precipitation of the same amount of chloride of mercury, by means of sulphuretted hydrogen, yields 85 638 of sulphide of mercury.

Now, in the former case the number 73.83 expresses directly the proportion of mercury contained in the analysed chloride; in the latter case we have to deduce this proportion by calculation, which may be accomplished by means of the following simple equation :-100 parts of sulphide of mercury contain 86-213 parts of mercury; how much mercury do 85.638 parts contain?

100 86-213: 85.638 : x = 73.83.

It will be readily understood from the preceding illustration, that all those forms and combinations into which the known constituents of a given compound are to be converted for the purpose of quantitative estimation must, of necessity, in the first place, admit of most accurate weighing, and that, in the second place, their composition must be correctly known. These two conditions are absolutely indispensable; for it is quite obvious, on the one hand, that accurate quantitative analysis must be altogether impossible if the substance the quantity of which it is intended to ascertain does not admit of correct weighing; and, on the other hand, it is equally evident, that if we do not know the exact composition of a new product, we lack the most indispensable element for our subsequent deductions.

ANALYSIS BY MEASURE, or VOLUMETRICAL ANALYSIS, is based upon a very different principle from that of analysis by weight; viz., it effects the quantitative determination of a body, by converting it from a certain definite state to another equally definite state, by means of a fluid of accurately known composition and action, and under circumstances permitting the analyst to mark with rigorous precision the exact point when the conversion is accomplished and terminated. The following example will serve to illustrate the principle of this method:Permanganate of potassa added to a solution of sulphate of protoxide of iron, acidified with sulphuric acid, immediately converts the protoxide of iron to sesquioxide; the permanganic acid, which is characterized by its intense color, yielding up oxygen and changing to protoxide of manganese, which combines with the sulphuric acid present to colorless sulphate of protoxide of manganese. If, therefore, to an acidified fluid containing protoxide of iron, we add, drop by drop, a solution of permanganate of potassa, the red color imparted to the fluid by every fresh drop added, continues for some time to disappear again upon stirring; but at last a point is reached when the coloration imparted to the fluid by the last drop added remains: this point marks the termination of the conversion of the protoxide of iron to sesquioxide.

Now, by accurately determining the strength, or power of action of the solution of permanganate of potassa-which is done simply by making it act upon a known quantity of protoxide of iron in solution, and correctly noting how much of it is required to effect the conversion of that protoxide to the state of sesquioxide-we get a standard which will enable us to determine the exact amount of protoxide of iron present in any given solution. Thus, we will assume, for instance, that we have found it takes exactly 100 parts of our solution of permanganate of potassa to peroxidize 2 parts of protoxide of iron; if now, in testing, with this standard solution of permanganate of potassa any given solution containing protoxide of iron in unknown proportion, we find that

100 parts of our standard fluid are required to peroxidize the iron, we know at once that the examined fluid contained exactly 2 parts of protoxide of iron; if 50 parts are required, we know that 1 part of protoxide of iron was present, &c. &c. Accordingly, by simply measuring the quantity used of our standard solution of permanganate of potassa, we arrive at once at an accurate knowledge of the corresponding amount of protoxide of iron.

As the process of measuring is mostly resorted to, in preference to that of weighing, for determining the quantity used of the standard fluid, we give to this analytical method the name of analysis by measure, or volumetrical analysis. It generally leads to the attainment of the object in view with much greater expedition than is the case with analysis by weight. To this brief intimation of the general purport and object of quantitative analysis and the general mode of proceeding in analytical researches, I have to add that certain qualifications are essential to those who would devote themselves successfully to the pursuit of this important branch of the science of chemistry. These qualifications, are, 1, theoretical knowledge; 2, skill in manipulation; and 3, strict conscientiousness.

The preliminary theoretical knowledge required consists in an acquaintance with the qualitative branch of analytical chemistry; together with some practice in simple arithmetic. A previous knowledge of qualitative analysis enables us to understand all the various methods proposed for isolating substances in order to determine their weight; whilst practice in simple arithmetical calculations enables us to deduce from our analytical results the composition of the analysed substance in equivalents, to test the correctness of the method we have pursued, and to control the results arrived at. To this knowledge must be joined the ability of performing the necessary practical operations. This is an axiom generally applicable in all practical sciences, but more particularly in quantitative chemical analysis. The most extensive and solid theoretical acquirements will not enable us, for instance, to determine the amount of common salt present in a solution of that substance, if we are without the requisite dexterity to transfer a fluid from one vessel to another without the smallest loss. The various operations of quantitative analysis demand great aptitude and manual skill, which can be acquired only by practice. But even the possession of the greatest practical skill in manipulation, joined to a thorough theoretical knowledge, will still prove insufficient to insure a successful pursuit of quanti. tative researches, unless combined also with a sincere love of truth and a firm determination to accept none but thoroughly verified and confirmed results.

No one who has ever been engaged in quantitative analysis can deny that cases will sometimes happen in which doubts may be entertained as to whether the results of the operation are correct, or even where the operator is positively convinced that the result of his process cannot be quite correct. Thus, for instance, a small portion of the substance under investigation may be spilled, or some of it lost by decrepitation; or the analyst may have reason to doubt the accuracy of his weighing; or it may happen that two analyses of the same substance do not exactly agree. In all such cases it is indispensable that the operator should be conscientious enough to repeat the whole process over again. He who is not animated with this sincere devotion to science and is afraid of en

countering labor and difficulties in the pursuit of truth-he who would be satisfied with mere assumptions or suppositions and guess-work, where the attainment of positive certainty is the object, must be pronounced just as deficient in the necessary qualifications for quantitative analytical researches, as he who is wanting in theoretical knowledge or in practical skill. He, therefore, who cannot firmly and fully rely upon the accuracy of his operations and labors-he who cannot swear to the correctness of his results, may indeed occupy himself with quantitative analysis for his own private amusement, but he ought never to publish as correct and positive the results of his operations and researches, since such a proceeding might be eminently injurious to others, by misleading them and might, in the end, even prove greatly detrimental to the interests of true science; nor would it be prudent for him to apply such results to any practical purpose of his own, since this would be sure to turn out very little advantageous to himself.

The domain of quantitative analysis may be said to extend over all matter, that is, in other words, anything corporeal may become the object of quantitative investigation. The present work, however, is intended to embrace only the substances used in pharmacy, arts, trades, agriculture, and manufactures.

Quantitative analysis may be subdivided into two branches, viz., analysis of mixtures, and analysis of chemical compounds. This division. may appear at first sight of very small moment, yet it is necessary that we should establish and maintain it, if we would form a clear conception of the value and utility of quantitative research. The quantitative analysis of mixtures has not the same aim as that of chemical compounds; and the method applied to secure the correctness of the results in the former case is different from that adopted in the latter. The quantitative analysis of chemical compounds rather subserves the theoretical purposes of science, whilst that of mixtures belongs to the practical purposes of life. If, for instance, I analyse the salt of an acid, the result of the analysis will give me the constitution of that acid, its combining proportion, saturating capacity, &c. &c. ; or, in other words, the results obtained will enable me to answer a series of questions of which the solution is important for the theory of chemical science: but if, on the other hand, I analyse gunpowder, alloys of metals, medicinal mixtures, ashes of plants, &c. &c., I have a very different object in view; I do not want in such cases to apply the results which I may obtain to the solution of any theoretical question in chemistry, but I want to render a practical service either to the arts, trades, or manufactures, or to some other science. If in the analysis of a chemical compound, I wish to control the results obtained, I may do this in most cases by means of calculations based on stachiometric data, but in the case of a mixture a second analysis is necessary to confirm the correctness of the results afforded by the first.

The preceding remarks clearly show the immense importance of quantitative analysis. It may, indeed, be averred that chemistry owes to this branch its elevation to the rank of a science, since quantitative researches have led us to discover and determine the laws which govern the combinations and transpositions of the elements. Stochiometry is entirely based upon the results of quantitative investigations; all rational views respecting the constitution of compounds rest upon them as the only safe and solid basis.

Quantitative analysis, therefore, forms the strongest and most powerful lever for chemistry as a science, and not less so for chemistry in its applications to the practical purposes of life, to trades, arts, manufactures, and likewise in its application to other sciences. It teaches the mineralogist the true nature of minerals, and suggests to him principles and rules for their recognition and classification. It is an indispensable auxiliary to the physiologist; and no one can deny that agriculture has derived of late, and will continue to derive, incalculable benefit from it. We need not expatiate here upon the advantages which medicine, pharmacy, and every branch of industry derive, either directly or indirectly, from the practical application of its results. On the other hand, the benefit thus bestowed by quantitative analysis upon the various sciences, arts, &c., has been in some measure reciprocated by some of them. Thus whilst stachiometry owes its establishment to quantitative analysis, the stachiometrical laws afford us the means of controlling the results of our analyses so accurately as to insure their correctness, and to justify the reliance which we now generally place on them. Again, whilst quanti-, tative analysis has advanced, and continues to advance, the progress of arts and industry, our manufactures in return supply us with the most perfect platinum-glass- and porcelain-vessels, and articles of india-rubber, without which it would be next to impossible to conduct our analytical operations with the minuteness and accuracy to which we have now attained.

Although the aid which quantitative analysis thus derives from stachiometry, and the arts and manufactures, greatly facilitate its prac tice, it must be admitted that the pursuit of this branch of chemistry to any satisfactory purpose, requires, notwithstanding, considerable expenditure of time. I would therefore advise every one desirous of becoming an analytical chemist, to arm himself with a considerable share of patience, reminding him that it is not at one bound, but gradually, and step by step, that the student may hope to attain to that skill and precision in his operations that may justify reliance upon the correctness of his results. However mechanical, protracted, and tedious the operations of quantitative analysis may appear to be, the attainment of accuracy will amply compensate for the time and labor bestowed upon them; whilst, on the other hand, nothing can be more disagreeable than to find, after a long and laborious process, that our results are incorrect or uncertain. Let him, therefore, who would render the study of quantitative analysis agreeable to himself, from the very outset endeavor, by strict, nay, scrupulous adherence to the rules and conditions of this science, to attain to correct results, at any sacrifice of time. There cannot be a better and more immediate reward of labor than that which springs from the attainment of accurate results and perfectly corresponding analyses. The satisfaction enjoyed at the success of our efforts is surely in itself a sufficient motive for the necessary expenditure of time and labor, even without looking to the practical benefits which we may derive from our operations.

The following are the substances treated of in this work :

I. METALLOIDS, or NON-METALLIC ELEMENTS.

Oxygen, Hydrogen, Sulphur, [Selenium,] Phosphorus, Chlorine, Iodine, Bromine, Fluorine, Nitrogen, Boron, Silicon, Carbon.