=24. Therefore the length of the cone is 24 inches. From

CA

=

this take Ce = 12 = 2, and the length of the trumpet is 22 inches. The diameter at the mouth is 2 C e, 4 inches. With this instrument one voice should be as loud as 144.

If it were required to approximate the sound only four times, making it 16 times stronger than the natural voice at the same distance, the angle ACB must be 29°; A e must be 2 inches, AB must be 1d inches, and e f must be d of an inch.

It is easy to see, that when the size of the ear-end is the same in all, the diameters at the outer end are proportional to the approximating powers, and the length of the cones are proportional to the magnifying powers.

We shall find the parabolic conoid the preferable shape for an acoustic trumpet; because the sounds come into the instrument in a direction parallel to the axis, they are reflected so as to pass through the focus. The parabolic conoid must therefore be cut off through the focus, that the sounds may not go out again by the subsequent reflections; and they must be received into a cylindrical pipe of d of an inch in diameter. Therefore the parameter of this parabola is d of an inch, and the focus is th of an inch from the vertex. This determines the whole instrument; for they are all portions of one parabolic conoid. Suppose that the instrument is required to approximate the sound 12 times, as in the example of the conical instrument. The ordinate at the mouth must be 12 times the 6th of an inch, or 2 inches; and the mouth diameter is 4 inches, as in the conical instrument. Then, for the length, observe, that DC in Plate VI. Fig. 7. is th of an inch, and MP is 2 inches, and AC isth of an inch and DC2: MP-AC: AP. This will give AP 12 inches, and CP 11ths; whereas in the conical tube it was 22. In like manner an instrument which approximates the sounds 4 times, is only 14th inches long, and

14th inches diameter at the big end. Such small instruments may be very exactly made in the parabolic form, and are certainly preferable to the conical. But since even these are of a very moderate size when intended to approximate the sound only a few times, and as they can be accurately made by any tin-man, they may be of more general use. One of 12 inches long, and 3 inches wide at the big end, should approximate the sound at least 9 times.

A general rule for making them.-Let m express the approximating power intended for the instrument. The length

at the mouth is. The diameter at the small end is al

ways of an inch.

In trumpets for assisting the hearing, all reverberation of the trumpet must be avoided. It must be made thick, of the least elastic materials, and covered with cloth externally. For all reverberation lasts for a short time, and produces new sounds which mix with those that are coming in.

We must also observe, that no acoustic trumpet can separate those sounds to which we listen from others that are made in the same direction. All are received by it, and magnified in the same proportion. This is frequently a very great inconvenience.

There is also another imperfection, which we imagine cannot be removed, namely, an odd confusion, which cannot be called indistinctness, but a feeling as if we were in the midst of an echoing room. The cause seems to be this : Hearing gives us some perception of the direction o the sounding object, not indeed very precise, but sufficiently so for most purposes. In all instruments which we have described for constipating sounds, the last reflections are made in directions very much inclined to the axis, and inclined in many different degrees. Therefore they have the appearance of coming from different quarters; and instead of the perception of a single speaker, we have that of a sounding

surface of great extent. We do not know any method of preventing this, and at the same time increasing the sound.

There is an observation which it is of importance to make on this theory of acoustic instruments. Their performance does not seem to correspond to the computations founded on the theory. When they are tried, we cannot think that they magnify so much: Indeed it is not easy to find a measure by which we can estimate the degrees of audibility. When a man speaks to us at the distance of a yard, and then at the distance of two yards, we can hardly think that there is any difference in the loudness; though theory says, that it is four times less in the last of the two experiments; and we cannot but adhere to the theory in this very simple case, and must attribute the difference to the impossibility of measuring the loudness of sounds with precision. And because we are familiarly acquainted with the sound, we can no more think it four times less at twice the distance, than we can think the visible appearance of a man four times less when he is at a quadruple distance. Yet we can completely convince ourselves of this, by observing that he covers the appearance of four men at that distance. We cannot easily make the same experiment with voices.

But, besides this, we have compared two hearing trumpets, one of which should have made a sound as audible at the distance of 40 feet as the other did at 10 feet distance; but we thought them equal at the distance of 40 and 18. The result was the same in many trials made by different persons, and in different circumstances. This leads us to suspect some mistake in Mr. Lambert's principles of calculation: and we think him mistaken in the manner of estimating the intensity of the reflected sounds. He conceives the proportion of intensity of the simple voice and of the trumpet to be the same with that of the surface of the mouth-piece to the surface of the sonorous hemisphere, which he has so ingeniously substituted for the trumpet. But this seems to suppose, that the whole surface, generated by the revolution of the quad

rantal arch TEG round the axis CG (Plate VI. fig. 4), is equally sonorous. We are assured that it is not; For even if we should suppose that each of the points Q, R, and S (Plate VI. fig. 3.), are equally sonorous with the point P, these points of reflection do not stand so dense on the surface of the sphere as on the surface of the mouth-piece. Suppose them arranged at equal distances all over the mouth-piece, they will be at equal distances also on the sphere, only in the direction of the arches of great circles which pass through the centre of the mouth-piece. But in the direction perpendicular to this, in the circumference of small circles having the centre of the mouth-piece for their pole, they must be rarer in the proportion of the sine of their distance from this pole. This is certainly the case with respect to all such sounds as have been reflected in the planes which pass through the axis of the trumpet; and we do not see (for we have not examined this point) that any compensation is made by the reflexion which is not in planes passing through the axis. We therefore imagine, that the trumpet does not increase the sound in the proportion of g E2 to T' (Plate

VI. fig. 5.), but in that of

g E2
to
GE

g T2
CT

E2

to g

Mr. Lambert seems aware of some error in his calculation, and proposes another, which leads nearly to this conclusion, but founded on a principle which we do not think in the least applicable to the case of sounds.

MARINE TRUMPET.

THIS

HIS is a stringed instrument, invented in the 16th century by an Italian artist Marino or Marigni, and called a trumpet, because it takes only the notes of the trumpet, with all its omissions and imperfections, and can therefore execute only such melodies as are fitted for that instrument. It is a very curious instrument, though of small musical powers, because its mode of performance is totally unlike that of other stringed instruments; and it deserves our very particular attention, because it lays open the mechanism of musical sounds more than any thing we are acquainted with; and we shall therefore make use of it in order to communicate to our readers a philosophical theory of music, which we have already treated in detail as a liberal or scientific art

The trumpet marine is commonly made in the form of a long triangular pyramid, ABCD, (Plate VI. fig. 8.) on which a single string EFG is strained over a bridge F by means of the finger pin L. At the narrow end are several frets 1, 2, 3, 4, 5, &c. between E and K, which divide the length EF,