, a current, or stream of air, especially when it is moved by some natural cause.

Winds are denominated from the point of the compass or horizon they blow from; as the east Wind, north Wind, south Wind, &c.

Winds are also divided into several kinds; as general, particular, perennial, stated, variable, &c.

Constant or Perennial Winds, are those that always blow the same way; such as the remarkable one between the two tropics, blowing constantly from east to west, called also the general trade-Wind.

Stated or Periodical Winds, are those that constantly return at certain times. Such are the sea and land breezes, blowing from land to sea in the morning, and from sea to land in the evening. Such also are the shifting or particular trade Winds, which blow one way during certain months of the year, and the contrary way the rest of the year.

Variable or Erratic Winds, are such as blow without any regularity either as to time, place, or direction. Such as the Winds that blow in the interior parts of England, &c: though some of these claim their certain times of the day; as, the north-Wind is most frequent in the morning, the west-Wind about noon, and the south-Wind in the night. |

General Wind, is such as blows at the same time the same way, over a very large tract of ground, most part of the year; as the general trade-Wind.

Particular Winds, include all others, excepting the general trade Winds.

Those peculiar to one little canton or province, are called topical or provincial Winds. The Winds are also divided, with respect to the points of the compass or of the horizon, into cardinal and collateral.

Cardinal Winds, are those blowing from the four cardinal points, east, west, north, and south.

Collateral Winds, are the intermediate Winds between any two cardinal Winds, and take their names from the point of the compass or horizon they blow from.

In Navigation, when the Wind blows gently, it is called a breeze; when it blows harder, it is called a gale, or a stiff gale; and when it blows very hard, a storm.

For a particular account of the trade-Winds, monsoons, &c, see Philos. Trans. number 183, or Abridg. vol. 2, p. 133. Also Robertson's Navigation book 5, sect. 6.

A Wind blowing from the sea, is always moist; as bringing with it the copious evaporation and exhalations from the waters: also, in summer, it is cool; and in winter warm. On the contrary, a Wind from the continent, is always dry; warm in summer, and cold in winter. Our northerly and southerly Winds however, which are usually accounted the causes of cold and warm weather, Dr. Derham observes, are really rather the effect of the cold or warmth of the atmosphere. Hence it is that we often find a warm southerly Wind suddenly change to the north, by the fall of snow or hail; and in a cold frosty morning, we find the Wind north, which afterward wheels about to the southerly quarter, when the sun has well warmed the air; and again in the cold evening, turns northerly, or easterly.

Physical Cause of Winds. Some philosophers, as Descartes, Rohault, &c, account for the general Wind, from the diurnal rotation of the earth; and from this general Wind they derive all the particular ones. Thus, as the earth turns eastward, the particles of the air near the equator, being very light, are left behind; so that, in respect of the earth's surface, they move westwards, and become a constant easterly wind, as they are found between the tropics, in those parallels of latitude where the diurnal motion is swiftest. But yet, against this hypothesis, it is urged, that the air, being kept close to the earth by the principle of gravity, would in time acquire the same degree of velocity that the earth's surface moves with, as well in respect of the diurnal rotation, as of the annual revolution about the sun, which is about 30 times swifter.

Dr. Halley therefore substitutes another cause, capable of producing a like constant effect, not liable to the same objections, but more agreeable to the known properties of the elements of air and water, and the laws of the motion of fluid bodies. And that is the action of the sun's beams, as he passes every day over the air, earth, and water, combined with the situation of the adjoining continents. Thus, the air which is less rarefied or expanded by heat, must have a motion towards those parts which are more rarefied, and less ponderous, to bring the whole to an equilibrium; and as the sun keeps continually shifting to the westward, the tendency of the whole body of the lower air is that way. Thus a general easterly Wind is formed, which being impressed upon the air of a vast ocean, the parts impel one another, and so keep moving till the next return of the sun, by which so much of the motion as was lost, is again restored; and thus the easterly Wind is made perpetual. But as the air towards the north and south is less rarefied than in the middle, it follows that from both sides it ought to tend towards the equator.

This motion, compounded with the former easterly Wind, accounts for all the phenomena of the general trade-Winds, which, if the whole surface of the globe were sea, would blow quite round the world, as they are found to do in the Atlantic and the Ethiopic oceans. But the large continents of land in this middle tract, being excessively heated, communicate their heat to the air above them, by which it is exceedingly rarefied, which makes it necessary that the cooler and denser air should rush in towards it, to restore the equilibrium. This is supposed to be the cause why, near the coast of Guinea, the wind always sets in upon the land, blowing westerly instead of easterly.

From the same cause it happens, that there are such constant calms in that part of the ocean called the rains; for this tract being placed in the middle, between the westerly Winds blowing on the coast of Guinea, and the easterly trade-Winds blowing to the westward of it; the tendency of the air here is indifferent to either, and so stands in equilibrio between both; and the weight of the incumbent atmosphere being diminished by the continual contrary Winds blowing from hence, is the reason that the air here retains not the copious vapour it receives, but lets it fall in so frequent rains.

It is also to be considered, that to the northward of the Indian ocean there is every where land, within the usual limits of the latitude of 30°, viz, Arabia, Persia, India, &c, which are subject to excessive heats when the sun is to the north, passing nearly vertical; but which are temperate enough when the sun is removed towards the other tropic, because of a ridge of mountains at some distance within the land, said to be often in winter covered with snow, over which the air as it passes must needs be much chilled. Hence it happens that the air coming, according to the general rule, out of the north-east, to the Indian sea, is sometimes hotter, sometimes colder, than that which, by a circulation of one current over another, is returned out of the south-west; and consequently sometimes the under current, or Wind, is from the north-east, sometimes from the south-west.

That this has no other cause, appears from the times when these Winds set, viz, in April: when the sun begins to warm these countries to the north, the southwest monsoons begin, and blow during the heats till October, when the sun being retired, and all things growing cooler northward, but the heat increasing to the south, the north-east Winds enter, and blow all the winter, till April again. And it is doubtless from the same principle, that to the southward of the equator, in part of the Indian ocean, the north-west Winds succeed the south-east, when the sun draws near the | tropic of Capricorn. Philos. Trans. num. 183; or Abridg. vol. 2, pa. 193.

But some philosophers, not satisfied with Dr. Halley's theory above recited, or thinking it not sufficient for explaining the various phenomena of the Wind, have had recourse to another cause, viz, the gravitation of the earth and its atmosphere towards the sun and moon, to which the tides are confessedly owing. They allege that, though we cannot discover aërial tides, of ebb or flow, by means of the barometer, because columns of air of unequal height, but different density, may have the same pressure or weight; yet the protuberance in the atmosphere, which is continually following the moon, must, say they, occasion a motion in all parts, and so produce a Wind more or less to every place, which conspiring with, or being counteracted by the Winds arising from other causes, makes them greater or less. Several dissertations to this purpose were published, on occasion of the subject proposed by the Academy of Sciences at Berlin, for the year 1746. But Musschenbroek will not allow that the attraction of the moon is the cause of the general Wind; because the east Wind does not follow the motion of the moon about the earth; for in that case there would be more than 24 changes, to which it would be subject in the course of a year, instead of two. Introd. ad Phil. Nat. vol. 2, pa. 1102.

And Mr. Henry Eeles, conceiving that the rarefaction of the air by the sun cannot simply be the cause of all the regular and irregular motions which we find in the atmosphere, ascribes them to another cause, viz, the ascent and descent of vapour and exhalation, attended by the electrical fire or fluid; and on this principle he has endeavoured to explain at large the general phenomena of the weather and barometer. Philos. Trans. vol. 49, pa. 124.

Laws of the Production of Wind.

The chief laws concerning the production of Wind, may be collected under the following heads.

1. If the spring of the air be weakened in any place more than in the adjoining places, a Wind will blow through the place where the diminution is; because the less elastic or forcible will give way to that which is more so, and thence induce a current of air into that place, or a Wind. Hence, because the spring of the air increases, as the compressing weight increases, and compressed air is denser than that which is less compressed; all Winds blow into rarer air, out of a place filled with a denser.

2. Therefore, because a denser air is specifically heavier than a rarer; an extraordinary lightness of the air in any place must be attended with extraordinary Winds, or storms. Now, an extraordinary fall of the mercury in the barometer shewing an extraordinary lightness of the atmosphere, it is no wonder if that foretels storms of Wind and rain.

3. If the air be suddenly condensed in any place, its spring will be suddenly diminished: and hence, if this diminution be great enough to affect the barometer, a Wind will blow through the condensed air. But since the air cannot be suddenly condensed, unless it has before been much rarefied, a Wind will blow through the air, as it cools, after having been violently heated.

4. In like manner, if air be suddenly rarefied, its spring is suddenly increased; and it will therefore flow through the air not acted on by the rarefying force. Hence a Wind will blow out of a place, in which the air is suddenly rarefied; and on this principle probably it is, that the sun, by rarefying the air, must have a great influence on the production of Winds.

5. Most caves are found to emit Wind, either more or less. Musschenbroek has enumerated a variety of causes that produce Winds, existing in the bowels of the earth, on its surface, in the atmosphere, and above it. See Introd. ad Phil. Nat. vol. 2, pa. 1116.

6. The rising and changing of the Winds are determined by weathercocks, placed on the tops of high buildings, &c. But these only indicate what passes about their own height, or near the surface of the earth. And Wolfius assures us, from observations of several years, that the higher Winds, which drive the clouds, are different from the lower ones, which move the weathercocks. Indeed it is no uncommon thing to see one tier of clouds driven one way by a Wind, and another tier just over the former driven the contrary way, by another current of air, and that often with very different velocities. And the late experiments with air balloons have proved the frequent existence of counter Winds, or currents of air, even when it was not otherwise visible, nor at all expected; by which they have been found to take very different and unexpected courses, as they have ascended higher and higher in the atmosphere.

Laws of the Force and Velocity of the Wind.

Wind being only air in motion, and the motion of a fluid against a body at rest, creating the same resistance as when the body moves with the same velocity through the fluid at rest; it follows, that the force of the Wind, and the laws of its action upon bodies, may be referred to those of their resistance when moved through it; and as these circumstances have been treated pretty fully under the article Resistance of the Air, there is no occasion here to make a repetition of them. We there laid down both the quantity and laws of such a force, upon bodies of different shapes and sizes, moving with all degrees of velocity up to 2000 feet per second, and also for planes set at all degrees of obliquity, or inclination to the direction of motion; all which circumstances having, for the first time, been determined by real experiments.

As to the Velocity of the Wind: philosophers have made use of various methods for determining it. The method employed by Dr. Derham, was by letting light downy feathers fly in the air, and nicely observing the distance to which they were carried in any number of half seconds. He says that he thus measured the velocity of the Wind in the great storm of August 1705, which he found moved at the rate of 33 feet in half a second, or 45 miles per hour: whence he concludes, that the most vehement Wind does not fly at the rate of above 50 or 60 miles an hour; and that at a medium the velocity of Wind is at the rate of 12 or 15 miles per hour. Philos. Trans. number 313, or Abridg. vol. 4, p. 411.

Mr. Brice observes however, that experiments with feathers are liable to much uncertainty; as they hardly | ever go forward in a straight direction, but spirally, or else irregularly from side to side, or up and down.

He therefore considers the motion of a cloud, by means of its shadow over the surface of the earth, as a much more accurate measure of the velocity of the Wind. In this way he found that the Wind, in a considerable storm, moved at the rate of near 63 miles un hour; and when it blew a fresh gale, at the rate of 21 miles per hour; and in a small breeze it was near 10 miles an hour. Philos. Trans. vol. 56, p. 226.

The velocity and force of the Wind are also determined experimentally by various machines, called anemometers, wind-measurers, or wind-gages; the description of which see under these articles.

In the Philos. Trans. for 1759, p. 165, Mr. Smeaton has given a table, communicated to him by a Mr. Rouse, for shewing the force of the Wind, with several different velocities, which I shall insert below, as I find the numbers nearly agree with my own experiments made on the resistance of the air, when the resisting surfaces are reduced to the same size, by a due proportion for the resistance, which is in a higher degree than that of the surfaces.

N. B. The table of my results is printed in pa. 111, vol. 1, under the article Anemometer; where it is to be noted, that the numbers in the third column of that table, for the velocity of the Wind per hour, are all erroneously printed, only the 4th part of what each of them ought to be; so that those numbers must be all multiplied by 4.

A Table of the different Velocities and Forces of the Wind, according to their common appellations.
Velocity of thePerpendi-
Windcular force
on one sq.Common appellations of the
Miles= feetfoot, in a-Winds.
in onein oneverdupois
11.47.005Hardly perceptible.
22.93.020}Just perceptible.
45.87.079}Gentle pleasant wind.
1014.67.492}Pleasant brisk gale.
2029.341.968}Very brisk.
3044.014.429}High Winds.
4058.687.873}Very high.
5073.3512.300A storm or tempest.
6088.0217.715A great storm.
80117.3631.490A hurricane.
100146.7049.200{A hurricane that tears
up trees, and carries
buildings &c before it.

The force of the Wind is nearly as the square of the velocity, or but little above it, in these velocities. But the force is much more than in the simple ratio of the surfaces, with the same velocity, and this increase of the ratio is the more, as the velocity is the more. By accurate experiments with two planes, the one of 17 3/2 square inches, the other of 32, which are nearly in the ratio of 5 to 9, I found their resistances, with a velocity of 20 feet per second, to be, the one 1.196 ounces, and the other 2.542 ounces; which are in the ratio of 8 to 17, being an increase of between 1/5 and 1/6 part more than the ratio of the surfaces.

Wind-Gage, in Pneumatics, an instrument serving to determine the velocity and force of the Wind. See Anemometer, Anemoscope, and the article just above concerning the Force and Velocity of the Wind.

Dr. Hales had various contrivances for this purpose. He found (Statical Essays, vol. 2, p. 326) that the air rushed out of a smith's bellows, at the rate of 68 3/4 feet in a second of time, when compressed with a force of half a pound upon every square inch lying on the whole upper surface of the bellows. The velocity of the air, as it passed out of the trunk of his ventilators, was found to be at the rate of 3000 feet in a minute, which is at the rate of 34 miles an hour. The same author says, that the velocity with which impelled air passes out at any orifice, may be determined by hanging a light valve over the nose of a bellows, by pliant leathern hinges, which will be much agitated and lifted up from a perpendicular to a more than horizontal position by the force of the rushing air. There is also another more accurate way, he says, of estimating the velocity of air, viz, by holding the orisice of an inverted glass siphon full of water, opposite to the stream of air, by which the water will be depressed in one leg, and raised in the other, in proportion to the force with which the water is impelled by the air. Descrip. of Ventilators, 1743, p. 12. And this perhaps gave Dr. Lind the idea of his Wind-gage, described below.

M. Bougner contrived a simple instrument, by which may be immediately discovered the force which the Wind exerts on a given surface. This is a hollow tube AABB (fig. 14, pl. 30), in which a spiral spring CD is fixed, that may be more or less compressed by a rod FSD, passing through a hole within the tube at AA. Then having observed to what degree different forces or given weights are capable of compressing the spiral, mark divisions on the rod in such a manner, that the mark at S may indicate the weight requisite to force the spring into the situation CD: afterwards join at right angles to this rod at F, a plane surface CFE of any given area at pleasure; then let this instrument be opposed to the Wind, so that it may strike the surface perpendicularly, or parallel to the rod; then will the mark at S shew the weight to which the force of the Wind is equivalent.

Dr. Lind has also contrived a simple and easy apparatus of this kind, nearly upon the last idea of Dr. Hales mentioned above. This instrument is fully explained at the article Anemometer, vol. 1, pa. 111, and a figure of it given, pl. 3, fig. 4.

Mr. Benjamin Martin, from a hint first suggested by Dr. Burton, contrived an anemoscope, or Wind-gage, of a construction like a Wind-mill, with four sails; but the axis which the sails turn, is not cylindrical, but conical, like the fusee of a watch; about this susee winds a cord, having a weight at the end, which is | wound always, by the force of the Wind, upon the sails, till the weight just balances that force, which will be at a thicker part of the fusee when the Wind is strong, and at a smaller part of it when it is weaker. But although this instrument shews when a Wind is stronger or weaker, it will neither shew what is the actual velocity of the Wind, nor yet its force upon a square foot of direct surface; because the sails are set at an uncertain oblique angle to the Wind, and this acts at different distances from the axis or centre of motion. Martin's Phil. Brit. vol. 2, p. 211. See the fig. 5, plate 3, vol. 1.

Wind-Gun, the same as Air-Gun; which see.

Wind-Mill, a kind of mill which receives its motion from the impulse of the Wind.

The internal structure of the Windmill is much the same with that of watermills: the difference between them lying chiefly in an external apparatus, for the application of the power. This apparatus consists of an axis EF (fig. 11, pl. 36), through which pass perpendicular to it, and to each other, two arms or yards, AB and CD, usually about 32 feet long: on these yards are formed a kind of sails, vanes, or flights, in a trapezoid form, with parallel ends; the greater of which HI is about 6 feet, and the less FG are determined by radii drawn from the centre E, to I and H.

These sails are to be capable of being always turned to the wind, to receive its impulse: for which purpose there are two different contrivances, which constitute the two different kinds of Windmills in common use.

In the one, the whole machine is supported upon a moveable arbor, or axis, fixed upright on a stand or foot; and turned round occasionally to suit the wind, by means of a lever.

In the other, only the cover or roof of the machine, with the axis and sails, in like manner turns round with a parallel or horizontal motion. For this purpose, the cover is built turret-wise, and encompassed with a wooden ring, having a groove, at the bottom of which are placed, at certain distances, a number of brass truckles; and within the groove is another ring, upon which the whole turret stands. To the moveable ring are connected beams ab and se; and to the beam ab is fastened a rope at b, having its other end fitted to a windlass, or axisin peritrochio: this rope being drawn through the iron hook G, and the windlass turned, the sails are moved round, and set fronting the wind, or with the axis pointing straight against the wind.

The internal mechanism of a Windmill is exhibited in fig. 12; where AHO is the upper room, and HoZ the lower one; AB the axle-tree passing through the mill; STVW the sails covered with canvas, set obliquely to the wind, and turning round in the order of the letters; CD the cogwheel, having about 48 cogs or teeth, a, a, a, &c, which carry round the lantern EF, having 8 or 9 trundles or rounds c, c, c, &c, together with its upright axis GN; IK is the upper millstone, and LM the lower one; QR is the bridge, supporting the axis or spindle GN; this bridge is supported by the beams cd, XY, wedged up at c, d and X; ZY is the lifting tree, which stands upright; ab and ef are levers, whose centres of motion are Z and e; fghi is a cord, with a stone i, going about the pins g and h, and serving as a balance or counterpoise. The spindle tN is fixed to the upper millstone IK, by a piece of iron called the rynd, and fixed in the lower side of the stone, which is the only one that turns about, and its whole weight rests upon a hard stone, fixed in the bridge QR at N. The trundle EF, and its axis Gt, may be taken away; for it rests by its lower part at t by a square socket, and the top runs in the edge of the beam w. By bearing down the end f of the lever fe, b is raised, which raises ZY, and this raises YX, which lifts up the bridge QR, with the axis NG, and the upper stone IK; and thus the stones are fet at any distance. The lower or immoveable stone is fixed upon strong beams, and is broader than the upper one: the flour is conveyed through the tunnel no into a chest; P is the hopper, into which is put the corn, which runs through the spout r into the hole t, and so falls between the stones, where it is ground to meal. The axis Gt is square, which shaking the spout r, as it goes round, makes the corn run out; rs is a string going about the pin s, and serving to move the spout nearer to the axis or farther from it, so as to make the corn run faster or slower, according to the velocity and force of the wind. And when the wind is strong, the sails are only covered in part, or on one side, or perhaps only one half of two opposite sails. Toward the end B of the axletree is placed another cogwheel, trundle, and millstones, with an apparatus like that just described; so that the same axis moves two stones at once; and when only one pair is to grind, one of the trundles and its spindle are taken out: xyl is a girth of pliable wood, fixed at the end x; the other end l being tied to the lever km, moveable about k; and the end m being put down, draws the girth xyl close to the cogwheel, which gently and gradually stops the motion of the mill, when required: pq is a ladder for ascending to the higher part of the mill; and the corn is drawn up by means of a rope, rolled about the axis AB, when the mill is at work. See Mill.

Theory of the Windmill, Position of the Sails, &c.

Were the sails set square upon their arms or yards, and perpendicular to the axletree, or to the wind, no motion would ensue, because the direct wind would keep them in an exact balance. But by setting them obliquely to the common axis, like the sails of a smokejack, or inclined like the rudder of a ship, the wind, by striking the surface of them obliquely, turns them about. Now this angle which the sails are to make with their common axis, or the degree of weathering, as the mill-wrights call it, so as that the wind may have the greatest effect, is a matter of nice enquiry, and has much occupied the thoughts of the mathematician and the artist.

In examining the compound motions of the rudder of a ship, we find that the more it approaches to the direction of the keel, or to the course of the water, the more weakly this strikes it; but, on the other hand, the greater is the power of the lever to turn the vessel about. The obliquity of the rudder therefore has, at the same time, both an advantage and a disadvantage. It has been a point of inquiry therefore to find the position of the rudder when the ratio of the advantage over the disadvantage is the greatest. And M. Renau, in | his theory of the working of ships, has found, that the best situation of the rudder is when it makes an angle of about 55 degrees with the keel.

The obliquity of the sails, with regard to their axis, has precisely the same advantage, and disadvantage, with the obliquity of the rudder to the keel. And M. Parent, seeking by the new analysis the most advantageous situation of the sails on the axis, finds it the same angle of about 55 degrees. This obliquity has been determined by many other mathematicians, and found to be more accurately 54° 44′. See Maclaurin's Fluxions, p. 733; Simpson's Fluxions, prob. 17, p. 521; Martin's Philos. Britan. vol. 1, p. 220, vol. 2, p. 212; &c.

This angle, however, is only that which gives the wind the greatest force to put the sail in motion, but not the angle which gives the force of the wind a maximum upon the sail when in motion: for when the sail has a certain degree of velocity, it yields to the wind; and then that angle must be increased, to give the wind its full effect. Maclaurin, in his Fluxions, p. 734, has shewn how to determine this angle.

It may be observed, that the increase of this angle should be different according to the different velocities from the axletree to the further extremity of the sail. At the beginning, or axis, it should be 54° 44′; and thence continually increasing, giving the vane a twist, and so causing all the ribs of the vane to lie in different planes.

It is farther observed, that the ribs of the vane or sail ought to decrease in length from the axis to the extremity, giving the vane a curvilinear form; so that no part of the force of any one rib be spent upon the rest, but all move on independent of each other. The twist above mentioned, and the diminution of the ribs, are exemplified in the wings of birds.

As the ends of the sail nearest the axis cannot move with the same velocity which the tips or farthest ends have, although the wind acts equally strong upon them both, Mr. Ferguson (Lect. on Mech. pa. 52) suggests, that perhaps a better position than that of stretching them along the arms directly from the centre of motion, might be, to have them set perpendicularly across the farther ends of the arms, and there adjusted lengthwise to the proper angle: for in that case both ends of the sails would move with the same velocity; and being farther from the centre of motion they would have so much the more power, and then there would be no occasion for having them so large as they are generally made; which would render them lighter, and consequently there would be so much the less friction on the thick neck of the axle, when it turns in the wall.

Mr. Smeaton (Philos. Trans. 1759), from his experiments with Windmill sails, deduces several practical maxims: as,

1. That when the wind falls upon a concave surface, it is an advantage to the power of the whole, though every part, taken separately, should not be disposed to the best advantage. By several trials he has found that the curved form and position of the sails will be best regulated by the numbers in the following table.

6th Parts of AngleAngle with
the radius orwith thethe plane of
37218 middle.
577 1/212 1/2
683 7 end.

2. That a broader sail requires a greater angle; and that when the sail is broader at the extremity, than near the centre, this shape is more advantageous than that of a parallelogram.

3. When the sails, made like sectors of circles, joining at the centre or axis, filled up about 7-8ths of the whole circular space, the effect was the greatest.

4. The velocity of Windmill sails, whether unloaded, or loaded so as to produce a maximum of effect, is nearly as the velocity of the Wind; their shape and position being the same.

5. The load at the maximum is nearly, but somewhat less than, as the square of the velocity of the wind.

6. The effects of the same sails at a maximum, are nearly, but somewhat less than, as the cubes of the velocity of the wind.

7. In sails of a similar figure and position, the number of turns in a given time, are reciprocally as the radius or length of the sail.

8. The effects of sails of similar figure and position, are as the square of their length.

9. The velocity of the extremities of Dutch mills, as well as of the enlarged sails, in all their usual positions, is considerably greater than the velocity of the wind.

M. Parent, in considering what figure the sails of a Windmill should have, to receive the greatest impulse from the wind, finds it to be a sector of an ellipsis, whose centre is that of the axletree of the mill; and the less semiaxis the height of 32 feet; as for the greater, it follows necessarily from the rule that directs the sail to be inclined to the axis in the angle of 55 degrees.

On this foundation he assumes four such sails, each being a quarter of an ellipse; which he shews will receive all the wind, and lose none, as the common ones do. These 4 surfaces, multiplied by the lever, with which the wind acts on one of them, express the whole power the wind has to move the machine, or the whole power the machine has when in motion.

A Windmill with 6 elliptical sails, he shews, would still have more power than one with only four. It would only have the same surface with the four; since the 4 contain the whole space of the ellipsis, as well as the 6. But the force of the 6 would be greater than that of the 4, in the ratio of 245 to 231. If it were desired to have only two sails, each being a semiellipsis, the surface would be still the same; but the power would be diminished by near 1-3d of that with 6 fails; because the greatness of the sectors would much shorten the lever with which the wind acts.

The same author has also considered which form, among the rectangular sails, will be most advantageous; | i. e. that which shall have the product of the surface by the lever of the wind, the greatest. The result of this enquiry is, that the width of the rectangular sail should be nearly double its length; whereas usually the length is made almost 5 times the width.

The power of the mill, with four of these new rectangular sails, M. Parent shews, will be to the power of four elliptic sails, nearly as 13 to 23; which leaves a considerable advantage on the side of the elliptic ones; and yet the force of the new rectangular sails will still be considerably greater than that of the common ones.

M. Parent also considers what number of the new sails will be most advantageous; and finds that the fewer the sails, the more surface there will be, but the power the less. Farther, the power of a Windmill with 6 sails is denoted by 14, that of another with 4 will be as 13, and another with 2 sails will be denoted by 9. That as to the common Windmill, its power still diminishes as the breadth of the sails is smaller, in proportion to the length: and therefore the usual proportion of 5 to 1 is exceedingly disadvantageous.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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WILKINS (Dr. John)