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 eiucidation 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 vi cinity 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 5 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 early 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 equivalent 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

D1092 × 30 × 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 em ployment of elastic vapour produced from water at high tem peratures.

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°

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

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 ordinary 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 3 atmospheres, or 45 inches of mercury: at temps. 308-84, 320-3, 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 ma

chine.

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 clopile as an impelling power for a stampingengine so early as 1629. Brancas's was, in fact, an immense

blow-pipe, turning a wheel. The hint so obscurely exhibited in the Marquis of Worcester's Century of Inventions, was car ried into effect by Captain Savery.

2. If the steam be admitted into the bottom of a hollow cylinder, to which a solid piston is adapted, the piston will be forced upwards by the difference between the elastic forces of steam and common air; and the steam being then condensed, the piston will descend by the pressure of the atmosphere, and so on successively. This is the principle of the steam-engine first contrived by Messrs. Newcomen and Cawley, of Dartmouth. This is sometimes called the atmospherical engine, and is commonly a forcing pump, having its rod fixed to one end of a lever, which is worked by the weight of the atmosphere upon a piston at the other end, a temporary vacuum being made below it by suddenly condensing the steam that had been admitted into the cylinder in which this piston works, by a jet of cold water thrown into it. A partial vacuum being thus made, the weight of the atmosphere presses down the piston, and raises the other end of the straight lever, together with the water, from the well. Then immediately a hole is uncovered in the bottom of the cylinder, by which a fresh_quantity of hot steam rushes in from a boiler of water below it, which proving a counterbalance for the atmosphere above the piston, the weight of the pump-rods, at the other end of the lever, carries that end down, and raises the piston of the steam-cylinder. The steam hole is then immediately shut, and a cock opened for injecting the cold water into the cylinder of steam, which condenses it to water again, and thus making a vacuum below the piston, the atmosphere again presses it down and raises the pump-rods, as before; and so on con tinually.

3. When the cylinder is full of steam, if a valve be opened by which the steam is allowed to escape into another vessel, where a jet of cold water is introduced, the condensation is much more complete, and the heat of the cylinder being preserved, the steam possesses its full elasticity.

This improvement was made by Mr. Watt, and completely changed the character of the steam-engine. In the old engines the power was diminished to half its real value, so that the moving force, instead of reaching 15 lbs. on each square inch of the area of the piston, was reduced to about 8 lbs. In this engine of Mr. Watt's the moving force is not less than 12 lbs. upon each square inch of the piston.

4. A farther improvement has been made on this engine, by injecting the steam into the cylinder, alternately above