(12.) The effects of the same sails at a maximum are nearly, but somewhat less than, as the cubes of the velocity of the wind.

(13.) The load of the same sails at a maximum is nearly as the squares, and the effect as the cubes of their number of turis in a given time.

(14.) When sails are loaded so as to produce a maximum 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 27; 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 winds, &c. we need not wonder if this kind of mill is in reality found to have not above one-eighth or one-tenth of the power of the common sort; as has appeared in some attempts of this kind."

51. Another first mover, of whose effects it may be proper to give some account, is fired gunpowder. These effects are too violent and sudden to allow of their being applied to many practical purposes (the chief use of gunpowder being in the discharge of balls and shells from guns and mortars); but they are so prodigious and extraordinary, and are so important in the art of war, that it may be naturally expected we should give some estimate of them in this place.

Now to understand the force of gunpowder it must be considered that whether it be fired in a vacuum or in air, it produces by its explosion a permanently elastic fluid: and it appears from experiment that the elasticity or pressure of the fluid produced by this firing of gunpowder is, cæteris paribus, directly as its density.

To determine the elasticity and quantity of this fluid produced from the explosion of a given quantity of gunpowder, Mr. Robins premises, that the elasticity increases by heat, and diminishes by cold, in the same manner as that of the air; and that the density of this fluid, and consequently its weight, is the same with the weight of an equal bulk of air, having the same elasticity and the same temperature. From these principles, and from the experiments by which they are established (for a detail of which we must refer to the book itself), he concludes that the fluid produced by the firing of gunpowder is nearly of the weight of the generating powder itself; and that the volume or bulk of this air or fluid, when expanded to the rarity of common atmospheric air, is about 244 times the bulk of the said generating powder.-Count Saluce, in his Miscel. Phil. Mathem. Soc. Priv. Taurin. p. 125, makes the proportion as 222 to 1; which he says agrees with the computation of Messrs. Hauksbee, Amontons, and Belidor.

Hence it would follow that any quantity of powder fired in

any confined space, which it adequately fills, exerts at the instant of its explosion against the sides of the vessel containing it, and the bodies it impels before it, a force at least 244 times greater than the elasticity of common air, or, which is the same thing, than the pressure of the atmosphere; and this without considering the great addition arising from the violent degree of heat with which it is endued at that time; the quantity of which augmentation is the next head of Mr. Robins's enquiry. He determines that the elasticity of the air is augmented in a proportion somewhat greater than that of 4 to 1, when heated to the extremest heat of red-hot iron; and supposing that the flame of fired gunpowder is not of a less degree of heat, increasing the former number a little more than 4 times, makes nearly 1000; which shews that the elasticity of the flame, at the moment of explosion, is about 1000 times stronger than the elasticity of common air, or than the pressure of the atmosphere. But, from the height of the barometer, it is known that the pressure of the atmosphere upon every square inch is on a medium of 143 lb; and therefore 1000 times this, or 14750 lb. is the force or pressure of the flame of gunpowder, at the moment of explosion, upon a square inch, which is very nearly equivalent to 6 tons and a half.

This great force, however, diminishes as the fluid dilates itself, and in that proportion, viz. in proportion to the space it occupies, it being only half the strength when it occupies a double space, one-third the strength when the triple space, and so on.

Mr. Robins further supposed the degree of heat above mentioned to be a kind of medium heat; but that in the case of large quantities of powder the heat will be higher, and in very small quantities lower; and that therefore in the former case the force will be somewhat more, and in the latter somewhat less, than 1000 times the force of the atmosphere.

He further found that the strength of powder is the same in all variations in the density of the atmosphere: but that the moisture of the air has a great effect upon it; for the same quantity which in a dry season would discharge a bullet with a velocity of 1700 feet in one second, will not in damp weather give it a velocity of more than 12 or 1300 feet in a second, or even less, if the powder be bad, and negligently kept. Robins's Tracts, vol. 1, p. 101, &c. Further, as there is a certain quantity of water which, when mixed with powder, will prevent its firing at all, it cannot be doubted but every degree of moisture must abate the violence of the explosion; and hence the effects of damp powder are not difficult to account for.

The velocity of expansion of the flame of gunpowder, when fired in a piece of artillery, without either bullet or other body

before it, is prodigiously great, viz. 7000 feet per second, or upwards, according to the experiments of Mr. Robins. But M. Bernoulli and M. Euler think it is still much greater.

Dr. Hutton, after applying some requisite corrections to Mr. Robins's numbers, and after remarking that the powder does not all inflame at once, as well as that about of it consists of gross matter not convertible into an elastic fluid, gives v = × log. of) for the initial velocity of any

125

nq 16+9

p+w 2180 ad2

ball of given weight and magnitude, and n = 2log. for the value of the initial force n of the powder in atmospheric pressures: where a = length of the bore occupied by the charge, b=whole length of the bore, d=diameter of the ball, w=its

a

weight, 2p=weight of the powder, q=. In his experiments and results he found n to vary between 1700 and 2300; and the velocity of the flame to vary between 3000 and 4732; specifying, however, the modification in his computations which would give more than 7000 feet per second for that velocity. Taking 2200 for an average value of n, and substituting 47 for its square root in the above formula for v, it becomes v=

.

8875 (16+4 × log. of -) for the velocity of the ball, a

theorem which agrees remarkably well with the doctor's numerous and valuable experiments. (Tracts, vol. iii. pp. 290-315.)

In a French work entitled" Le Mouvement Igné, considéré principalement dans la charge d'une Pièce d'Artillerie," published in 1809, there are advanced, among some notions which we apprehend few philosophers will be inclined to adopt, some which may demand and deserve a careful consideration. The author of this work observes that if a fluid draws its force, partly from a gaseous or aëriform matter, and partly from the action of caloric, which rarefies that deriform matter; then its density in the process of dilatation, will follow the inverse ratio of the spaces described, and at the same time the intensity of the heat will follow the same ratio: so that the force of the totality of the fluid will conform to the inverse ratio of the squares of the spaces described. He then investigates two classes of formula: the first appertain to fluids which possess simply the fluid or aeriform elasticity, which are free from all heat exceeding the temperature of the atmosphere; whether there be one or many gaseous substances signifies not, provided their temperature agrees with that of the atmosphere; for when these dilate they conform to the inverse ratio of the spaces described. The

second relate to those which derive their elasticity as well from the aëriform fluids as from the matter of heat which pervades them, and which are denominated fluids of mixt elasticity, to distinguish them from those of simple or purely aëriform elasticity: these fluids, in dilating, conform to the inverse ratio of the squares of the spaces described. Thus the celerity of action of mixed elastic fluids, is to that of simple elastic fluids, as s2 to s; whence it follows that mixed elastic fluids are more prompt and energetic in their action than others; and hence also is inferred why the fluid produced by the combustion of gunpowder is more impetuous and more terrible in its operation than atmospheric air, however compressed it may be. The force exerted by the caloric to dissolve a quantity of powder, is regarded as equal to that possessed by the fluid which results from that dissolution, and is named force of dissolution of powder by fire: and the surface of least resistance, is that (as of the ball) which yields to the action of the fluid. The gunpowder subjected to experiment by this author, was of seven different qualities, varying from 1000 the density of water, down to 946 the density of the powder used by sportsmen. It was found by theory, and confirmed by experiment, that the real velocity with which the elastic fluid considered under the volume of the powder, and penetrated by a degree of heat capable of quadrupling the volume, would expand when it had only the resistance of the atmosphere to surmount, is 2546 49 feet, that is, about 2734-4 feet English.

Comparing the several forces which were calculated for the same quantity of powder in three different circumstances:

1. When the fluid has only to surmount the atmospheric pressure, it has a force of dissolution which is proper to it, and which, in a charge of 8lbs. of powder, specific gravity 944-72, for a 24-pounder, acts upon the surface of least resistance with an energy equivalent to 9747-8074 pounds.

2. The fluid, retarded in its expansion by a surface of least resistance, whose tenacity (occasioned by the compactness and pressure of the wadding, &c.) T = 31 pounds, acquires by its elasticity a force = 52839 1463 pounds, at the instant when that surface yields to its action.

3. If the tenacity T 298 pounds, the force of the fluid at the moment when the resisting surface yields to it will be equivalent to 417371-4275 pounds.

If each of these forces be divided by the surface of least resistance, the quotient will indicate the force of each fluid filament, namely,

1. That of the force of dissolution

173 63 grains. =923.26 grains. =7433.99 grains.