the Vths. N. B. These temperaments are calculated by the author. We have found some of them a little different. Thus we make the temperament of CG only 108. Below this we have set down the measures of the perfect intervals, which are to be compared with the differences of the logarithms in column third.

418. We presume not to decide on the merits of this temperament: Only we think that the temperaments of several thirds, which occur very frequently, are much too great; and many instances of the 6th, which is frequent in the flat key, are still more strongly tempered. A temperament however, which very nearly coincides with Dr. Young's, has great reputation on the continent. This is the temperament by Mr. Kirnbergher, published at Berlin in 1771, in his book called Die Kunst des reinen Satzes in der Musik. The eminent mathematician Major Templehoff has made some important observations on this temperament, and on the subject in general, in an essay published in 1775, Berlin. Dr. Young's is certainly preferable.

The monochord is thus divided by Kirnbergher:

We conclude this article (perhaps too long) by earnestly recommending to persons who are not mathematically disposed, the sliding scales, either circular or rectilineal, containing the octave divided into 301 parts; and a drawing of Plate VI. fig. 2. on card paper, of proper size, having the quarter-comma about two inches, and a series of scales corresponding to it. This will save almost the whole of the calculation that is required for calculating the beats, and for examining temperaments by this test. To readers of more information, we earnestly recommend a careful perusal of Smith's Harmonics, second edition. We acknowledge a

great partiality for this work, having got more information from it than from all our patient study of the most celebrated writings of Ptolemy, Huyghens, Euler, &c. It is our duty also to say, that we have got more information concerning the music of the Greeks from Dr. Wallis's appendix to his edition of Porphyrius's Commentary on Ptolemy's Harmonics, than from any other work.

The superior asked them in what manner the governor had warned so many of them in so short a time, at such a distance from his own residence? They told him that it was by the trumpet: and that every person heard at his own door the distinct terms of the order. The father had heard nothing; but they told him that none heard the trumpet but the inhabitants of villages to which it was directed. This is a piece of very curious information; but, after allowing a good deal to the exaggeration of the reverend Jesuits, it cannot, we think, be doubted, but that the Peruvians ac tually possessed this stentorophonic art. For we may observe that the effect described in this narration resembles what we now know to be the effects of speaking trumpets, while it is unlike what the inventor of such a tale would naturally and ignorantly say. Till speaking trumpets were really known, we should expect the sound to be equally diffused on all sides, which is not the case; for it is much stronger in the line of the trumpet than in any direction very oblique to it.

About the middle of the last century, Athanasius Kircher turned his attention to the philosophy of sound, and in different works threw out many useful and scientific hints on the construction of speaking trumpets, but his mathematical illustrations were so vague, and his own character of inattention and credulity so notorious, that for some time these works did not attract the notice to which they were well entitled.

About the year 1670 Sir Samuel Morland, a gentleman of great ingenuity, science, and order, took up the subject, and proposed as a question to the Royal Society of London, What is the best form for a speaking trumpet? which he called a stentorphonic horn. He accompanied his demand with an account of his own notions on the subject (which he acknowledged to be very vague and conjectural), and an exhibition of some instruments constructed according to his views. They were in general very large conical tubes, sud

denly spreading at the very mouth to a greater width. Their effect was really wonderful. They were tried in St. James's park; and his Majesty K. Charles II. speaking in his ordinary colloquial pitch of voice through a trumpet only 5 feet long, was clearly and most distinctly heard at the distance of a thousand yards. Another person, selected we suppose for the loudness and distinctness of his voice, was perfectly understood at the distance of four miles and a half. The fame of this soon spread; Sir Samuel Morland's principles were refined, considering the novelty of the thing, and differ considerably from Father Kircher's. The aerial undulations (for he speaks very accurately concerning the nature of sound) endeavour to diffuse themselves in spheres, but are stopped by the tube, and therefore redundulate towards the axis like waves from a bank, and, meeting in the axis, they form a strong undulation a little farther advanced along the tube, which again spreads, is again reflected, and so on, till it arrives at the mouth of the tube greatly magnified, and then it is diffused through the open air in the same manner, as if all proceeded from a very sonorous point in the centre of the wide end of the trumpet. The author distinguishes with great judgment between the prodigious reinforcement of sound in a speaking trumpet and that in the musical trumpet, bugle-horn, conch shell, &c.; and shows that the difference consists only in the violence of the first sonorous agitation, which can be produced by us only on a very small extent of surface. The mouth-piece diameter therefore of the musical trumpet must be very small, and the force of blast very considerable. Thus one strong but simple undulation will be excited, which must be subjected to the modifications of harmony, and will be augmented by using a conical tube*. But a speaking trumpet must make

Accordingly the sound of the bugle-horn, of the musical trumpet, or the French horn, is prodigiously loud, when we consider the snall passage through which a moderate blast is sent by the trumpeter.

no change on the nature of the first undulations; and cach point of the mouth-piece must be equally considered as the centre of sonorous undulations, all of which must be reinforced in the same degree, otherwise all distinctness of articulation will be lost. The mouth-piece must therefore take in the whole of the mouth of the speaker.

When Sir Samuel Morland's trumpet came to be general. ly known on the continent, it was soon discovered that the speaker could be heard at a great distance only in the line of the trumpet; and this circumstance was by a Mr. Cassegrain (Journ. des Sçavans 1672, p. 131.) attributed to a defect in the principle of its construction, which he said was not according to the laws of sonorous undulations. He proposed a conoid formed by the revolution of a hyperbola round its assymptote as the best form. A Mr. Hase of Wirtemberg, on the other hand, proposed a parabolic conoid, having the mouth of the speaker placed in the focus. In this construction he plainly went on the principle of a reflection similar to that of the rays of light; but this is by no means the case. The effect of the parabola will be to give one reflection, and in this all the circular undulations will be converted into plane waves, which are at right angles to the axis of the trumpet. But nothing hinders their subsequent diffusion; for it does not appear that the sound will be enforced, because the agitation of the particles on each wave is not augmented.

We do not fully

The subject is exceedingly difficult. comprehend on what circumstance the affection or agitation of our organ, or simply of the membrana tympani, depends. A more violent agitation of the same air, that is, a wider oscillation of its particles, cannot fail to increase the impulse on this membrane. The point therefore is to find what concourse of feeble undulations will produce or be equivalent to a great one. The reasonings of all these restorers of the speaking trumpet are almost equally specious, and each points out some phenomenon which should characterise the princi