tion. All sounds, whether acute or grave, are found to travel through the atmosphere with the same celerity. Nor are these the only objections which may be urged. If the atmosphere suffered by the passage of sound such excessive commotion as to vibrate in each successive pulse through a range of five times its density, the conditions of the problem would be totally changed, since the previous investigation was grounded on a supposition that the limits of oscillation are infinitely small. The hypothesis advanced, so far from correcting the result of calculation, would, therefore, occasion a complete derangement.

But though Lagrange rightly determined the equation of aerial pulses, he was unable to effect its complete integration. Might not the difference proceed from his omitting all the powers of the differentials beyond the second? In such delicate processes, the example of Clairaut should teach us caution. That able geometer, on revising his investigation of the precession of the equinoxes, and resuming some terms which he had before neglected, obtained a result conformable to nature, and exactly the double of what was at first assigned. Till the integral calculus has arrived at much greater perfection, it will often be requisite for the analyst in the solution of dynamical questions, to descend from his elevation, and seek to simplify the differential expressions by a sober and judicious application of the principles of physicks.

Imagine a string of particles or physical points A, B, C, D, E, F, &c. in a state of rest or mutual balance. If A were pushed nearer to B, and then suddenly abandoned, it would recoil with a motion exactly similar to the oscillation of a pendulum. The time of this relapse might easily be determined from a comparison of the force of gravity with that of elasticity, or from the number of particles contained in a

column of equipoise. The minute interval between the adjacent particles, being now divided by the duration of each fit of contraction, will give the velocity with which the vibratory influence shoots along the chain of communication. This simple investigation leads still to the same result as before. But it proceeds on assumptions which are evidently incorrect; for it supposes the pulses to follow each other in accurate succession, every contraction terminating as the next begins. Since the particles, however, do not exist in a state of insulation, while B repels A, it must likewise press against C; and C, in its turn, must gradually affect D. Before the contraction of A and B is completed, that of B and C is, therefore, partially performed; and this anticipated influence may even extend to the remoter particles. Nor is the system of mutual action at all materially disturbed by such anticipations. Each pulsation is performed in the same way as if it were quite detached; only the succeeding one is partly accomplished before the regular period of its commencement. The velocity of aërial undulation is in this way much accelerated. To estimate the quantity of correction due to that cause, does not require any great. profusion of calculus; but it would lead us into a tedious digression, altogether foreign to the nature of this journal.

We cannot, however, dismiss the conjecture proposed by M. Laplace, without remarking, that it serves at least to elucidate the explication which professor Leslie has given of the curious phenomenon hypothetically and inaccurately termed the radiation of heat. Having established, by experiment, that such dispersion never takes place but in some species of gas, and that the impression is not conveyed by the actual transfer of the heated portion of the fluid, the conclusion hence appeared irresistible, that this communication

of heat must be performed, by means of the only other motion of which an elastick medium is susceptible, or by its internal oscillations. The author has, indeed, stated the result of induction with excessive brevity; nor has he at all sought to varnish over a subject which is naturally difficult. To comprehend the process distinctly, would require some attention and reach of thought, not quite in the taste of the multitude of chymical amateurs. It is the present fashion to exclaim against theory, and yet indolently to admit the most vague and flimsy assumptions. The principle of the transmission of heat by the agency of aërial pulsation, has not, therefore, attracted that notice, which, from its extent and precision, it so justly deserves. But when it shall be fully developed and strengthened by the concurring analogies, we have no doubt of its being generally embraced as the true exposition of the mode which Nature employs for producing an important class of operations in the physical world. Let AM, BN, CO, DP, &c. represent a series of atmospherick pulses, each pulse being composed of two distinct portions, which alternately contract and dilate. The part A, relapsing from a state of expansion, delivers its surplus heat to M, which now expands, and has consequently its capacity enlarged. This M, next contracting, abandons its heat to the absorption of B, which comes in turn to dilate. The charge of heat is, therefore, conveyed through the atmosphere, and with the rapidity of sound, by a successive transfer along the chain of undulating spaces. In like manner, an impression of cold might be communicated to distant objects by the system of internal vibrations, the primary contraction being followed by a corresponding expansion in regular sequence. It forms no solid objection, that the existence of those hot or cold pulses is not cognizable to the senses. If we had not recourse

to analogical deduction, we should not have discovered that sound itself is propagated through the atmos phere by means of internal vibrations. But such aërial vibrations do not always produce sound. A certain quickness in the succession of pulses seems necessary to make an impression on our organ of hearing; and the peculiar influence of a hot or cold surface may disperse itself in gentle undulations, without exciting in the air that tremor which causes noise.

Experiments on the Propagation of Sound through solid Bodies and through Air in very long Tubes. By M. Biot.

It is well known that air is not essential to the propagation of sound, which can be transmitted through any elastick medium, solid, liquid or gaseous. The celerity of its flight is also much greater in the denser substances. This fact has been ascer tained in Denmark and England, by direct experiments on the sound conducted through beams of wood. and stretched wires; through water and sheets of ice. It was very conspicuous in the observations made by Hassenfratz in the subterranean quarries extended under the site of Paris. The ingenious Chladni proposed to determine the relative swiftness of transmission through a solid body, merely from the note which a rod of the given materials yields when excited into a tremor by friction.

M. Biot, whose attention is ever alert, has seized the occasion of some considerable improvements now going forward in the capital of France, to repeat similar experiments with great precision. The pipes intended to convey water to that metropolis consist of cylinders of cast iron, each eight feet three inches in length; the joints are secured by a collar of lead nearly half an inch thick, covered with pitched cotton rag, and strongly compressed by screws. Into

one end of the compound pipe, was inserted an iron hoop, holding a bell with a clapper, and at the other end, the observer was stationed. In these observations, M. Biot was occasionally assisted by M. Bouvard or M. Malus, colonel of artillery, and by Martin, a chronometer maker. On striking the clapper at once against the bell and the inside of the tube, two distinct sounds were heard at the remote extremity, the one sent through the iron, and the other conducted along the air. The interval between those sounds was measured by a chronometer that marked half seconds. In the first experiment, the pipe consisted of 78 pieces; its length, exclusive of the lead rings was 647 feet; and the interval between the two sounds was ascertained, from a mean of fifty trials, to be .542". But the ordinary propagation of sound through the atmosphere would, at that temperature, have required .579"; and consequently the difference, .037", must give the time of transmission through the metallick tube. In another experiment, the assemblage of pipes, including the leaden joints extended to 2550 feet, or nearly half a mile; and on a medium of 200 trials the two sounds were heard at the interval of 2.79 seconds. The time which sound would take, according to the calculation, to travel the same distance through the air, is 2.5 seconds; whence the difference .29" marks the time of conveyance along the combined tubes. But M. Biot was enabled, by ingeniously varying the experiment, to arrive directly at that conclusion, without employing any previous computation. He concludes, from numerous combined trials, that the true quantity was .26"; and, therefore, that sound is transmitted ten or twelve times faster through cast iron than through the atmosphere.

These experiments sufficiently confirm the results of abstract theory. Perhaps cast iron is more

languid in its tremors than the purer, malleable iron. Chladni had assigned the celerity of vibration through iron and glass at 17500 feet in a second; and Leslie had shown, in one of the curious notes annexed to his book on heat, that through a fir board, the velocity of impulsion, which he proved to be the same as that of vibration, is 17300 feet in a second. We wish that some experiments, on a large scale, were made on the time of the transmission of sound through water. They could not fail, we are sure, to lead to consequences highly instructive in the economy of nature.

Besides the paper which we have now analyzed, this volume contains several chymical dissertations of no ordinary value, though the length of our preceding observations will prevent us from going very fully into their examination. There are one or two, however, on which we shall subjoin a few remarks.

On the relation between the Oxydation of Metals, and the capacity of Saturation of their Oxyds by Acids. By M. Gay-Lussac. Read at the Institute, December 5th, 1808. Mr. Dalton, in his "New System of Chymical Philosophy," published in the beginning of 1808, maintains, that bodies combine only in certain definite proportions, and that all metallick oxyds of the same class possess the same quantity of oxygen, and differ from each other solely in the proportion of metallick matter they contain. According to his theory, one portion of metal, in its first state of oxydation, requires, for its saturation, one portion of acid. Now, it is well known that some metals, when highly oxydated, take more acid to dissolve them than when oxydated in an inferiour de gree. Of course, it follows, that one portion of metal, in its second state of oxydation, ought, if it takes up more acid, to take up at least twice as much as it did in the first; or, to employ a more gene

ral form of expression, it should always be found, that the quantity of acid in metallick salts, so constituted, is directly proportional to the quantity of oxygen in the oxyd-the very principle which M. Gay-Lussac endeavours to demonstrate in this memoir. We shall not pretend to determine the claims to originality which our author tacitly makes, or to risk a conjecture whether or not he is indebted to Mr. Dalton. That the principle maintained by both, is the same, we conceive to be undeniable; and it is certain that M. GayLussac was in possession of the English work, if not before, at least within twenty-four days after this memoir was read (and long before it was published) as he expressly refers to it, in another paper of that date, as a work with which he was familiar.

The facts advanced by our author, in support of the principle, consist chiefly in the phenomena which occur during the precipitation of one metal by another. Thus, when neutral solutions of acetate of lead, sulphate of copper, and nitrate of silver, are precipitated by zink, iron, and copper, respectively, it is inferred, as no gas appears to be extricated, that merely a transfer of the oxygen and acid is made from one metal to the other.

By similar facts and reasonings, the principle is extended to salts containing metals at their maximum of oxydation; and then it is applied to the sulphites by means of a calculation depending on two facts. The change of sulphurick acid, by heat, into oxygen and sulphurous acid gas; and the curious circumstance that, during the conversion of sulphite into sulphate of lead, the neutral state of the salt undergoes no alter ation. Our author, in an observation at the end of this memoir, attempts to prove, that the quantity of sulphur in sulphurets, formed by the action of sulphurated hydrogen or the hydrosulphurets on metallick

salts, is directly proportional to the quantity of oxygen previously combined with the metal.

We have not entered into a minute analysis of this memoir, nor pointed out the particular application of the author's conclusions, because the hypothesis which he endeavours to establish, appears to us to stand in need of much additional confirmation. The series of facts on which it rests, strikes us at first sight, as far too narrow and limited for the basis of so extensive an inference; and some of the experiments referred to in proof of its truth, seem to us contradictory to each other. Our author no where adverts to the nature of the sub and super acid salts, the very existence of either of which equally opposes the hypothesis that the quantity of acid is, in all cases, directly proportional to the quantity of oxygen in the oxyd. As a parti cular instance, let us take the subsulphate of iron, produced by exposing a solution of the green sulphate. to the atmosphere. It is well known, that, during its formation, the liquid becomes sensibly acid;-but how is this phenomenon to be reconciled with the hypothesis, according to which, as the metal acquires more. oxygen, it should possess a greater capacity for acid, and retain that with which it was combined, with additional force? To remove this objection, it would be necessary to prove, that the acid, in this case, exists only in mechanical mixture with the oxyd, and not in chymical union, which is highly improbable.. Many other instances of a similar mature might be quoted.

The spirit of theory and generalization, in short, is evidently too much indulged throughout this memoir; and the ingenious author is so fully satisfied of the truth of his hypothesis, though countenanced. but by a few insulated facts, that he does not scruple to set it up as the very standard and test of truth, by which the accuracy of the laborious

experience of other philosophers is to be estimated and controlled. He has, in some other of his late inquiries (which we hope to be able to refer to on a future occasion) as well as in this, followed the path originally struck out by Mr. Dalton, and pursued by him with much industry and talent. The idea of uniform proportions, in all chymical combinations, has received support from some other chymists of high authority; but the fact, we conceive, is still very far from being established; nor can we investigate too rigorously, or receive with too much caution, general principles which are intended to be applied to correct the results of actual experiment and analysis. The quantities of elementary materials which form compound bodies, and the nature of their arrangements, are scarcely susceptible of rigorous demonstration. As yet, a few facts only have been compared in relation to these numerical doctrines; and any decision upon them will be premature. We hope soon to be enabled to resume this important subject, with better grounds of conclusion. In the mean time, we would earnestly recommend the most minute experimental inquiry, in all cases in which mathematicks are applied to chymistry. To use the words of Boerhaave: " egregia illius ancilla est—non alia prejor domina." 1. Of the Action of Vegetable Acids on Alcohol, both with and without the intervention of a Mineral Acid. 2. Of the Combination of Acids with Vegetable and Animal Substances. By M. Thenard. Read at the Institute, November 23, 1807.

The new facts detailed in the first memoir are processes for forming compounds by distilling the oxalick, malick, citrick, gallick, and tartarous acids, respectively with alcohol and a mineral acid. The substances thus produced are all analogous to each other, and to the oil of benzoin discovered by Scheele; and, according

to M. Thenard's experiments, they are entirely free from the mineral acid employed. These facts are both new and curious; and others are brought forward which are also curious, but not new. Such, for instance, are some of our author's experiments respecting acetick ether, particularly the process by which he succeeded in procuring it without the intervention of a mineral acid. Few chymists, we conceive, can be ignorant of this method, as it was known as long ago as 1759, when the count de Lauragais made it publick. His results, indeed, were considered as incorrect by Scheele; but their accuracy has since been well established by M. Pelletier and Dr. Henry, as well as by the experiments of M. Thenard himself. Whether this neglect towards the inquiries of these gentlemen, was intentional or not, on the part of our author, is of very little consequence; for, whilst the records of chymical discovery exist, philosophers may rest assured that justice will be done to their labours, sooner or later, by the enlightened part of mankind.

Led by a train of reasoning, like that which M. Thenard followed in concluding the experiments of Scheele on acetick ether and oil of benzoin to be inconclusive, we cannot but think the investigation, here brought forward, of the same description; and that much remains to

be done, before the nature of the new substances will be fully understood. They are considered by our author, as combinations merely of the vegetable acids and alcohol; and he asserts, that the mineral acid employed in the operation, acts no other part than that of condensing the vegetable acid and alcohol; and of inducing in each a state that disposes them to combine. This is possible; but it is not demonstrated by any experiments he has described, Independent of the failure of all his attempts to form the combination directly, there are many reasons