place a small figure, but in such a manner, that its head may be exactly in the focus.

This mirror must be placed at the distance of eight or ten feet from a wall opposite to it, and parallel to its surface: the wall must have in it an aperture, equal to the surface of the mirror, concealed by a very fine curtain, that the sound may easily pass through it. Provide also a second mirror of the same form, with a similar figure, and place it behind the wall at the distance of two or three feet from it, and opposite to the former, with the figure in its focus. It may be readily conceived, that when a person only whispers into the ear of the small figure behind the wall, a person standing near that placed in the focus of the opposite _mirror, will hear very distinctly the words whispered into the ear of the former. In this manner, the person who asks a question, standing near the first figure, hears the answer which is whispered into the ear of the other behind the wall.

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In order to conceal entirely the apparatus which duces this effect, and to render it much more extraordinary, the pretended concave magic mirror may be covered with a piece of gauze, which will not prevent the transmission of the sounds from the one focus to the other.

The Memoirs of the Academy of Sciences at Paris, for the year 1692, speak of a very remarkable echo in the court of a gentleman's seat, called Le Genetay, in the neighbourhood of Rouen. It is attended with this singular phenomenon, that a person who sings or speaks in a low tone does not hear the repetition of the echo, but only his own voice; while, on the other hand, those who listen hear only the repetition of the echo, but with surprising variations; for the echo seems sometimes to approach and sometimes to recede, and at length ceases when the person who speaks removes to some distance in a certain direction. Sometimes only one voice is heard, sometimes several, and sometimes one is heard in the right, and another on the left. An explanation of all these phenomena, deduced from the semi-circular form of the court, may be seen in the above collection.

EXPERIMENTS RESPECTING THE VIBRATIONS OF MUSICAL STRINGS, WHICH FORM THE BASIS OF THE THEORY OF MUSIC.

If a string of metal or cat-gut, such as is used for musical instruments, made fast at one of its extremities, be extended in a horizontal direction over a fixed bridge, and a weight be suspended from the other extremity, so as to stretch it; this string, when struck, will emit a sound produced by reciprocal vibrations which are sensible to the sight.

If the part of the string made to vibrate be shortened, and reduced to one half of its length, any person who has a musical ear will observe, that the new sound is the octave of the former: that is to say, twice as sharp.

If the vibrating part of the string be reduced to twothirds of the original length, the sound it emits will be the fifth of the first.

If the length be reduced to three-fourths, it will give the fourth of the first.

If it be reduced to, it will give the third major; if to, the third minor. If reduced to, it will give what is called the tone major; if to, the tone minor; and if to, the semi-tone, or that which in the gamut is between mi and fa, or si and sol.

The same results will be obtained if a string be fastened at both ends, and,, and of it be successively intercepted by means of a moveable bridge.

(See the following table relating to this subject.) ·

Such is the result of a determinate degrée of tension applied to a string, when the length of it has been made to vary. Let us now suppose that the length of the string is constantly the same, but that its degree of tension is varied. The following is what we are taught by experiment on this subject:

If a weight be suspended at one end of a string of a determinate length, made fast by the other, and if the tone it emits be fixed, when another weight quadruple of the former is applied, the tone will be the octave of the former; if the weight be nine times as heavy, the tone will be the octave of the fifth; and so on: so that the tones will become acute in the ratio of the square roots of the weights.

The size of the strings has an effect in regard to the tones, as well as the different lengths of the string, and the weight by which it is stretched; for it is proved by experiment, that a string twice as small in diameter as another, every thing else being the same, emits a tone which is the octave of that of the other; and that if the diameter is only a third of that of the other, the tone is the octave of the fifth of that other string, following the order of the diatonic scale.

We may thence conclude, that the tones of the musical strings are in the direct ratio of the square root of the weights by which they are stretched, and in the inverse ratio of the lengths and diameters of these strings.

Consequently, to bring into unison strings which differ in length and diameter, and which are stretched by different weights, the compound ratio thence resulting must be exactly the same, in order that the frequency of the vibration in one may be compensated by the slowness of another. Thus, two strings of the same size, the lengths of which are as 2 to 1, and the stretching weights as 4 to 1, will have their vibrations isochronous, that is to say, they will be in unison: two strings, the diameters of which are as 2 to 1, and the lengths as 1 to 2, stretched by equal weights, will be in unison also, as well as those which, being of

equal lengths, have their diameters as 2 to 1, and the stretching weight as 4 to 1.

We may conclude, therefore, that two strings, the diameters of which are as 3 to 2, and the lengths as 1 to 3, cannot be in unison, unless the weights, by which they are stretched, be to each other in the same ratio as 1 to 4.

To determine the number of the vibrations made by a string of a given length and size, when stretched by a given weight.

A very ingenious method, invented by M. Sauveur, for finding the number of these vibrations, may be seen in the Memoirs of the Academy of Sciences, for 1700. Having observed, when two organ-pipes, very low, and having tones very near to each other, were sounded at the same time, that a series of pulsations or beats were heard in the sounds; and by reflecting on the cause of this phenomenon, he found that these beats arose from the periodical meeting of the coincident vibrations of the two pipes. Hence he concluded, that if the number of these pulsations, which took place in a second, could be ascertained by a stop watch, and if it were possible also to determine, by the nature of the consonance of the two pipes, the ratio of the vibrations which they made in the same time, he should be able to ascertain the real number of the vibrations made by each.

We shall here suppose, for example, that two organpipes are exactly tuned, the one to mi flat, and the other to mi: it is well known, that as the interval between these two tones is a semi-tone minor, expressed by the ratio of 24 to 25, the higher pipe will perform 25 vibrations while the lower performs only 24; so that at each 25th vibration of the former, or the 24th of the latter, there will be a pulsation: if 6 pulsations, therefore are observed in the course of 1 second, we ought to conclude, that 24 vibrations of the one and 25 of the other take place in the tenth of a second: