Higher Mathematics for Chemical Students (1911)

• The statement of a law of nature involves the formation of a concept, or general idea, in which the likenesses of phenomena are collected, and the differences, in so far as they are not intimately involved in the nature of the case, are eliminated.
  • Introduction

• To a person whose experience has never been brought into relation with the object sulphur, the name signifies nothing; to the scientist... his concept involves the ideas of specific gravity, crystalline form, element, atom, and the like, derived from past experiences. His concept is distinguished from the other by involving... number or quantity.
  • Introduction

• The earliest chemical theory was qualitative in the strictest sense; the so-called Aristotelean doctrine of the four elements assumed that air, water, earth, and fire, were qualities impressed on a primal matter; and the changes of material bodies were explained by the assumption that properties could be taken up by, and impressed upon, or removed from, the base-stuff. Transmutation as a possibility followed at once, and centuries of vain endeavour were required to impress the fact of its impossibility, leading to the true concept of element.
  • Introduction

• The quantitative investigations of Black on the burning of lime and magnesia alba, in which the balance (previously characterized by the French chemist Jean Rey as "an instrument for clowns") was applied at every turn, led to the rejection of a hypothetical "principle of causticity," and replaced it by a "sensible ingredient of a sensible body," fixed air.
  • Introduction

• The extension of Black's method by the physicist Lavoisier led to the downfall of the purely qualitative theory of phlogiston, and gave to chemistry the true methods of investigation, and its first great quantitative law—the law of conservation of matter.
  • Introduction

• Wenzel and Richter, the latter... of most pronounced mathematical temperament, laid the foundations of stoichiometry, or "the art of measuring the chemical elements".
  • Introduction

• Dalton, the mathematical tutor, following up the lead of Newton, combined the whole of the results of quantitative measurement which had accumulated up to his time, in a comprehensive theory, based on the concept of the chemical atom.
  • Introduction

• The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory.
  • Introduction

• As an instance of the remarkably far-reaching effect which a single mathematico-physical concept has had upon the development of chemical theory, one has but to recall the state of chemistry just before the revival of Avogadro's law by Cannizzaro, to be impressed by its confusion. Relying solely upon their "chemical instinct," the leaders of the various schools of chemical thought had developed each his own theoretical system. ...a host of ...conceptions strove for supremacy. The strife was stilled, order and unity were restored, as soon as Avogadro's great idea was seen in its true light, and the concept of the molecule was introduced into chemistry. A formula which had required pages of reasoning from a purely chemical standpoint to establish, and that insecurely, was fixed by a single numerical result.
  • Introduction

• There are not wanting, even to-day, chemists who advocate "purely chemical" methods in chemistry, and cannot appreciate the value of physical evidence in conjunction with mathematical calculations. We can only hope that their number is decreasing exponentially with time.
  • Introduction

• From the time when Guldberg and Waage gave quantitative form to the speculations of the physicist Berthollet, a clear conception of chemical equilibrium, in sharp contrast to an anthropomorphic theory of affinity dating back to Hippocrates and Barchausen, has yielded rich and abundant fruit.
  • Introduction Note: Johann Conrad Barchusen was the author of Pyrosophia (1698)

• The philosopher Comte has made the statement that chemistry is a non-mathematical science. He also told us that astronomy had reached a stage when further progress was impossible. These remarks, coming after Dalton's atomic theory, and just before Guldberg and Waage were to lay the foundations of chemical dynamics, Kirchhoff to discover the reversal of lines in the solar spectrum, serve but to emphasize the folly of having "recourse to farfetched and abstracted Ratiocination," and should teach us to be "very far from the litigious humour of loving to wrangle about words or terms or notions as empty".
  • Introduction

• An explanation of a phenomenon is regarded, apparently instinctively, as the most general possible when it is a mechanical explanation. The "mechanism" of the process is the ultimate goal of experiment. Now this mechanism in general lies beyond the range of the senses; either by reason of their limitations, as in the case of the atomic structure of matter, or by the very nature of the supposed mechanism, as in the theory of the ether. The only way to bridge the gap between the machinery of the physical process and the world of sense-impressions is to think out some consequence of that mechanism. This we will call the hypothesis. The hypothesis, resting still on the mechanical basis, is yet beyond the range of direct experimental investigation; but if, by mathematical reasoning, a consequence of the hypothesis can be deduced, this will often lie within the range of experimental inquiry, and thus a test of the soundness of the original mechanical conception may be instituted.
  • Introduction

• Disagreement between theory and experiment has proved a most potent agent in broadening theoretical views, and in making clear the necessity for new concepts or hypotheses.
  • Introduction

• It is necessary to guard against a possible danger... of submitting too readily to the result of a so-called "crucial experiment". Very few experiments can, in the nature of things, be really crucial. One so-called "crucial experiment" which decided between Newton's corpuscular theory of light and Huyghens' wave-theory, viz. the relation between the law of refraction and the velocity of light, was not at all decisive.
  • Introduction

• We perceive clearly that theories and hypotheses are not accepted or rejected outright; they have their periods of activity, and then lie dormant for a time, only to be revived in a new form later on.
  • Introduction

• The fundamental materials from which we construct our picture of the universe may appear in different shapes, but there is really very little discontinuity between what seem at first sight very different views.
  • Introduction

• It is clear, however, that the distinguishing mark of the whole development of theoretical chemistry and physics is the elimination of the anthropomorphic elements, especially specific sense-impressions, from the concepts. This process is called by Prof. M. Planck the objectification of the physical system.
  • Introduction Note: Max Planck, "Acht Vorlesungen iiber theoretische Physik" (1910)

• In early physical systems we have optics dealing with phenomena perceived by the eye; acoustics treating of auditory percepts, and so on. The subjective concepts of "tone" and "colour" have now been replaced by the objectified concepts of frequency of vibration; and wave-length. The object of this process of elimination is, according to Planck, the striving towards a unification of the whole theoretical system, so that it shall be equally significant for all intelligent beings.
  • Introduction

A Short History of Chemistry (1937)

• The earliest applications of chemical processes were concerned with the extraction and working of metals and the manufacture of pottery. ...The irruption of an iron using race or races into Mediterranean sites ...introduced the Iron Age... but many of the oldest arts still survived in almost their original form. The potter, for example, still used nearly the same materials and appliances as Neolithic man.

• Side by side with the production of metals, the Egyptians and the inhabitants of Mesopotamia perfected the arts of making glazed pottery... and the production of glass. ...vessels were baked in tall closed furnaces. "Egyptian blue" was made in Egypt by heating silica with malachite and lime... applied with soda as a blue glaze on faience, and the blue glass is also colored with copper. Some early... Egyptian and Babylonian blue glass are coloured with cobalt.

• The blue dye indigo was obtained from the indigo plant by the Egyptians more than 4000 years ago. ...The famous and valuable "purple of Tyre" was perhaps first made in Crete in very early times... obtained at great cost... from tiny marine molluscs. ...The scarlet dye mentioned in the Bible was obtained from the kermes insect (hence the name "crimson").

• The first clear expression of the idea of an element occurs in the teachings of the Greek philosophers. ...Aristotle ...who summarized the theories of earlier thinkers, developed the view that all substances were made of a primary matter... On this, different forms could be impressed... so the idea of the transmutation of the elements arose. Aristotle's elements are really fundamental properties of matter... hotness, coldness, moistness, and dryness. By combining these in pairs, he obtained what are called the four elements, fire, air, earth and water... a fifth, immaterial, one was added, which appears in later writings as the quintessence. This corresponds with the ether. The elements were supposed to settle out naturally into the earth (below), water (the oceans), air (the atmosphere), fire and ether (the sky and heavenly bodies).

• A great number of our common ideas and ways of looking at the world were really shaped for us by the Greeks of antiquity, and... incorporated into the scientific knowledge of today. Such ideas as those of matter, force, element, number, space, time, etc., came to us from the ancient Greeks.

• We find Theophrastus (315 B.C.) describing... the manufacture of white lead... "lead is placed in an earthen vessel over sharp vinegar, and after it has acquired some thickness of a kind of rust... they open the vessels and scrape it off. ...repeating over and over again... til it is wholly gone. What has been scraped off they then beat to a powder and boil with water for a long time, and what at last settles to the bottom is white lead.

• In Alexandria two streams of knowledge met and fused together... The ancient Egyptian industrial arts of metallurgy, dyeing and glass-making... and... the philosophical speculations of ancient Greece, now tinged with ancient mysticism, and partly transformed into that curious fruit of the tree of knowledge which we call Gnosticism. ...the result was the "divine" or "sacred" art (...also means sulphur) of making gold of silver. ...during the first four centuries a considerable body of knowledge came into existence. The treatises written in Greek... in Alexandria, are the earliest known books on chemistry. ...The treatises also contain much of an allegorical nature... sometimes described as "obscure mysticism." ...the Neoplatonism which was especially studied in Alexandria... is not so negligible as has sometimes been supposed. ...The study of astrology was connected with that of chemistry in the form of an association of the metals with the planets on a supposed basis of "sympathy". This goes back to early Chaldean sources but was developed by the Neoplatonists.

• The Greek chemical treatises contain... a great amount of practical chemical information... fusion, calcination, solution, filtration, crystallization, sublimation and especially distillation; and methods of heating include the open fire, lamps, and the sand and water baths. Nearly all this practical knowledge... the Arabs... derived... from the very source we are now considering.

• The Alexandrian chemists were very near to a recognition of gases.

• The Chinese early learned to work in metals; bronze occurs in the 11th-10th centuries B.C., useful iron from about 500 B.C. At a later period they made brass... True porcelain was first made about A.D. 600. They were probably in possession of mercury at an early date, and learnt how to decompose cinnabar into mercury and sulphur, and recompose it from these materials.