same way. On the contrary, an operation group may have elements enjoying special privileges and hence it has more extensive contact in the actual world of thought.

A little study of the stated problem revealed the interesting fact that when the number of tables is any power of 2 the substitutions of a well-known type of substitution groups and its group of isomorphisms exhibit directly how the players can be arranged so that each one will play once and only once with, and twice and only twice against, each of the others in a certain series of games. To make myself perfectly clear, I may say that if 8 tables, or 32 players, are involved, one can write directly by means of a certain regular substitution group of order 32 a set of possible arrangements so that in 31 successive games each one of these 32 players would play once and only once with each of the others and twice and only twice against each of them. This was, however, not the first solution of the general problem in question. In fact, about twenty years ago Professor E. H. Moore published a different solution of it in Volume 18 of the American Journal of Mathematics under the title "Tactical Memoranda."

I have referred to this matter here mainly for the purpose of emphasizing the fact that intellectual penetration is often attended by the most unexpected by-products, but I should also be pleased to have people know that certain kinds of recreation can easily be enriched by making use of results which the mathematician developed for a totally different purpose. Science should and does enrich both work and play. More than a thousand years ago the Hindu astronomer Brahmagupta said:

As the sun obscures the stars, so does the proficient eclipse the glory of other astronomers in an assembly of people by the recital of algebraic problems, and still more by their solution.

6 H. T. Colebrooke, "Algebra with Arithmetic

The playful question, Where do the finger nails find so much dark dirt to put under them? may serve to arouse a thoughtful attitude on the part of the boy who has been taught to keep his hands clean. In fact, our play and recreation are perhaps as fundamentally affected by questions of science as our serious work and the victrolas and moving pictures should have a marked influence on the popular attitude towards science in view of the fact that they reach so many people. If it is true that the greatest service which science is rendering the human race is the reduction of superstition, it is clear that the efficiency of science depends largely upon its popularity.

The hypothesis that space and the operations of nature are discontinuous clearly excludes the hypothesis that they are continuous, but it is interesting to note that the mathematics relating to the discontinuous does not exclude that relating to the continuous. On the contrary, there are the most helpful interrelations between these two types of mathematics. Such a subject as number theory, relating decidedly to discrete quantities, has been greatly extended by analytic methods relating to continuous quantities, and, on the other hand, processes relating to the study of continuous functions are largely based upon those relating to the discontinuous.

This may perhaps tend to show that even if our hypotheses in regard to the continuity of space and the operations of nature have to be largely modified, as seems now probable, the mathematical methods of attack may require less modification than might at first appear to be necessary. The language which mathematics has provided for science includes not only concepts relating to the continuous and the discontinuous, but fortunately it also shows relations between these concepts and these relations and Mensuration from the Sanscrit," by Brahmagupta and Bhascara, 1817, p. 379.

ment.

In view of the age of this language and its contact with various sciences it may be readily understood why mathematical history occupies a prominent place in the history of science. In fact, the history of science constitutes one of the fields where scientists may find common interests most fully represented, even if the past is too rich in events to be studied completely. It may therefore be appropriate on this occasion to refer to a few recent developments relating to the history of mathematics, especially since the interest in the history of science has increased rapidly during recent decades, as is partly evidenced by the efforts that are now being made to establish an institute of historical scientific research in our land.

One of the most interesting questions relating to the early history of mathematics is the use of positional values of numbers and the closely connected use of a symbol for zero. Until a decade or two ago it was commonly assumed by mathematical historians that the use of zero as a positional number symbol originated in India, and this view has not yet been entirely abandoned, notwithstanding the fact that the Babylonians employed numbers with positional value and a symbol which seems to have fulfilled the main function of our zero several centuries before the Christian era. On the other hand, the first definite evidence of the use of zero among the Hindus falls in the second half of the first millennium of this era.

In view of these facts it is extremely interesting to note the early use of zero, in connection with numbers having positional value, by the Maya, a people inhabiting the Atlantic coast plains of southern Mexico and northern Central America. One of the worthy alumni of your university recently

Special interest attaches to the occurrence of zero-symbols and the principle of local value among the inhabitants of the flat lands of Central America, at a period as early as the beginning of the Christian era, if not much earlier. It would seem that in this invention, the Maya in Central America possessed priority over Asiatic people by a margin of five or six centuries.7

If further investigation will lead mathematical historians to agree that the zero as a symbol in a numerical notation with positional value was actually first used in America, according to the preserved records, it will effect a very fundamental change as regards interest in the early mathematical attainments of the American aborigines. Unfortunately these early mathematical attainments failed to become the source of extensive further developments on American soil. They exhibit clearly that central concepts may be discovered independently and they direct attention to the danger in trying to establish one source for a particular concept in historical investigation. They also show that the small strip of country marked now by Boston has not always been the intellectual

hub of America.

The history of some of the mathematical attainments of the Maya people has recently been made more easily accessible through the publication of "An Introduction to the Study of the Maya Hieroglyphs," prepared by S. G. Morley and published as Bulletin 57 of the Bureau of American Ethnology, Smithsonian Institution of Washington. On page 92 of this bulletin a dozen different symbols for zero are noted and on page 131 numbers varying from 21 to 12,489,781, and involving the use of zero, are represented in the Maya. notation. It is of interest to note that the 7 F. Cajori, SCIENCE, N. S., Vol. 44 (1916), p. 715.

value of a unit in a higher position is always 20 times the value of a unit in the next lower position, except in the case of the third place, where its value is only 18 times that of the second place.

In historical research and elsewhere, the mathematician seeks cordial cooperation with other scientists, and he regrets that the confusion of tongues, resembling the experiences at the tower of Babel, is making it more and more difficult to understand each other. In the case of scientists this confusion is mainly due to a rapid growth of language in various directions. May we not hope that as many theories which were supposed to be distinct suddenly exhibited profound connections, so also this extensive language will tend towards unity and simplicity as we see more clearly the fundamental underlying principles. Science knows no bounds in method or in subjectmatter and the artificial limitations set by man for his own convenience in making a start must break down before the onward march of truth. All science is a unit and all scientific investigators should be inspired by their common interests.

UNIVERSITY OF ILLINOIS

G. A. MILLER

SCIENTIFIC EVENTS FORESTRY ORGANIZATION FOR THE WAR A 66 FORESTRY regiment," made up of foresters, practical woodsmen, loggers, portable sawmill operators and others experienced in lumbering operations, for service in France, will, it is announced, be raised immediately. The Forest Service, at the request of the War Department, will prepare plans for the organization and equipment of the force and will aid in securing suitable men. The regiment will form a unit of the Engineer Corps now being recruited to be sent abroad as soon as it can be organized and equipped.

The organization of this regiment is the result of a suggestion made by the British

Commission. Similar forces have been raised in Canada and are rendering valuable services. The object of the American forestry regiment, it is said, will be to convert available timber into material suitable for bridges, railroads, trenches and other construction work with the least possible waste. At the same time the cutting will be done under the supervision of technical experts in cooperation with the French foresters. In this way the permanent damage to the forests incident to furnishing the imperatively needed timber, it is hoped, will be kept as small as possible.

The regiment will be organized in units capable of handling all kinds of woods work and will include a number of portable sawmill outfits. It will be officered by trained foresters and expert lumbermen who are thoroughly familiar with producing and delivering lumber. It will carry complete equipment for all kinds of woods work. The classes of men desired comprise axemen, teamsters, tiecutters, millwrights, saw-filers, sawyers, portable sawmill men, farriers, blacksmiths, lumberjacks, cooks and carpenters, as well as motorcycle and motor-truck operators. As rapidly as enlistments are secured, the men will be assembled at six central points, which have already been designated.

EXPEDITIONS OF THE SMITHSONIAN
INSTITUTION

A LETTER from Mr. H. C. Raven recounts the collection of many kinds of wild rats, shrews, bats, squirrels, etc., made in the East India Islands. The first shipment received at the National Museum included 319 mammals and about 300 birds. Mr. Raven recently explored the central part of Borneo, thence working southward by cart and pack train, and is now supposed to be in the southern part of the island. Another collection of miscellaneous matter just received from Mr. Raven includes ethnological specimens, mammals, birds, also reptiles, shells and insects.

Mr. Arthur deC. Sowerby, who has been exploring in China for the National Museum, has not been very successful owing to the conditions there, but managed to visit Shanghai and several places on the lower Yangtze. A

letter from him reports as follows: "My recent trip, to Che Kiang was brought to a summary close by the outbreak in that region. I could not get any transport and very nearly had my retreat cut off. Nothing can be done until the provinces have come to an agreement as to just how the government is to be run. There is only north Chili (a province of China) left to work in and I hope to go there in the autumn. China is in such an unsettled state that if it were not for the war in Europe it would be attracting everybody's attention. Conditions are no better than they were during the revolution of 1911."

Dr. W. L. Abbott, who has enabled the institution to take part in much field work during the past thirty years, and who is now financing the explorations of Mr. Raven, has made a short collecting trip to Santo Domingo. On this island, which was the scene of Dr. Abbott's earliest expedition, in 1883, he collected a number of mammals, birds, reptiles, mollusks, insects and Indian relics.

Mr. John B. Henderson, a regent of the Smithsonian Institution, has conducted a series of dredgings from his yacht Eolis off Key West, Florida. Owing to the exceptionally good weather conditions and to the fact that the Gulf Stream had receded much farther off shore than is usual, the party was enabled to carry on most successful operations upon the Pourtales Plateau. This is a strip of rocky bottom off the Florida Keys extending some forty or fifty miles and lying between the depths of 100 and 200 fathoms. It is one of the richest localities in American waters with a fauna peculiarly its own. The material collected covers all groups of marine invertebrates.

Dr. Paul Bartsch, of the National Museum staff, and Mr. John B. Henderson, also collected in Cuba, the Florida Keys, and in Florida, where marine invertebrates were secured by dredging. The Cerion Colonies composed of land mollusks from the Bahamas, planted some time ago by Dr. Bartsch in the Florida Keys, as an experiment to discover the effect of the environment, were examined. Observations and notes were also made on the birds seen on the islands visited.

APPROPRIATIONS OF THE GENERAL EDUCATION BOARD

THE General Education Board, disbursing moneys from the John D. Rockefeller Fund for the promotion of education, has announced annual appropriations amounting to $878,004. It is announced also that since the University of Chicago has raised $3,461,500 for its medical school, subscriptions of the General Education Board and of the Rockefeller Foundation, amounting to $2,000,000, become valid at once.

By a final gift of $350,000 to the Johns Hopkins Medical School the board announced that it had completed its contribution of $1,750,000 for full-time medical teaching in that institution. When the board announced the first of its gifts for the reorganization of the departments of medicine, surgery and pediatrics in Johns Hopkins, the total contributions were set at $1,400,000.

Aims of the board in making the gift were expressed then by the Rev. F. T. Gates, then chairman, in these words: "We think it important that the clinical subjects should be cultivated and taught by men freed from the distraction involved in earning their living through private practise. They will henceforth be in a position to do any service that either science or humanity demands." fund thus completed is known as the William H. Welch Endowment for Clinical Education and Research.

The

In announcing the release of the money for the University of Chicago the board added that its policy was to " use its funds with a view to inducing others to cooperate toward the same ends. Thus its contributions for nearly all purposes are supplemented by other gifts secured through the cooperation of the General Education Board."

Annual appropriations to other funds and for other educational purposes as planned in former years were:

To Monmouth College, Monmouth, Ill., $60,000 toward a total of $250,000.

To Ottawa University, Ottawa, Kan., $100,000 toward a total of $400,000.

For professors of secondary education in state universities, $35,130.

For state agents for rural schools, $53,200. For rural education of negroes, $50,974. For current support of negro colleges and industrial schools, $102,200.

For farm demonstrations, including canning club work and boys' corn and tomato clubs in Maine and New Hampshire, $36,500.

Additional appropriations for various projects, aggregating $80,000, of which the sum of $50,000 was given for the purpose of promoting educational studies and research.

In making this last appropriation of $50,000 for educational research the board is continuing a policy begun two years ago.

It was also announced that Frederick T. Gates, who has been Mr. Rockefeller's adviser in benefactions for many years, had resigned from the chairmanship of the board. He is to be succeeded by Dr. Wallace Buttrick, who has been secretary. Mr. Buttrick's place is taken by Dr. Abraham Flexner.

THE RAMSAY MEMORIAL FUND

As was noted in SCIENCE at the time a public meeting was held last October at University College, London, to consider the best means of establishing a memorial to the late Sir William Ramsay. We learn from Nature that since then the organization of the appeal has been set up and is now complete. Mr. H. H. Asquith has consented to act as president of the fund, whilst the vice-presidents include the ambassadors and ministers of allied and neutral powers, Mr. Lloyd George, the president of the Board of Education, the president of the Royal Society and the chancellors of the universities of Cambridge, Glasgow and London. The general committee, consisting of the subscribers, is under the chairmanship of Lord Rayleigh. Lord Glenconner and Professor J. N. Collie share the office of honorary treasurer, and Dr. Smiles is acting as honorary secretary.

An executive committee, formed under the chairmanship of Sir Hugh Bell, has drawn up an appeal, which is at present only privately issued, but will shortly be circulated publicly. The committee aims at obtaining a sum of £100,000, and whilst the final form to be taken by the memorial will be submitted to the subscribers, and will necessarily depend on the

amount obtained, the objects recommended are: (1) The provision of Ramsay Research Fellowships, tenable wherever the necessary equipment may be found; and (2) the establishment of a Ramsay Memorial Laboratory of Engineering Chemistry in connection with University College, London, where Sir William Ramsay's most important discoveries were made during his twenty-six years' tenure of the chair of chemistry. The committee has also in mind the inclusion of other forms of memorial, such as the institution of a Ramsay Medal for Chemical Research.

The sum already obtained by the private efforts of Sir William Ramsay's friends and from their own generosity amounts to about £13,500. This includes the donation of £5,000 from Messrs. Brunner, Mond, Ltd.; £1,000 each from the Rt. Hon. Lord Glenconner, Sir Hugh Bell, Sir Ralph C. Forster, Sir Robert Hadfield, Mr. Robert Mond and Mr. Hugh Brunel Noble; and £500 each from the president of the British Science Guild and Miss Lilias Noble.

SCIENTIFIC NOTES AND NEWS

THE New York Academy of Sciences has been compelled to postpone the celebration which had been planned, but on the evening of May 28 the following program was given in honor of the one hundred years of scientific activity of the academy:

The relation of pure science to the national crisis: Professor Michael Idvorsky Pupin, president of the academy.

The academy's scientific survey of Porto Rico: Dr. Nathaniel Lord Britton.

Our first hundred years-a summary: Dr. John Hendley Barnhart.

PROFESSOR T. H. MORGAN, of Columbia University, has been elected a foreign member of the Linnean Society, London.

DR. ISAIAH BOWMAN, director of the American Geographical Society, was in April awarded the Bonaparte-Wyse gold medal of the Geographical Society of Paris for his explorations in and publications on South America.