Nothing is now wanting to ascertain the quantity of the refractive power of the glafs, but to know the real or tangible thickness of the plate. For this purpofe the Author firft meafures that thicknefs with a calliper compafs, and then applies his microscope and micrometer to measure the interval between the points of the compafs. By means of these two inftruments this diftance is determined with fuch precision, 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 last measure is accordingly fufceptible of greater accuracy than the former t. The refractive power of the glafs 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 diminifhed 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 poffefled 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 diftance of the lens must not be lefs than two-thirds of the thickness of the piece of glass, whofe farther furface is to be viewed through it. It is, however, undoubtedly advantageous to employ a lens of a fhort 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 meafure 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 fmall 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 glafs. 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 moft 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 fhall 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 analy fis of the excellent telescope above mentioned, the final result of his inquiries and experiments is given in a table, which exhibits the radij of curvature, thicknefs, foci, and refpective distances of all the glaffes which conftitute it.

MECHANIC 8.

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

The utility of a fixed and univerfal standard of weight, and the inconveniences refulting from the varieties now in ufe throughout the commercial world, are as universally known and acknowledged, as is the difficulty, or rather the moral impoffibility, of fetaling one invariable ftandard, which the European nations would agree to adopt. Such a measure being evidently impracticable, the French miniftry have lately very laudably interefted themfelves in the practicable, but difficult fcheme of afcertaining at leaft the real value of the different weights used throughout Europe, or rather of difcovering the exact propor. tion which they bear to thofe ufed in France. For this purpofe the king's ambafladors 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 ftandard, must be of common benefit to all the countries comprehended in them.

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

and

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

ART. VIII.

Hiftoire de l'Academie Royale des Sciences, &c.-The Hiflory 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 I. Obfervations on the Motion of the Quickfilver in Barometers of various Diameters, and charged in different Manners. By the Cardinal de Luynes.

THE 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 inAtrument 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 a 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 immense tube, it will eafily be imagined, fupported a longer column of quickfilver than the reft, and was accordingly ufed 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 likewife, 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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line in diameter, carefully charged with boiling quickfilver, forms a cheap inftrument, and which may be depended upon, as to the regularity of its motions; which were found to correfpond exactly with thofe of the quickfilver in much larger tubes, even in thofe of near one-fourth of an inch in diameter.

Of all the methods of filling the tubes of barometers, the Author found that to be the worft (though it has been recommended by fome as one of the moft excellent) in which the mercury is introduced into the tube by means of a tunnel, with a long capillary ftem reaching nearly to the bottom of it. In a tube, thus filled, he found that the quickfilver stood 8 lines below the ftandard. He obferves too, that the previous washing the internal furface of a tube with spirit of wine, is a ftill more prejudicial practice; as a barometer, thus treated, ftood an inch lower than it ought to do. But we have some reafon to fufpect that the Author has not been accurate in this experiment; particularly, in the drying the tube; and that this remarkable low nefs of the mercury was in fome measure owing to the claftic vapour which is very readily generated in vacuo, in a very moderate degree of heat, from even a small quantity of moiffure.

MEMOIR II. and III. Obfervations on the Circulation of Air in Mines; together with an Account of the most effectual Methods of promoting it. Firft and fecond Memoirs. By M. Jars.

It is well known, that the inconveniences and fatal accidents attending the working of coal-pits and other mines, principally derive their origin from the ftagnation of the air within them; and that the prevention of thefe dangers is only to be effected, by producing a mation in the air contained in thefe fubterraneous cavities: fo that the mephitic, inflammable, and other noxious exhalations, continually ariling in them, may be expelled by a current of fresh air introduced from without.

In thefe memoirs the Author throws confiderable light on this fubject, by offering a theory founded on a great number of obfervations, made in the different mines which he has vifited in various parts of Europe. Of thefe obfervations we fhall felect one, which is undoubtedly founded on just hydroftatical principles; and of which we may poffibly fucceed in giving an intelligible account, without the affiftance of plates. A general knowledge of the Author's theory may be of great fervice in directing thofe, who are engaged in works of this kind, where to fink the Airfhafts, or other fpiracles, to the greatest advantage; and may prevent them from incurring very great and unneceffary expences, in the digging them, as it were, at random, and in fituations where they cannot poffibly, for the reafons hereafter explained, produce the beneficial effects expected from them.

In his vifits to the mines of Cheiffy, in the Lionnois, as well as to fome others which are funk under the declivity of a hill, M. Jars obferved, that, in the winter, there was a regular current of air which entered the galleries, or the horizontal paffages leading to the mine, at their mouths, which open towards the bottom of the hill; and that the air at the fame time came out of the Air-fhafts, or perpendicular paflages, that are funk down to thefe galleries, and which have their mouths towards the top of the hill. In the fummer-time, he obferved, that there was a current likewife, but that it now moved in a contrary direction; entering at the mouth of the air fhaft, and paffing out at that of the gallery or adit . In the spring and autumn, fcarce any motion of the air was perceptible; and accordingly thefe particular mines, he obferves, as well as many others, are abandoned at these feafons, on account of the atter impracticability of working them, arifing from this ftagnation; though the caufe of it was not known.-The following manner of confidering the fubject will probably explain the cause or rationale of thefe different appearances.

We may confider the gallery at the bottom of the hill, together with the perpendicular Air-fhaft, afcending from one extremity of it, and an imaginary tube, parallel to the Airfhaft, and fuppofed to afcend from the other extremity, as a horizontal tube, to the ends of which two perpendicular tubes of equal length or height are connected, and which is preffed by two columns of air, each extending to the top of the atmofphere. Suppofing the air contained in these two perpendicular tubes to be of equal gravity at equal heights above the gallery; no reason can be given why the air, contained in this compound tube, fhould have a motion in any direction whatever. But if thefe two columns, though equal in height, confift of a fluid, the temperature of which in one of the legs of the com pound tube fometimes differs from that of the fluid contained in the other, a difference will take place in its denfity and weight; the two columns will not at thefe times be in equilibrio with each other; the heavier column will confequently defcend and the lighter will rife; in fhort, the whole fluid will be put in motion, which will continue as long as the caufes which produced it continue to exift.

Now the air contained within the perpendicular Air-fhaft (or rather that part of it which is at a certain depth below the

We fpeak from memory only, not having the work at hand; but there are fome observations, in one of Dr. Franklin's Letters, &c. on intermittent or periodical currents of air, moving alternately up and down a chimney, where there is no fire, at different times of the day, which have a near relation to the prefent fubject.

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