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A Text-Book of Physics

Revised Edition

By L. B. SPINNEY, Professor of Physics at Iowa State College. Cloth, Octavo, about 625 pages. To be ready in September.

In revising this book the author has aimed primarily to increase its teachability and to make the discussions clearer. Among the important changes are: a rearrangement of the chapters on electricity, the introduction of recent investigations concerning X-rays, an amplified consideration of Newton's laws, the use of both the ray and wave front in diagrams for reflection of light, and a description of the vacuum tube with its application in radiotelegraphy and radiotelephony. New problems have been provided throughout the book.

Plane Trigonometry

By JOHN W. YOUNG and FRANK M. MORGAN, Professors of Mathematics at Dartmouth College. Cloth, 12mo, 122 pages, $1.50.

This new Plane Trigonometry emphasizes the numerical aspects and applications of the subject. It embodies the characteristic features of the widely approved sections devoted to trigonometry in the authors' earlier work, " Elementary Matematical Analysis."

Logarithmic and Trigonometric Tables Revised

Edition

Prepared under the direction of EARLE R. HEDRICK, Professor of Mathematics in the University of Missouri. Cloth, 12mo. To be ready in September.

This revised edition of the widely used "Macmillan Tables" contains several tables not included in the earlier book. New tables are added to complete the tables of hyperbolic functions; a table of haversines will be welcomed by those interested in navigation; tables of factors of composite numbers, logarithms of primes, compound interest, annuities, depreciation, etc., are among the new sections.

Vertebrate Zoology

By HORATIO H. NEWMAN, Professor of Zoology and Embryology in the University of Chicago. Cloth, Octavo, 432 pages, $3.00.

This volume is intended for use as a textbook in college courses in vertebrate zoology and comparative anatomy. Professor Newman approaches his subject from the dynamic rather than structural point of view; thus the physiological, phylogenetic, ecological and evolutionary aspects of vertebrates are particularly emphasized. Careful attention is given to the anatomical facts and data of extant species of animals, but the forms are placed in their setting and viewed as modern end-products of the evolutionary process.

Essentials of Psychology

Revised Edition

By W. B. PILLSBURY, Professor of Psychology in the University of Michigan.
Cloth, 12m0, 428 pages, $1.90.

In preparing this revised edition the book has been entirely reset. The chapter on Emotion has been largely rewritten, the chapter on Memory has been expanded, there is a new chapter on Types of Mind, dealing with some of the more general results of mental testing; and numerous minor changes have been made in every chapter. At various points in the book reference is made to the theories and research of Freud, Pawlaw, Watson, and other important psychologists whose influence has been most marked in recent years. The questions and exercises at the end of chapters have been revised and improved.

THE MACMILLAN COMPANY

PUBLISHERS

NEW YORK

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THE STRUCTURE OF THE UNIVERSE1 THE phrase, “ the structure of the universe," is apt to bring to mind only the great and majestic forms which are revealed to us by the telescope, the stars, nebula and galaxies. In the present discussion however I wish to include in one view the entire range of physical things from the infinitesimal to the infinite; for to the mathematician there is no such thing as absolute size-a thing is either large or small only by comparison. Up to the present time we have succeeded in extending our vision equally, so to speak, in both directions. We find ourselves almost midway in a series of physical units. On the one side we have the electrons, atoms and molecules, and on the other we have the ordinary masses, stars and galaxies. The galaxies are more or less definite aggregations of stars. The stars are amazingly great organizations of hot gases. The gases in turn are resolved into their constituent molecules; the molecules yield up their atoms, and finally we find that the atoms are built up of two kinds of electrons. Each physical unit is analyzed into units of the next lower order, and synthesized into those of the next higher order. Each unit is an organization endowed with the proper amount of energy to carry on its existence and to insure its identity.

Our direct vision is bounded on the one side by the electrons and on the other side by the galaxies. But the common properties of energy and organization lead us naturally to imagine that the electrons in their turn are organizations of still smaller units, let us call them sub-electrons; and the sub-electrons are organizations of still smaller units, and so on, ad infinitum. Turning to the other end of the series we can fancy that there are organ

1 Read before the Chicago chapter of the Sigma Xi, March 11, 1920.

izations of galaxies, say super-galaxies, and still higher organizations of super-galaxies, and so on without limit. To be sure this is mere speculation and rests upon no direct physical evidence. But let us not forget that even in the days when the atom was our smallest physical unit there were many men who refused to regard it as such upon grounds which were purely metaphysical. The mere fact that the physicists have been able to take one more step down the series by conquering the extraordinary experimental difficulties, and that the astronomers in their turn are beginning to perceive in the spiral nebulæ other galaxies than our own is quite encouraging to the purely metaphysical notion that the series of physical units is an unending one, without bottom and without top.

Thus we have a conception of an infinite, three-dimensional continuum of space about which we can move at will, at least within certain limits; a conception of an infinite one-dimensional continuum of time through which we move always in one direction, without choice on our part; and finally, a conception of an infinite one-dimensional series of physical units in which our position is fixed-it is only in thought that we can move along this series. If to these we add energy and consciousness, neither of which admit the notion of dimensions, we have perhaps exhausted the catagory of fundamental conceptions.

The physicists and astronomers have nothing to do with consciousness objectly. They are interested only in the conceptions of space, time, the series of physical units, and energy. In particular, they are interested in the properties of the physical units, the nature of their wonderful organizations and the flow of energy which is associated with them. The astronomers, fortunately, are able to furnish us with photographs of the objects with which they deal, so that we are able to study them more or less thoroughly one at a time. No two of the galaxies are alike in detail although in their broad outlines there are striking similarities. The globular cluster is one type of organization of which

we have some eighty specimens, and the spiral cluster is another, and of these we have some hundreds of thousands.

Descending from the galaxies to the stars we are unable to make out the structural details notwithstanding their vast size, owing to their still more vast remoteness. Only one specimen, our own sun, is sufficiently friendly to submit to anything like a close inspection. Nevertheless a classification of the stars according to their colors and their types of spectra is entirely possible. Thus the inherently brilliant white Orion-type stars have continuous spectra, save for a few broad lines of absorption due to helium and hydrogen, with a complete absence of the metallic lines. The brightest part of the spectrum is in the violet. Then come the stars of the solar type with the yellow as the brightest part of the spectrum, with many lines of hydrogen and the metals. Then the orange stars with metallic lines and absorption bands due to chemical compounds. Finally, the deep red stars with heavy absorption bands due to carbon compounds. The individualities of the stars, however, are preserved for no two of the spectra are exactly alike.

Nothing need be said with respect to ordinary masses, for they are matters of our everyday experience. No two leaves even from the same tree are exactly alike. But when we descend to the stage of the molecules the situation is very different. The physicists have not yet given us any photographs of them to study, and no one can say that he has ever seen a molecule. Their numbers are so amazingly great that an individual study of them is quite out of the question. Nevertheless, as the chemists assure us, classification is quite possible, and their variety is astonishingly great. But when we study the properties of even a single variety and attempt to work out their structural organizations we must not forget that it is only the properties common to large numbers which stand out and characterize the variety. If the human race could be studied only through the statistics of population, we might arrive at the conclusion that the Chinese are a

variety of the human race, but that one Chinaman was just like another. Analogy would lead us to doubt whether all the molecules even of water are alike. Could they be examined individually and in detail, marked differences would probably be found.

The case is similar with respect to the atoms, although the number of varieties of atoms seems to be limited while the number of varieties of molecules does not. Our information with respect to atoms is largely statistical. But even so, the chemists are recognizing the isotopes of the various elements, and certainly two varieties of lead are now known where previously we had but one; illustrating beautifully the principle that differences and individuality tend to grow with increasing acquaintance.

When we descend one more step in the scale of the physical units and reach the electrons, we are so remote from our own position in the scale and our acquaintance with these units is so far from being intimate that it is not surprising that we regard all positive electrons as being alike, and all negative electrons as being alike. We seem to have reached that ultimate simplicity for which the mind is always seeking. Nor is our information with respect to the electron entirely statistical, for Millikan has performed the amazing feat of measuring their electrical charges one at a time, and finds that in this respect they actually are measurably alike. So far then as we think of the electron as possessing the single property of the electrical charge we are justified in assuming that they are all alike. The human mind, however, is incurably speculative, and few of us, I fancy, would be willing to admit that this is their only property, or that the electrons really are all identical, or that the electron is not still further resolvable into smaller units.

Since the beginning of the present century the physicists have been very busy with the atom. The phenomena of radioactivity and of the X-rays have led them along a brilliantly lighted path in their exploration of its interior, and they have supplied us with verbal pictures of considerable clearness. The elec

trical charge of a positive electron is numerically equal to the electrical charge of a negative electron, but its mass is nearly two thousand times greater while its diameter is only one two-thousandths as great. If we could apply the ordinary notions of density to these statements we should have to say that the density of a positive electron is ten million million times the density of a negative electron, although its electrical charge is equal. But the ordinary notions of density perhaps do not apply.

If we accept the picture that a hydrogen atom consists of a negative electron moving in a circular orbit about a positive electron, we have so far as relative sizes and distances are concerned a veritable planetary system, except that the diameter of the satellite is two thousand times the diameter of the primary, for their distances apart are relatively as great as between the sun and Neptune. The nucleus of a helium atom has two free positive electrical charges and two negative satellites; lithium has three, and so on; there is a chemical element for each integral multiple up to 92 which belongs to the element uranium, with perhaps a half dozen gaps in the entire series; and furthermore, there is no chemical element which does not fit into the series. We have therefore a complete ordering of the chemical elements upon a purely numerical basis, which makes intelligible the periodic law of these elements which has been long known by the chemists on the basis of their chemical properties.

Notwithstanding the brilliant achievements of the physicists in their work with the atom their analysis is by no means completed. Many fascinating questions remain to be answered. For example, are all of the elements merely hydrogen atoms locked together in a very tight embrace, and if so will a sufficiently violent bombardment separate them? Rutherford's success in obtaining hydrogen from nitrogen by a bombardment with a-particles is certainly suggestive. If the answer is to be in the affirmative, what is the nature of this embrace? How do the electrons, positive and negative, arrange themselves?

How are the lines in the spectrum to be accounted for? And how does an atom radiate energy, anyway? It is a delightful situation for the mathematical physicist to face, for he has already achieved a very solid foothold, and we may be sure he will not be slow to push his advantage.

If the private affairs of the atom belong to the domain of the physicist, their social affairs belong to the chemist. And what tremendously social creatures they are! Few of them are content to live by themselves. The vast majority of them cling more or less tenaciously to other atoms or groups of atoms, and these groups are the chemists' molecules, the smallest particles of what we call ordinary matter. This grouping is not a mere random affair. The atoms exhibit a distinct choice not only as to their associates but as to the manner in which they will associate together. Just as the physicist has his problems as to the structure of the atoms so the analytical chemist is busy breaking up the almost infinite variety of molecules he finds about him to learn what atoms enter into their structure and what are the relations which exist between those atoms. In this endeavor he has been highly successful and the great majority of molecules he can read as an open book, but the subtile strain of carbon molecules will doubtless tax his ingenuity for a long time to come. On the other hand, the synthetic chemist is slowly learning how to coax the atoms into those particular groups which either his theory tells him are possible or for which nature herself has already furnished an example. In the domain of ordinary masses the architect and engineer, the painter and sculptor and the skilled artisans of a thousand varieties have learned how to build up their structures to suit their various purposes. But the physicists have not yet dreamed of building up an electron nor an atom. The biologists have little hope of ever constructing a living organism. The geologists are content to examine their rocks and to make the past live again in their vision; while the astronomers in the very nature of things must maintain a respectful distance

from the objects which engage their interest. Outside the domain of ordinary masses it is the synthetic chemist alone who can engage in the process of physical construction, the building up of those units which are the object of their study. The world is very greatly their debtor to-day, and this debt will increase enormously as the chemists rise higher and higher in their ability to control the groupings of the atoms in the molecules.

Our greatest familiarity and closest intimacy with nature naturally lies in that portion of the scale of physical units to which we ourselves belong, viz: ordinary masses. It is here that the geologists and biologists are at home. But so infinitely varied is the aspect here presented to us that these sciences divide and subdivide in their study of particular phases of things that we seem to have a whole host of sciences. To geology belong such sciences as meteorology, geography, paleontology, and mineralogy. Biology divides into the two great branches, zoology and botany, and these two branches subdivide and split up very much like the cells, about which they are so fond of talking, until one is actually lost in their numbers. Resting securely above these, at least so far as complexity of their phenomena is concerned, are the psychologists and sociologists.

Would an inhabitant of an atom, supposing him to be as small relatively as we are to the earth, find the world about him as complicated and varied as we find ours to be? Would he require a thousand and one different sciences, of which we do not even dream, in order to interpret what was going on about him and adapt things to his use as we are doing? Fortunately science does not have to answer, for there is no evidence. Science always turns away disdainfully when there is no evidence, and rightly so. It is none of her affair. But the same human being, if he is a scientist, is also a philosopher and a speculator. Perhaps he is a scientist because he is a philosopher and a speculator. At any rate, we can not but be impressed with the richness and luxuriance of our own field of units when we compare it with the poverty with which our mental pictures

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