Windmill, a building containing machinery driven by the action of wind upon a set of wings or sails. Windmills are of two kinds, one revolving in a vertical, the other in a horizontal plane. The principal parts of the machinery of a vertical windmill are: 1, an axis in the top of the building, inclined (as the impulse of the wind is very commonly exerted in a line descending at such an angle) to the horizontal at 10° or 15°, on which are the wings; 2, the wings, consisting of as many sail frames, with sails stretched on them, which, if four, are at right angles with each other, and that in all cases are mainly rectangular to the axis, their length being from 30 to 40 ft. each; 3, a large toothed wheel upon the horizontal axis already referred to, carried about with it by the action of the wind on the sails, and of course standing at the angle of 10° to 15° with the vertical, the teeth of which engage with those of a pinion upon - 4, a truly vertical axis rising through the middle of the mill, and thus impart a movement of rotation to this, and (in case of grinding) to the upper millstone.

The first named, or as it may be called horizontal axis, is supported at its innermost end near the centre of the base of a dome or cover surmounting the mill; while its opposite extremity is let through a perforation in one side of the dome, and projects far enough beyond to receive the ends of the long timbers, or "whips," to which the sails are affixed. The suddenly varying and often extreme pressure of the wind upon the wings renders it necessary that the supports of the horizontal axis, and all parts of the wings projecting from it, shall have great strength. Against the rim of the principal wheel upon.this axis a brake can be brought to act, so as to stop the motion of the machinery. In the ordinary kind of wings, beginning at about six feet from the axis along each of the six whips, project on one or both sides of the whip a series of wooden pieces or staves, at right angles with the whip, usually growing shorter toward its extremity, and having their ends further joined by a continuous lath or strip of wood; the whole thus forms a sort of lattice, upon which the sail is to be stretched.

The lattice and canvas are inclined to the line of the axis and of the wind at such an angle that, as in case of the obliquely set sails of vessels, the total force of the wind is resolved into components, a considerable one of which takes effect in the direction at right angles to the axis, and produces the revolution. But the different parts of the sail have not the same angle in respect to the line of the wind. The velocity of revolution of each wing increases from its inner to its outer end; and mathematical considerations show that the inclination of the sail to the wind should increase as the velocity increases, the best effect being obtained when at different lengths along the wing the inclinations are about those here named: at | the length of the wing from the centre, 70°; at1/3, 71°; at ½,72°; at 2/3,74°; at 1,77½°; at the end, 83°. Other authorities give the inclinations from 60° to 80°. The result is that the surfaces of the sails are not oblique planes, but curving, or rather warped outward, in going from the centre to the extremities.

Mr. Sraeaton found that the velocity of the extremity of the sails is often to that of the wind in a ratio greater than that of 2 to 1; and according to Euler, when the velocity is that of 2 to 1, the efficiency of the mechanism is greatest. When the tower or mill is of timber and small, it is so fixed upon a strong column or axis entering its base, which is also sufficiently elevated, that the whole tower can be turned around so as to bring the axis of the machine in a line with the wind, by means of a long lever projecting from it below. In the case of stone and all large and heavy towers, the dome only is turned, carrying the axis and sails with it into the required position, while the vertical wheel merely travels about the pinion, and the connection is not broken. The turning of the dome to the wind is effected in different ways: 1, by the employment of a toothed wheel engaging in a rack on its inner side, and turned by means of a so-called endless cord, by a man below working a winch; 2, by a method invented by Sir W. Cubitt, consisting of a set of small vanes, placed in an upright position upon a long arm projecting in the same line with the horizontal axis, and by their revolution turning a shaft and pinion, and acting upon teeth surrounding the exterior of the dome and moving it; 3, by the much more simple and quite as effective means of having a single large vane extending behind the axis, and with its plane vertical, so that it, and consequently the axis, shall always be in the direction of the wind. - In situations in which the great height of the vertical sails would be objectionable, the horizontal windmill is sometimes used.

It has six or more wings, usually of plain boards, set upright the whole height of the tower, being attached to upper and lower disks or platforms, and the whole is turned by the force of the wind about a vertical axis at its middle part. If the wings are fixed in position, they are set obliquely to the direction in which the wind will strike them. Outside of the whole is then placed a screen or cylindrical arrangement of boards not intended to revolve, these boards being also set obliquely and in planes lying in opposite course to those of the wings. The result is, that from whatever direction the wind may blow against the tower, it is always admitted by the outer boards to act on the wings most freely on, that half of the side it strikes, on which the wings are turning away. But with an equal area of the wings, the power of the horizontal is always much less than that of the vertical windmill. Sir David Brewster concludes that the ratio is no less than that of 1 to 3 or 4. - Mr. Smeaton found that the efficiency of the sails is greater as they are broader at the extremity than near the centre, up to but not beyond a greatest breadth equal to one third the length of the wing; that if the total area of sails exceed seven eighths of the area of the circle described by the wings in their revolution, the velocity is diminished; that the maximum of work is obtained when the velocity of the wings as loaded with the work performed is to that they would have without load as 2 to 3; and that when the work is a maximum, the velocity of the sails still varies nearly with that of the wind.

The variations in the pressure of the wind being considerable, and sometimes sudden and extreme, it becomes desirable to provide for regulating the sails accordingly; and a large share of the more recent inventions in connection with windmills have this for their object. The old plan is attended with much trouble and delay; in it the canvas, by means of a rope to each wing, can be taken in or let out, or that of each wing ft made in three portions controlled by separate ropes; in either case, the mill must be stopped, and a man must usually ascend the wings successively for the purpose. One of the inventions in connection with the improvement of windmills was patented in 1861 by Mr. A. Giraudat of New York. In this, all necessity of a turning dome and horizontal axis is simply obviated, while in fact the wind wheel can be conveniently erected above the roof of any building, its axis descending through the roof to machinery within; and this machinery can be of almost any sort requiring moderate or ordinary power; for one important application of it, the running of sewing machines, a patent was obtained in July, 1862. The wind wheel is constructed simply with four or eight horizontal arms, on which solid square or oblong sails (rather tables) are carried, and by the revolution of which the vertical axis supporting them, and the machinery connected with it, are directly turned.

The sails swing on the arms so as to be brought down perpendicular to a wind striking them on one side, and lifted toward a horizontal position, so as to prove ineffective when it strikes them on the other. For regulating the velocity, each sail can slide in from the end of its arm to near the axis; and it is caused to slide one way or the other by the action of a heavier and of a lighter weight on parts of a sort of endless cord attached to it, and both meanwhile upheld by means of iron links at the ends of the respective arms. If the impulse of the wind becomes excessive, the weights are by centrifugal force thrown outward, and the action draws the sail in toward the axis, where it can exert less effect, while the small weight slides up the link to allow of this; when the excessive impulse ceases, the heavier weight and link return to a more nearly vertical position, and the lighter weight, sliding down the link, returns the sail to the end of the arm.