Maxim 5. When the sails are loaded so as to produce a maximum at given velocity, and the velocity of the wind increases the load containing the same: first, the increase of effect, when the increase of the velocity of the wind is smaller, will be nearly as the squares of those velocities; secondly, when the velocity of the wind is double, the effects will be Learly as 10 to 274; but thirdly, when the velocities compared are more than double of that where the given load produces a maximum, the effects increase nearly in a simple ratio of the velocity of the wind.

Maxim 6. If sails are of a similar figure and position, the number of turns in a given time will be reciprocally as the radius or length of the sail. Marim 7. The load at a maximum that sails of a similar figure and position will overcome, at a given distance from the centre of motion, will be as the cube of the radius.

Maxim 8. The effect of sails of similar figure and position are as the square of the radius.

Maxim 9. The velocity of the extremity of Dutch sails, as well as of the enlarged sails, in all their usual positions when unloaded, or even loaded to a maximum, are considerably quicker than the velocity of the wind.

Mr. Ferguson remarks, that it is almost incredible to think with what velocity the tips of the sails move when acted upon by a moderate wind. He several times counted the number of revolutions made by the sails in 10 or 15 minutes; and, from the length of the arms from tip to tip, has computed, that if an hoop of the same size were to run upon plain ground with equal velocity, it would go upwards of 30 miles in an hour.

RULES FOR MODELLING THE SAILS OF WINDMILLS.

FIG. 127 is a front view of one of the four sails of a windmill. The letters of reference will serve to explain the terms made use of in the following description:

1. The length of the arm, or whip A A, reckoned from the centre of the great shaft B to the outermost bar 19, governs all the rest.

2. The breadth of the face of the whip A, next the centre, is one-thirtieth of the length of the whip, its thickness at the same end is three-fourths of the breadth, and the back-side is made parallel to the face for half the length of the whip, or to the tenth bar; the small end of the whip is square, and at its end is one-sixtieth of the length of the whip, or half the breadth at the great end.

3. From the centre of the shaft B to the nearest bar 1 of the lattice, is one-seventh of the whip; the remaining space of six-sevenths of the whip is equally divided into 19 spaces, so as to make 19 bars; one-ninth of one of these spaces is equal to the mortises for the bars, the tenons of which are made square where they enter and go through the whip, and consequently the mortises must be square also.

4. To prepare the whip for mortising, strike a gage-score at about threefourths of an inch from the face on each side, and the gage-score, on the leading side 4, 5, will give the face of all the bars on that side; but on the other side, the faces of all the bars will fall deeper than the gage-score, according to a certain rule. To find the space to be set off for this purpose for each bar, construct a scale in the following manner:

5. Extend the compasses to any distance at pleasure, so that six times

that extent may be greater than the breadth of the whip at the seventh bar; set those six spaces off upon a straight line for a base, at the end of which raise a perpendicular; set off three spaces upon the perpendicular, and divide the two spaces that are farthest from the base line into six equal parts each, so that this quantity of two spaces may be equally divided into 12 spaces, marked out by 13 points; from each of these points draw a line to the opposite end of the base, as so many rays to a centre, and the scale is finished.

6. To apply this scale to any given case, set off the breadth of the whip at the last bar, (that is, the bar at the extremity of the sail,) from the centre of the scale along the base towards the perpendicular; and at this point raise a perpendicular to cut the ray nearest to the base; also set off the breadth of the whip at the seventh bar in the same manner, and at this point erect another perpendicular to cut the thirteenth radius. From the intersection of the perpendicular (drawn upon the breadth of the last bar) with the first of the thirteen radii, to the intersection of the other perpendi cular with the thirteenth radius, draw an oblique line cutting all the rest, and the distances of each of these last-mentioned points of intersection from the base line is the space which the face of each bar is distant from the gageline on the driving side.

7. These distances give a difference set off for each bar till the seventh, which same must be set off for all the rest to the first.

8. These mortises must be square to the leading side of the whip.

9. When the mortises are cut, let the face of the whip be sloped off so as to agree with the face of the bars in every part.

10. Two-fifths of the whip are the length of the last or longest bar.

11. Five-eighths of the longest bar must be on the driving side of the whip, and three-eighths on the leading side, each being reckoned from the middle of the whip.

12. The proportion of the mortises already given determines the size of the bars at the mortises, but their thickness must be diminished each way, so as to be only one-half at the ends; but the face must be kept of equal breadth all the way.

13. The leading side goes no farther than the fourth bar, and there only projects one-third of the projection of the last bar.

14. All the bars on the driving side are made hollowing in the arch of á circle, which begins to spring one-third of the length of the bars on the driving side from the whip; and the sweep is such, that if a straight line be applied to the face of the bar from the whip to the end, the face of the bar should leave the straight line about the breadth of the bar.

15. There ought to be three uplongs, as 3, 2, 10,- -to the driving, and two to the leading side, as 5, 4, to strengthen the lattice. Dr. Rees's Cyclopædia.

Mr. Richard Hall Gower, a gentleman in the sea-service of the East India Company, has made some judicious experiments with a view of determining the proper angles of weather which ought to be given to the vanes of a vertical windmill: his general conclusion is, that each vane should be a spiral, generated by the circular motion of a radius, and of a line moving at right angles to the plane of a circular motion. The construction he deduces from his inquiries is simple, being this:

The length, breadth, and angle of weather at the extremity of a vane being given; to determine the angles of weather at different distances from the centre.

K

Let AB, fig. 129, be the length of the vane; BC its breadth; and BCD the angle of the weather at the extremity of the vane, equal to 20 degrees. With the length of the vane A B, and breadth BC, construct the isosceles triangle ABC: from the point B draw B D perpendicular to CB, then B D is the proper depth of the vane.

Divide the line A B into any number of parts, (five for instance,) at those divisions draw the lines 1 E, 2 F, 3 G, and 4 H, parallel to the line BC; also, from the points of division 1, 2, 3, and 4, draw the lines 1 I, 2 K, 3 L, and 4 M, perpendicular to 1 E, 2 F, 3G, &c. all of them equal in length to BD. Join EI, FK, GL, and HM: then the angles 1 EI, 2 F K, 3G L, and H M, are the angles of weather at those divisions of the vane; and if the triangles be conceived to stand perpendicular to the plane of the paper, the angles I, K, L, M, and D, becoming the vertical angles, the hypothenuse of these triangles will, as before suggested, give a perfect idea of the weathering of the vane as it recedes from the centre.

METHOD OF CLOTHING AND UNCLOTHING THE SAILS WHILE IN

MOTION.

MR. JOHN BYWATER, of Nottingham, took out a patent in 1804, for a method of clothing and unclothing the sails of windmills while in motion, by which the mill may be clothed either in whole or in part, in an easy and expeditious manner, by a few revolutions of the sails, whether they be going fast or slow, leaving the surface smooth, even, and regular in breadth from top to bottom; and in like manner the cloth, or any part of it, may be rolled or folded up to the whip at pleasure, by simple and durable machinery.

Fig. 130, Nos. 1, 2, 3, are front views of the sails as unclothed, halfclothed, and clothed.

Fig. 131, a ring of iron, or other material, about 4 inches wide, and of an inch thick, whose diameter must be sufficient to embrace the shaft-head, to which it must be well secured by the stays a a.

Fig. 132, a bevelled wheel, without arms, made of iron, stayed on the edge of the ring so as to turn easily.

Fig. 133, a spur wheel of iron, without arms, made to turn easily on four pins fixed into four ears bb bb, in the back of the ring; which pins are turned up at their ends to keep it steady.

Fig. 134 is one of the four spindles of iron, or other material, with a spur nut a, and a bevelled nut b; this spindle passes through fig. 131 at ecce, and the nut a works into the spur-wheel as seen in fig. 135, aaaa. The four bevelled nuts (fig. 134) work into the bevelled wheels at the end of four cylinders iiii fig. 130, Nos. 1, 2, 3, and so turn them; and two of these spindles must be shorter than the others when the stocks are not flush. These cylinders are made of wood of about 3 inches diameter, and are to be placed at the outside of the leading edge of each sail, round which the cloth is rolled (one edge being fastened on for that purpose) when the sail is unclothed. A gudgeon from the end of each cylinder runs into an iron fastened to the shaft-head, and is kept in its place by a nut screwed to its end. The other end has a gudgeon b, which turns in the eye of the cross iron h, at the points of the whips; ffff four cylinders, similar to iiii, placed on the inside the whips; one behind each sail to clothe the sails, by means of ropes o o o o, &c. fastened to them and the edge of the cloth. At the end of each of these four cylinders a nut or wheel is

fixed, eeee, to work into the bevelled wheel; fig. 132, whose teeth decline from the centre in proportion as these work from it, which declination must be reversed when the sails turn in the contrary way, and gudgeons to run into irons either projecting from the ring or fastened to the shaft-head like the other cylinders. The gudgeons g keep these cylinders steady in the cross iron h at the point of the whips, and stays of any shape or number will keep them from springing.

Now, suppose the mill fully clothed, as at 3, all the parts of the machinery revolve with it undisturbed until a lever, fig. 136, which is fastened to the braces or fencing, by the centre pin a, fig. 137, on which it turns, and whose end b is weighted to hang down towards the breast of the mill, is brought into an horizontal direction by pulling a string attached to the end a within-side the mill, which end b stops the stud b, projecting from the inner surface or back-front of the spur-wheel, fig. 135; consequently the four spur-nuts a, at the end of the spindle, fig. 134, and seen at aaaa, fig. 135, roll round the spur-wheel, and the bevelled nuts b at the other end of the spindle work into the bevelled wheels of the outside cylinders iiii, at 1, 2, 3, in a straight direction behind them, and so turning the cylinders roll the cloth on them till it is rolled up to the whip. The lever is then driven sideways (its spring e returning it again) from the stud in the back face of the spur-wheel by the following contrivance:

A screw, b, fig. 138, is cut on the gudgeon of any one of the cylinders behind the sail, and a piece of iron, c, is tapped to fit it. The end of this iron runs into a slot in the iron d, made fast to the shaft-head, to prevent the iron e from turning with the cylinder, but allows it to slide up and down so as to press on that on the iron a, which has the eye in it, and raises the end a just high enough to drive the lever aside when the cloth is all rolled up, the thread of the screw adjusting it to what number of revolutions you choose to employ for that purpose. The point-end of the iron a, is that part of it which pushes aside and passes the lever, fig. 136, and moves on its centre c, and must be carried under the spur-wheel so as to act behind it for that purpose. By letting go the string the miller may at any time leave the cloth on the sail where he chooses, likewise the sails may be clothed, or any part thereof, by a lever, similar to a, stopping the stud a, on the edge of the bevelled wheel, fig. 132, and driven off in a manner similar to the spur-wheel.

Fig. 139 is a stay of wood, fixed to the stock or whip at n nnn, 1, 2, 3, to prevent the cylinders from springing too much. In the inside there is left room enough for the cloth to be rolled upon the cylinder through its lips in the eye of this stay. In order to keep the strings, which go over the edge of the shrouds oooo, &c. tight in all weathers, a cord, passing over a spring of any sort or shape, placed under the sail, is fastened to and wound about the upper ends of the cylinders, in a direction contrary to the strings and cloth. To prevent the strings from being driven downwards by the centrifugal force, a ring or two are left on to run along the rods in the old manner as p, Nos. 2, 3.

The width of the cloth, diameter of the cylinders, and number of revolutions you choose to employ to roll up your cloth, must determine the size of the wheels. In order to fold the cloth instead of rolling it, one end of it must be fastened to the whip and lines passed across the outside of it through loops fastened to its edge, and consequently over the edge of the shrouds, and connected with the cylinder or

roller, of any shape, placed under the sail, or elsewhere, the other ends of the lines must be connected with the said cylinder or roller; and when the cloth is drawn up in folds towards the whip, so much of these lines will be rolled on the cylinder one way, and off from it the other, as will be sufficient to let out the cloth again when the same cylinder, turning the contrary way, draws the cloth on the sail. By this mode the patentee gets rid of four cylinders, with their appendages, the work being in other respects the same as in rolling the cloths; but since folding gives a surface much inferior in many respects to rolling, and induces inconveniences and accidents from which the rolled surface is free, he advises the rolling, rather than for a small saving to endure the inconveniences of folding.

If a sudden gust of wind should arise in the absence of the miller, so as to drive the mill faster than a given velocity, a pair of centrifugal balls, like the governor of a steam engine, may be so placed as to adjust the lever so that it may immediately unclothe itself.

BAINES'S VERTICAL WINDMILL SAILS.

MR. ROBERT RAINES BAINES, of Myton, Kingston upon Hull, secured to himself in June 1815, by patent, an improvement in the construction of vertical windmill sails.

Fig. 140 represents six sails; the stocks or arms marked A are the same as used for common vertical windmills; the sails marked B are made of canvass, and fastened to the front sides of the said stocks or arms along the edges marked a, a, and to the rods or bars marked D, at or near the point marked b, and are also extended by the rods or bars marked E, which are inserted into or fixed to the backs thereof, and by rods or bars marked m, which are inserted into or fastened to the edges of the said sails; each sail is also connected by a bar or rod marked F, as hereinafter described, with the next following sail. The shafts or rods marked C are fastened to the stocks or arms marked A, at or near d, d, by loops or otherwise, so as to allow them to move as hinges do. The bars or rods marked D are each of them connected with the shafts or rods marked C by a joint, which will allow the said bars or rods marked D to move from the wind independent of the shafts or rods marked C, in case it should blow against the back sides of the said sails, but will not allow the said bars or rods marked D to move from the wind independent of the said shafts or rods marked C, when the wind blows against the front sides of the said sails. The bars or rods marked F connect the corners marked e of each sail with the corner of the next following sail at or near the point marked b, leading behind such following sail, and which bars or rods are fastened by hooks, or other proper means, at or near their points, bent to such an angle that if the wind should blow against the back sides of the said sails and force them forward, the said bars or rods will be unhooked and set at liberty A rim or circle marked G is fixed by screws or otherwise upon the said stocks or arms marked A, for the purpose of supporting the fulcra or props marked H. At I is represented the head or end of a rod or bar which passes through