compute the velocity of sound. I have mentioned it that they may compare it with the hypothesis-if any thing so simple can be called a hypothesis-which I shall now employ, and from which I have investigated in Thomson's Annals for May 1821, all the known laws of gaseous bodies, except one with which I was then unacquainted. It is there assumed, that air consists of a number of very small particles continually infringing on one another, and the sides of the vessel containing them, having no property but absolute hardness. The laws of collision for such bodies are demonstrated in the preceding number, exactly agreeing, as I have since found, in some of the principal points with those delivered by Huygens and Wren. However, in the present inquiry, we shall have no need to have recourse to these laws. We may keep nearer the beaten tract by considering the particles perfectly elastic, and yet not affect the legitimacy of our proceedings. Now, if in an air so constituted, no disturbance be given to the motions of the particles, they will settle into corresponding motions throughout the whole extent of the air, and the medium will appear to enjoy a perfect repose; for the mutual collisions, if corresponding through the whole medium, are not considered a disturbance. But if the motions of any of the particles of this air be disturbed, the disturbance will affect their collisions on the adjacent particles, and hence the collisions of these on the next, and so on to the limits of the air, at the rate at which the particles propagate their motions. Should the disturbance be a violent displacement of the air, as that, for example, occasioned by the collision of the bodies, an aerial wave will be generated, which will travel from part to part of the medium, with no sensibly greater velocity than the slightest disturbance. For if we suppose the collision to give a great individual excess of motion to a sphere of particles a foot diameter, by the time it is propagated to the extremities of a sphere a hundred feet diameter, it would, if equally divided among them, amount individually to only a th of its original quantity; and if distributed among the superficial particles only, to a th of what it was. So that 1 1,000,000 1 10,000 22 before it arrives to 50 feet from the origin of disturbance, that is to and part of the distance which sound passes over in a second, it would be so attenuated as to be altogether insensible. The same is likewise equally true in a tube. For since the mass of the tube is so great, compared with that of the included air, and the air instantly imparts its motion to the sides of the tube, all effect from any individual excess is destroyed, perhaps more rapidly than it would be in the open air. Thus the uniform velocity of sound, and its equal propagation in loud and low sounds, are very obvious consequences. The intensity depends on the magnitude of the aerial wave or quantity of particles disturbed, and the quality of sound I conceive on the nature of the disturbance, that is, on the sort of derangement given to the motions of the particles. But with this we have at present no concern; our object is to estimate the velocity of sound. In the Annals already alluded to, I have deduced the properties of gases from general views of their motions, without descending to particulars; but in the problem we have in hand, this is not enough. We must discover such a system of motion as may subsist and satisfy the general laws of airs, and from this investigate the mean elasticity, and the mean velocity of the particles reduced to any rectilinear direction. Let us suppose, then, that a quantity of air is enclosed in a cubical vessel, whose faces are opposite to the four cardinal points, and the zenith and nadir. Now, if we suppose the particles to meet and strike in sixes simultaneously, one from each of the above six points, and that after collision they separate, each retracing its path, a medium might be composed which would continue its internal motions and existence ad infinitum, if not disturbed. Each particle would, on this view, constantly run forwards and backwards in the same track, meeting, at one extremity, always one set of five particles, and at the other another set of five particles. Let N denote the number of the particles in unity space, then 2 1 NI is the length of a particle's path in its going, and the length in its going and N returning. If, therefore, V be the velocity per 1" of a particle, Again, м being the mass of a particle, v м is its momentum. But, because to conserve the motions, the particles are reflected back and made to retrace their paths, 2 v м is the force of collision, or the intensity of a particle's direct stroke on the containing side. Moreover, the space and number of particles being the same, the mean distance run by each and the mean number of collisions would be the same, with the same velocity, in whatever manner the particles do really perform their motions; but the intensity of collision on the side would be very different. For since the angle of incidence of any one particle may vary from 0° to 90°, the intermediate angle 45° is the mean angle in which it can strike the side. Consequently, 2 VM √2 particle on the side containing the air; and if this be drawn into the number force per second of a particle. This again multiplied by N3, the number of particles which strike against unity area of the side, gives the mean force per second of the air in unity space against the side, D being the density of the air. But if g be the velocity of a falling body by the force of gravity at the end of a second, and E the elasticity of the air or weight it will support, e g will also be the total action of the air per second. Equating these two expressions, we have for the mean velocity of the particles, preserving to each its mean action on the containing side; or for the mean rectilinear velocity of the particles in any given direction; that is, by what we have before said, the velocity with which sound or any disturbance in the air is propagated. Before we proceed farther, let us just glance at a curious consequence of the above theorem. I have hitherto said nothing of the nature or laws of heat. But by experiments we know that E is as D × (F+448) in every gas, F being the Fahr. temperature. Therefore, by the preceding theorem, V2 is as F +448; that is, if the hypothesis we have assumed of the nature of air be true, the Fahr. temperature plus 448 is proportional to the square of the velocity of the particles, and, consequently, heat must consist in motion. Conversely, if heat consist in motion, the simplest, and hence, according to the laws followed by nature the true constitution of aeriform bodies, is that which we have supposed. The theory of heat which appears to me to be most consistent with phenomena, is, indeed, the Newtonian, namely, that heat is nothing but corpuscular motion; and that the quantity of heat in any body, is as the sum of all the motions of its particles; and if the body be uniformly hot, that its temperature is proportional to the motion or momentum of any one of its particles. But to return: we have by M. Biot, g = 9.8088 metres at Paris, Traité de Physique, tome ii, p. 15, or =9·8088 × 3.28085=32·18122 English feet; and D= E bm (1+00375 c) Therefore, v=g bm (1+0075 c) √2, b being the altitude of the barometer, m the ratio of the weight of a given volume of mercury to that of air, and C the cent. temperature. When C=0 and b=,76 metres, M. Biot makes m=10463; therefore v = √9·8088×·76 × 10463 × √2 × (1+00375 c)=332·1241+00735 c metres, or 1089.65 √ F + 448 English feet,. (3) in perfectly dry air. At the temperature of melting ice it is 1089.65 feet, while the experiments of Dr. Moll, which are considered to be the most accurate hitherto made, reduced to the same temperature and state, give 1089-74 feet, or '09 more. This result it will have been observed, has been obtained without any extra hypothesis of the effect of condensation, &c., on the temperature and elasticity, and by a simple direct process from the definition only of an air. Let us now compare the theorem with some of the best experiments that we have, by which a better opinion may be formed of its accuracy and accordance with nature. Captain Parry at Port Bowen, observed the velocity of sound to be 1035.96 feet per second, the temperature being -15°31 Fahr. This is the mean of all the experiments recorded in Phil. Trans. for 1828, p. 97, except those of January 10th, in which there appears to be some error, and those of June 4th, made in a strong wind. By our theory the velocity should be 1034-6 feet, or 1.4 feet less. The French Academicians in 1738, found it to be 172:56 toises, or 1103.5 feet, at 42o.8 Fahr. (Connais. des Tems. for 1825, p. 370); by our theory, it is 1101·9, or 1·6 in defect. In the Cambridge Phil. Trans. and Phil. Mag. for June 1824, Dr. Gregory has published a set of experiments, the mean of which is 1107 feet, at 48.62 Fahr. Our theorem gives 1108-4 feet, or 14 too much. These experiments are justly celebrated for their great accuracy, considering the smallness of the bases employed. The Connaisance des Tems for 1825, contains the experiments of M. Arago and colleagues; the mean of the first set, made June 21st, 1822, was 1118-4 feet, at 60°-62 Fahr; and of the second set, the next day, 1130-3 feet, the temperature be ing 639.95 Fahr. At the same temperatures, we find by (3) for the velocities 1121.8 and 1125.4 feet, that is 3-4 too much, and 4.9 too little. Collecting these observations together, we have Thus the mean difference is half a foot in defect, much within what is due in the last experiments to the vapour, according to Laplace, Con. des for 1825, p. 272, As I shall have to enter more fully into this subject in my Mathematical Principles of Natural Philosophy before alluded to, I shall not trouble the Association with the ordinary consequences of (2), and the method of allowing for the influence of vapour. There are, however, one or two facts relative to the INTENSITIES OF SOUND IN DIFFERENT AIRS, which I can hardly pass over, lest from their not being quite so obvious, it should be supposed the present theory of airs does not apply to them. According to our views of the nature of airs, it is evident that the intensity of sound, from the same cause at the same distance, the temperature being the same, would be directly as the number of particles acted on or displaced; that is, as the number in a given space, whether the cause of sound be in the same air under different compressions, or in different airs; for since the temperatures are as the momenta of the particles, and these are supposed to be the same, the force on the tympanum of the ear will be as the number which strikes it. In the same air, at a given temperature, the intensity will therefore be as the elasticity. But in different airs by (2) e, d, n representing the м v being equal to m v. N n same things in another gas, and the temperature If therefore E D n d =e That is in different gases, of the same elasticity and temperature, the intensities are as the square roots of the densities or specific gravities, and inversely as the velocities with which sound is propagated. Thus the tones or intensities become measures of the velocities, when applied to different gases. But in order that the measures may hold good, it is evident that the airs must be individually homogeneous; that is, in each gas the particles must throughout be of the same size, or at least of the same mass. If the airs, or one of them, contain particles of unequal masses, the same relation between the intensities, specific gravities, and velocities, will not hold; and hence the tones or intensities furnished by the different gases, will present us with the means of looking into their internal constitution, or of deciding whether an air under examination, be homogeneous, or a mechanical mixture of heterogeneous particles. Those who understand the experiments and researches which have been made on the pulses, tones, &c., in the various gases, for the purpose of |