Academy of Sciences found, that sound moved at the rate of 1172 Parisian feet in a second. Gassendus makes its velocity to be 1473 feet in a second; Mersenne 1474; Duhamel, in the History of the Academy of Sciences, 1338; Newton 968; and Derham, in whose measure Flamsteed and Halley concurred, 1142. Though it is difficult to determine among so many authorities, the last estimate, viz 1142 per second, has been generally adopted in this country..

It is to be observed that, according to Derham's experiments, the temperature of the air, whether dry or moist, cold or hot, causes no variation in the velocity of sound. This philosopher had often an opportunity of seeing the flash and hearing the report of cannon fired at Blackheath, 9 or 10 miles distant, from Upminster, the place of his residence; but whatever might be the state of the weather, he always counted the same number of half seconds, between the moment of seeing the flash and that of hearing the report, unless any wind blew from either of these places, in which case the number of the seconds varied from 111 to 112. It may be readily conceived, that if the wind impelled the fluid put into a state of vibration, towards the place of the observer, the vibrations would reach him sooner than if the fluid had been at rest, or had been impelled in a contrary direction.

But notwithstanding what Derham has said, we can hardly be persuaded that the velocity of sound is not affected by the temperature of the air; for when the air is heated, and consequently more rarefied or elastic, the vibrations must be more rapid: observations on this subject ought to be carefully repeated.

An inaccessible distance then may be measured by means of sound. For this purpose provide a pendulum that swings half seconds, which may be done by suspending from a thread a ball of lead, half an inch in diameter, in such a manner, that there shall be exactly 9 inches, or 9 between the centre of the ball and the point of suspension; then the moment you perceive the flash of a cannon, or musket, let go the pendulum, and count how many. vibrations it makes till the instant when you hear the report if you then multiply this number by 571 feet, you will have the distance of the place where the musket or cannon was fired.

We here suppose the weather to be calm, or that the wind blows only in a transversal direction; for if the wind blows towards the observer from the place where the cannon or gun is fired, and if it be violent, as many times 12 feet as there have been counted half seconds must be added to the distance found; and in the contrary case, that is to say, if the wind blows from the observer, towards the quarter where the explosion is made, they must be subtracted. It is well known that a violent wind makes the air move at the rate of about 24 feet per second, which is nearly the 48th part of the velocity of sound. If the wind be moderate, a 96th may be added or subtracted; and if it be weak, but sensible, a 192d: but this correction, especially in the latter case, seems to be superfluous; for can we ever flatter ourselves that we have not erred a 192d part in the measuring of time?

This method may be employed to determine the distance of ships at sea, or in a harbour, when they fire guns, provided the flash can be seen, and the explosion heard. During a storm also, the distance

of a thunder-cloud may be determined in the same manner. But as a pendulum is not always to be obtained, its place may be supplied by observing the beats of the pulse, for when in its usual state, each interval between the pulsations is almost equal to a second; but when quick and elevated, each pulsation is equal to only two thirds of a second.

ARTICLE III.

How sounds may be propagated in every direction without confufion.

This is a very singular phenomenon in the propagation of sounds; for if several persons speak at the same time, or play on instruments, their different sounds are heard simultaneously, or all together, either by one person, or by several persons, without being confounded in passing through the same place in different directions, or without damping each other. Let us endeavour to account for this phenomenon.

The cause no doubt is to be found in the property of elastic bodies. For let us conceive a series of globules equally elastic, and all contiguous, and let us suppose that a globule is impelled with any velocity whatever against the first of the series: it is well known that in a very short time the motion will be transmitted to the other extremity, so that the last globule will have the same motion communicated to it as if it had been itself immediately impelled. Now if two globules with unequal velocities impel at the same time the two extremities of the series, the globule a, for example, the extremity A, and the globule b the extremity B (fig. 1 pl. 15), it is

certain, from the well known properties of elastic bodies, that the globules a and b, after being a mo ment at rest, will be repelled, making an exchange of velocity, as if they had been immediately impelled against each other.

If we suppose a second series of globules, intersecting the former in a transversal direction, the motion of this second series will be transmitted by means of the common globule, from one end to the other of this series, in the same manner as if it had been alone. The case will be the same if two, three, four or more series cross the first one, either in the same point or in different points. The particular motion communicated to the beginning of each series, will be transmitted to the other end, as if that series were alone.

This comparison may serve to shew how several sounds may be transmitted in all directions, by the help of the same medium; but it must be allowed that there are some small differences.

For, in the first place, we must not conceive the air, which is the vehicle of sound, to be composed of elastic globules, disposed in such regular series as those here supposed: each particle of air is no doubt in contact with several others at the same time, and its motion is thereby communicated in every direc tion. Hence it happens that the sound, which would reach to a very great distance almost without diminution, if communicated as here supposed, experiences a considerable decrease, in proportion as it recedes from the body which produced it. Though the movement by which sound is transmitted be more complex, there is reason to believe that it is reduced, in the last instance, to something similar to what has been here described,

The second difference arises from the particles of air by which the organ of hearing is immediately affected, not having a movement of translation, like the last globule of the series, which proceeds with a greater or less velocity, in consequence of the shock that impels the other extremity of the series. But the movement in the air consists merely of an undulation or vibration, which, in consequence of the elasticity of its aerian particles, is transmitted to the extremity of the series, such as it was received at the other. It must be observed that the sonorous body communicates to the air, which it touches, vibrations isochronous with those which it experiences itself; and that the same vibrations are transmitted from the one end to the other of the series, and always with the same velocity: for we are taught by experience that a grave sound, ceteris paribus, does not employ more time, than an acute one, to pass through a determinate space.

ARTICLE IV.

Of Echoes; how produced; account of the most remarkable echoes, and of some phenomena respecting them.

Echoes are well known; but however common this phenomenon may be, it must be allowed that the manner in which it is produced is still involved in considerable obscurity, and that the explanation given of it does not sufficiently account for all the circumstances attending it.

All philosophers almost have ascribed the formation of echoes to a reflection of sound, similar to that experienced by light, when it falls on a polished body. But, as D'Alembert observes, this explana