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eafy method of finding proper formula for the conftruction of achromatic object-glafles, formed of three lenfes likewise, but not contiguous to each other; and defcribes the manner of employing these formule to the greatest advantage. He afterwards adds fome ufeful tables, by which the calculation is confiderably abridged; together with fome reflections on the aberration which may ftill remain. An anfwer is given to fome objections proposed by M. Euler to fome of the doctrines contained in the preceding memoirs; accompanied with a few remarks on the structure of the eyes of fifhes; from which M. D'A. endeavours to prove that the entire deftruction of the colorific aberration is not neceffary. The memoir is terminated by fome reflections on the combination of proper eye-glaffes, with these achromatic object-glaffes, and a few confiderations on fome other objects relative to the perfection of telescopes. We fhall only add, that the Author here, as in the preceding memoirs, ftrongly urges the abfolute neceffity of fcrupulously attending to and afcertaining the precife ratio of the refractive and difperfive powers of the glafs to be used in the construction of a compound object glafs: as the fmalleft error in this article is capable of producing a colorific aberration, greater than that arifing from the spherical figure, in the reflecting and common dioptrical telescopes.

MEMOIR II. On fome Experiments relative to Dioptrics. By the

Duke de Chaulnes.

In the preceding memoir the further improvement of the achromatic telescope was attempted by analytical reasoning and calculation, a priori: in the prefent ingenious effay the noble Author purfues a different and contrary courfe, and endeavours to accomplish the fame end by obfervations made a pofteriori; that is, by a fcrupulous examination of an excellent inftrument of that kind already constructed. Having procured a telescope, made by Mr. Dollond, which was found greatly to exceed any of the fame dimenfions, which that excellent artist afterwards endeavoured to form on the fame principles, he was ftrongly incited to discover, if poffible, all the elements of its conftruction to which it owed its fuperiority.

The difficulty of this undertaking will obviously appear, when it is confidered that the three combined object glaffes of this telescope were infeperably fixed in a cell, or at least could not be separated from each other without, perhaps irreparably, difordering fo valuable an inftrument; which might poffibly, in a great meafure, derive its fuperior excellence from certain circumftances, that might be confiderably affected by fuch an attempt. He here defcribes the different methods which he employed in order to ascertain the various elements, fuch as the refpective foci, thickness, radii of curvature, refracting powers,

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&c. of the different lenfes. Many of his expedients appear equally new and ingenious; but are not eafily to be defcribed without a reference to the numerous plates that accompany and illuftrate this very inftructive Memoir; in which the Author labours in analyzing this lucky bit of Mr. Dollond's, with all the zeal of a chemift in decompounding a valuable noftrum. For the more minute particulars therefore of this optical analyfis, we must refer to the article itself.

We have formerly + given a concife account of the noble Author's new and curious application of the microfcope and micrometer united, to the conftruction and graduation of a fmall and accurate aftronomical fector. Thefe inftruments were of the greateft ufe to him in the prefent inquiry, and may in many cafes be advantageously employed, both by the theoretical and practical optician. We thall endeavour, therefore, in order to give a fpecimen of their utility, to convey to our Readers a general idea of the Author's new method of determining, by their means, the mean refractive power of any par ticular kind of glafs, to the greatest exactnefs: as this is a defideratum, according to our obfervation in the preceding article, of the greatest importance in the theory of the achromatic telescope.

We fhall not enumerate the inconveniences attending the common method of determining this element, by means of prifms formed of the glafs to be examined. According to the Author's method the glafs is first ground into a plate, the furfaces of which are perfectly plain and parallel to each other. Over each of thefe furfaces he fprinkles a little of the duft, that is, feathers of a butterfly's wing, or fome other equally minute microscopical object; in order that these furfaces may be perceived the more diftinctly. The plate is then placed before the microfcope, at that precife diftance at which he can fee the nearest furface, or rather the fmall objects fcattered upon it, with the greatest distinctnefs. From this point he fets out, and proceeds till, by a regular motion given to the microfcope towards the piece of glafs, he can fee its farther furface with the fame exactnefs. We cannot, without figures, explain the apparatus by which this motion is effected, and its quantity measured. It will be fufficient to fay, that the space moved through by the microfcope is afcertained with the greatest accuracy, by means of his micrometrical apparatus; which thus gives him the apparent, or, as we may call it, the visible thicknefs of the glafs, diminished by its own refractive power; and this, without the hazard, as he affirms, of erring more than the 50th part of a line in the admeasurement.

+ See Appendix to Vol. xlii. p. 500.

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Nothing is now wanting to ascertain tne quantity of the refractive power of the glafs, but to know the real or tangible thickness of the plate. For this purpose the Author first meafures that thickness with a calliper compafs, and then applies his microscope and micrometer to meafure the interval between the points of the compafs. By means of thefe two inftruments this diftance is determined with fuch precifion, that, on repeating the operation feveral times on the fame piece of glass, he never found a difference equal to the 400th part of a line. This laft meafure is accordingly fufceptible of greater accuracy than the former t. The refractive power of the glass is then eafily and immediately deduced from thefe data; that is, by comparing the real thickness of the plate with its apparent thicknefs; the latter of which is diminished in proportion to the refractive power of the glafs. In a table the refults are given of the Authors examination of 15 different kinds of glafs by this method; from which it appears, that almost all the different fpecimens poffeffed different degrees of refrangibility, and that actual experiments alone, made with the particular glafs that is to be employed, can give its refractive power with the accuracy abfolutely requifite in the conftruction of an achromatic telescope.

The Author afterwards defcribes the apparatus with which He measures the other remarkable property poffeffed by the various fpecies of glafs, and which feems to be independent on their general or mean refractive power: we mean their refpec

In the first operation, that is, in meafuring the apparent thicknefs of the glafs, fome degree of uncertainty arifes from hence; that though there is undoubtedly an advantage in ufing a thick plate of glafs, yet, in that cafe, a great magnifier, or lens, of a thort focal distance, cannot be employed, on account of the too great distance of the farther furface of the plate from the lens. In fact, the focal distance of the lens must not be less than two-thirds of the thickness of the piece of glafs, whofe farther furface is to be viewed through it. It is, however, undoubtedly advantageous to employ a lens of a short focus; as there is lefs latitude or uncertainty in eftimating the point at which the object is feen moft diftinctly through it. But if, in order to avail himself of this advantage, the obferver makes choice of a thin fpecimen of the glafs to be examined, the advantage hence arifing will appear to be in fome measure counterbalanced, when we confider, that though the uncertainty in determining the true focal distance of the lens is lefs in a great than in a small magnifier; yet, on the other hand, the remaining poffible error is distributed through a fmaller space, and confequently may be relatively greater, in a thin than in a thick piece of glass. The Author found, by experience, that a lens of half an inch focus, and a plate of 8 or 9 lines in thicknefs, formed the most favourable combination for this purpose.

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tive qualities of difperfing the differently coloured rays in different degrees. The diftinction between these two properties is indeed the bafis on which the whole theory of the achromatic telescope is founded. His method feems to be fufceptible of a confiderable degree of precifion, and appears capable of being applied, with great advantage, to the determination of this effential element. We shall only add, that the different methods defcribed in this memoir exhibit many marks of an inventive mechanical genius in the Author; and that, with refpect to the more particular object of this article, or the analyfis of the excellent telescope above mentioned, the final result of his inquiries and experiments is given in a table, which exhibits the radii of curvature, thicknefs, foci, and refpective distances of all the glaffes which conftitute it.

MECHANICS.

MEMOIR. On the Proportion between the Weights used in France, and thofe of foreign Countries. By M. Tillet.

The utility of a fixed and universal standard of weight, and the inconveniences refulting from the varieties now in ufe throughout the commercial world, are as univerfally known and acknowledged, as is the difficulty, or rather the moral impoffi bility, of fettling one invariable ftandard, which the European nations would agree to adopt. Such a measure being evidently impracticable, the French miniftry have lately very laudably interested themselves in the practicable, but difficult fcheme of afcertaining at leaft the real value of the different weights used throughout Europe, or rather of discovering the exact proportion which they bear to thofe ufed in France. For this purpose the king's ambaffadors and refidents in foreign parts received particular inftructions, not only to procure the best information concerning the weights employed in thofe countries where they refided, but likewife to fend over exact and well-authenticated fpecimens of each. This memoir contains an account of the methods purfued, in the courfe of an elaborate examination of the different weights that had been procured, by the commiffaries appointed by the Academy; the refult of which is given in 31 tables, containing the exact value of these weights, and of their various fubdivifions, which are ufed in as many of the principal cities of Europe; and which are all reduced to the Poids de Marc and its fubdivifions in France, as to a common measure. We need not dwell on the utility of these very extenfive tables, formed with the moft fcrupulous accuracy, and which, though adapted to the French standard, must be of common benefit to all the countries comprehended in them.

This volume is terminated by a fhort enumeration of different machines, prefented to and approved by the Academy ;

and

and by an account of the continuation of the Hiftories of the Arts that have been printed in 1767. These are, the art of Organbuilding; of making Tennis-balls, &c. of Leather-dreffing; of the Vermicelli-maker; and of the Miller, Baker, and Perriwigmaker. B...y.

ART. VIII.

Hiftoire de l'Academie Royale des Sciences, &c.-The Hiflor of the Royal Academy of Sciences at Paris; together with the Mathematical and Phyfical Memoirs for the Year 1768. 4to. Paris.

1770.

GENERAL PHYSICS. MEMOIR 1. Obfervations on the Motion of the Quickfilver in Barometers of various Diameters, and charged in different Manners. By the Cardinal de Luynes.

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HE defign of the Author of this memoir was to afcertain, by a regular feries of experiments, how far the fize or bore of a tube, intended for a barometer, influences the height of the mercury; and in what degree the perfection of that inftrument is affected by the different methods that have been practifed in filling the tube. For this purpose he made a variety of experiments with tubes of different fizes; the leaft of which was capillary, being only two-thirds of a line in diameter; and the largeft 13 lines, requiring no less than 18 pounds of quickfilver to fill it. For this laft he was obliged to contrive particular apparatus, in order to enable him to fubject the mercury, put into it at different times, (to the amount of only 3 or 4 inches each time,) to a boiling heat; and afterwards to invert it into the bafon. This immenfe tube, it will easily be imagined, fupported a longer column of quickfilver than the reft, and was accordingly used by the Author'as a ftandard.

From the whole of his experiments we collect, that the advantage of employing very large tubes is not very confiderable. In the great tube of above 13 lines in diameter, the mercury ftood only one line higher than in another tube, the bore of which was little more than 2 lines, or the fixth of an inch; and even the capillary tube above-mentioned fupported a column only 2 lines fhorter than this laft; that is, 3 lines lower than that of his ftandard barometer; all the three having been alike charged with boiling mercury. It appears likewise, that this capillary tube, thus charged, fuftained as long a column as a tube of 2 lines bore which contained quickfilver only moderately heated; but that in this laft-mentioned tube, the mercury was 2 lines lower, than in one of the fame bore, in which the mercury was made to boil violently. The Author afterwards obferves, that a capillary tube, only two-thirds of a

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