will, by degrees, in paffing on from the place of emergence, become tinged at its edges with colours. This he tried, by refracting light with prifms of glafs placed within a prifmatic veffel of water. By theorems deduced from this experiment he infers, that the refractions of the rays of every fort, made out of any medium into air, are known by having the refraction of the rays of any one fort; and alfo that the refraction out of one medium into another is found as often as we have the refractions out of them both into any third medium. On the contrary, the Swedish philofopher obferves, that, in this experiment, the rays of light, after paffing through the water and the glafs, though they come out parallel to the incident rays, will be coloured; but that the fmaller the glafs prifm is, the nearer will the refult of it approach to Newton's defcription. 35. This paper of M. Klingenftierna being communicated to Mr Dollond by M. Mallet, made him entertain doubts concerning Newton's report, and determined him to have recourfe to experiment. He therefore cemented together two plates of parallel glafs at their edges, fo as to form a prifmatic veffel, when stopped at the ends or bafes; and the edge being turned downwards, he placed in it a glafs prifm, with one of its edges upwards, and filled up the vacancy with clear water; fo that the refraction of the prifm was contrived to be contrary to that of the water, in order that a ray of light, tranfmitted through both thefe refracting mediums, might be effected by the difference only between the two refractions. As he found the water to refract more or lefs than the glass prifm, he diminished or increafed the angle between the glass plates, till he found the two contrary refractions to be equal; which he difcovered by viewing an object through this double prifm. For when it appeared neither raifed nor depreffed, he was fatisfied that the refractions were equal, and that the emergent rays were parallel to the incident. Now, according to the prevailing opinion, he obferves, the object fhould have appeared through this double prifm in its natural colour; for if the difference of refrangibility had been in all refpects equal in the two equal refractions, they would have rectified each other. But this experiment fully proved the fallacy of the received opinion, by fhowing 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, was yet as much infected with prifmatic colours, as if it had been feen through a glass wedge only whofe refracting angle was near 30 degrees. 36. This experiment is the very fame with that of Sir Ifaac Newton's above-mentioned, notwithftanding the refult was so remarkably different; but Mr Dollond affures us, that he used all poffible precaution and care in his procefs; and he kept his apparatus by him, that he might evince the truth of what he wrote, whenever he thould be properly required to do it. He plainly faw, however, that if the refracting angle of the water veffel could have admitted of a fufficient increase, the divergency of the coloured rays would have been greatly diminished, or entirely rectified; and that there would have been a very great refrac tion without colour, as he had already produced a great difcolouring without refraction; but the inconveniency of fo large an angle as that of the prismatic vessel must have been, to bring the light to an equal divergency with that of the glafs prism whofe angle was about 60°, made it necef fary to try fome experiments of the fame kind with fmaller angles. Accordingly, he got a wedge of plate glafs, the angle of which was only 90; and ufing it in the fame circumftances, 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 glafs; that is, till the image of the object, though confiderably refracted by the excefs 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 meafure, the refraction by the water was about of that by the glass. 37. As thefe experiments clearly proved that different fubftances made the light to diverge very differently, in proportion to their general refrac tive power, Mr Dollond began to fufpect that such variety might poffibly be found in different kinds of glafs, especially as experience had already fhown that fome of the kinds made much better object-glaffes in the ufual way than others; and as no fatisfactory cause had been affigned for fuch difference, he thought there was great reason to prefume that it might be owing to the different divergency of the light in the fame refractions. He therefore ground wedges of different kinds of glass, and applied them together; fo that the refractions might be made in contrary directions, to difcover whether the refraction and the divergency of the colours would vanifh together. It was not till the end of 1757 that he undertook it; when he difcovered a difference far beyond his hopes in the refractive qualities of different kinds of glass, with refpect to the divergency of colours. The yellow or ftraw-coloured foreign fort, commonly called Venice glass, and the English crown glass, proved to be very nearly alike in that refpect; though, in general, the crown glass seemed to make the light diverge leaft. The common English plate glafs made the light diverge more; and the white cryftal, or English flint glass, moft of all. 38. He now examined the particular qualities of every kind of glass that he could come at, not to amufe himself with conjectures about the cause of this difference, but to fix upon two forts in which it should be the greatest; and he foon found these to be the crown glass and the white flint glafs. He therefore ground one wedge of white flint, of about 25°; and another of crown glass, · of about 29°: which refracted very nearly alike, but their power of making the colours diverge, was very different. He then ground several others of crown glafs to different angles, till he got one which was equal, with refpect to the divergency of the light, to that in the white flint glass: for when when they were put together, fo as to refract in contrary directions, the reflected light was entirely free from colours. Then measuring the refraction of each wedge with these different angles, he found that of the white glafs to be to that of the crown glafs nearly as two to three: and this proportion held very nearly in all fmall angles; fo 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 difperfion of the rays. 39. In a letter to M. KLINGENSTIERNA, quoted by M. Clairaut, Mr Dollond fays, that the fine of incidence in crown glass is to that of its general refraction as I to r53, and in flint glafs as 1 to 1583. To apply this to practice, Mr Dollond went to work upon the object-glaffes of telescopes; not doubting but that, upon the fame principles upon which a refracted colourless ray was produced by prifms, it might be done by lenfes only, made of fimilar materials. And he fucceeded, by confidering, that, in order to make two fpherical glaffes 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 muft evidently be in the convex lens. Alfo, as the convex glafs is to refract the moft, it appeared from his experiments, that it must be made of crown glafs, and the concave of white flint glass. Farther, as the refractions of spherical glaffes are in an inverse ratio of their focal diftances, it follows that the focal diftances of the two glaffes fhall be inversely as the ratios of the refractions of the wedges; for being thus proportioned, every ray of light that paffes through this combined glafs, at whatever distance it may pafs from its axis, will conftantly 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. 40. Notwithstanding our author had thefe clear grounds in theory and experiment to go upon, he found that he had many difficulties to fruggle with: For, 1. The focal diftances, as well as the particular furfaces, muft be very nicely proportioned to the denfities or refracting powers of the glaffes, which are very apt to vary in the fame fort of glafs made at different times. 2. The centres of the two glasses must be placed truly in the common axis of the telescope, otherwife the defired effect will be in a great measure deftroyed. 3. There are four furfaces to be wrought perfectly fpherical; all of which require the greatest accuracy throughout the whole work. At length, however, after numerous trials, he conftructed refracting telescopes, with fuch apertures and mag. nifying powers, under limited lengths, as, in the opinion of the beft judges, far exceeded any thing that had been produced before, representing objects with great diftinctness, and in their true colours. 41. It was objected to Mr Dollond's discovery, that the small difperfion of the rays in crown glafs is only apparent, owing to the opacity of that ki of gfs which does not transmit the fainter coloured rays in a fufficient quantity; but this objection is answered by M. BEGUELIN. As Mr Dollond did not explain the methods which he took, in the choice of different spheres proper to deftroy the effect of the different refrangibility of the rays of light; and as the calculation of the dif perfion of the rays, in fo complicated an affair, is very delicate; M. CLAIRAUT endeavoured to make out a complete theory of it; as without fome affiftance of this kind, it is impoffible to conftruct telescopes of equal goodness with those of Mr Dollond. Befides, Mr Dollond only gave his proportions in general, whereas the greateft pof fible precifion is neceffary. 42. With a view, therefore, to affift the artist, he endeavoured to afcertain the refractive power of different kinds of glass, and their property of feparating the rays of light, by the following methods. He made ufe of two prifms placed clofe to one another, as Mr Dollond had done: but he placed them in a darkened room; and when the image of the fun tranfmitted through them was perfectly white, he concluded that the different refrangibility of the rays was corrected. To af. certain with more ease the true angles that prifms ought to have, to deftroy the effect of the difference of refrangibility, he conftructed one which had one of its furfaces cylindrical, with several degrees of amplitude. Thus, without changing his prifms, he had the choice of an infinity of angles; among which, by examining the point of the curve furface, which, receiving the folar ray, gave a white image, he could easily find the true one. He alfo afcertained the proportion in which different kinds of glass feparated the rays of light, by measuring, with proper precautions, the ob long image of the fun, made by tranfmitting a beam of light through them. In making these experiments, he hit upon an eafy method of proving the greater refractive power of English flint glass above the common French glass, both with refpect to the mean refraction, and the different refrangibility of the colours; for having taken two prifms of these two kinds of glafs, but equal in all other refpects, and placed them fo that they received at the fame time two rays of the fun with the fame degree of incidence, be faw, that of the two images, that which was produced by the English flint-glafs was a little higher up on the wall than the other, and longer by more than one half. 43. M. CLAIRAUT was affifted in these experiments by M. De TOURNIERES, and the refults agreed with Mr Dollond's in general; but whereas Mr Dollond had made the difperfion of the rays in glafs and in water to be as 5 to 4, these gentlemen, who ufed more precautions, found it to be as 3 to 2. For the theorems and prob. lems deduced by M. Clairaut from these new principles, we refer the reader to Mem. Acad. Par. 1756, 1757 44. The labours of M. Clairaut were fucceeded by thofe of M. D'ALEMBERT, which feem to have given the makers of these achromatic telescopes all the aid that calculations can afford them. This excellent mathematician likewife proposed a variety of new confiructions of these telescopes; at the fame time he points out feveral methods of correcting the errors to which they are liable: as by placing the object-glaffes, in fome cafes, at a fmall fmall distance from one another, and fometimes by ufing eye-glaffes of different refractive powers. He shows, that telescopes may be made to advantage, confifting of only one object-glafs, and an eye-glafs of a different refractive power. This fubject he confidered at large in one of the Opufcules Mathematiques. We have alfo 3 of his memoirs upon this fubject, among thofe of the French academy, in 1764, 1765, and 1767. 45. Notwithstanding Mefits Clairaut and D'Alembert feemed to have exhaufted the bnfinefs of calculation, on the subject of Mr Dollond's telescopes, no ufe could be made of their labours by foreign artists. For ftill the telescopes made in England, according to no exact rule, as foreigners fuppofed, were greatly fuperior to any made elsewhere, though under the immediate direction of thofe able calculators. For this M. BEGUELIN affigned several reasons: 1. Their geometrical theorems were too general, and their calculations too complicated, for the ufe of work men: 2. In confequence of neglecting fmall quantities, which thefe calculators profeffedly did, to make their algebraical expreffions more commodious, their conclufions were not fufficiently exact: But 3. What he thought to be of the moft conf-quence, was the want of an exact method of measuring the refractive and difperfing powers of the different kinds of glafs; and for want of this, the greatest precision in calculation was altogether ufelefs. 46. Thefe confiderations induced this gentleman to take another view of this fubject; but ftill he could not reconcile the actual effect of Mr Dollond's telefcopes with his own conclufions: fo that he imagined, either that he had not the true refraction and difperfion of the two kinds of glafs given him; or elfe, that the aberration which ftill remained after his calculations, muft have been deftroyed by fome irregularity in the furfaces of the lenfes. He finds feveral errors in the calculations both of M. D'Alembert and Clairaut. 47. M. Euler, who firft gave occafion to this inquiry, being perfuaded both by his reafoning and calculations, that Mr Dollond had difcovered no new principle in optics, and yet not being able to controvert Mr SHORT's teftimony in favour of the goodnefs of his telescopes, concluded that this extraordinary effect was owing, in part, to the crown glafs not tranfmitting all the red light, which would otherwife have come to a different focus, and have diftorted the image; but principally to his happening to hit on a juft curvature of his glafs, which he did not doubt would have produced the fame effect if his lenfes had all been made of the fame kind of glafs. He alfo imagined that the goodnefs of M; Dollond's telefcope might be owing to the eye-glafs. At length, however, M. Euler was convinced of the reality and importance of Mr Dollond's difcoveries; and frankly acknowledged, that he fhould perhaps never have been brought to affent to it, had not his friend M. Clairaut affured him, that the experiments of the English optician might be depended upon. 48. However, the experiments of M. Zeiher of Peterburgh gave him the most complete fatisfac tion, with respect to this new law of refraction. This gentleman demonftrated, that it is the lead in the compofition of glafs that gives it this remarkable property, that while the refraction of the mean rays is nearly the fame, that of the extremes differs confiderably. And, by increasing the quantity of lead in the mixture, he produced a kind of glafs, which occafioned a much greater separation of the extreme rays than the flint-glafs which Mr Dollond had made use of. By this evidence, M. Euler owns that he was compelled to renounce the principle which, before this time, had been confidered as inconteftible, viz. that the difperfion of the extreme rays depends upon the refraction of the mean; and that the former varies with the qualities of the glass, while the latis not affected by it. 49. From these new principles M. Euler deduced theorems concerning the combinations of the lenfes; and, in a manner fimilar to M. Clairaut and D'Alembert, points out methods of constructing achromatic telescopes. While he was employed upon this fubject, he informs us, that he received a letter from M. Zeiher, dated Petersburgh, 30th January 1764, in which he gives him a particular account of the fuccefs of his experiments on the compofition of glass: and that, having mixed minium and fand in different proportions, the refult of the mean refraction and the difperfion of the rays varied according to the following 50. TABLE. Proportion of Mean refraction Difperfion of minium to from air into the rays in flint. glafs. comparison of crown-glafs. III. IV. I 1000 3550 : 1080 : 1000 3259 1000 2207 : : ICOO 1000 1000 1800 10001354 : 1000 : 1000 V. VI. 2 : 11830 : 11787 11732 : : 11742 : : 11664 : 51. By this table it is evident, that a greater quantity of lead not only occafions a greater difperfion of the rays, but also confiderably increases the mean refraction. The firft of these kinds of glafs, which contains three times as much minium as flint, will appear very extraordinary; fince, hitherto, no tranfparent fubftance has been known, whofe refractive power exceeded the ratio of two to one, and that the difperfion occafioned by this glafs is almoft five times as great as that of crown glafs, which could not be believed by thofe who entertained any doubt concerning the fame property in flint-glafs, the effect of which is threetimes as great as crown glass. 52. M. EULER announces to us another difcovery of M. ZEIHER, no lefs furprising than the former, and which difconcerted all his fchemes for reconciling the above-mentioned phenomena. As the fix kinds of glafs mentioned in the above table were compofed of nothing but minium and flint, M. Zeiher propofed mixing alkaline falta with them, to give the glafs a confiftence more proper for dioptric ufes; and was surprised to find this mixture greatly diminished the mean refraction, almost without making any change |