SOCIETIES AND ACADEMIES

THE AMERICAN MATHEMATICAL SOCIETY THE one hundred and eighty-ninth regular meeting of the society was held at Columbia University on Saturday, February 24. The morning session sufficed for the presentation of the brief list of papers. The attendance included twenty-six members. Professor H. S. White occupied the chair, being relieved by Professor Kasner. The council announced the election of the following persons to membership in the society: Professor H. P. Kean, McHenry College; Mr. Ralph Keffer, Harvard University; Mr. H. C. M. Morse, Harvard University; Dr. F. D. Murnaghan, Rice Institute; Mr. G. E. Raynor, University of Washington; Dr. S. P. Shugert, University of Pennsylvania; Mr. G. W. Smith, University of Illinois; Mr. J. S. Taylor, University of California; Dr. L. E. Wear, University of Washington; Dr. H. N. Wright, University of California. Four applications for admission to membership were received.

It was decided to hold the next summer meeting of the society at Cleveland, Ohio, on September 4-5. The Mathematical Association of America will meet at Cleveland on September 6-7.

By the will of the late Professor L. L. Conant, of the Worcester Polytechnic Institute, who was a member of the society from 1892 to his death in 1916, the sum of $10,000 is left to the society, subject to Mrs. Conant's life interest. The will provides that the income of this bequest "shall be offered once in five years as a prize for original work in pure mathematics." This generous gift, a noble monument to the donor, should do much for the promotion of higher mathematical aims in this country. For many years the society has consistently pursued these aims, with a success far outrunning what might have been expected from its modest financial resources. With greater means in the way of general or special funds, it could accomplish still more. To anyone who is able to give for science, the society presents itself as an experienced and beneficent administrator.

At the annual meeting, the council placed itself on record as desiring to cooperate with the National Research Council in forwarding the interests of research. At the February meeting a committee was appointed to confer with the chairman of the Mathematics Committee of the Research Council, Professor E. H. Moore, in regard to the selection of the members of that committee.

The following papers were read at this meeting: A. R. Schweitzer: "The iterative compositions of a function of n + 1 variables (n=1, 2, 3 ... ).”

A. R. Schweitzer: "Functional equations based on iterative compositions.''

D. F. Barrow: "An application of Fourier's series to probability."

Edward Kasner: "Degenerate cases in the theory of the conduction of heat."

J. E. Rowe: "The equation of a rational plane cubic derived from its parametric equations (second paper)."

R. L. Moore and J. R. Kline: "The most general closed plane point set through which it is possible to pass a simple continuous plane arc."

H. S. White: "New proof of a theorem of von Staudt and Hurwitz.''

Henry Taber: "On the structure of finite continuous groups. '

The next meeting of the society will be held at the University of Chicago on April 6-7. The San Francisco Section will meet at Stanford University on April 7. F. N. COLE, Secretary

OKLAHOMA ACADEMY OF SCIENCE

THE Oklahoma Academy of Science held its eighth annual meeting in Oklahoma City, December first and second, with President C. N. Gould in the chair. The following papers were presented:

AGRICULTURE

"Effects of Soil Types on the Root Development of Cotton and Kaffir," by Wallace MacFarlane.

ARCHEOLOGY

"Types of Stone Implements," by J. B. Thoburn.

CHEMISTRY

"Errors in the Determination of the Coefficient of Viscosity Gases by the Capillary Method," by I. M. Rapp.

"Sulfur in Petroleum," by Chas. K. Francis. "Effect of Para Substituents in the Acylation of Aromatic Amines,'' by L. Chas. Raiford and A. F. Whipple.

"Oxidation of Ethyl Alcohol to Acetaldehyde," by Wm. J. Becker.

"Infra-red Absorption of Naphthalene," by A. H. Stang.

"Visibility Curves of the Green Mercury Line and Its Satellites," by A. F. Reiter.

ECONOMICS

"Setting the Clock Ahead," by Joseph M. Perkins.

"The Lumber Industry of Oklahoma," by John Cullen.

"Progress of Work in the Cretaceous Area of Oklahoma," by C. W. Shannon.

"New Volcanic Ash Theory," by Chas. N. Gould.

"Manganese Deposits Near Bromide, Oklahoma," by Geo. E. Burton.

"The Distribution of the Sand Dunes of Oklahoma," by Bryan Hendon.

"Oil Seeps," by Elbert E. Boylan. "A 'Gas Blow-out,'"' by V. V. Waite. "The Elephants of Oklahoma" (by title), by E. B. Wilson.

"The Early Vertebrates of Oklahoma" (by title), by M. G. Mehl.

"Granite Situation in North-Central Kansas'' (by title), by Everett Carpenter.

MATHEMATICS

"English Experiences in Teaching Calculus to Trades-school Students," by A. Press.

"A Shorter Proof of a Theorem on Fourier's Series" (by title), by W. H. Cramblet.

BIOLOGY

"A Flock of Hawks," by Chas. N. Gould. "Platanus occidentalis," by Chas. N. Gould. "Past and Future of the Buffalo," by Frank Rush.

"Reproductive Organs of Birds and Their Activities" (by title), by T. C. Carter.

"Biological Significance of Bones, Teeth and

Shells Found in the Caves of Eastern Oklahoma," by H. H. Lane.

"Further Observations on the Effect of Acohol on White Mice," by L. B. Nice.

"Speech Development of a Child from Eighteen Months to Six Years," by Mrs. Margaret Morse Nice.

"The Murine Opossum, an Accidental Immigrant in Oklahoma,'' by H. H. Lane.

"On a Collection of Moths and Butterflies from Costa Rica," by H. H. Lane.

"Some Personal Observations on the Habits of the Butcher's Shrike," by C. W. Shannon. "Observations on Demoder folliculorum" (by title), by G. K. Stanton.

"The Relation of Vegetation to Stratigraphy" (by title), by Floyd Absher.

"The Hawks of Oklahoma" (by title), by Joe Matthews.

The Committee on Publications reported that arrangements had been made whereby the University of Oklahoma would assume responsibility for publishing the proceedings, the academy paying what it can and the state assuming the balance. The report was accepted. The committee appointed on publication for the coming year consists of the president, treasurer, secretary and

curator.

The committee on membership presented the names of forty new members which were accepted.

Professor C. W. Shannon, director of the Oklahoma Geological Survey reported that the Biological Survey working in connection with the academy had established many nature study clubs in the public schools of the state during the past year. Report accepted.

A committee was appointed to work to get better laws passed in Oklahoma for the protection of wild life. Mr. Frank Rush, United States forester, in charge of the buffalo herd, in the Washita Mountain Reservation, was made chairman of this committee.

The treasurer's report was read and accepted. The following officers were elected for the coming year:

President, L. Chas Raiford, A. & M. College; First Vice-president, M. M. Wickham, Southeastern State Normal School; Second Vice-presi. dent, A. F. Reiter, Phillips University; Treasurer, H. H. Lane, University of Oklahoma; Secretary, L. B. Nice, University of Oklahoma; Curator, Fritz Aurin, Oklahoma Geological Survey.

L. B. NICE,

Secretary

its relation to engineering seems to-day to be in an intermediate stage of its asymptotic evolution from the state of a follower to that of an absolute dictator. The first reason why this evolution has to follow this general course is that application must needs precede correlation.

Man like the other animals from the very first can survive only as he applies nature's laws to his needs, as he conforms to them, so that he begins applying them inconceivably earlier than he begins to formulate them or even to be capable of formulating them.

The second reason lies in the unfathomable complexity of the laws on which engineering must needs be based.

The engineering of the savage is military. His existence depends on his power to kill his enemies and incidentally his game by means of weapons made from the materials at hand. Of these materials he knows only certain prominent properties irrelated to each other and to the rest of nature. If this knowledge can be said to consist of laws they are only the most minute fragments when compared even with the fragments of laws which we have joined up. They are fragments comminuted to the second degree. The explanation of these fragments the savage has never sought. Yet the laws themselves were as complex when our forefathers were naked as they are to-day. The Bornean or Fiji knows that wood is strong, stone stronger, and iron stronger still, though corruptible by rust. Armed with this and all other knowledge which he has he destroys those who else would destroy him. The survival is not of those who formulate knowledge but of those who best apply it, and so there evolves a race which applies successfully the laws which it may never even think of thinking of.

By and by evolution lifts certain men

so far up out of the imperative need of ceaseless viligance lest they be slain by their fellows or by nature as to give them the opportunity to consider their environment, and note the analogies between phenomena which at first seem irrelated. These are the first men of science. Before them the ratio of observed to correlated phenomena was that of a small body to zero, and hence was infinity. With them that ratio fell from infinity to finiteness, but it was still extremely small.

As the accumulation of observed phenomena goes on and with it the organization and elaboration of society, certain men come to excel their fellows sufficiently in their mastery of this knowledge, and in their ingenuity in applying it, to become recognized as a special class, engineers. More slowly the accumulation of observed analogies becomes so great that those who master it become recognized in their turn as a class, the natural philosophers or men of science.

These philosophers address themselves at first to correlating phenomena, which, however familiar, are known as yet only empirically, and thus to explaining that which engineering has long known how to do, has known in part since the days of Assyria, of Homer, and of Kephren. But this is to trail after engineering, to explain its exploits as the minstrel glorifies those of the warrior. By and by science becomes able, through its accumulation of correlations, to point out to the engineer how he may better his service to man. But this is to snatch a share in the leadership, and add it to the continuing labor of correlation.

From this time on science increases continuously the share which it has in the direction of engineering. It is engaged ever more and more in discovering and simultaneously correlating new knowledge, and less and less in the gradually vanishing

work of the correlation of the old empirical knowledge with which alone engineering formerly worked. With the completion of this latter task science might come to be the sole guide of engineering, but for two considerations.

First, as engineering adopts the knowledge which science has correlated it simultaneously unearths new uncorrelated knowledge. Science indeed correlates this in turn, but not instantaneously, so that engineering has always at its hand both that which science has correlated and its own empirical discoveries which science has not yet had time to arrange. As optimists we may well expect that this uncorrelated knowledge will form a gradually decreasing fraction of the whole, but can we expect it ever to vanish completely? Must not science's approach to exclusive leadership be asymptotic?

We begin to get a glimmering of the vastness of the scheme of creation when we remember that every lengthening of man's artificial vision by means of telescope and camera, every new strengthening of telescope, sensitizing of plate, and lengthening of exposure brings a proportional increase in the number of visible suns, telling us that even at that inconceivable distance we have not begun to approach the limit of the discoverable universe. When we turn from telescope to microscope and thence to the inferred constitution of matter, we find with every new refinement of observation and inference a proportional addition of new wonders, a proportional increment in the complexity of natural phenomena. Hence while we may speculate that, as there must be a place where the stars end, so there must be a degree beyond which the subdivision of matter can not go, and a limit to the number of nature's laws, we may well ask whether either that limit or the limit of stellar space will be reached in

that little throb in the pulse of the universe which we call the habitable period of this earth. Will man survive long enough to complete the discovery of all laws, so that no uncorrelated phenomena will remain for the engineer to unearth?

The second of the two considerations which tend to postpone the completion of science's leadership is that the beautiful as distinguished from the useful and the good will increase without limit its demands upon the work of the engineer. Though the beautiful itself should in time be capable of complete mathematical analysis, who shall say that that time, now seemingly so inconceivably remote, can arrive during man's earthly stay?

HENRY M. HOWE

OUR PSYCHOLOGICAL ASSOCIATION AND RESEARCH1

THE American Psychological Association, like the infants who are among the objects of our study, celebrated its first birthday some months after it was born. We are thus able to hold at the same time our

twenty-fifth meeting and mark the completion of nearly twenty-five years of activity. This period covers the working life of most of us and about half the adult life of the science in which we work. Wundt's "Physiologische Psychologie," published in 1874, may be taken to mark the coming of age of the experimental work of Weber, Helmholtz and Fechner. But if psychology as a science was made in Germany, the raw materials were contributed from many nations, many centuries, many sciences; and the leading strings attaching us to Germany were severed at about the time when this association was organized.

1 Address given on the occasion of the celebration of the twenty-fifth anniversary of the American Psychological Association, New York, December 28, 1916.