Farded by the fides and bottom of the channel in which it moves. But it is alfo gratuitous to fuppofe, that the velocity of the cloud is the velocity of the ftratum of air between the cloud and the earth; we are almost certain that it is not. It is proved by Dr HUTTON of Edinburgh, that clouds are always formed when two parcels of air of different temperatures mix together, each containing a proper quantity of vapour in the state of chemical folution. Different ftrata of air often flow in different directions for a long time. In 1781, while a great fleet rendezvouzed in Leith Roads during the American war, there was a brisk E. wind for about five weeks; and, during the laft fortnight of this period, there was a brisk current at the height of about of a mile. This was diftinctly indicated by frequent fleecy clouds at a great diftance, above a lower ftratum of thefe clouds, which were driving all this time from the E. A gentleman who was at the fiege of Quebec in 1759 informed us, that one day while there blew a gale from the W. so that the ships at anchor in the river were obliged to ftrike their top mafts, and it was with the utmoft difficulty that fome well manned boats could row against it, car rying fome artillery ftores to a poft above the town, feveral shells were thrown from the town to destroy the boats; one of the fhells burft in the nir near the top of its flight, which was about half a mile high. The fmoke of this bomb remained in the fame spot for above a quarter of an hour, like a great round ball, and gradually diffipated by diffufion, without removing many yards from its place. When, therefore, two ftrata of air come from different quarters, and one of them flows over the other, it will be only in the contiguous furfaces that a precipitation of vapour will be made. This will form a thin fleecy cloud; and it will have a velocity and direction which neither belongs to the upper nor to the lower ftratum of air which produced it. Should one of these ftrata come from the E, and the other from the W. with equal velocities, the cloud formed between will have no motion at all; should one come from the E. and the other from the N. the cloud will inove from the NE. with a greater velocity than either of the ftrata. So uncertain then is the information given by the clouds, either of the velocity or the direction of the wind. A thick smoke from a furnace will give us a much lefs equivocal Ineafure; and this, combined with the effects of the wind in impelling bodies, or deflecting a loaded plane from the perpendicular, or other effects of this kind, may give us measures of the different currents of wind with a precision sufficient for all practical ufes.

Mr JOHN SMEATON, the celebrated engineer, has given in the Philof. Tranf. Vol. 5. the velocities of wind correfponding to the ufual denominations in our language. Thefe are founded on a great number of obfervations made by himfelf in the course of his practice in erecting wind-mills; and are as follow: Miles. per hour.

Feet. per fecond.

Names.

Hurricane, tearing up

trees, overturning buildings, &c.

See alfo fome valuable experiments by MrSmeaton on this subject, in the Philof. Trans. for 1760 and 1761.

One of the most ingenious and convenient me thods for measuring the velocity of the wind is to employ its preffure in fupporting a column of water, in the fame way as Mr Pitot measures the velocity of a current of water. It was first propofed by Dr JAMES LYND of Windfor, a gentleman eminent for his great knowledge in all the branches of natural science, experiment, and prac tical application. His ANEMOMETER Confists of a glass tube of the form ABCD (fig. 55.), open at both ends, and having the branch AB at right angles to the branch CD. This tube contains a few inches of water or any fluid; (the lighter the better;) it is held with the part CD upright, and AB horizontal and in the direction of the wind; that is, with the mouth A fronting the wind. The wind acts in the way of preffure on the air in AB, compreffestit, and caufes it to prefs on the furface of the liquor; forcing it down to F, while it rifes to E in the other leg. The velocity of the wind is concluded from the difference Eƒ between the heights of the liquor in the legs. As the wind does not generally blow with uniform velocity, the liquor is apt to dance in the tube, and render the obfervation difficult and uncertain; to remedy this, it is proper to contract very much the communication at C between the two legs. If the tube has half an inch of diameter, a hole of one fiftieth of an inch is large enough; indeed the hole can hardly be too fmall, nor the tubes too large.

This inftrument gives the proportions of the ve locities of different currents with the greatest precifion; for in whatever way the pressure of wind is produced by its motion, the different preffures are as the fquares of the velocities: if, therefore, we can obtain one certain measure of the velocity of the wind, and obferve the degree to which the preffure produced by it raifes the liquor, we can at all other times observe the pressures and compute the velocities from them, making proper allowances for the temperature and the height of the mercury in the barometer; because the velocity will be in the fubduplicate ratio of the denfity of the air inverfely when the preffure is the fame.

The VELOCITY of the wind is ufually estimated that which would be acquired by falling from a

height which is to Effig. 55. as the weight of water is to that of an equal bulk of air. Thus, fuppofing air to be 840 times lighter than water, and that Efts of an inch, the velocity will be about 62 feet per fecond, which is that of a very hard gale, approaching toja ftorm. Hence we fee that the scale of this inftrument is extremely fhort, and that it would be a great improvement to make the leg CD not perpendicular, but very much floping; or perhaps the following form of the inftrument will give it all the perfection of which it is capable. Let the horizontal branch AB (fig. 56.) be contracted at B, and continued horizontally for everal inches BG of a much smaller bore, and then turned down for 2 or 3 inches GC, and then upwards with a wide bore. To use the inftrument, hold it with the part DC perpendicular; and (having sheltered the mouth A from the wind) poor in water at D till it advances along GB to the point B, which is made the beginning of the kale; the water in the upright branch ftanding at fan the fame horizontal line with BG. Now, turn the mouth A to the wind; the air in AB will be compreffed and will force the water along BG to I, and cause it to rife from fto E; and the range fE will be to the range BF on the fcale, as the lection of the tube BG to that of CD. Thus, if the width of DC be an inch, and that of BG, we hall have 25 inches in the scale for one inch of real preffure Eƒ.

But it has not been demonstrated in a very fasadory manner, that the velocity of the wind is that acquired by falling through the heights of a column of air whole weight is equal to that of the column of water Ef. Experiments made with PITOT's tube in currents of water, fhow that feveral corrections are neceffary for concluding the velocity of the current from the elevations in the tube: thofe corrections may however be made, and fafely applied to the prefent cafe; and then the inftrument will enable us to conclude the velocity of the wind immediately, without any fundamental comparison of the elevation, with a velocity actually determined upon other principles. The chief ufe which we have for this information is in our employment of wind as an impelling power, by which we can actuate machinery or na. vigate hips. These are very important applications of pneumatical doctrines, and merit a particular confideration; and this naturally brings us to the laft part of this branch of our object, viz. the confideration of the impulfe of air on bodies expofed to its action, and the refiftance which it appoles to the paffage of bodies through it. This fubject is of the greatest importance; being the foundation of that art which has done the greatest honour to the ingenuity of man, and the greateft fervice to human fociety, by connecting together the moft diftant inhabitants of this globe, and making a communication of benefits which would otherwife have been impoffible; we mean the art of NAVIGATION or Seamanship. Of all the machines which human art has conftructed, SHIP is not only the greatest and most magnificent, but alfo the most ingenious and intricate; and the clever feaman poffelles a knowledge founded on the most difficult and abftrufe doctrines of mecha ics. The feaman probably cannot give any ac

count of his own fcience; and he poffeffes it rather by a kind of habit than by any process of reafoning; but the success and efficacy of all the mechanifm of this complicated engine, and the propriety of all the maneuvres which the feaman practifes, depend on the invariable laws of mechanics; and a thorough knowledge of thefe would enable an intelligent perfon, not only to understand the machine and the manner of working it, but to improve both.

But although this fubject employed the genius of Newton, who confidered it with great care, and his followers have added more to his labours on this fubject than on any other, it still remains in a very imperfect state. A minute difcuffion of it cannot be expected in this short treatise; in which we can only give fuch a general ftatement of the moft approved doctrine on the subject as shall enable our readers to conceive it diftinctly, and judge with intelligence and confidence of the practical deductions which may be made from it. It is evidently a branch of the general theory of the impulse and refiftance of fluids, which fhould have been treated of under the article HYDRAU LICs, but was then deferred till the mechanical properties of compreffible fluids fhould be confidered. It was thought very reasonable to suppose that the circumstances of elafticity would introduce the fame changes in the impulfe and refiftance of fluids that it does in folid bodies. It would greatly divert the attention from the dif tinctive properties of air, if we fhould in this place enter on this fubject, which is both extenfive and difficult. We reckon it better therefore to take the whole together, under the article RsSISTANCE of FLUIDS, and confine ourselves at prefent to what relates to the impulfe and refiftance of air alone; anticipating only a few of the general propofitions of that theory, in order to understand the application which may be made of it.

Suppofe a plane furface, of which a C (fig. 57 pl. 282.) in the fection, expofed to the action of ftream of wird blowing in the direction QC, perpendicular to a C. The motion of the wind will be obftructed, and the furface a C preffed forward. And as all impulfe or preffure is exerted in a direction perpendicular to the furface, and is refifted in the opposite direction, the furface will be impelled in the direction CD, the continuation of QC. And as the mutual actions of bodies depend on their relative motions, the force acting on the furface a C will be the fame, if we shall fuppofe the air at reft, and the surface moving equally fwift in the oppofite direction. The refiftance of the air to the motion of the body will be equal to the impulfe of the air in the former cafe. Thus refiftance and impulfe are equal and contrary. If the air be moving twice as faft, its particles will give a double impulfe; but in this cafe a double number of particles will exert their impulfe in the fame time; the impulfe will therefore be fourfold; and in general it will be as the fquare of the velocity; or if the air and body be both in motion, the impulfe and refiftance will be proportional to the fquare of the relative velocity.

This is the firft propofition on this fubject, and it appears very confonant to reafon. There will

therefore

therefore be fome analogy between the force of the air's impulse or the refiftance of a body, and the weight of a column of air incumbent on the furface; for it is a principle in the action of fluids that the heights of the columns of fluid are in the fquares of the velocities which their preffures produce. Accordingly the ad propofition is, that the abfolute impulfe of a stream of air, blowing perpendicularly on any furface, is equal to the weight of a column of air which has that furface for its bafe, and for its height the space through which a body muft fall in order to acquire the velocity of the air.

3dly, Suppofe the furface AC equal to a C no longer to be perpendicular to the stream of air, but inclined to it in the angle ACD, which we fhall call the angle of incidence; then by the refolution of forces, it follows, that the action of each particle is diminished in the proportion of radius to the fine of the angle of incidence, or of AC to AL, AL being perpendicular to CD. Again: Draw AK parallel to CD. It is plain that no air, lying farther from CD than KA is, will ftrike the plane. The quantity of impulfe therefore is di minished still farther, in the proportion of a C to KC, or of AC to AL. Therefore, on the whole, the abfolute impulse is diminished in the proportion of AC to AL; hence the propofition, that the impuife and refiitance of a given furface are in the proportion of the fquare of the fine of the angle of incidence.

4thly, This impulfe is in the direction PL, perpendicular to the impelled furface, and the fur. face tends to move in this direction: but fuppofe it moveable only in fome other direction PO, or that it is in the direction PO that we wish to employ this impulfe, its action is therefore oblique; and if we wish to know the intenfity of the impuife in this direction, it must be diminished ftill farther in the proportion of radius to the confine of the angle LPO or fine of CPO. Hence the general propofition: The effective impulfe is as the furface, as the fquare of the velocity of the wind, as the iquare of the fine of the angle of incidence, and as the fine of the obliquity jointly, which we may exprefs by the fymbol RS-V* fin. I. fin. O; and as the impulfe depends on the denfity of the impell. ing fluid, we may take in every circumftance by the equation RS·D'V2. fin.1 I. fin. O. If the impulfe be estimated in the direction of the ftream, the angle of obliquity ACD is the fame with the angle of incidence, and the impulfe in this direction is as the furface, as the fquare of the velocity, and as the cube of the angle of incidence jointly. From these premifes it follows, that if ACA' be a wedge, of which the base AA' is perpendicular to the wind, and the angle ACA bifected by its direction, the direct or perpendicular impulfe on the bafe is to the oblique impulie on the fides as radius to the fquare of the fine of half the angle ACA. The fame must be affirmed of a pyramid or cone ACA', of which the axis is in the direction of the wind. If ACA' (fig. 58.) reprefent the fection of a folid produced by the revolution of a curve line APC round the axis CD, which lies in the direction of the wind, the impulfe on this bo. dy may be compared with the direct impulfe on its bafe, or the refiftance to the motion of this bo

dy through the air may be compared with t direct refiftance of its bafe, by refolving its furta into elementary planes Pp, which are coincide with a tangent plane PR, and comparing the in pulfe on Pp with the direct impulfe on the co refponding part Kk of the bafe. Thus it follow that the impulfe on a sphere is one half of the in pulfe on its great circle, or on the base of a cyli der of equal diameter.

A very important inference arises from this do trine, to determine the most advantageous po tion of a plane furface, when required to mo in one direction, while it is impelled by the win blowing in another. Thus, Let AB (pl. 281. f 59) be the fhip's fail, CA the direction in whic the wind blows, and AD the line of the ship courfe. It is required to place the yard AC fuch a pofition that the impulfe of the wind upo the fail may have the greatest effect poffible in in pelling the ship along AD. Let AB, Ab, be tw pofitions of the fail very near the beft pofition but on oppofite fides of it. Draw BE, be, per pendicular to CA, and BF, bf, perpendicular t AD, calling AD radius; it is evident that BE, BE are the fines of impulfe and obliquity, and tha the effective impulfe is BEX BF, or be2 x bf. Thi must be a maximum. Let the points B,. b, con tinually approach and ultimately coincide; th chord b B will ultimately coincide with a ftraigh line CBD touching the circle in B; the triangle CBE, be are fimilar, as alfo the triangles DBF Dbf: therefore BE: be=BC2: be, and BF bf BD: bD; and BEX BF: be2xbf=CB1× BD cbxbD. Therefore when AB is in the best po fition, fo that BEX BF is greater than bxbf we fhall have CBX BD greater than CbxbD, o cBX BD is alfo a maximum. This we know to be the cafe when CB=2BD: therefore the fai must be fo placed that the tangent of the angle of incidence fhall be double of the tangent of the angie of the fail and keel. In a common windmill the angle CAD is neceffarily a right angle; for the fail moves in a circle to which the wind is perpendicular: therefore the best angle of the fail and axle will be 54°.44 nearly.

Such is the theory of the RESISTANCE and IMPULSE of the air. It is extremely simple, and of eafy application. When a ftream of air is obftructed by a folid body, or when a folid body moves along in the air, the air is condented before it and rarefied behind. There is therefore a preffare on the anterior parts, arising from this want of equilibrium in the elafticity of the air. This must be fuperadded to the force ariling from the impetus or inertia of the air.

Experiments on this subject are not numerous; at least fuch as can be depended on. The first that have this character are thofe published by Mr Robins in 1742, in his treatise on Gunnery. They were repeated with fome additions by the Chevalier Borda, and fome account of them published in the Mem. of the Acad. of Sciences in 1763. In the Philos. Tranf. Vol. LXXIII. there are fome experiments on a larger fcale by Mr Edgeworth.

In all thefe experiments the refiftances were found very exactly in the proportion of the fquares of the velocities; but they were found confider

ably