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has recourse to reasoning; and gives a formula for ascertaining the expansion in a certain heat.

Another irregularity in the expanfion of the air is produced by the inequality of the compreffing force; a formula for correcting this is alfo added. The Author mentions another correction which is to be applied to the height of a mountain, as it is ufually found from obfervations of the barometer. This arifes from the diminution of gravity, in afcending or defcending from the furface of the earth.

Having enumerated all the caufes which produce variations in the density of the air, Mr. Playfair proceeds to investigate the effect of them all together, and after an integral calculus, managed with great ingenuity, he obtains a univerfal formula for the distance, between the two places of observation, in the following infinite feries, where, bbyp, log. of the height of the mercury in the lower barometer, B = hyp. log. of that in the upper one, H= the height of the mercury in the lower thermometer, b = that in the upper one, m=.00245 the expansion of the air for an increase of 1o of heat according to Fahrenheit's thermometer at 32°, r = 32, p = 4342.9 &c. and g hyp, log. (1-m).

p.b-B.

1 + rg + { r2g2 + 1⁄2 r3g3 &c. ad inf.

1+{g.H+b+ & g2. H2 + Hb + b2 &c. If, inftead of the hyperbolical logarithms, Briggs's be used, then p becomes 10000. And the two firft terms of the feries will be found to be precifely M. de Luc's formula, which was discovered by that ingenious and indefatigable obferver, without any inquiry into the principles on which it depends, but merely deduced from a number of obfervations, made in different fituations, and different ftates of the atmosphere.

Mr. Playfair adds numerous remarks, tending to fhew what particular parts of this univerfal expreffion are the corrections that must be made for particular effects. He mentions alfo feveral circumstances neceffary for perfecting the art of barometrical measurement, which are not yet determined; and recommends fuch methods as he thinks will ascertain, or at least contribute to increase our knowlege of, thofe facts which feem wanting to complete the theory.

On the Ufe of negative Quantities in the Solutions of Problems by algebraical Equations. By William Greenfield, M. A. F. R. S. Edin. Profeffor of Rhetoric at Edinburgh.

In this paper Mr. Greenfield demonftrates the two following propofitions: ift, Where the problem allows us to confider x, one of the unknown quantities, as capable of existing in two oppofite fituations, which may be represented by adREV. July, 1788. dition

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dition and fubtraction; then the equation which expreffes the conditions required of x in one of thefe fituations, and whofe pofitive roots determine the magnitudes of x in that fituation; the fame equation, by its negative roots, will determine the magnitudes of x in the oppofite direction. 2d, Where the problem allows us to confider a, any of the known quantities, as capable of exifting in two fuch oppofite fituations; then the equation which expreffes the conditions of the problem, upon the fuppofition that a is in one of thefe fituations, will be reduced to the equation expreffing the conditions of the problem on the contrary fuppofition, by fimply changing the fign of the terms involving the odd powers of a.' Thefe are not new propofitions. Mr. Greenfield has however demonftrated them in a manner that we do not recollect to have seen before.

Experiments and Obfervations upon a remarkable Cold which accompanies the Separation of Hoar-froft from a clear Air. By Patrick Wilfon, M. A. F. R. S. Edin. Prof. of Aftronomy at Glafgow.

In the 64th volume of our Review, p. 275, and 67th vol. p. 127, we gave an account of Mr. Wilfon's experiments, by which it appeared that there is a conftant difference of temperature between the fnow and the air at a few feet above its furface; the fnow being the coldeft. In the prefent memoir, Mr. Wilfon offers fome conjectures as to the caufe of this phenomenon, and adds the relation of more experiments made with a view to eftablifh the facts. His general conclufions are, That when bodies attract hoar-froft from a clear air, there is a cold produced at their furfaces; and that this cold does not originate from any peculiar qualities of bodies upon which the hoar-froft fettles, any farther than as fome bodies are capable of attracting from the air more or less of it in a given time. That the difpofition of the air of thus parting with hoar-froft, and the cold which accompanies that feparation, has a conftant dependence on the general ferenity of the atmosphere, and is always interrupted by the fky being overcaft with clouds or fogginefs, especially near the place of obfervation.'

Though Mr. Wilfon's experiments afforded fufficient examples of cold produced on the feparation of hoar-frost from the air, he relates the particulars of one fet of experiments, from which it appears that the phenomenon of an excefs of cold at the furface of the fnow took its rife from a manifeft evaporation. To enumerate the particulars of thefe experiments would take more room than we can allow; we must therefore refer the curious meteorologift to the memoir itfelf.

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An Account of a Method of making a Wine, called by the Tartars KOUMISS; with Obfervations on its Ufe in Medicine. By John Grieve, M. D. F. R. S. Edin.

The Author of the prefent memoir gives the following receipt for making the Koumifs, as he obtained it from a Ruffian nobleman, who went into that part of Tartary, where it is made, for the fake of ufing it medicinally.

Take of fresh mare's milk, of one day, any quantity; add to it a fixth part of water, and pour the mixture into a wooden veffel; use then, as a ferment, an eighth part of the foureft cow's milk that can be got; but, at any future preparation, a small portion of old Koumifs will better anfwer the purpose of fouring; cover the veffel with a thick cloth, and fet it in a place of moderate warmth; leave it at reft 24 hours, at the end of which time, the milk will have become four, and a thick fubftance will be gathered on the top; then with a stick made at the lower end in the manner of a churn-ftaff, beat it till the thick fubftance above mentioned be blended intimately with the fubjacent fluid. In this fituation, leave it again at reft for 24 hours more; after which, pour it into a higher and narrower veffel, resembling a churn, where the agitation must be repeated as before, till the liquor appear to be perfectly homogeneous; and, in this ftate, it is called Koumifs; of which the tafte ought to be a pleasant mixture of sweet and four. Agitation must be employed every time before it be used.'

From the foregoing account, the Koumifs appears to be foured milk: on the authority of Mr. Oferetskowsky, Dr. Grieve fays that it yields, by diftillation, an ardent spirit.

The Author relates fome cafes of Phthifis and Tabes, which the use of the Koumifs had completely cured.

An Improvement of the Method of correcting the obferved Distance of the Moon from the Sun, or a Fixed Star. By the Rev. Thomas Elliot.

Every attempt to facilitate or fimplify the practice of aftronomy, especially when that science is applied to the art of navigation, merits the attention of mankind. Mr. Elliot's inveftigation of the problem is fcientific and elegant; and his practical rule is concise. The methods now ufed in our navy are fufficiently exact, yet it must be confeffed that their prolixity, and dependence on Tables, render them, and indeed all others, fubject to error or mistake.

Account of a remarkable Agitation of the Waters of Loch Tay. By the Rev. Tho. Fleming.

Loch Tay is about 15 miles long, and one broad. On Sept. 12, 1784, by an unknown caufe, its waters were violently agitated, and the river which iffues from it was feen to run back,

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and its waters for fome time were dried up. Similar commotions, though much less violent, were observed for several days. No accounts could be obtained of any earthquake in the neighbourhood, and the weather was remarkably calm, the wind being gentle, from the N. E. and the barometer ftanding at 291.

Abstract of the Register of the Weather kept at Branxholm, for Ten Years, ending Dec. 31, 1783. By his Grace the Duke of Buccleugh.

This valuable meteorological Diary contains, 1ft, The quantity of rain; 2d, The height of the barometer; 3d, Of the thermometer; 4th, The direction of the wind. In addition to the abftract, the Duke gives a comparative view of the depth of rain at Branxholm, Dalkeith, and Langholm, for five years. Theory of the Earth; or an Investigation of the Laws obfervable in the Compofition, Diffolution, and Refloration of Land upon the Globe. By James Hutton, M. D F R. S. Edin.

The theory of the Earth, which Dr. Hutton here delivers, is diffufe, and at the fame time fomewhat invelloped in obfcurity. Sixteen pages are employed in pursuing,' what our Author calls general or preparatory ideas,' in which he confiders the Earth as a machine, conftructed on chemical as well as mechanical principles.' He fays, the globe of this earth is evidently made for man;' and after fome high encomiums on this lord of the creation, he adds, man, therefore, fhould be made the first fubject of enquiry.' This enquiry, however, the Doctor confines to an ascertainment of the period in which mankind were created. The Mofaic hiftory, he fays, places this beginning of man at no great distance; and he thinks that no documents can be found in natural hiftory by which a high antiquity can be attributed to the human race. He then proceeds to fhew, that we poffefs many monuments which prove that marine animals had exifted long before the human fpecies. This inquiry gives rife to a long difquifition on marble or lime-ftone, which terminates the first part (containing preparatory ideas) of the present memoir.

The fecond part is An investigation of the natural operations employed in confolidating the ftrata of the globe.' The Author fays, there are just two ways in which porous or spongy bodies can be confolidated, and by which, fubftances may be formed into maffes of a natural fhape and regular ftructure. One of thefe is fimple congelation from a fluid ftate, by means of cold; the other is accretion; and this includes a feparatory operation, as well as that by which the folid is to be produced.' In difcuffing this part of his fubject, Dr. H. is extremely diffufe; he thinks that water is not the menftruum by which the consolidating matter was introduced into the interstices of ftrata, but that

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confolidation is effected by means of heat and fufion; he fupposes filiceous matter to be infoluble in water, and thence concludes that no filiceous cryftallizations, or confolidations, can be otherwise produced than by fufion; from fimiliar arguments, he concludes that all mineralization with fulphureous fubftances is performed by heat and fufion. The variety of fulphureo-metallic fubftances, in point of compofition, is almoft indefinite; the confolidation of these heterogeneous maffes cannot be performed by water, unless each of their component parts be foluble in water. The Doctor fays, phlogifton, which is a principal ingredient in these compounds, refufes aqueous folution.' Does he mean, by that expreffion, that phlogifton cannot be united with water? Metals, especially when in their native ftate, he thinks, cannot ever be produced from folution, because the phlogifton is infoluble in water. A familiar experiment will fhew, that phlogifton may, in folution, be detached from one body and united with another: to a folution of blue vitriol in water put a fmall piece of pure iron; the vitriolic acid will part with the calx of copper and feize the calx of the iron, while the phlogifton of the iron unites itself to the calx of the copper, and the precipitate will be pure copper in its metallic form.

Were we to follow the Doctor through the whole of his arguments, by which he concludes fufion to be the cause of all confolidation, we should extend our article beyond measure, and for little other purpose than to fhew the fallacy of his conclufions; we fhall therefore proceed to the third part of the memoir, which is entitled, Inveftigation of the natural operations employed in the production of land above the furface of the fea.'

Heat is again produced as the powerful agent of nature in raifing the land above the waters. Subterraneous fires are (and in this we perfectly coincide with our Author) the most probable cause of the irregularities in the furface of our present Earth, or in those internal parts which human industry hath hitherto explored *.

In the fourth part of the memoir, Dr. Hutton is retrograde; for, after having confidered thofe operations by which the ftrata of the Earth had been confolidated and then elevated above the level of the fea, he inveftigates the fource whence those materials, from the combination of which the land was formed, were derived. In this part of his inquiry, he treads nearly the fame ground with the late ingenious Mr. Whitehurft, in fuppofing the prefent Earth formed from the materials of a preceding Earth. He advances however much farther, and supposes a regular fucceffion of Earths from all eternity! and that the fucceffion will

* See Review, vol. lxxv. p. 12, et feq. where these operations are defcribed.

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