In plate 13, fig. 12, ABC is a pyramidical frame for supporting the moving parts. DE is an upright axis, on which is framed FG, an arm for carrying the sails at a proper distance from the centre of the upright axis. H is a barrel on the upright axis, on which is wound a cord; which, being drawn by the hand, gives a circular motion to the axis, and to the arm FG; and so carries the axis of the sails in the circumference of a circle, whose radius is DI, thus causing the sails to strike the air, and turn round on their own axis.

At L is fixed the end of a small line, which passing through the pulleys M, N, O, terminates on a small cylinder or barrel on the axis of the sails, and, by winding on it, raises p the scale, where the weights are placed for trying the power of the sails. This scale, moving up and down in the direction of the upright axis, receives no disturbance from the circular motion.

QR two parallel pillars standing on the arm FG, for supporting and keeping steady the scale P; which is kept from swinging by means of ST two small chains, which hang loosely round the two pillars. w is a weight, for bringing the centre of gravity of the moveable part of the machine into the centre of motion of the axis DE.

vx is a pendulum, composed of 2 balls of lead, which are moveable on a wooden rod, and thus can be so adjusted, as to vibrate in any time required. This pendulum hangs on a cylindrical wire, on which it vibrates, as on a rolling axis. Y is a perforated table for supporting the axis of the pendulum.

The pendulum being so adjusted as to make 2 vibrations in the time that the arm FG is intended to make one turn; the pendulum being set a vibrating, the experimenter pulls by the cord z, with sufficient force to make each half revolution of the arm to correspond with each vibration, as equal as possible, during the number of vibrations that the experiment is intended to be continued. A little practice renders it easy to give this motion with all the regularity that is

instead of a weight, as in the former; which was certainly best for the purposes of measuring the impulse of the wind, or resistance of plains: but the latter is more applicable to experiments on windmill-sails; because every change of position of the same sails will occasion their meeting the air with a different velocity, though urged by the same weight.-Orig.

* In all the following experiments, the angle of the sails is counted from the plane of their motion; that is, when they stand at right angles to the axis, their angle is denoted 0°, this notation being agreeable to the language of practitioners, who call the angle so denoted, the weather of the sail, which they denominate greater or less, according to the quantity of this angle.-Orig.

20 turns of the sails raised the weight...

Velocity of the centre of the sails, in the circumference of the great

circle, in a second

Continuance of the experiment

N° Wt. in the scale. Turns.

2. ..6

1......0 lb. .... 108......

......

3......63

4... 7

5......7

Product.

0

85......510

81......526

78......546

73......547) max.

520

0...... 0

11.3 inches.

6 feet.

.. 52 seconds.

The weight of the scale and pulley was 3 oz.. and 1 oz. suspended on one of the radii, at 124 inches from the centre of the axis, just overcame the friction, scale, and load of 7 lb.. and placed at 141 inches, overcame the sameresistance with 9 lb. in the scale..

Reduction of the preceding Specimen.

N° 5 being taken for the maximum, the weight in the scale was 7 lb. 8 oz. which, with the weight of the scale and pulley 3 oz. makes 7 lb. 11 oz. equal to 123 oz.; this added to the friction of the machinery, the sum is the whole resistance.* The friction of the machinery is thus deduced: since 20 turns of the sails raised the weight 11.3 inches, with a double line, the radius of the cylinder will be .18 of an inch; but had the weight been raised by a single line, the radius of the cylinder being half the former, viz. .09, the resistance would have been the same: we shall therefore have this analogy; as half the radius of the cylinder, is to the length of the arm where the small weight was applied; so is the weight applied to the arm, to a 4th weight, which is equivalent to the sum of the whole resistance together; that is, .09: 12.5 :: 1 oz. 139 oz.; this exceeds 123 oz. the weight in the scale, by 16 oz. or 1 lb. which is equivalent to the friction; and which, added to the above weight of 7 lb. 11 oz. makes 8 lb. 11 oz. = 8.69 lb. for the sum of the whole resistance; and this, multiplied by 73 turns,, makes a product of 634, which may be called the representative of the effect produced.

In like manner, if the weight 9 lb. which caused the sails to rest after being in motion, be augmented by the weight of the scale and its relative friction, it will become 10.37 lb. The result of this specimen is set down in N° 12 of table 3, and the result of every other set of experiments there contained, were made and reduced in the same manner.

* The resistance of the air is not taken into the account of resistance, because it is inseparable from the application of the power.- Orig.

TABLE III. Containing Nineteen Sets of Experiments on Windmill Sails of various
Structures, Positions, and Quantities of Surfaces.

{

135 35 66
2 12 12

70

3 15

15 105 69

4 18

18 96 66 7.0

42 7.56 lb 12.59 lb. 318 404sq.in. 10:7

10:6.6 10:8.3 10:10.15

10:7.1 10:10.15

10:7

5 9

261

66 7.0

462 404

12

295

10:11.4

10:12.8

10:13.

Observations and Deductions from the preceding Experiments.

I. Concerning the best Form and Position of Windmill Sails. In table 3, N° 1, is contained the result of a set of experiments on sails set at the angle which the celebrated Mons. Parent, and succeeding geometricians for many years, held to be the best, viz. those whose planes make an angle of 55° nearly with the axis; the complement of which, or angle that the plane of the sail makes with the plane of their motion, will therefore be 35°, as set down in col. 2 and 3. Now if we multiply their number of turns by the weight they lifted when working to the greatest advantage, as set down in col. 5 and 6, and compare this product (col. 8) with the other products contained in the same column, instead of being the greatest, it turns out the least of all the rest. But if we set the angle of the same planes at somewhat less than half the former, or at any angle from 15° to 18°, as in N° 3 and 4, that is, from 72° to 75° with the axis, the product will be increased in the ratio of 31:45, and this is the angle most commonly made use of by practitioners, when the surfaces of the sails are planes.

If nothing more was intended than to determine the most efficacious angle to make a mill acquire motion from a state of rest, or to prevent it from passing into rest from a state of motion, we shall find the position of N° 1 the best; for if we consult col. 7, which contains the least weights that would make the sails pass from motion to rest, we shall find that of No 1, (relative to the quantity of cloth) the greatest of all. But if the sails are intended, with given dimensions, to produce the greatest effect possible in a given time, we must entirely reject those of N° 1; and if we are confined to the use of planes, conform ourselves to some angle between N° 3 and 4, that is, not less than 72°, nor greater than 75°, with the axis.

The late celebrated Mr. Maclaurin has judiciously distinguished between the action of the wind on a sail at rest, and a sail in motion; and, in consequence, as the motion is more rapid near the extremities than towards the centre, that the angle of the different parts of the sail, as they recede from the centre, should be varied. For this purpose he has furnished us with the following theorem.* Suppose the velocity of the wind to be represented by a, and the velocity of any given part of the sail to be denoted by c; then the effort of the wind on that part of the sail will be greatest, when the tangent of the angle in which the

9cc 3c

wind strikes it, is to radius, as √2+ + to 1.' This theorem then assigns

4aa

2a

the law, by which the angle is to be varied according to the velocity of each part of the sail to the wind: but as it is left undetermined what velocity any one given part of the sail ought to have in respect to the wind, the angle that any one part of the sail ought to have, is left undetermined also; so that we are still at a loss. for the proper data to apply the theorem. However, Mr. S. being willing to avail himself of it, and considering that any angle from 15° to 18° was best suited to a plane, and of consequence the best mean angle, he made the sail, at the middle distance between the centre and the extremity, to stand at an angle of 15° 41' with the plane of the motion; in which case the velocity of that part of the sail, when loaded to a maximum, would be equal to that of the wind, or c = a. This being determined, the rest were inclined according to the theorem, as follows:

Angle with
the axis.

Angle of weather.

• Maclaurin's Account of Sir Isaac Newton's Philosophical Discoveries, p. 176, art. 29.-Orig,

The result was according to N° 5, being nearly the same as the plane sails, in their best position: but being turned round in their sockets, so that every part of each sail stood at an angle of 3o, and afterwards of 6°, greater than before, that is, their extremities being moved from 9° to 12° and 15°, the products were advanced to 518 and 527 respectively. Now from the small difference between those two products, we may conclude, that they were nearly in their best position, according to N° 7, or some angle between that and N° 6: but from these, as well as the plane sails and others, we may also conclude, that a variation in the angle of a degree or two makes very little difference in the effect, when the angle is near upon the best.

It is to be observed, that a sail inclined by the preceding rule will expose a convex surface to the wind: whereas the Dutch, and all our modern millbuilders, though they make the angle to diminish, in receding from the centre towards the extremity, yet constantly do it in such manner, as that the surface of the sail may be concave towards the wind. In this manner the sails made use of in N° 8, 9, 10, 11, 12, and 13, were constructed; the middle of the sail making an angle with the extreme bar of 12°; and the greatest angle (which was about of the radius from the centre) of 15° with it. Those sails being tried in various positions, the best appears to be that of N° 11, where the extremities stood at an angle of 74° with the plane of motion, the product being 639 greater than that of those made by the theorem in the ratio of 9: 11, and double to that of N° 1; and this was the greatest product that could be procured without an augmentation of surface. Hence it appears, that "when the wind falls on 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."

Having thus obtained the best position of the sails, or manner of weathering, as it is called by workmen, the next point was to try what advantage could be made by an addition of surface on the same radius. For this purpose, the sails made use of had the same weather as those N° 8 to 13, with an addition to the leading side of each of a triangular cloth, whose height was equal to the height of the sail, and whose base was equal to half the breadth: of consequence the increase of surface on the whole was a 4th part, or as 4: 5. Those sails, by being turned round in their sockets, were tried in 4 different positions, specified in N° 14, 15, 16, and 17; whence it appears that the best was when every part of the sail made a greater angle by 240, with the plane of the motion, than those without the addition, as appears by N° 15, the product being 820: this exceeds 639 more than in the ratio of 4: 5, or that of the increase of cloth. Hence it appears, that "a broader sail requires a greater angle; and that when