Dividing again these latter values by the length of the charges, we shall have for the mean force of each elementary fluid particle

J. Force of dissolution

2. When T = 31 lbs. force elastic

= 0·14205 grains.

075540 grains. 6.08174 grains.

3. When T = 298 lbs. force elastic It appears, however, that equal charges of powder of the same quality, employed in the same piece, produce very different velocities, the more considerable being the resistance to the expansion of the fluid, the less the velocity becomes. Thus, it is found that when T 31 lbs. the velocity of the ball when expelled at the mouth of the piece is 1563.6 feet; when T 298 lbs. v 1350·9 feet.

The following table will exhibit, in one view, the velocities with which a 24 pound ball issues from the mouth of a gun, when propelled with the several charges expressed in the first column. 1st. According to the theory developed in the volume from which we have made these extracts. 2dly. According to the experiments of M. Lombard at Auxerre, on guns for land service. 3dly. According to the experiments of M. Teixier de Norbec, at Toulon, on guns for sea service. 4thly and 5thly. According to the determinations of Mr. Robins and Dr. Hutton.

Charges Veloc. from Theory Mean Veloc. fromExperim. Velocities.

of

when when

velocity

Powder. T=31 T= 298 from theory. Lombard. Norbec. Robins. Hutton.

It is the prodigious celerity of expansion of the flame of fired gunpowder which is its peculiar excellence, and the circumstance in which it so eminently surpasses all other inventions, either ancient or modern: for as to the momentum of these projectiles only, many of the warlike machines of the ancients produced this in a degree far surpassing that of our heaviest cannon shot or shells; but the great celerity given to them cannot be approached with facility by any other means than the explosion of powder.

52. Since the important invention of the Steam-engine, another species of first movers has come under the consideration of the mechanical investigator, namely, such as arise from the volatilisation of different fluids. Of these the one most commonly chosen is the STEAM raised from hot water, which is an

elastic fluid, and which when raised with the ordinary heat of boiling water is almost 3000 times rarer than water, or more than 5 times rarer than air, and then has its elasticity equal to that of the common atmospheric air: by great heat it has been found that the steam may be expanded into 14000 times the space of water, and then exerts a force of nearly 5 times the pressure of the atmosphere: and there is no reason to suppose this is the limit: indeed some accidents which have happened prove clearly that the elastic force of steam may at least equal that of gunpowder.

The observations on the different degrees of temperature acquired by water in boiling, under different pressures of the atmosphere, and the formation of the vapour from water under the receiver of an air-pump, when with the common temperatures the pressure is diminished to a certain degree, shew clearly that the expansive force of vapour or steam is different in the different temperatures, and that in general it increases in a variable ratio as the temperature is raised. Previous to describing the method which has been adopted to measure the force of steam under different temperatures, it will be proper to describe briefly the method by which the Chemists account for the production of aëriform fluids.

53. The term Caloric is used to denote the cause, whatever it may be, of heat, and of the phenomena which accompany heat: it is now almost universally admitted to be a highly elastic fluid. Every body is, according to its nature, capable of containing under a given volume a certain quantity of caloric, either greater or less: this property was first observed by Dr. Black, and the English chemists designated it by the term Capacity of a body to contain the matter of heat. Professor Wilcke and M. Lavoisier first made use of the term specific caloric, denoting by it the quantity of caloric respectively necessary to elevate to the same number of degrees' the temperature of several bodies of equal weight.

Substances volatilised and reduced to gas or aëriform fluids, are nothing else than ordinary solid or fluid bodies which by some circumstance are found superabundantly combined with caloric, in such a manner that the constituent particles of these bodies are separated the one from the other, by a quantity of ambient, caloric much more considerable than that which surrounds the same particles in the natural state of the bodies. The extreme elasticity of the caloric the effect of which is augmented by its condensation, and the weakening of the reciprocal attraction or of the cohesion of the particles of the bodies (a weakening or diminution produced by the increased distance of those particles) concur to diminish the density of the bodies

in such a manner that they become reduced to an aëriform

state.

54. As to the elasticity of gaseous fluids thus formed, it appears in great measure to be produced by the elasticity of caloric itself, which, when bodies are reduced to the gaseous state, occupy a very great part of their volume. This eminent elasticity of caloric tends continually to produce expansion; on the other hand, this fluid, by a particular destination of nature, is more or less disseminated between the molecule of all bodies, in such sort that we may say with M. Lavoisier that even in the solid state these moleculæ do not touch, but, as it were, swim in the caloric at a certain distance from each other. There must, therefore, be a perpetual contest between the expansive force of caloric which tends to disseminate the moleculæ, and the cohesive attraction of the molecule which tends to join them together. From the reciprocal intensity of these two powers results the solid and liquid states of bodies: thus, water only differs from ice by the greater or less condensation of caloric, which permits more or less of the molecule of the liquid to yield to the effect of their attraction or reciprocal cohesion.

When substances pass from the liquid to the aëriform state, there is a third power to combine with the expansive effort of t caloric, and the aggregative or attractive effort of the molecula; namely, the pressure of the atmosphere, or of any elastic fluid whatever which compresses the fluid, and opposes itself to the separation of its parts. This third power has a certain influence also upon the passage from the solid to the fluid state, but it is most frequently (in this case) very small, and even evanescent in comparison of the resistance arising from the mutual cohesion of the moleculæ. The contrary effect has place in the course of the passage from the liquid to the gaseous or aëriform state; the cohesion of the fluid molecule being extremely small, the elasticity of the caloric has scarcely any thing to surmount to produce volatilisation besides the pressure of the atmosphere, or gas which actually compresses it.

55. Hence it results that the same liquid under different pressures ought to volatilise at different temperatures. M. Lavoisier proved the truth of this result, by placing ether under the receiver of an air-pump, and producing volatilisation solely by taking off a part of the pressure of the atmosphere. See Chymie, tome 1. pa. 9. And we know by many experiments of M. Deluc and others, that water boils the more speedily as it is less pressed by the weight of the atmosphere.

Lavoisier notices a curious consequence of what has been here said; which is, that if our planet revolved upon its axis. with such a velocity as to lessen the pressure of the atmosphere,

or if the temperature of the air were raised, then several fluids. which we now see under a liquid state would only exist in the aeriform state; for example, if under the temperature of summer the pressure of the atmosphere were only equivalent to 20 or 24 inches of the barometrical tube, that pressure would not retain ether in the fluid state, it would be changed into gas; and the like would happen, if while the pressure of the air was equivalent to 28 or 30 inches of the mercury the habitual temperature were 105 or 110 degrees on Fahrenheit's scale.

56. The principles which have been here exhibited are sufficient for the understanding of all which relates to the action of water or other fluids reduced to vapour. Now, it has appeared from frequent experiments that water heated in common air volatilises at 80° of Reaumur's thermometer, or 212° of Fahrenheit's, the height of the barometer being 28 French, or 29.9 English inches: and spirits of wine under a like pressure volatilises at between 63° and 64° of Reaumur, or nearly 175° of Fahrenheit. The expansive force of the vapour must, therefore, in both these cases, according to the principles just explained, be measured by a column of mercury of 28 French, or 29.9 English inches, in like manner as such a column measures the pressure of the atmosphere, or the elasticity of common air. And at any more elevated temperatures the elastic force of the vapour will surpass the pressure of the atmosphere by a quantity which has a certain relation with the excess of the temperature above those just stated.

57. Till lately there was wanting on this important subject a series of exact and direct experiments by means of which, having given the temperature of the heated fluid, the expansive force of the steam rising from it might be known, and vice versa. There was likewise wanting an analytical theorem expressing the relation between the temperature of the heated fluid and the pressure with which the force of the steam was in equilibrio. These desiderata have, however, been lately supplied by M. Bettancourt, an ingenious Spanish philosopher, after a method which shall now be concisely explained.

58. M. Bettancourt's apparatus consists of a copper vessel or boiler, with its cover firmly soldered on: this cover has three orifices which close up with screws: at the first the water or other fluid is put in and out; through the second passes the stem of a thermometer which has the whole of its scale or graduations above the vessel, and its ball within, where it is immersed either in the fluid or in the steam according to the different circumstances; through the third hole passes a tube, making a communication between the cavity of the boiler and one branch of an inverted syphon, which contains mercury,

and acts as a barometer for measuring the pressure of the elastic vapour within the boiler. In the side of the vessel there is a fourth hole into which is inserted a tube with a turncock, making a communication with the receiver of an air-pump, in order to extract the air from the boiler, and to prevent its return.

The apparatus being prepared in good order, and distilled water introduced into the boiler at the first hole, and then stopped, as well as the end of the inverted syphon or barometer, M. Bettancourt surrounded the boiler with ice, to lower the temperature of the water to the freezing point, and then, having extracted all the air from the boiler by means of the air-pump, the difference between the columns of mercury in the two branches of the barometer shewed the measure of the elastic force of the vapour arising from the water in that temperature. Then lighting the fire below the boiler, he gradually raised the temperature of the water from 0 to 110° of Reaumur's thermometer, that is, from 32° to 27910 of Fahrenheit's thermometer; and for each degree of elevation in the temperature he observed the height of the mercurial column which measured the elasticity or pressure of the vapour.

These experiments were repeated various times and with dif ferent quantities of water in the vessel; their results were arranged in different columns for the sake of comparison, and it appeared that the pressures for different temperatures agreed very nearly, however much the quantity of fluid in the vessel was varied. It was also seen that the increase in the expansive force of the vapour is at first very slow; but increases gradually unto the higher temperatures, where the increase becomes very rapid, as will be obvious from an examination of the tables in some of the following pages.

59. To express the relation between the degrees of temperature of the vapour and its elastic force, this philosopher employs a method suggested by M. Prony, which consists in imagining the heights of the columns of mercury measuring the expansive force to represent the ordinates of a curve, and the degrees of heat the corresponding abscissæ of that curve; making the ordinates equal to the sum of several logarithmic ones which contain two indeterminates, and ascertaining these quantities in such manner that the curve may agree with a tolerable number of observations taken throughout the whole extent of the change of temperature, from the lowest to the highest extreme of the experiments. Then a formula or equation to a curve is investigated, and when the curve corresponding to that equation is constructed, if it coincide (with the exception of a few trifling anomalies) with the curve constructed by the results of the experiments, the formula may be looked upon as correct,