VII. When the Odds on each game are 7 to 4.

5 times running,

· . are.

very near 3 to 1

⚫ near 84 to 1

3 out of 4,

IX. When the Chance on each game is 4 to 7.

Against winning

⚫ are.

72 to 49, or 1

to 1

65 to 56, or 7 to 6

6 times running,

5 out of 6,

4 out of 6,

5 times running,

4 out of 5,

X. When the Odds on each game are 2 to 1.

XI. When the Chance on each game is §, or 1 to 2.

143

ACOUSTICS AND MUSIC.

THE ancients seem to have considered sounds under no other point of view than that of music; that is to say, as affecting the ear in an agreeable manner: it is even very doubtful whether they were acquainted with any thing more than melody, and whether they had any art similar to that which we call composition. The moderns, however, by attending to the philosophy of sounds, have made many discoveries in this department, so much neglected by the ancients; and hence has arisen a new science, distinguished by the name of Acoustics. Acoustics have for their object the nature of sounds considered, in general, both in a mathematical and philosophical view. This science, therefore, comprehends music, which considers the ratios of sounds, so far as they are agreeable to the ear, either by their succession, which constitutes melody, or by their simultaneiety, which forms harmony. We shall here give a brief account of every thing most curious and interesting in regard to this science.

Definition of sound; how diffused and transmitted to our organs of hearing-experiments on this subject-different ways of producing sound.

Sound is nothing else but the vibration of the particles of the air, occasioned either by some sudden agitation of a certain mass of the atmosphere, violently compressed or expanded, or by the communication of the vibration of the insensible parts of a hard and elastic body.

These are the two best known ways of producing sound. The explosion of a pistol, or of any other kind of fire-arms, produces a report or sound, because the air or elastic fluid, contained in the gunpowder, being suddenly dilated, compresses the external air with great violence: the latter, in consequence of its elasticity, re-acts on the surrounding atmosphere, and produces in its moleculæ an oscillatory motion, which occasions the sound, and which extends to a greater or less distance, according to the intensity of the cause that gave rise to it.

The other method of producing sound, is to excite in an elastic body, vibrations sufficiently rapid to occasion, in the surrounding parts of the air, a similar motion. Thus an extended string, when struck, emits a sound; and its oscillations, that is to say, its motion backward and forward, may be distinctly seen. The elastic parts of the air struck by the string, during the time it is vibrating, are themselves put into a state of vibration, and communicate this motion to the neighbouring ones. Such also is the mechanism by which a bell produces its sound: when struck, its vibrations are sensible to the hand which touches it.

That air is the vehicle of sound, may be proved by the following experiment: if a bell be suspended in the receiver of an air-pump, the sound of it decreases in proportion as the air is exhausted, and at last becomes totally insensible when a complete vacuum has been formed.

Sound always ceases when the vibrations of the sonorous body cease, or become too weak. This may be proved also by an experiment; for when the vibrations of a sonorous body are damped by any soft body, the sound seems suddenly to cease; in a piano-forte, therefore, the quills are furnished with bits of cloth, that by touching the strings when they fall down, they may damp their vibrations. On the other hand, when the sonorous body is, by its nature, capable of continuing its vibrations for a considerable time, as is the case with a large bell, the sound may be heard for a long time after.