Definite economic problems can very rarely be dealt with by merely quantitative methods.
The elementary use of graphic methods is qualitative rather than quantitative; i.e.
Lavoisier may be justly regarded as the founder of modern or quantitative chemistry.
The researches of Julius Thomsen and others have shown that in many cases definite conclusions regarding constitution can be drawn from quantitative measurements of the heats of combustion; and in this article a summary of the chief results will be given.
It may be surmised that the quantitative measures of most physical properties will be found to be connected with the chemical nature of substances.
Lavoisier was the first investigator to study fermentation from a quantitative standpoint.
Richter contributed to the knowledge of the quantitative composition of salts.
The conclusion that each element had a definite atomic weight, peculiar to it, was the new idea that made his speculations fruitful, because it allowed of quantitative deduction and verification.
The first exact quantitative study of electrolytic phenomena was made about 1830 by Michael Faraday (Experimental Researches, 1833).
In connexion with the problem of universals, he held that the diversity of individuals depends on the quantitative division of matter (materia signata), and in this way he attracted the criticism of the Scotists, who pointed out that this very matter is individual and determinate, and, therefore, itself requires explanation.
An exact and conscientious worker, he did much to improve and systematize the processes of analytical chemistry and mineralogy, and his appreciation of the value of quantitative methods led him to become one of the earliest adherents of the Lavoisierian doctrines outside France.
The problem is a very difficult one and cannot be regarded as definitely settled, but it is difficult to understand why all this additional complexity in the division of the nucleus should be necessary if the final result is only a quantitative separation of the chromatin.
Various methods have been devised for the quantitative determination of phenol.
Lavoisier, and the quantitative by N.
For the quantitative determination of cobalt, it is either weighed as the oxide, C0304, obtained by ignition of the precipitated monoxide, or it is reduced in a current of hydrogen and weighed as metal.
Fleming, " A Note on a Form of Magnetic Detector for Hertzian Waves adapted for Quantitative Work," Proc. Roy.
He emphasized that the practical training should include (1) the qualitative and quantitative analysis of mixtures, (2) the preparation of substances according to established methods, (3) original research - a course which has been generally adopted.
Such a determination is qualitative, the constituent being only detected or proved to be present, or quantitative, in which the amount present is ascertained.
His text-books on the subject, of which the Qualitative appeared in 1841, and the Quantitative in 1846, have a world-wide reputation, and have passed through several editions.
It must remain constant for the same substance at any temperature and in any form) that quantitative relations between refractivity and chemical composition can be derived.
The most important subjects of his inquiries are enumerated by Forbes under the following five heads: - (1) The laws of polarization by reflection and refraction, and other quantitative laws of phenomena; (2) The discovery of the polarizing structure induced by heat and pressure; (3) The discovery of crystals with two axes of double refraction, and many of the laws of their phenomena, including the connexion of optical structure and crystalline forms; (4) The laws of metallic reflection; (5) Experiments on the absorption of light.
This section treats of the qualitative detection and separation of the metals, and the commoner methods employed in quantitative analysis.
By his insistence upon the use of the balance as a quantitative check upon the masses involved in all chemical reactions, Lavoisier was enabled to establish by his own investigations and the results achieved by others the principle now known as the " conservation of mass."
The methods of chemical analysis may be classified according to the type of reaction: (I) dry or blowpipe analysis, which consists in an examination of the substance in the dry condition; this includes such tests as ignition in a tube, ignition on charcoal in the blowpipe flame, fusion with borax, microcosmic salt or fluxes, and flame colorations (in quantitative work the dry methods are sometimes termed " dry assaying "); (2) wet analysis, in which a solution of the substance is treated with reagents which produce specific reactions when certain elements or groups of elements are present.
In quantitative analysis the methods can be subdivided into: (a) gravimetric, in which the constituent is precipitated either as a definite insoluble compound by the addition of certain reagents, or electrolytically, by the passage of an electric current; (b) volumetric, in which the volume of a reagent of a known strength which produces a certain definite reaction is measured; (c) colorimetric, in which the solution has a particular tint, which can be compared with solutions of known strengths.
Since then the subject has been extensively studied, more particularly by Alexander Classen, who has summarized the methods and results in his Quantitative Chemical Analysis by Electrolysis (1903).
We shall here consider the qualitative and quantitative determination of these elements.
Fresenius, Qualitative and Quantitative Analysis, Eng.
Cohn (Quantitative, 1903); F.
The principal object of this more recent research has been the determination of the quantitative amount of chemical change associated with the passage for a given time of a current of strength known in electromagnetic units.
Owing to the difficulty of determining the magnetization I and the susceptibility K with accuracy, it has not yet been possible to submit this formula to a quantitative test, but it is said to afford an indication of the results given by actual experiment.
" The variety of individuals," says Albert, " depends entirely upon the division of matter," and Aquinas says the principle of the diversity of individuals of the same species is the quantitative division of matter," which his followers render by the abbreviated phrase materia quanta.
It is part of the general theory of quantitative relation, and in its elementary stages is a suitable subject for graphical treatment (ï¿½ 31).
In quantitative estimations it is generally weighed as oxide, after precipitation as sulphide or carbonate, or in the metallic form, reduced as above.
Quantitative methods are divided into four groups, which we now pass on to consider in the following sequence: (a) gravimetric, (0) volumetric, (7) electrolytic, (5) colorimetric.
It has been the habit of biologists to use the terms variation, selection, elimination, correlation and so forth, vaguely; the new school, which has been strongly reinforced from the side of physical science, insists on quantitative measurements of the terms. When the anatomist says that one race is characterized by long heads, another by round heads, the biometricist demands numbers and percentages.
It is in the adaptation of biological conceptions and methods, in the positive contributions of jurisprudence, law and history, in the rigorous application, where possible, of quantitative tests, that the explanation of the present position of economics is to be found.
A tolerably evident shortcoming of such a doctrine is that, while declaring the quantitative determination of matter to be the individual element in the individual, it gives no account of how such quantitative determination arises.
No quantitative determination of the amount of gold in solution is available.
Since the earliest quantitative analyses of sea-water were made by Lavoisier in 1772, Bergman in 177 4, Vogel in 1813 and Marcet in 1819 the view has been held that the salts are present in sea-water in the form in which they are deposited when the water is evaporated.
Schott gives the following as the result of measurements of transparency by means of a white disk at 23 stations in the open ocean, where quantitative observations of the plankton under i square metre of surface were made at the same time.
The thermal G G detectors are especially useful for the purpose of quantitative measurements, because they indicate the true effective or square root of mean square value of the current or train of oscillations passing through the hot wire.
It is clear, however, that an equal quantitative division and distribution of the chromatin to the daughter cells is brought about; and if, as has been suggested, the chromatin consists of minute particles or units which are the carriers of the hereditary characteristics, the nuclear division also probably results in the equal division and distribution of one half of each of these units to each daughter cell.
The formulation of the atomic theory by John Dalton gave a fresh impetus to the development of quantitative analysis; and the determination of combining or equivalent weights by Berzelius led to the perfecting of the methods of gravimetric analysis.
The quantitative precipitation of metals by the electric current, although known to Michael Faraday, was not applied to analytical chemistry until O.
Quantitative Inorganic Analysis.
Combustion is a familiar example of the transformation of chemical energy into heat and light; the quantitative measures of heat evolution or absorption (heat of combustion or combination), and the deductions therefrom, are treated in the article Thermochemistry.
Taylor Jones showed in 1897 that only a small proportion of the contraction exhibited by a nickel wire when magnetized could be accounted for on Kirchhoff's theory from the observed effects of pulling stress upon magnetization; and in a more extended series of observations Nagaoka and Honda found wide quantitative divergences between the results of experiment and calculation, though in nearly all cases there was agreement as to quality.
His version of the methodological assumption of constancy in the quantitative aspects of phenomena, seems a very unsuitable basis for a philosophy of progress.
Since molecular refractions are independent of temperature and of the state of aggregation, it follows that molecular dispersions must be also independent of these conditions; and hence quantitative measurements should give an indication as to the chemical composition of substances.
Julian, Textbook of Quantitative Chemical Analysis (1904); A.