Popular Science Monthly/Volume 56/April 1900/A Hundred Years of Chemistry I
A HUNDRED YEARS OF CHEMISTRY. |
By F. W. CLARKE,
CHIEF CHEMIST, UNITED STATES GEOLOGICAL SURVEY.
IT is hardly an exaggeration to say that chemistry, as a science, is the creation of the nineteenth century. Chemical facts, indeed, were known even in remote antiquity; some principles were dimly anticipated long before the century began; Boyle had given the first rational definition of an element; the principal gases had been discovered; great foundations were laid, ready for the superstructure. But the making of bricks is not architecture, nor does the accumulation of details constitute a science. The scattered facts are needful preliminaries, but only with the discovery of laws and the development of broad generalizations does true science begin.
That truth can be born from error may seem paradoxical, but, nevertheless, the statement is exact. False hypotheses stimulate investigation, and so truth comes at last to light. In the history of chemistry this principle is clearly illustrated. During the eighteenth century the doctrine of phlogiston was generally accepted; this led to exhaustive researches upon combustion, and from these the science of chemistry received its present shape. Becher and Stahl had taught that every combustible substance contained a combustible principle—phlogiston—and that to the elimination of this principle the phenomena of combustion were due. According to this theory, a metal was regarded as a compound of its calx, or oxide, with phlogiston; hydrogen became a compound of water with phlogiston, and so the truth was curiously inverted. The doctrine was vigorously and ingeniously defended, and, although it was overthrown by Lavoisier, it had persistent supporters even after the present century began.
The weak point of the phlogistic theory was its practical disregard of the phenomena of weight. That the calx weighed more than the metal was well known, but quantitative considerations were subordinated to those of quality, and the form of matter was studied rather than its mass.
In 1770 the scientific career of Lavoisier began, and the balance became a chief instrument in chemical research. The constancy of weight during chemical change was experimentally established, and what had been a philosophical speculation—the increatability and indestructibility of matter—became a doctrine of science, a datum of knowledge instead of a hypothetical belief. In 1774 Priestley and Scheele independently discovered oxygen, and with the aid of the balance the phenomena of combustion were rendered intelligible. The foundations of chemistry were laid, and upon them the nineteenth century has built. Lavoisier, the greatest of the founders, fell a victim to the guillotine; the judge who condemned him refused all appeals for mercy, saying "the republic has no need for savants," but the necessity which judicial ignorance could not foresee presently made itself felt. France, at war with all Europe, her ports closed to supplies from without, fell back upon her own resources. Saltpeter was needed for her guns, alkali for her industries, and the chemist was called upon for help. The stress of continued warfare stimulated intellectual activity, and one result was the creation of chemical processes which revolutionized more than one industry. The dependence of modern civilization upon science then began to be recognized—a dependence which is, perhaps, the chief characteristic of the present century.
With the opening of the new century a period of great activity began. The constancy of matter was well established, and the fundamental distinction between elements and compounds was clearly recognized; two starting points for exact research had been gained. Only a small number of elements, however, had been identified as such; of some substances it was doubtful whether they were elementary or not, but the mine was open and a rich body of ore was in sight. Furthermore, the utility of research had become evident, so that intellectual curiosity received a new stimulus and a new direction. Theory and practice became partners, and have worked together to this day.
Between the years 1803 and 1808 one of the greatest advances in scientific chemistry was made, when John Dalton announced and developed his famous atomic theory. In this we find a notable illustration of the difference between metaphysics and science. The conception of matter as made up of atoms, as discrete rather than continuous, was a commonplace of philosophical speculation. It had been taught by Democritus and Lucretius; it was the theme of wordy wrangles during centuries; Swedenborg, Higgins, and other writers had sought to apply it to the discussion of chemical phenomena; but it remained only a speculation, unfruitful for discovery. Up to the time of Dalton it had led to nothing but intellectual gymnastics.
A good scientific theory is never a product of the unaided imagination; it must serve some purpose in the correlation of phenomena which suggest it to the mind. This was the case with Dalton's discovery, which grew out of his observations upon definite and multiple proportions. That every chemical compound has a fixed and definite composition was recognized by Lavoisier, and by other chemists before him; but the fact was disputed by Berthollet, and its verity was not established until 1808. Dalton went a step further, and found that to every element a definite combining number could be assigned, and that when two elements united in more than one proportion even multiples of that number appeared. Thus, taking the hydrogen weight as unity, oxygen always combines with other elements in the proportion of eight parts or some simple multiple thereof, and so on through the entire list of elementary bodies. Each one has its own combining weight, and this was the law for which Dalton sought an adequate explanation. Fractions of the weights did not appear, fractional atoms could not exist; the two thoughts were connected by Dalton. Chemical union, to his mind, became a juxtaposition of atoms, whose relative weights were indicated by their combining numbers, and so the atomic conception for the first time was given quantitative expression. The facts were co-ordinated, the special laws were combined in one general theory, and the mere suppositions of other men were supplanted by a precise statement, which is a corner stone of chemistry to-day. The doctrine led at once to investigations, it rendered possible the discovery of new truth, chemical formulæ and chemical equations were developed from it; without its aid the growth of chemical science would probably have been slow. The nature of the atoms may be in doubt, they may be divisible or indivisible, but the value of the theory is independent of such considerations. It gives adequate expression to known laws, and it can only be set aside, if ever, by absorption into some wider and deeper generalization.
The same year which saw the completion of Dalton's theory (1807) was also signalized by the remarkable discoveries of Sir Humphry Davy, who decomposed the alkalies and proved them to be compounds of metals. In 1810 chlorine, which was previously thought to be a compound, was proved to be elementary, and this fact was emphasized a year later by the discovery of iodine. These researches gave precision to the conception of an element, and prepared the way for later investigations upon many other oxides. All the so-called "earths"—lime, magnesia, alumina, and so on—were now seen to be oxy-compounds of metals, and an intelligent interpretation of all forms of inorganic matter became possible. The first step in the chain of research was the discovery of oxygen itself; from that, and from the teachings of Lavoisier, the later discoveries logically followed.
While the investigations of Dalton and of Davy were still incomplete, other chemists were actively studying the properties of gases and exploring the fertile border-land between chemistry and physics. In 1805 Gay-Lussac and Humboldt determined the composition of water by volume; in 1808 Gay-Lussac extended these observations, and found that in all compound gases simple volumetric relations existed; and in 1811 the entire subject was generalized into Avogadro's law. Avogadro showed that equal volumes of gases, compared under equivalent conditions, must contain equal numbers of molecules, and although the force of his discovery was not fully appreciated until much later, it is now recognized as one of the fundamental propositions of both physics and chemistry. For the first time the distinction between atoms and molecules was clearly stated, and from the density of a gas the relative weight of its molecule could be calculated. Avogadro's law rounded out and completed the atomic theory, and to its application much of the advance in organic chemistry is due. Equally striking, but less far-reaching in its consequences, was the discovery announced by Dulong and Petit in 1819, when it was shown that the specific heat of an element was inversely proportional to its atomic weight. Otherwise stated, this law asserts that the atoms of all the elements have the same capacity for heat, and an important check upon determinations of atomic weight was thus provided.
The next twenty years in the history of chemistry were years of detail rather than of permanent generalizations. The multitudinous verification of known laws, the development of experimental methods, especially methods of analysis, the discovery of new elements, the preparation of numberless new compounds, occupied the attention of most workers. This period, which may be called the Berzelian period, was enormously fruitful in results, although but few of the theories then proposed have survived to the present day. During this period the name and influence of Berzelius overshadowed all others, and his marvelous researches, carried out in a laboratory which was hardly more than a kitchen, were of almost incredible variety. For the crude symbols of Dalton, Berzelius substituted a system of chemical formulæ which could be used in chemical equations; in 1818 and 1826 he published tables of atomic weights, determined with far greater exactness than ever before; he discovered five new elements and a multitude of compounds, devised methods of research, and proposed theories which, though later to be overthrown, for many years dominated chemical science. His electro-chemical experiments led him to his dualistic theory of compounds, which interpreted each compound as made up of two parts—one positive, the other negative. The electro-positive oxides were basic, the electro-negative groups were acid; chemical affinity was electrical attraction between the two opposites; chemical union implied a neutralization of one by the other. These ideas were more than speculation, for they rested upon experiment and led to further experimental research; but they went too far, and therefore could not last. The theory, however, contained much that was true, and the formulæ developed by it gave the first general suggestion of what is now known as chemical structure or constitution. The later study of organic compounds led up to the modern views.
Although Berzelius and many other chemists did some work upon organic compounds, their era was chiefly identified with inorganic researches. Mineral chemistry received a great deal of attention, the relatively simple acids, bases, and salts were studied, but the compounds of carbon were thought to be more complex and received less consideration. To-day, at the close of the century, nearly seventy thousand organic compounds are known, and of these comparatively few were discovered before the year 1830. Since then organic chemistry has been the dominant line of investigation.
Among the earlier chemists of the nineteenth century it was commonly supposed that organic and inorganic matter were radically different, and that the former could only be produced by the operation of a peculiar vital force. To this view there were some dissentients, Berzelius among them, but experimental proof for their contention was lacking. In 1827, however, Wöhler succeeded in transforming the inorganic ammonium cyanate into the organic urea, and the barrier was broken down. The era of synthetic chemistry had begun. Still earlier, in 1823, Liebig had found that silver cyanate and silver fulminate possessed the same percentage composition; in 1825 Faraday discovered an isomer of ethylene; and Wöhler's research now gave a third example of the same kind. Two different substances could contain the same elements in the same proportions, and to explain this fact Berzelius inferred different arrangements of atoms within the molecule, and suggested that their mode of union might be determined. A working theory, however, was still lacking, and without it progress was necessarily slow. The dualistic hypothesis explained the phenomena only in part, and as the known facts increased in number it had to be abandoned.
Two important investigations paved the way for an advance. In 1832 Liebig and Wöhler, studying benzoic acid, found that it and its derivatives contained in common a group of atoms, not isolable by itself, to which they gave the name of benzoyl. The conception of such a group, a compound radicle, already existed, but it lacked clearness, and now for the first time it became truly a scientific idea. The search for, and the identification of, compound radicles began to occupy the attention of chemists, and a definite line of attack upon organic matter was recognized.
Two years later the second great step was taken. Dumas, studying the action of chlorine upon acetic acid, showed that the chlorine could replace hydrogen atom for atom, or volume for volume, and that his observations explained other reactions which had been unintelligible hitherto. This research led him to the famous theory of substitutions, which at first was received with ridicule, but soon found general acceptance. Electro-chemical conceptions, the Berzelian doctrines, were then in vogue, and it seemed strange, even absurd, to suppose that electro-negative chlorine could be substituted for electro-positive hydrogen. But the facts were stronger than the preconceived ideas, and the latter soon gave way. In this discovery by Dumas the first germs of the modern theory of valence are to be found.
For the study of inorganic substances, however, the dualistic theory was long retained, with the result that inorganic chemistry degenerated to a great extent into analysis and compound making, without any general conceptions which could stimulate scientific advance. It became a science of details rather than of principles, and was soon overshadowed by the organic branch. In the latter, theory after theory sprang up, flourished, and died away, each one having partial truth, but none being exhaustive and final. Still, the intellectual activity led to discoveries, and the warfare between doctrines, unlike the warfare between men, was productive of good instead of destruction. From the conflict of ideas the truth gradually emerged, and a new system of chemical philosophy was developed. The theory of compound radicles, the nucleus theory, the theory of types, the conception of conjugated compounds, followed rapidly one after the other, until in the discovery of valence all discrepancies were reconciled, structural chemistry came into existence, and a single doctrine, applicable alike to organic and inorganic substances, had possession of the field.
The theory of valence was a logical outgrowth from its predecessors, whose valuable features it included in a wider generalization, but it was the work of no one master mind. Many chemists contributed to its up-building, Frankland and Kekulé being among the leaders; but its foundations are to be detected in the atomic theory itself, from which it is legitimately derived. To understand its full significance we must take a step backward in history, and trace the change in atomic weights from their first form to the modern system.
In the early days of the atomic theory, in the determinations by Wollaston, Berzelius, and others, attention was chiefly paid to the atomic weights in their aspect of combining numbers. They were primarily of use as factors in chemical calculations, and chemists naturally sought for their simplest expressions, with little regard to theoretical considerations. The laws of Avogadro, of Dulong and Petit, had, indeed, been announced, but the adjustment of the atomic weights to meet their requirements was long neglected. The importance of the adjustment was not realized, for it was obscured by the prevailing dualistic theory, but without it the deeper general relations of the atoms could not appear. Accordingly, a system of chemical formulae grew up which was based upon a deceptive apparent simplicity of ratios, and by which the theory of valence could not be even suggested. The old formula for water, HO, expressed only its composition by weight, ignoring its composition by volume; it failed, therefore, to accord with Avogadro's law or to give the slightest hint as to the relations which are now covered by the conception of chemical structure. A part of the existing knowledge was accurately symbolized, but the larger part was ignored, a state of affairs which could not last, although the change came about but slowly.
The incentive to reform came from two sources. Physics, in the kinetic theory of gases, gave a new demonstration of the truth of Avogadro's law, and led chemists to realize more clearly than before the distinction between atoms and molecules. Soon it was seen that the molecule was the smallest particle of matter which could exist as such, while the atom was the smallest particle which could take part in any chemical change. The metaphysical atom was really the modern molecule; the chemical atom was a new conception, due to the discoveries of chemistry alone. This distinction was found to hold good even for elementary bodies, and it became evident that free hydrogen or oxygen must contain two atoms to the molecule, while phosphorus and arsenic contained four. With mercury the atom and the molecule are identical, but in most cases the greater complexity exists, and the elements as we see them are compounds of like atoms with each other. That hydrogen can unite with hydrogen, oxygen with oxygen, carbon with carbon, is a conception to which the early chemists never attained, but which is a necessary consequence of Avogadro's law in its application to observed phenomena.
The second impulse toward change originated in the study of organic compounds, and gained its force from the struggle between contending theories. The advocates of each theory sought for evidence in its favor, and so innumerable discoveries were made, compound radicles were recognized in great numbers, and the mass of data became so overwhelming that for a while chaos reigned. Classification of compounds became imperatively necessary, and to that all speculation was subordinated. In 1842 Schiel found that the alcohols formed a regular series, with progressive variation in their properties; Dumas observed a similar relation among the fatty acids, and so something like order began to appear.
In 1843 Charles Gerhardt proposed to use the law of Avogadro as a basis for the determination of atomic weights. This involved the doubling of many existing values, especially the atomic weights assigned to oxygen, carbon, and sulphur. At first the proposition was violently opposed, and even ridiculed, but by slow degrees it managed to make its way, although it was not until after 1858 that it began to find anything like general acceptance. In that year Cannizzaro put forth his revision of the atomic weights, adjusted to accord with physical laws, and a new era in chemistry began. The modern theories of chemistry became possible, and the many researches in which they had been foreshadowed received a clearer meaning. Cannizzaro did not stand alone; his work was but the capstone of a structure which had long been growing; Liebig, Dumas, Laurent, Gerhardt, Wurtz, Graham, Williamson, and Frankland were among the builders. But at last chemical and physical evidence were brought into full convergence, and each gave emphasis to the other.
During the formative period of the new doctrines, between 1840 and 1858, many discoveries were made which helped toward the final consummation. Even earlier than this the researches of Graham upon the phosphoric acids had familiarized chemists with the idea that different substances might have very different combining powers, and other polybasic acids were found to exist among organic compounds. The discovery by Wurtz, in 1849, that the hydrogen of ammonia was replaceable by organic radicles, forming the compound ammonias or amines, was a logical extension of the theory of substitutions; and the recognition at about the same time, by Hofmann, of ammonia as a distinct type upon which many other substances could be modeled, was another long step forward. In 1851 Williamson argued that nearly all inorganic and many organic molecules could be represented as analogous in structure to water, and a year later, as a result of his researches upon the organo-metallic bodies—zinc ethyl, tin ethyl, etc.—Frankland expressed the belief that every elementary atom has a definite combining power which limits the number of other atoms capable of direct union with it. This was the theory of valence in its first and simplest form, undeveloped to its consequences, but unmistakably clear. To carbon compounds in general it was yet to be applied.
In 1858 the work of Cannizzaro appeared, and a general revision of chemical formulæ became necessary. The advanced views which a few chemists had held began to find a more general acceptance, and the significance of the change was gradually realized. In the same year Kekulé showed that the atom of carbon, had a combining capacity of four, and furthermore that in many organic compounds the carbon atoms were in part united with each other, and even linked, as it were, into chains. Still later, studying benzene, he found that its six carbon atoms were best regarded as joined together in the form of a closed ring, and with this conception the idea of chemical structure received at last a definite form. These linkages of atoms, these rings and their derivatives, could all be represented graphically to the eye, in accordance with the combining power of the several elements, and so the structural formulæ of modern chemistry came into vogue. Types, substitutions, compound radicles, were all covered by and included in the new generalization, and each of the older theories was seen to be but an expression of special cases, rather than of any general law. No truth was set aside, but all were co-ordinated.
To the non-chemical reader the foregoing passages may seem vague and abstruse, but in an essay of this scope greater elaboration is inadmissible. It is clear, however, that each forward step has been a logical development of the atomic theory, which, as we shall see later, does not end even here.
Thus, then, the chemical formulæ and atomic weights of Berzelius grew by slow degrees into the modern system, with its representations of structure and atomic linking. The internal architecture of the molecule was now revealed not to the imagination only, but to the eye of reason, and, speculative as the new conceptions may seem at first, they have led to astonishing practical consequences. The new formulæ at once indicated lines of research, and with their aid synthetic chemistry was greatly stimulated. True, many syntheses of organic compounds had already been made, but progress became more rapid and the work of discovery was systematized to a wonderful degree. In 1856 Perkin discovered the first of the coal-tar dyes, creating a new industry which has been assisted beyond measure by the structural symbols that came into use only a few years later. In 1868 alizarin, the coloring principle of madder, was made artificially from the hydrocarbon anthracene; a host of other colors, a veritable chemical rainbow, have been discovered; the synthesis of indigo has been effected; and within twenty years we have seen medicine enriched by a great variety of drugs, all prepared by purely chemical processes from the former waste material—coal tar. To most of this work, at least since 1865, Kekulé's conception of the benzene ring has been the guiding clew, and it is certain that without the theory the practice would have advanced much more slowly. Out of research for its own sake has come an enrichment of the world, which in any previous age would have been inconceivable.
The atomic theory, while replacing speculation in one sense, stimulated it in another. The human mind is always striving to get back of the known, to see what lies beyond the limits of visibility, and the conception of an element with its atomic weight opened up a field for the exercise of the imagination. What is an element ultimately? was an early question to ask. Are the elements really diverse, or do they manifest but one fundamental kind of matter? To such queries the atomic weights offered a promising line for investigation, and more than one mind began traveling along it. In 1815 Prout put forth the supposition that all atomic weights were even multiples of that assigned to hydrogen, and over this hypothesis a long warfare has raged. To-day it is practically abandoned by chemists, but the controversy which it provoked led to some of the most accurate investigations in the history of science, and so served to give precision to our knowledge. Without the instigation of Prout's hypothesis, which hinted at hydrogen as the ultimate form of matter, we might have been content with inferior determinations of atomic weight, and chemistry, as an exact science, would have suffered.
In due time, however, it was perceived that the elements could be arranged in groups, the members of each group having similar properties and forming similar compounds. Serial relations, analogous to those discovered among organic compounds, became manifest, and much thought was expended in seeking to trace out their meaning. The classification of the elements was more and more seen to be important, and regularities came to light which at first were unsuspected. Still, no general law, no one guiding principle, could be found so long as the old system of weights and formulæ was retained in common usage.
The adoption of Cannizzaro's atomic weights and the establishment of the theory of valence made possible a new attack upon the problem of classification. In 1864 Newlands arranged the elements in the order of their atomic weights, and showed that at regular intervals there was a periodic recurrence of certain characteristics. This observation, which foreshadowed the periodic law, was received with indifference and, to some extent, with ridicule, but the path had been found which soon led to a great discovery. In 1869 Mendelejeff published his celebrated memoir, and the periodic law took its place as a distinct addition to science. Almost simultaneously Lothar Meyer announced similar views, but independently, and controversy soon arose as to the relative merits of the two philosophers. With that controversy we have nothing to do, but the law itself deserves our fuller attention.
According to the periodic law, all the properties of the elements are periodic functions of their atomic weights, varying from substance to substance in a perfectly regular manner. The elements thus fall into periods, or octaves, as Newlands called them, of a very striking character. If, for example, we start with univalent lithium, the next higher element has a valence of two, the next of three, and then comes carbon, whose atom is quadrivalent. Following carbon, the combining power of successive elements decreases until we reach sodium, in which something like the properties of lithium recur. Above sodium the same rise goes on to the fourth element higher, silicon, which resembles carbon, and then follows the regular step-by-step falling away, to end with chlorine, the last member of the second period. This periodic rising and falling is characteristic of all the elements, and they were so tabulated by Mendelejeff as to be perfectly clear, with a clearness which is not to be given by words. In Mendelejeff's table certain gaps appeared, which he ascribed to the existence of undiscovered metals. Tor three of these he predicted the properties, starting out from the properties of their neighbors. This was a rash thing to do, but the venture has been fully vindicated. In 1875 Lecoq de Boisbandram discovered gallium, which filled one of the gaps; scandium and germanium filled the other two later. The predictions of Mendelejeff were fulfilled; atomic weight, specific gravity, fusibility, the character of the compounds to be formed, were all foreseen for each of the three new elements; and, so far as experiment has yet gone, his anticipations have been perfectly realized. Every good theory is prophetic; but few generalizations have been so strikingly verified in this respect as has the periodic law. In spite of some outstanding difficulties, yet to be explained, the law has served to great advantage in the classification of the elements, and it has had much to do with the late revival of inorganic chemistry. The latter branch of science, long comparatively neglected, has now gained new interest, and for it, in the near future, a great growth can be prophesied.
The immediate effect of the periodic law was to prove that the elements are connected with one another by general relations, and so to stimulate the belief in their possibly common origin. This view has many upholders, although it is also strongly opposed, but the weight of argument seems to be in its favor. On philosophic grounds it is at least more probable than the opposite opinion, which can not account in any way for the regularities which have been observed. From another source, partly physical and partly chemical, the theory of the unity of matter has received strong support, and this statement brings us to another of the greatest discoveries made during the nineteenth century—that of the spectroscope and spectrum analysis.
It was in 1860 that Kirchhoff and Bunsen added this new weapon to the arsenal of scientific research. The spectroscope itself, as an instrument, was an invention in the department of optics, but its applications to chemistry were among the most obvious and the most startling of its achievements. With its aid new elements were discovered—rubidium, cæsium, thallium, indium, and gallium; in many lines of investigation it found immediate use; but, more than all, it made possible the analysis of the heavenly bodies, and proved that the same kinds of matter exist throughout the visible universe. Before the day of the spectroscope all speculation upon the chemistry of the stars was in vain; with its advent the material unity of planets, suns, and nebulæ was made clear. To the astronomer, a new eye was given; to the chemist, a new laboratory. Three sciences were brought to a single focus, and each one gained in power thereby.
In its application to what may be called chemical astronomy, one achievement of the spectroscope was particularly notable—namely, the rehabilitation of the nebular hypothesis. When the gigantic telescope of Lord Rosse had resolved some nebulæ into clusters of stars, it was thought that all other nebulæ might be of the same character; the visible basis of the hypothesis was gone. But the spectroscope soon found among these celestial objects some which were truly clouds of incandescent gas, and so the nebular hypothesis received a new standing, becoming stronger than ever before. One point, however, was strange: these gaseous clouds were of the simplest composition; hydrogen and nitrogen were their chief constituents; how, then, could a world like ours originate from them?
Further investigation, to which Huggins and Secchi were the chief contributors, showed, however, that from nebula to planet there is a regular, progressive order of chemical complexity. The nebulæ are simple; in the hotter stars a few more elements appear; more still can be detected in colored stars and the sun; but the planets, represented by our earth, are most complex of all. So far the facts; the scientific imagination now comes into play. If suns and planets were derived by a process of condensation from such nebulæ as exist to-day, perhaps the process of evolution was attended by an evolution of the chemical elements themselves. Upon that supposition the facts become intelligible; without it the evidence is not easily co-ordinated. This hint, together with the suggestions offered by the periodic law, has made chemists more ready to consider the probable unity of matter, even though actual proof for or against the conception has not yet been attained. That the chemical elements are absolute and final few thinkers of to-day believe; the drift of opinion is mainly in one direction, but no element has yet been decomposed or transmuted into another. Some mathematical relations have been found connecting the atomic weights of certain elements with the wave lengths of their spectral lines, and this field of investigation is a promising one for the future. That the atomic weights are connected hardly admits of doubt; to the mass of the atom its rate of vibration must be related; to that vibration the lines in the spectrum are due. The clews are obvious, and it will be strange if they do not lead to important discoveries ere long.
[To be concluded.]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rule_Segment_-_Span_-_40px.svg/40px-Rule_Segment_-_Span_-_40px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rule_Segment_-_Span_-_40px.svg/40px-Rule_Segment_-_Span_-_40px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Rule_Segment_-_Flare_Left_-_12px.svg/12px-Rule_Segment_-_Flare_Left_-_12px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Rule_Segment_-_Span_-_5px.svg/5px-Rule_Segment_-_Span_-_5px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/28/Rule_Segment_-_Circle_-_6px.svg/6px-Rule_Segment_-_Circle_-_6px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Rule_Segment_-_Span_-_5px.svg/5px-Rule_Segment_-_Span_-_5px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Rule_Segment_-_Flare_Right_-_12px.svg/12px-Rule_Segment_-_Flare_Right_-_12px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rule_Segment_-_Span_-_40px.svg/40px-Rule_Segment_-_Span_-_40px.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Rule_Segment_-_Span_-_40px.svg/40px-Rule_Segment_-_Span_-_40px.svg.png)