tion, nor to infinitesimals, nor to vanishing quantities, nor even to limits except indirectly: that fluxions, and variations which are also fluxions, ought to be taught among the very elements of geometry and algebra: that curves are most easily conceived and understood from their equations, not from the sections of solids: that the sections of cones and of other solids may be very requisite in masonry, carpentry, civil and military engineering; but that the student of general science, without neglecting these sections, ought, soon after he knows the fourteenth proposition of Euclid's second book, and a little of algebra, to acquire the principles of fluxions, availing himself of that knowledge to render his progress continuous from Euclid through conics, which he will do by taking the equations to the ellipse, &c. from that to the circle: and that, if such a method be followed, a diligent student will leave our Universities with a competent knowledge of Newton, Euler, Lagrange, Monge, Laplace, and many others, and of any department of natural philosophy to which their mathematical researches are applicable. ARTICLE V. A Memoir on Iodine. By M. Gay-Lussac. (Concluded from p. 132.) Historical Note on the Discovery of Iodine. Ir was about two years after M. Courtois had discovered iodine that M. Clement announced it to the Institute on the 29th November, 1813. M. Courtois had observed several of its properties, and particularly that which it has of forming a very fulminating powder when treated with ammonia. He intended to have ascertained all its properties; but being prevented by the attention required by an extensive manufactory of nitre, he engaged M. Clement to continue his researches. M. Clement, from similar motives, could only consecrate to it a few moments. However, he obtained a great number of results, as may be seen by the note printed in the Ann. de Chim. lxxxviii. 304. He discovered that by the combination of iodine and phosphorus a gaseous acid is obtained; but he concluded from his experiments that this acid was composed of about + muriatic acid and iodine. M. Clement was employed in these experiments when Sir H. Davy came to Paris; and he thought that he could not better receive so distinguished a philosopher than by showing him the new substance, which he had likewise shown to мм. Chaptal and Ampere. I state these circumstances to answer a strange assertion which we find in the Journal of Messrs. Nicholson and Tilloch, No. 189, p. 69:-" It appears that this gas (iodine) was discovered above two years ago; but such is the deplorable state of scientific men in France, that no account of it was published till the arrival of our English philosopher there." It is Sir H. Davy of whom they speak. Soon after showing iodine to Davy, and communicating to him the result of his experiments, M. Clement read his note to the Institute, and concluded by announcing that I was going to continue the subject. On the 6th of December I read a note to the Institute on the subject, which was printed in the Moniteur of the 12th of December, and afterwards in the Annales de Chimie, lxxxviii. 311. It is needless to say here that the results which it contained determined the nature of iodine, and that I there established that it is a simple body analogous to chlorine. Nobody hitherto has disputed that I was the first who discovered the nature of iodine: and it is certain that Davy did not publish his results till more than eight days after having known mine. NOTE A. When we make iodine, an alkaline oxide, and water, act upon each other at once, there is formed in general an iodate and hydriodate, or, if you choose, an ioduret. The oxygen which acidifies the iodine may be furnished either by the alkaline oxide or by the water. Let us examine which of these two in all probability furnishes it. When we employ potash, we may admit that it is it which furnishes the oxygen to the iodine; for as iodine disengages oxygen from the potash at a red heat, we may conceive that the same thing takes place at the ordinary temperature by means of water; especially if we consider that here two products are formed, iodate and ioduret, and that there are of consequence two forces which tend to decompose a portion of the potash. The same thing may be said of soda, from which iodine likewise separates the oxygen at a red heat; and of all the oxides in which the oxygen is but weakly condensed. But is this necessarily the case also with all the other oxides? Iodine does not disengage the oxygen from barytes, strontian, lime, and magnesia, even at a very high temperature; and this circumstance, while it renders it more difficult to conceive the decomposition of a part of these alkalies by means of water, although there is then the concurrence of two affinities, renders very probable the existence of a limit beyond which the united affinities of the iodine for the metal, and the iodic acid for the metallic oxide, cannot overcome the affinity of the metal for oxygen. In this case the water may be decomposed; and I have no doubt that this is the fact. On the supposition that there exist only iodurets in solution in water, and no hydriodates, it is a necessary consequence that the oxygen is furnished to the iodine by the metallic oxide. But if there exist hydriodates, then the oxygen will be furnished by the water in all the cases in which they are formed. The question then reduces itself to this-do hydriodates exist? We shall examine it. But as it is the same with the hydro-chlorates, which are better known, we shall turn our more particular attention It may be stated, in the first place, against the existence of hydro-chlorates, that we must admit that on evaporating the water in which they are dissolved, they are changed into chlorurets, and that by redissolving these we reproduce the hydro-chlorates. to them. It is very true that crystallization is sufficient to change the hydro-chlorates of potash, soda, and barytes, into the state of chlorurets. But this does not happen with the hydro-chlorates of lime and magnesia. A high temperature is necessary to deprive the first of the whole of its water. And how can we affirm that a part of that water is not the result of the oxygen and hydrogen which constituted the hydro-chlorate? That of magnesia requires likewise a high temperature to be decomposed, and the chlorine finds still sufficient hydrogen to be changed into hydro-chloric acid. Here then is a decided case in which hydro-chloric acid, and we may add hydriodic acid, are not able to reduce magnesia, though in circumstances most favourable to their action. But if we cannot deny the existence of hydro-chlorate and hydriodate of magnesia, by what certain character can we know that those of lime cannot exist at the ordinary temperature of the atmosphere? When a solution of chloruret of calcium is mixed with subcarbonate of ammonia, the chlorine must pass to the state of hydrochloric acid in order to combine with the ammonia. And if we can admit that water is decomposed at the moment of precipitation in order to furnish hydrogen to the chlorine, and oxygen to the calcium, nothing in that case prevents us from admitting that the act of crystallizing is sufficient to convert an hydro-chlorate into a chloruret, and that the solution of a chloruret in water converts it into a hydro-chlorate; for it is the difference of solubility of subcarbonate of lime and hydro-chlorate of ammonia which occasions the double exchange of the bases and acids; and consequently it is on account of that difference of solubility that the water is decomposed. If we mix together chalk and muriate of ammonia, we reproduce by heat subcarbonate of ammonia and chloruret of calcium. Thus, though we refuse to admit that the chloruret of calcium is changed into hydro-chlorate by solution in water, we must still allow that the elements of water may be separated or united by a trifling change of temperature. What I have just said of the hydro-chlorate of lime applies to most of the other hydro-chlorates and hydriodates; and I might mention other analogous facts. But I ask this only to be granted me, that water in certain circumstances may be formed or decomposed by the same forces which produce the double decomposition of salts. These forces being in general very weak, since a slight change in temperature is sufficient to vary the nature of double decompositions, it will be obvious that solution in water and crystallization may determine the decomposition and formation of this liquid. But in that case the reason which I assigned in favour of the existence of chlorurets and iodurets dissolved in water, does not appear to me to have the same force. It may be alleged, on the other hand, in favour of the existence of chlorurets in solution in water, that when they are dissolved only a very slight change of temperature takes place; while if the water were really decomposed, the variation would be very great. The temperature produced by the solution of a solid body being the result of two opposite causes, it is difficult to distinguish the heat owing to the combination of the liquid with the solid from that which is owing to the change of state in the solid. But independent of this consideration, I must remark, that some of the chlorurets produce cold when dissolved in water, and others heat. Thus the chloruret of sodium sinks the temperature of the water about 3.5°, while that of calcium raises it more than 108°. Farther, if it be demonstrated that the forces, which determine the double saline decompositions, are sufficient to operate the separation of the elements of water and their union in the circumstances of which we are speaking, we ought to admit that the state of condensation of the oxygen and hydrogen in water is little different from that which they experience in the hydro-chlorate, and then the variations of temperature owing to the separation or re-union of these two elements ought to be but little sensible. Besides, my object is not to prove that only hydro-chlorates exist in solution in water. I believe, on the contrary, that according to the nature of the substance with which the chlorine is combined, the chlorurets may dissolve in water without undergoing decomposition, or be changed into hydro-chlorates during that solution. To acquire still further light on that head, I supposed that on mixing a solution of sulphate of ammonia with that of chloruret of calcium or barytes, there ought to be produced a great deal of heat, if these metals were not combined with oxygen; for having to pass into the state of oxide in order to combine with sulphuric acid, the decomposition of the water must necessarily take place, and its oxygen experiencing a great condensation on uniting to the calcium or barium, there ought to be a very sensible disengagement of heat. On mixing solutions of chloruret of calcium and sulphate of ammonia nearly in equal volumes, the temperature scarcely rose half a degree, though such a quantity of sulphate of lime was formed that the whole mixture became solid. The solution of chloruret of barium treated in the same way produced an elevation of about 3.5°. From these facts it would seem that in the solution of chloruret of calcium the metal is in the state of an oxide, while in that of chloruret of barium the metal is still in the metallic state, Analogy, to which one should not yield too blindly in chemistry, but which ought not to be neglected when founded on a numerous series of phenomena, furnishes still, as we shall see, some probabilities in favour of the existence of the hydro-chlorates. It cannot be doubted that sulphur, and even phosphorus, approach a good deal to chlorine and iodine, and that of course their combinations have an analogy with each other. But if we dissolve in water the sulphuret of potassium, we obtain a combination the edour of which announces the presence of hydro-sulphuric acid, and which allows that acid to escape by the action of a moderate heat. In the same way, when phosphuret of potassium is dissolved, phosphureted hydrogen gas is disengaged. The water then in these different circumstances is decomposed: in the first case, in consequence of the affinity of potassium for oxygen, and of sulphur for hydrogen; and in the second, in consequence of the same affinities, together with that of phosphorus for oxygen, since at the same time phosphorous acid is formed. Further, I have already remarked that among the chlorurets, iodurets, and sulphurets, it is those one of whose elements has more affinity for oxygen than the other for hydrogen, that are soluble in water. Hence after the unequivocal existence of hydro-chlorate and hydriodate of magnesia; after the proofs which I have given that water, either in dissolving a chloruret, or in abandoning it, may be decomposed or formed by the same forces that determine the double saline decompositions; and after the analogies which I have just stated, I think we may admit that most of the chlorurets, iodurets, and sulphurets, in solution in water, those at least whose metals have a great affinity for oxygen, may be considered as hydro-chlorates, hydriodates, and hydro-sulphates. I do not, however, deny the existence of the chlorurets, &c. in solution in water. On the contrary, I admit as a principle that we ought to have a chloruret or a hydro-chlorate in solution, according as the forces which act in order to decompose water are smaller or greater than those which keep its elements united. NOTE B. On Acidity and Alkalinity. All the combinations which bodies form may be divided into two sets. In the one there is perfect neutrality; in the other, acidity or alkalinity. Neutrality may not only exist in the saline combinations, but likewise in many others. Thus the ethers formed by the combination of an acid with alcohol, the soaps with an alkaline or acid basis, are so many compounds in which the respective properties of the constituents disappear completely. In the acid or alkaline combinations, on the contrary, the peculiar properties of one of the constituents still show themselves. From the idea of neutrality derived principally from the saline combinations, we regard, as performing the function of an alkali, all the bodies which saturate either completely or in part the properties of acids; and as acids, all bodies that saturate the properties of alkalies. We consider, further, the neutral state as resulting from a certain constant ratio between the body which possesses the properties of acids, and that which possesses those of alkalies. In every other ratio the compound is acid or alkaline. But in all cases the acidity or alkalinity which is in excess is less than before the combination; and this excess may be exactly measured by the c |