must be used, and ciircful cori'ections must be made for chaiifjes of pressure and temperature. When water is used to eontine the gas, some in- accuracy is introduced, since all gases are more or less soluble in water. In technical work, how- ever, a very high degree of accuracy is but rarely required. The technical analysis of gases has assumed great practical importance, owing to the extension of the use of gaseous fuels.
Accuracy. The accuracy of analytical work varies within wide limits, according to the pur- pose which an analysis is intended to serve. The most accurate analyses are those made to deter- mine the proportions by weight, in which the various elements unite with each other. Thus, the proportion in which silver and chlorine unite forms one of the best determined constants of nature. In determining the proportion in which magnesium unites with chlorine, a series of de- terminations has been obtained, agi'eeing so per- fectly with each other that a loss or gain of only one-twentieth of a milligram of the magnesium chloride analyzed corresponds to the difference between the highest or lowest results and the average. Xo such accuracy is attainable in com- mercial or technical work. Nor, if attainable, would it he of any value, since it is but seldom possible to obtain samples representing precisely the average composition of large quantities of material.
The aim of the commercial and technical ana- lyst is usuallj- not to attain extreme accuracy, but to olitain results which he knows to be cor- rect within certain limits. Thus, if an analyst is required to find the percentage of copper in a .sample representing a large cargo of ore, in order to fix its commercial value, he can deter- mine the copper by the electrolytic method to within about one part in four hundred without undue expenditure of time or labor. If the ob- ject of the analysis is to enable the superin- tendent of the smelting furnace to make up charges of a suitable content of copper, a much quicker volumetric process is used : the results are then less accurate than those of the electro- lytic ])rocess, but still much more accurate than is necessary for the purposes of the smelter. When it becomes necessary to determine the amount of substances which occur in relatively very small quantities, it is impossible to avoid relatively large errors. For instance, in deter- mining the amount of phosphorus in a specimen of steel, where the total amount is only about one part in a thousand, the analyst is not sur- prised to find that, in spite of all care, differences of 2 per cent, occur between the results of deter- minations made carefully and under exactly the same conditions.
History. Systematic chemical analysis only dates from the latter half of the eighteenth cen- tury, although chemists of an earlier period had accumulated observations which made it possible to test for the presence of many substances. Bergman (173.5-84) first attempted to give a plan for systematic qualitative analysis of in- organic substances in the wet way. Until the work of Lavoisier (1743-94) had shown the im- portance of relations by weight, quantitative de- terminations attracted little attention, although such determinations were by no means entirely wanting. After the triumph of Lavoisier's views, the importance of quantitative analysis was fully seen ; and the labors of Klaproth ( 1743- SI7), Proust (17o.5-lS2(i),and Vauquelin (1763- 1829), rapidly enriclied chemistry with new methods. But it is to Berzelius "( 1779-1848) that quantitative analysis owes the heaviest debt. Berzelius published tables of the atomic weights of all the elements well known at that time, and some of his values for these important constants have scarcely been improved on since. In the course of these researches an immense number of new methods were developed. Two of his pupils, Heinrich Rose (179.5-1864) and Fried- rich Wfihler (1800-82), not only added to the meth.ods in use, but published comprehensive works on inorganic analysis. The final edition of Rose's work, published after his death by his pupil, R. Finkener, remains an invaluable work to the analyst of to-day. Although K. R. Fre- senius (1818-97) added many new methods, his gi'eat service, which secures him a conspicu- ous place in the histoi-y of analytical chemistry, was the collection and comparison of the various methods in use, the publication of text-books, ^'hich ha^'e formed the models of most others since published, and the founding of a periodical devoted to analytical chemistry. The last editions of his standard works are in the hands of every analyst.
Volumetric analysis was introduced by Gay- Lussae (1778-1850) : but although he gave the first of his important processes to the world as early as 1824. it was not until the publication of Fr. Mohr's text-book on the subject that volumetric analysis began to rank in importance with gravimetric methods. The ultimate an- alysis of organic bodies was attempted with some success by Lavoisier and Berzelius. Gay-Lussac, in 1815, introduced the use of cupric oxide, and Liebig (1803-73) gave the process essentially its present form. Dumas (1800-84) introduced, in 1830, the method for the determination of nitro- gen by direct measurement of the liberated gas, which is still preferred in strictly scientific work to the easier method devised by Kjeldahl. Many attempts were made to analyze gases in the eighteenth ceTitury and in the beginning of the nineteenth, but it is to Bunsen (1811-99) that we owe the perfection of the methods at present in use for gas analysis. The first edition of his text-book, Gasometnsche Methoden, w"as published in 1857. The improvements since that time have been principally in the direction of adapting the methods to rapid work for tech- nical purposes.
Bibliography. Rose, Handbuch der analy- tischen f'hemir. completed by Finkener (Leipzig, 1867-71): Mohr, Lehrhuch der chemisch-analy- tischrn Tilriniirtliodrn, edited by Classen (Brunswick, 1886), and Chemifsrh-tecluufiche TJntcrsnclnmgs-Methoden, edited by Lunge (Ber- lin, 1900) ; Fresenius, Manual of Qualitative Chemical Anab/sis, translated by Wells (New York, 1897) : Fresenius, Anleitxinq sur qiianti- tativen chemischen Anahi-ic (Brunswick, 1875- 87) ; Hempel, iletlioda of fla.i Aiialysin, trans- lated by Dennis (New York, 1892) ; Treadwell, Kiirzcs Lehrhuch der anaUjtischen Chemie (Leip- zig and Vienna, 1899).
AN'ALYT'IC GEOM'ETRY. Geometry treated by means of algebra. Geometric conditions are expressed by equations which, after certain transformations, are interpreted again in geometric concepts. The powerful algebraic method is thus made use of for discovering and demon-
