at a given velocity, and the velocity of the wind increases, the load continuing the same; then the increase of effect, when the increase of the velocity of the wind is small, will be nearly as the squares of these velocities: but when the velocity of the wind is double, the effects will be nearly as 10 to 274; and 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. Hence our author concludes that windmills, such as the different species for draining water, &c. lose much of their effect by acting against one invariable opposition.

(15.) In sails 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.

(16.) 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.

(17.) The effects of sails of similar position and figure are as the square of the radius. Hence augmenting the length of the sail without augmenting the quantity of cloth, does not increase the power; because what is gained by length of the lever is lost by the slowness of the motion. Hence also, if the sails are increased in length, the breadth remaining the same, the effect will be as the radius.

(18.) The velocity of the extremities of the Dutch sails, as well as of the enlarged sails, either unloaded or even when loaded to a maximum, is considerably greater than that of the wind itself. This appears plainly from the observations of Mr. Ferguson, already related, concerning the velocity of sails.

(19.) From many observations of the comparative effects of sails of various kinds, Mr. Smeaton concludes, that the enlarged sails are superior to those of the Dutch construction.

(20.) He also makes several just remarks upon those windmills which are acted upon by the direct impulse of the wind against sails fixed to a vertical shaft: his objections have, we believe, been justified in every instance by the inferior efficacy of these horizontal mills.

"The disadvantage of horizontal windmills (says he) does not consist in this, that each sail, when directly opposed to the wind, is capable of a less power than an oblique one of the same dimensions; but that in an horizontal windmill little more than one sail can be acting at once: whereas in the common windmill, all the four act together; and therefore, supposing each vane of an horizontal windmill to be of the same size with that of a vertical one, it is manifest that the power of

a vertical mill will be four times as great as that of an horizontal one, let the number of vanes be what they will. This disadvantage arises from the nature of the thing; but if we consider the further disadvantage that arises from the difficulty of getting the sails back again against the wind, &c. we need not wonder if this kind of mill is in reality found to have not above oneeighth or one-tenth of the power of the common sort; as has appeared in some attempts of this kind."

Coulomb's Experiments.

5. M. Coulomb, whose experiments have tended to the elucidation of many parts of practical mechanics, devoted some time to the subject of windmills. The results of his labours were published in the Memoirs of the Paris Academy for 1781. The mills to which he directed his attention were in the vicinity of Lille, and were, in fact, oil mills. From the outer extremity of one sail to the corresponding extremity of the opposite sail, was 70 feet, the breadth of each sail 64 feet, of which the sail-cloth when extended occupies 54 feet, being attached on one side to a very light plank; the line of junction of the plank and of the sail-cloth, forms, on the side struck by the wind, an angle sensibly concave at the commencement of the sail, but diminishes gradually all along so as to vanish at the remoter extremity. The angle with the axis, at seven feet from the shaft, is 60°, and it increases continually, so as to amount to nearly 84° at the extremity. The shaft upon which the sails turn, is inclined to the horizon, in different angles in different mills, from 8 to 15 degrees.

Coulomb infers from his experiments,

(1.) That the ratio between the space described by the wind in a second, and the number of turns of a sail in a minute, is nearly constant, whatever be the velocity of the wind; the said ratio being about 10 to 6, or 5 to 3.

(2.) That with a wind whose velocity is 21 feet (English) per second, the quantity of action produced by the impulsion of the wind is equivalent to a weight of 1080 pounds avoirdupois raised 270 feet in a minute; the useful effect being equivaÎent to a weight of 1080 pounds raised 232 feet in the same time whence it results that the quantity of effect absorbed by the stroke of the stampers, the friction, &c. is nearly a sixth part of the quantity of action.

(3.) Suppose one of these mills to work 8 hours in a day. Coulomb regards its daily useful effect as equivalent to that

of 11 horses working at a walking-wheel, in a path of the usual radius.

(4.) It is observable that in most windmills the velocity at the extremity of the sails is greater than that of the wind. In some cases, indeed, these velocities have been found in about the ratio of 5 to 2. Now, it is evident that the impulsion of a fluid against any surface whatever can only produce pressure, or mechanical effect, when the velocity of the surface exposed to the impulse is less than that of the fluid; and that the pressure will be nothing when the velocity of the surface is equal to or greater than that of the fluid. Indeed, in the latter case, the pressure may operate against the motion of the sails, and be injurious. It is desirable, therefore, in order to derive from a windmill all the effect of which it is susceptible, so to adjust the number of the turns that the velocity of the extremity of the sails shall be less, or, at most, equal to that of the wind.

It would be highly expedient to make comparative experiments on windmills, with a view to the determination of that velocity of the extremity of the sails which corresponds with the maximum of effect.

6. If v denote the velocity of the wind in feet per second, t the time of one revolution of the sails, A the angle of inclination of the sails to the axis, and D the distance from the shaft or axle of rotation to the point which is not at all acted on by the wind, or beyond which the sail-cloth ought to be folded up; then theoretical considerations supply the following theorem: viz.

D1092 t v tan. A.

Ex. Suppose v = 30 feet per second, t = 2.25 seconds, and A = 75°; then

D= 1092 x 30 x 2.25 x 3.73205 = 27.509 feet.

This result agrees nearly with one of Coulomb's experiments, in which the velocity of the wind was 30 feet English per second, the sails made 17 turns in a minute, and they were obliged to fold off more than 6 feet from the extremity of each sail, of 34 feet long, to obtain a maximum of effect. The angle A at that distance from the tip of the sail was 75°

or 76°.

SECTION IV.-Steam and Steam-Engines.

The whole power of the steam-engine depends on the employment of elastic vapour produced from water at high temperatures.

Steam, in fact, is highly rarefied water, the particles of which are expanded by the absorption of caloric, or the matter of heat. Water rises in vapour at all temperatures, though this is usually supposed to take place only at the boiling point; when, however, the evaporation occurs below 212° (Fahr.) it is confined to the surface of the fluid acted upon : but, at that heat, 212°, steam is formed at the bottom of the water, and ascends through it, carrying off the heat in a latent form, and, therefore, preventing the elevation of temperature of the water itself. At the common pressure of the atmosphere, one cubic inch of water produces about 1700 cubic inches (or nearly a cubic foot) of aqueous vapour; but the boiling point varies considerably under different pressures, and these anomalies materially affect the the density of the vapour produced. Thus, in a vacuum water boils at about 70°; under common atmospheric pressure at 212°; and when pressed by a column of mercury 5 inches in height, water does not boil until it is heated to 217°; each inch of mercury producing by its pressure, a rise of about 1° in the ther

mometer.

According to the elaborate experiments of Dr. Ure, of Glasgow, the elastic force of this vapour at 212° is equivalent to the pressure of a column of mercury 30 inches high, or equal to about 15 lbs. avoirdupois on a square inch. At temp. 212°

226.3

....

30 inch. mercury 15 lbs. per sq. inch.

25.15

312 .... 166.

And Mr. Woolf has ascertained that at these temperatures, omitting the last, a cubic foot of steam will expand to about 5, 10, 20, 30, and 40 times its volume respectively; its elastic force, when thus dilated, being in each case equal to the ordi nary pressure of the atmosphere.

One pound of Newcastle coals converts 7 pounds of boiling water into steam; and the time required to convert a given

Some recent experiments made in France, by Messrs. Dulong and Arago, do not essentially differ in result from these of Dr. Ure. They find, at temp, 275-18 Fahr., an elasticity equal to atmospheres, or 45 inches of mercury: at temps. 308-84, 320-36, 331-70, 341-96, 350-78, and 358-88, the elasticities equivalent to 5, 6, 7, 8, 9, and 10 atmospheres, respectively. Temp. 439-34 an elasticity of 25 atmospheres, which was the limit of their experiment; but by computation they went to a temperature of 510-60, equivalent to an elasticity of 50 atmospheres.

quantity of boiling water into steam, is 6 times that required to raise it from the freezing to the boiling point.

It is found, also, that if a bushel of coals per hour applied to a well-constructed boiler, produces steam of the expansive force of 15 lbs. per square inch, it will tend to expand itself with a velocity of 1340 feet per second; then 2 bushels of coals, burnt under the same boiler, are capable of giving to the vapour an expansive force of 120 lbs. per square inch, and a velocity of expansion of 3800 feet per second. A bushel and half of coals would, with the same boiler, carry steam to the pressure of 50 lbs. on a square inch; which is as high as is regarded consistent with safety.

From these data it will be evident that when steam is merely employed to displace the air in a close vessel, and afterwards produce a vacuum by condensation, no more heat is necessary than what will raise the water employed to 212°: but if, on the contrary; steam capable of giving high pressures is required, a considerable increase of heat, as to 260°, 280°, will be necessary; and, of course, an augmentation of fuel, though not one that is strictly proportional, will be required. This, however, is a consideration upon which we cannot here enlarge.

We proceed to speak of the actual construction of the machine.

The principles and manner of operation of the steam-engines of Savery, Newcomen and Cawley, and of Watt, may be understood from the following brief explanations and remarks.

1. Let there be a sucking pipe with a valve opening upwards at the top, communicating with a close vessel of water, not more than thirty-three feet above the level of the reservoir, and the steam of boiling water be thrown on the surface of the water in the vessel, it will force it to a height as much greater than thirty-three feet as the elastic force of the steam is greater than that of air; and if the steam be condensed by the injection of cold water, and a vacuum thus formed, the vessel will be filled from the reservoir by the pressure of the atmosphere, and the steam being admitted as before, this water will also be forced up; and so on successively.

Such is the principle of the first steam-engine, said by the English to be invented by the Marquis of Worcester; while the French ascribe it to Papin though we believe the fact is that Brancas, an Italian, applied the force of steam ejected from a large œlopile as an impelling power for a stampingengine so early as 1629. Brancas's was, in fact, an immense