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solve. We proceed by assuming more or less arbitrarily a certain cause for each group of phenomena. Then, without reference to facts, we proceed to draw or 'deduce' all the conclusions that can be logically developed from the hypothesis.' We call this development the theory of the events in question. A comparison of the theoretical deductions with the observed facts. is the sole means of judging the correctness of the theory and of the hypothesis on which it is based. So long as facts and theory agree, we are justified in regarding the theory as accurate, but not as absolutely and infallibly true.

If the theoretical conclusions and the facts do not agree, then the hypothesis is false, or the extension of the theory has been incorrectly carried out, and the errors must be sought out and corrected. Hypotheses and theories contradicted by observation must be rejected; doubtful theories may often be usefully retained so long as they facilitate the survey of a large number of observations. The best supported theory must never be regarded as absolutely true: a high degree of probability is the utmost to which it can attain.

As examples of a few of the hypotheses which have attained this highest degree of probability, we may mention Newton's hypothesis that the heavenly bodies exert a mutual attraction on each other which is inversely proportional to the square of their distances; Huygen's hypothesis that light is an undulatory movement of the ether; and the hypothesis of Daniel Bernoulli and R. Clausius that in the gaseous state the particles are in rapid rectilinear motion; and many others might be cited.

If we ask how far a happily chosen hypothesis and a correct theory can carry us on the path of knowledge, we find we must be content if, by their aid, we can follow and discern the causal connection and the necessary results of phenomena until we arrive at certain values which remain unaltered in the various changes taking place. These unchangeable values are termed 'constants.' They may be real values or only express proportions or ratios of such things as number, weight, length, space or time. A 'constant' is not of necessity absolutely invariable. It is sufficient for our purposes if it does not undergo any appreciable change in the phenomena under investigation. Con

CHEMICAL THEORIES

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sequently the constants we arrive at, in a certain group of phenomena, need not of necessity form the limits of our knowledge, but may in turn form the subject of research, if we investigate the conditions under which they vary, and in this way arrive at constants of a higher order. But in spite of all the progress we have made the determination of the constants still remains the problem for investigation. We are content when we succeed in predicting the phenomena which result as a natural consequence from certain constants, and the varying relations which these constants bear to each other.

§ 4. Development of Chemical Theories.-The inductive method was first applied in chemistry at a comparatively late stage in its history. It was only at the end of the seventeenth, and more particularly during the eighteenth century that all the then known facts were systematically arranged and a logical classification of bodies into combustible and incombustible, burnt and unburnt, was made. The hypothesis which was employed to account for the difference between the two large classes of bodies proved incorrect. This hypothesis assumed the existence of a peculiar combustible principle, the so-called 'phlogiston,' in all combustible substances. Combustion consisted in the evolution of phlogiston. In recent times it has been shown that the phlogiston theory is not altogether devoid of truth. For what was formerly termed phlogiston is almost identical with our present notion of potential energy. It was during the two hundred years when the phlogiston theory prevailed that the application of inductive methods revealed the general truth that matter can neither be created nor destroyed. This discovery led to conclusions rendering the doctrine of phlogiston untenable, and resulting in its replacement by Lavoisier's theory of combustion. According to this theory the process of combustion is not due to an evolution of phlogiston, but to oxidation'-that is, to the combination of the combustible body with oxygen, one of the constituents of atmospheric air.

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During the period of quantitative analysis, which begins with this theory, great stress was laid on the investigation of the proportions by weight in which different substances unite together, and thus a new field of research was opened up, which rapidly acquired unexpected dimensions.

The most important result of this new development was to strengthen our knowledge of the fact that nothing is lost and nothing is gained when substances undergo chemical change. When substances unite together, the weight of the compound is exactly equal to the sum of the weights of the constituents. When several bodies act on each other, it was formerly a difficult matter to decide which were compounds and which were constituents; but by the light of this new law the question can easily be answered. When red-hot iron is hammered it yields forgescales, and on exposure to damp air it rusts. In either case it gains in weight; consequently it has combined with something, and not lost anything as was formerly supposed. It has combined with oxygen, and the increase in weight is equal to the weight of oxygen the metal has united with in its conversion into oxide (rust or forge scales). Consequently the oxide is the compound and the metal is a constituent; but in the last century the reverse was held to be the case. In this way quantitative chemistry' effected an accurate distinction between elementary bodies and their compounds, and imparted a degree of exactness to the methods of investigation, of which in previous centuries there had been no conception.

We are acquainted with about seventy bodies which have up to the present time resisted all attempts to decompose them. We therefore consider these substances as invariable in composition until the contrary is proved, and consequently regard them as the fundamental constants of chemistry. The aim of the science of chemistry is to investigate the laws which govern the combination of these elements, and to determine in what way the character and properties of the compounds are affected by the nature of the constituent elements.

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§ 5. Stochiometric Laws. The further investigation of the quantitative composition of chemical compounds led to the foundation of the science of stœchiometry by Jeremias Benjamin Richter. The most important facts of stochiometry were discovered almost simultaneously by Proust. The fact pointed out by Proust, that definite chemical compounds always contain their constituents in fixed and invariable proportions, was strongly disputed by no less an authority than C. L. Berthollet.

1 Tà σTOIXEîα, the constituents. μéтpov, the measure.

LAW OF MULTIPLE PROPORTIONS

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Richter's views on the laws which govern the combination of acids with bases to form salts remained for a long time neglected and almost unnoticed. The credit of establishing the value of these laws (so far as they were correct) belongs to J. J. Berzelius, who obtained important aid from an hypothesis propounded by John Dalton.

The fundamental law of stochiometry, discovered by Richter and confirmed and developed by Berzelius, states that all true chemical changes (i.e. changes of composition) take place between definite volumes or weights of the substances. This is equally true whether a substance decomposes into its constituents or is formed from its constituents, or when different compounds exchange one of their constituents.

When water is formed from its constituents 7.98 parts by weight of oxygen unite with one part by weight of hydrogen, never more or less, and the two constituents are produced in exactly these proportions when water is decomposed.

All other substances, whether elements or compounds, behave in the same way; that is to say, they only enter into combination or undergo decomposition in definite and fixed proportions by weight.

It often happens that the bodies unite together in several distinct proportions, but these different proportions always bear a simple relation to each other.

This empirical law is known as the law of multiple proportions. For example, there is another compound of hydrogen and oxygen, hydrogen peroxide, which contains 15.96 parts by weight of oxygen to 1 part by weight of hydrogen—that is, twice as much oxygen as unites with 1 part by weight of hydrogen in water. By mixing these two oxides of hydrogen a liquid is obtained in which the quantity of oxygen lies between that contained in water and in hydrogen peroxide. The resulting liquid is not a chemical compound, but merely a mechanical mixture, for its properties are those of its constituents, and the act of admixture is not followed by those changes in the material nature of the substances, which are characteristic of chemical combination.

Nitrogen forms a larger number of oxides, in which one part by weight of nitrogen is combined respectively with 0.5696, 1.1392, 1.7088, 2.2784, and 2.8480 parts by weight of oxygen.

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The relation between these quantities is expressed by the whole numbers 1, 2, 3, 4, 5.

The numbers indicating the proportions in which substances unite together are called 'combining weights,' or stœchiometric quantities. It is remarkable that they apply not merely to two given elements but to all elements without exception. For example, one part by weight of copper is combined with 0.1263 part by weight of oxygen in cuprous oxide, and with 0.2526 part by weight of oxygen (i.e. exactly double) in cupric oxide. The quantities of sulphur combined with one part by weight of copper in the sulphides are also in the proportion of 1 to 2, cupric sulphide containing 0-5062 and cuprous sulphide 0.2531 part by weight of sulphur; 0.2531 part by weight of sulphur on combustion unites with 0.2526 part by weight of oxygen. This is exactly the quantity of oxygen which unites with one part by weight of copper to form cupric oxide.

The combining weights for copper and sulphur and for copper and oxygen are also valid for the compounds of sulphur and oxygen. This rule is true of all elements. It may be generally expressed in the following words :

If we know the proportions by weight in which a series of elements unite with a certain given element, then these elements either unite with each other in the quantities represented by these proportions or in some simple multiple of them. If A, B, C, D represent the proportions by weight in which the different elements unite with a definite quantity of another element, then any compound of these elements can be represented by the formula

n. A+ n1. B+ng. C + nz . D + ...

when n, n, n,, n, represent whole (generally small) numbers. The values A, B, C, &c. are the fundamental constants of stachiometry.

§ 6. Atomic Hypothesis.-The stochiometric laws are purely empirical, and were discovered by induction. They have been confirmed by thousands of experiments, and their validity is independent of any hypothesis. But the human mind suspects a cause for every law, and is disinclined to acknowledge the existence of a law unless it can account for the cause of it.

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