Taboo and Totem
The practice of taboo and totemism, although one word comes to us from the South Seas and the other from the American Indians, is found all over the less civilized world, and—even more important—it explains many things in the social and religious life of more civilized communities. For instance, the account by modern students of Greek and Roman religion has had to be largely rewritten in the light of what we have learned in the last two generations about taboo and totemism.
The articlesTaboo(Vol. 26, p. 337) andTotemism(Vol. 27, p. 79) are both by Andrew Lang, author ofCustom and Mythand other standard works on folk-lore. It is unnecessary to outline these two articles here, as the two words have been defined, and the importance of the subject suggested. The reader should refer to the article onAndrew Lang(Vol. 16, p. 171), in which it is said that “he explained the irrational elements of mythology as survivals from earlier savagery....†idealized “savage animism ... maintained the existence of high spiritual ideas among savage races, and instituted comparisons between savage practices and the occult phenomena among civilized races.†His appreciation of the culture of the savage and his remarkably interesting style should induce the student to read Lang’s other and related articles in the Britannica, especially:
Family(Vol. 10, p. 158), (equivalent to 27 pages of this Guide), dealing particularly with the question of marriage as related to totemism, and the practices of marrying onlyoutof the tribe or totem, and of marrying onlywithinthe totem (see the articlesEndogamyandExogamy,Matriarchate,Polyandry,Polygamy,LevirateandCouvade).
Name(Vol. 19, p. 157), which discusses the relation of the name to the totem, the strange primitive custom of the individual’s having many names and concealing his true name, etc.; and also the articlesFairy(Vol. 10, p. 134) andMythology(Vol. 19, p. 128).
Religion
For special forms of superstition, read the articlesMagic,Shamanism,Witchcraft,DemonologyandLycanthropy, and in the field of religion,Religion,Primitive(Vol. 23, p. 63), by R. R. Marett, of Oxford University, author ofThe Threshold of Religion, etc. This article puts particular stress on the importance of ritual in early religion. Compare also the matter, already mentioned, onreligion in the article on North American Indians with the short articlesManitou(Vol. 17, p. 568) andGhost Dance(Vol. 11, p. 925). Besides, the student should roadOrdeal(Vol. 20, p. 173),Prayer(Vol. 22, p. 256),Ritual(Vol. 23, p. 370),Sacrifice(Vol. 23, p. 980),Animism(Vol. 2, p. 53), on the attempt to explain religion as due to the fear and worship of ghosts—andFetishism(Vol. 10, p. 295), by N. W. Thomas, government anthropologist to Southern Nigeria;Ancestor-Worship(Vol. 1, p. 945),Funeral Rites(Vol. 11, p. 329) andPurification(Vol. 22, p. 660), all by Dr. F. C. Conybeare, author ofMyth, Magic and Morals, etc.;Tree-Worship(Vol. 27, p. 235) andSerpent-Worship(Vol. 24, p. 676), both bearing on totemism, by S. A. Cook, author ofReligion of Ancient Palestine, etc.
Biographical Study
A course of reading on anthropology may well close with the study in the Britannica of the lives of some leaders in this science. The student will thus be familiarized with the theories of each great anthropologist—and will notice the manifold appeal of the science by seeing from what point each approached it—one from his interest in geology, another from travel, a third because of his studies in surgery or biology, another as a psychologist.
There is no single book in the English language, save the Britannica, in which the whole body of mathematical knowledge is examined and classified with special reference to the inter-relation of its various parts and to the results obtained in the neighboring domains of physics, chemistry, and engineering. Text-books necessarily have a somewhat narrow purpose, namely to teach the student how to solve problems in a single given field; wide views over the surrounding country can, therefore, seldom be afforded. The Britannica, however, does for English readers, what theEncyclopädie der Mathematischen Wissenchaftendoes for German, and more, in that in the Britannica the shadowy borderlands are illuminated and the roads cleared which connect the mathematical and the experimental sciences. In fact if anyone possessed every mathematical text-book that had ever been published, he would still findthe articles full of suggestion to him, for in them the whole subject has been presented, in all its complex bearings, logically and as a whole.
History
It is nearly 4,000 years since a mathematician was last deified in the person of Amenophis, and as far as can be ascertained only one other of his calling ever received this honour, and he also was an Egyptian who had entered into his godship a full thousand years earlier (Vol. 9, p. 46). To the ancient Egyptians mathematics owes the first fragmentary ideas of arithmetic and mensuration, but little else, for despite their amazing mechanical achievements very little record of purely mathematical knowledge has come down from them. It was the Greeks, starting with Thales (600 B.C.), who really created the sciences of geometry and numbers. To them we owe the great abstract ideas which dominate the science. The Greek period lasted till the capture of Alexandria by the Mohammedans, A.D. 640, at which time the Arabian school took shape, and to it we owe the development of algebra (al-jebr-wa’l-muqubala, which means the transposition and removal [of terms of an equation]). With the Renaissance the centre of scientific research shifted to Western Europe and from then on the boundaries of mathematical knowledge were rapidly extended, till to-day the subject is the common ground on which all the physical sciences meet. The student is referred to the articleMathematics(Vol. 17, p. 878), by A. N. Whitehead, fellow and senior lecturer in mathematics, Trinity College, Cambridge, for a brilliant exposition of the foundations of the subject.
The professed mathematician will, of course, not need any set guide to his reading, but it may be well to point out one or two articles which he will find especially worthy of his attention.
Leading Articles
The articleProbability, (Vol. 22, p. 376), by Professor Edgeworth, author ofMathematical Psychics, and numerous papers on the calculus of probabilities, gives, to the best of our belief, the only statement of the whole problem in the English language. That onAlgebraic Forms(Vol. 1, p. 620), by Major Macmahon, former president of the London Mathematical Society, includes a number of results not previously published. The articleElasticity(Vol. 9, p. 141), by A. E. H. Love, professor of natural philosophy in the University of Oxford, embodies the experience of a distinguished mathematician who has made this subject the object of his special study for years. Sir George Darwin (son of Charles Darwin) in the articleTide(Vol. 26, p. 938) summed up the results of his life’s work. The new electrical theory of the properties ofMatter(Vol. 17, p. 891) is discussed by Sir J. J. Thomson, professor of physics, Cambridge, who has done more than anyone else to develop it. There are many other valuable articles, e.g.,Geometry,Axioms(Vol. 11, p. 730), andGeometry,Non-Euclidean(Vol. 11, p. 724), by A. N. Whitehead;Units, Dimensions of(Vol. 27, p. 736), by Professor J. A. Fleming;EnergyandEnergetics(Vol. 9, p. 398 and p. 390), by Sir Joseph Larmor;Groups, by Prof. Burnside, author ofTheory of Groups of Finite Order. Articles which will be found highly useful to the engineer areMensuration(Vol. 18, p. 134);Earth, Figure of(Vol. 8, p. 801);Geodesy(Vol. 11, p. 607);Strength of Materials(Vol. 25, p. 1007).
Leading Contributors
The mathematician will at once recognize the peculiar fitness of the contributors to deal with the subjects allotted to them, and this fitness is the more noticeable in the following list, arranged in alphabetical order, which names and briefly describes the distinguishedmathematicians who have collaborated in the Britannica, and indicates the principal articles written by each.
H. F. Baker, Fellow and Lecturer of St. John’s College, Cambridge. Cayley Lecturer in Mathematics in the University. Author ofAbel’s Theory and the Allied Theory, etc.:
Differential Equation;Function,Functions of Complex Variables.
Ludwig Boltzmann, formerly Professor of Theoretical Physics in the Universities of Munich, Vienna, and Leipzig. Author ofLectures on the Theory of Gas;Lectures on Maxwell’s Theory of Electricity and Light:
Model.
W. Burnside, Professor of Mathematics, Royal Naval College, Greenwich. Hon. Fellow of Pembroke College, Cambridge. Author of theTheory of Groups of Finite Order, etc.:
Groups, Theory of
Arthur Cayley, formerly Professor of Pure Mathematics in the University of Cambridge. See the biographical article (Vol. 5, p. 589):
Curve(in part);Determinant;Equation;Numbers, Partition of;Surface(in part);Gauss, K. F.;Monge, G.
George Chrystal, Professor of Mathematics and Dean of the Faculty of Arts, Edinburgh University, Hon. Fellow and formerly Fellow and Lecturer, Corpus Christi College, Cambridge:
Perpetual Motion;Pascal(in part);Riemann, Georg.
Col. A. R. Clarke, Royal Medal of Royal Society 1887; in charge of trigonometrical operations of the Ordnance Survey 1854–1881:
Earth, Figure of the(in part);Geodesy(in part);Map,Projections(in part).
Agnes Mary Clerke, Author ofHistory of Astronomy in the 19th Century;The System of the Stars;Problems in Astrophysics; and many other astronomical books. See the biographical article (Vol. 6, p. 497):
Astronomy,History:Zodiac;Brahe, Tycho;Copernicus;Flamsteed;Halley;Huygens;Kepler, etc.
Lt. Col. C. F. Close, head of the Geographical Section, British General Staff, formerly British Representative on the Nyasa-Tanganyika Boundary Commission. Author ofText-Book of Topographical Surveying, etc.:
Maps,Projections(in part).
W. E. Dalby, Professor of Civil and Mechanical Engineering at the City and Guilds of London Institute, Central Technical College, South Kensington. Author ofThe Balancing of Engines, etc.:
Mechanics,Applied(in part); and several engineering subjects.
Sir George H. Darwin, late Fellow of Trinity College, Cambridge, and Plumian Professor of Astronomy and Experimental Philosophy in the University. President of the British Association, 1905. Author ofThe Tides and Kindred Phenomena in the Solar System, etc.:
Tide.
F. Y. Edgeworth, Professor of Political Economy in the University of Oxford, etc. Author ofMathematical Psychics, and numerous papers on the Calculus of Probabilities in thePhilosophical Magazine, etc.:
Probability.
E. B. Elliott, Waynflete Professor of Pure Mathematics, and Fellow of Magdalen College, Oxford. Formerly Fellow of Queen’s College, Oxford. President of the London Mathematical Society, 1896–1898. Author ofAlgebra of Quantics, etc.:
Curve, (in part);Geometry, IVAnalytical Geometry.
C. Everitt, Magdalen College, Oxford:
Algebra,History:Density;Light,Introduction,History, etc.
J. A. Ewing, Director of (British) Naval Education. Hon. Fellow of King’s College, Cambridge. Formerly Professor of Mechanism and Applied Mechanics in the University of Cambridge. Author of theStrength of Materials, etc.:
Strength of Materials, and several engineering subjects.
J. A. Fleming, Pender Professor of Electrical Engineering in the University of London. Fellow of University College, London. Formerly Fellow of St. John’s College, Cambridge, and Lecturer on Applied Mechanics in the University. Author ofMagnets and Electric Currents, etc.:
Units, Physical; and many articles on Electrical Science.
Rev. A. H. Frost:
Magic Square.
W. Garnett, Educational Adviser to the London County Council; formerly Fellow and Lecturer of St. John’s College, Cambridge. Principal and Professor of Mathematics, Durham College of Science. Author ofElementary Dynamics, etc.:
Energy(in part);Hydrometer;Kelvin, Lord.
J. W. L. Glaisher, Fellow of Trinity College, Cambridge. Formerly President of the Cambridge Philosophical Society and the Royal Astronomical Society, Editor ofMessenger of Mathematicsand theQuarterly Journal of Pure and Applied Mathematics:
Logarithm;Table, Mathematical;Legendre, A. M.;Napier, John.
J. H. Grace, Lecturer in Mathematics at Peterhouse and Pembroke College, Cambridge. Fellow of Peterhouse:
Geometry,Line Geometry.
Sir A. G. Greenhill, formerly Professor of Mathematics in the Ordnance College, Woolwich. Author ofDifferential and Integral Calculus with Applications;Hydrostatics;Notes on Dynamics, etc.:
Ballistics;Gyroscope and Gyrostat;Hydromechanics.
Sir Thomas Little Heath, Assistant-Secretary to the Treasury, London. Fellow of Trinity College, Cambridge. Author ofApollonius of Perga;Treatise on Conic Sections;The Thirteen Books of Euclid’s Elements, etc.:
Anthemius;Apollonius of Perga;Archimedes;Hero of Alexandria;Pappus of Alexandria;Porism, etc.
F. R. Helmert, Professor of Geodesy in the University of Berlin:
Earth, Figure of the(in part);Geodesy(in part).
O. M. F. Henrici, Professor of Mechanics and Mathematics in the Central Technical College of the City and Guilds of London Institute. Author ofVectors and Rotors;Congruent Figures, etc.:
Calculating Machines;Geometry, I.Euclidean; II.Projective; III.Descriptive;Perspective;Projection.
E. W. Hobson, Fellow and Tutor in Mathematics, Christ’s College, Cambridge. Stokes Lecturer in Mathematics in the University:
Fourier’s Series;Spherical Harmonics;Trigonometry.
A. E. Jolliffe, Fellow, Tutor and Mathematical Lecturer, Corpus Christi College, Oxford. Senior Mathematical Scholar, 1892:
Continued Fractions;Maxima and Minima;Series.
H. Lamb, Professor of Mathematics, University of Manchester, formerly Fellow and Assistant Tutor of Trinity College, Cambridge; Member of Council of Royal Society, 1894–1896. Royal Medallist, 1902. President of London Mathematical Society 1902–1904. Author ofHydrodynamics, etc.:
Dynamics;Harmonic Analysis;Mechanics, I.Theoretical;Vector Analysis;Wave.
A. E. H. Love, Sedleian Professor of Natural Philosophy in the University of Oxford. Hon. Fellow of Queen’s College; formerly Fellow of St. John’s College, Cambridge; Secretary to the London Mathematical Society:
Elasticity;Variations, Calculus of;Function,Functions of Real Variables;Infinitesimal Calculus.
W. H. Macaulay, Fellow and Tutor of King’s College, Cambridge:
Motion, Laws of.
Major P. A. Macmahon, Deputy Warden of the Standards, Board of Trade. Joint General Secretary, British Association. Formerly Professor of Physics, Ordnance College. President of London Mathematical Society, 1894–1896:
Algebraic Forms;Combinatorial Analysis;Cayley, Arthur.
G. B. Mathews, formerly Professor of Mathematics, University College of N. Wales, sometime Fellow of St. John’s College, Cambridge:
Algebra,Special Kinds of Algebra;Number.
J. Clerk Maxwell, former Professor of Experimental Physics in the University of Cambridge. See biographical article (Vol. 17, p. 929):
Capillary Action(in part);Diagram.
Simon Newcomb, former Professor of Mathematics and Astronomy, Johns Hopkins University, etc. See the biographical article (Vol. 19, p. 474):
Astronomy,Descriptive; and many other astronomical subjects.
J. H. Poynting, Professor of Physics and Dean of the Faculty of Science in the University of Birmingham. Formerly Fellow of Trinity College, Cambridge. Joint-author ofText-Book of Physics:
Acoustics;Gravitation(in part);Sound.
F. Purser, formerly Fellow of Trinity College, Dublin; Professor of Natural Philosophy in the University of Dublin; Member of the Royal Irish Academy:
Surface(in part).
J. Purser, formerly Professor of Mathematics in Queen’s College, Belfast. Member of the Royal Irish Academy:
Surface(in part).
W. J. M. Rankine, former Professor of Civil Engineering at Glasgow University. See the biographical article (Vol. 22, p. 894):
Mechanics,Applied(in part).
Hon. B. A. W. Russell, formerly Fellow of Trinity College, Cambridge. Author ofFoundations of Geometry;Principles of Mathematics, etc.:
Geometry, VI.Non-Euclidean(in part).
W. F. Sheppard, Senior Examiner in the Board of Education; formerly Fellow of Trinity College, Cambridge; Senior Wrangler, 1884:
Algebra,Principles of Ordinary Algebra;Arithmetic;Differences, Calculus of;Interpolation;Mensuration.
P. G. Tait, late professor of Natural Philosophy, Edinburgh University. Author ofElementary Treatise on Quaternions. Joint author with Lord Kelvin ofTreatise on Natural Philosophy:
Knot;Quaternions(in part);Hamilton, Sir William;Maxwell, James Clerk.
Rev. Charles Taylor, formerly Master of St. John’s College, Cambridge. Vice-Chancellor, Cambridge University, 1887–1888. Author ofGeometrical Conics, etc.:
Geometrical Continuity.
H. M. Taylor, Fellow of Trinity College, Cambridge; formerly Tutor and Lecturer. Smith’s Prizeman, 1865. Editor of the Pitt PressEuclid:
Newton, Sir Isaac.
Sir J. J. Thomson, Cavendish Professor of Experimental Physics and Fellow of Trinity College, Cambridge. Presidentof the British Association, 1909–1910. Author ofA Treatise on the Motion of Vortex Rings;Application of Dynamics to Physics and Chemistry:
Matter; and several articles on Electrical Science.
J. Walker, Christ Church, Oxford. Demonstrator in the Clarendon laboratory. Formerly Vice-President of the Physical Society. Author ofThe Analytical Theory of Light, etc.:
Polarization of Light;Refraction,Double Refraction.
A. N. Whitehead, Fellow and Lecturer in Mathematics, Trinity College, Cambridge. Author ofA Treatise on Universal Algebra, etc.:
Geometry VI.Non-Euclidean Geometry(in part);Geometry VII.Axioms on Geometry;Mathematics.
These are the men who are responsible for the mathematical sections of the Britannica. A fuller list of articles on mathematical subjects is given below.
No greater homage has ever been paid to the progress of American science than when the planning and supervision of the astronomical section of the new Encyclopaedia Britannica was entrusted to the late Prof. Simon Newcomb, who was also the only American save Benjamin Franklin ever elected an associate of the French Institute. His death occurred some time before the Britannica was completed, but he had already finished the articles which he had undertaken personally to contribute, and read a great number of the other articles which had, at his suggestion, been assigned to eminent astronomers in various parts of the world. His famous hand-book,Popular Astronomy, has been translated into all the European languages, and into Japanese as well; but the unlimited resources in the way of collaboration which the editorial organization of the Britannica put at his disposal, enabled him to assemble in these volumes a complete body of astronomical knowledge which is the greatest of his educational achievements.
The making of a lens for a great telescope is the most difficult undertaking in all craftsmanship, and the mounting of the telescope itself a triumph of mechanical ingenuity. Yet the stars and planets have been guide-posts for the shepherd and the sailor throughout the ages, and have told the farmer when to sow and when to reap, and, even in our day, observations made by an amateur, through a common field-glass, have in more than one instance yielded results of serious value.
A Few Facts
Progress is from one point of view so slow that astronomers are now compilingdata regarding fixed stars of which the motion cannot be deduced for centuries to come; yet some of the changes to be observed are so swift that solar prominences often rise at the rate of 350,000 miles an hour, and have been seen to rise to that height. The temperature of the sun’s envelope, 6000° C., greatly exceeds any that we can artificially create, and would convert into gas any substance we know; and for every unit of heat it sends to the earth, a hundred million other units, poured into space, are absolutely lost for any purposes of mechanical effect.
Astronomy deals with objects so minute that even a shooting star evolving, as it passes through our atmosphere, so much light that we can trace its course with the naked eye, may be no larger than a grain of sand; deals, too, with objects of so shadowy a nature that the white clouds in our sky are, in comparison, solid blocks; and deals, again, with distances and surfaces so vast that numerical description fails to convey any impression but one of confusion.
It is not easy to conceive, when we see a balloon in the air, the remainder that would exist if the bag, the car, and the cordage were all subtracted. There would be, until the gas mixed with the atmosphere, a sphere of gas. The stars, our sun included, seem to be masses of incandescent gas, possessing fairly definite boundaries, and not far from spherical in shape; the nebulae seem also to be masses of incandescent gas, irregular in form and having no clearly marked limits; even the nucleus of a comet is apparently not solid enough to be opaque; and as the four great planets also seem to be gaseous, it is probable that only the smaller bodies, like our earth, the moon, and Mars, are solid.
To the rule that we can handle none of the matter that originates beyond the limits of our atmosphere, the meteorites supply an exception. Seventy years ago, a mass of stone, cold and invisible, flying through the aether of space at the rate of some hundred thousand miles an hour, entered our atmosphere, became so hot, as the air’s friction checked its speed, that bits of its surface, fused to crust, flicked off and floated in the air, leaving a shining trail; then as its speed was reduced to some three hundred miles an hour, cooled until it was no hotter than a laundress likes her iron to be. At Mhow, in India, as it made a dent in the earth, it killed a man—the only man known to history who has died so uncanny a death. But near Wold Cottage, in Yorkshire, England, thirty years before, another meteorite had fallen only ten yards from a labourer; and only thirty years ago another arrived on a Yorkshire railway line, forty yards from a gang of platelayers. The largest meteoric mass known weighs about fifty tons, but most of them seem to have split in the course of their journey; and at Hessle, a hundred thousand fragments spread, like grapeshot from a giant gun, over an area of some thirty square miles. SeeMeteorite(Vol. 18, p. 262).
Life on Mars
Although the closest scrutiny has not discovered in any meteorite a shred of life, even the lowest, we obtain, from another source, and by a different method of observation, evidence—as yet inconclusive,—that not only life, but intelligent life exists beyond our planet. As in respect of other astronomical problems, the Britannica is singularly clear, impartial and authoritative in its treatment of this question. The articleMars(Vol. 17, p. 761) was written by Professor Newcomb, but Professor Percival Lowell contributes a summary of the recent investigations and deductions relating to Mars with which his name is associated. In 1877, Schiaparelli, adopting the old belief now abandoned by all astronomers, that oceans occupied the darker-coloured regions of Mars, observed dark streaks connecting these dark patches, and, believing them to bestrips of water, described them by the Italian word “canale,†by which he meant channels, or natural bodies of water. An absurd misconception of his meaning gave wide currency to the idea that these strips were artificialcanals, a manifest impossibility, as they are many miles in width. No canal, properly so called, could be so wide, and no reservoir could conceivably be so extensive. There is, in the existence of such patches, even if they were bodies of water, as no one now believes them to be, not the slightest indication of excavation. In 1894, Professor Lowell, an American astronomer of great authority, established, for the special purpose of observing Mars, the Lowell Observatory at Flagstaff, in Arizona, 7,250 feet above sea level, in singularly clear, dry air, equipped with a twenty-four-inch telescope. This observatory unquestionably commands greater penetration than any other, and Professor Newcomb says that the work there upon Mars “has been continued with such care and assiduity that its results must take precedence of all others.†Professor Lowell’s first announcement that he had detected evidences of the existence of extensive artificial canals, which would of course absolutely prove Mars to be inhabited by intelligent creatures, was received with derision by many critics who jumped to the conclusion that he meant artificial canals many miles in width. Fuller statements from Professor Lowell showed that he believed Schiaparelli’s wide strips to be not water,but areas of vegetation lying on each side of artificial irrigating canals of no extraordinary width, by a network of which water is brought to, and distributed throughout, the temperate and equatorial zones of Mars from the extreme North and South, as the polar snow caps melt; and that this irrigation gives the rainless area a seasonal fertility, just as the melting of Abyssinian snows fecundates the distant valley of the lower Nile. These strips, according to Professor Lowell and other observers, are at one season of a bluish-green colour suggesting prosperous vegetation, then fade to a paler shade or in some places to a tawny brown. The strips are thousands of miles in length, perfectly straight. No one claims to have seen the artificial canals, but if there are areas of vegetation, they must be due to irrigation performed by waterways. If continued observations confirm the existence of these strips, it will become certain that they are not telescopic illusions, but the results of engineering operations on a scale unknown to our planet. The readings indicated in this chapter will yield a survey of this special field, as of all other fields of current research in astronomy, and give new interest to current investigations.
A brief account of some of the principal astronomical articles is printed here in tabular form, and a fuller list, alphabetically arranged, follows this topical outline.