ical Association, are: Drs. W. T. Councilman, Harvey Cushing, Walter B. Cannon, Fritz B. Talbot, James S. Stone, George Holmes, David L. Edsall and Francis W. Peabody, Boston; William G. MacCallum and Warfield T. Longcope, New York; Lewellys F. Barker and Theodore C. Janeway, Baltimore, and Rollin T. Woodyatt, Ludvig Hektoen and Harry G. Wells, Chicago.

THE advisory commission of the Council of National Defense and the National Research Council have sent six American men of science to England and France to study problems arising out of the war. Members of the party and the subjects in which they will specialize are: Dr. Joseph S. Ames, Johns Hopkins University, aeronautical conditions; Dr. Richard P. Strong, Harvard University, camp sanitation; Dr. Linsley R. Williams, assistant health commissioner of New York State; George A. Hulett, Princeton University, chemistry of explosives; Dr. Harry Fielding Reid, Johns Hopkins University, scientific map making and photography from airplanes, and Dr. George R. Burgess, of the Federal Bureau of Standards, metals suitable for guns and rigid dirigibles. The party is accredited to the American Embassies in London and Paris.

SIX professors of the University of Minnesota have been asked by the war department to act as a scientific research board for the district of the state of Minnesota. The duties asked of them will require a considerable portion of their time from now on. These men are Professor John J. Flather, head of the department of mechanical engineering, Dean George B. Frankforter of the school of chemistry, Dr. L. G. Rowntree, head of the department of medicine, Professor R. W. Thatcher, head of the department of agricultural chemistry, L. W. McKeehan of the department of physics, F. R. McMillan, of the department of structural engineering. Dean Frankforter and Professor Flather acted upon a special navy board which made an inventory of Minnesota resources last summer and the figures

which they gathered at that time will be of inestimable value in the present crisis.

Ar the annual dinner and initiatory exercises of the Washington University chapter of Sigma Xi, the president of the chapter, Dr. B. M. Duggar, discussed "Some Materials and Problems in Plant Pathology."

DR. CHARLES BASKERVILLE, director of chemical laboratories of the College of the City of New York, delivered an illustrated address at the Franklin Institute, Philadelphia, on April 19, his subject being "The Hydrogenation of Oils."

AT the recent meeting of the West Virginia Scientific Society Dr. Ludvig Hektoen, of the University of Chicago, delivered an address on "Recent Investigations of Infantile Paralysis."

MR. WILLIAM BOWIE, chief of the division of geodesy, delivered recently an address before. the Geological Society of Washington, D. C., on Some Evidences of Isostasy."

66

DR. R. A. PEARSON, president of the Iowa State College, has been made chairman of a committee which will include one member from each congressional district of the state of Iowa and whose duty will be to organize the farmers of the state in the interest of food conservation and increased production. The creation of such a committee was recommended by a conference of the leading men of the state held at the state house on April 3 at the call of Governor Harding. The governor will appoint the other members of the committee. The conference recommended an emergency appropriation by the legislature of $100,000 for 1917 and an equal amount for 1918 to be used under the supervision of the extension department of the Iowa State College in a campaign to increase the food production of Iowa.

PROFESSOR A. D. WILSON, director of agricultural extension work of the University of Minnesota, has been appointed by the government to direct the work of farm production and labor conservation in the northwest during the continuance of the war.

PROFESSOR JOSEPH JASTROW, of the University of Wisconsin, is giving a series of lectures

Human Nature."

HERBERT WILLIAM CONN, professor of biology in Wesleyan University and Connecticut State bacteriologist, has died at the age of fiftyeight years.

THE death is announced of Emil von Behring, professor in the University of Marburg, discoverer of diphtheria antitoxin. He was born in West Prussia in 1854. In 1901 he received the Nobed prize in medicine, and was made a member of the hereditary nobility.

THE death is announced of Dr. Narcisse E. Dionne, librarian of the Legislature of Quebec, and formerly professor of archeology of Laval University. Dr. Dionne was the author of a number of important biographical and historical works, and in 1907 served as general secretary of the fifteenth International Congress of Americanists, which was held at Quebec.

THE Southern Society for Philosophy and Psychology held its twelfth annual meeting on April 12 and 13, 1917, at Randolph-Macon Woman's College, Lynchburg, Va. It was voted to extend the scope of the society so as to include "experimental education," and to hold the next meeting at Peabody College for Teachers, Nashville, Tenn. The following officers were elected: President, Professor E. K. Strong, Jr., Peabody College, Nashville; Vicepresident, Dr. T. V. Moore, Catholic University of America, Washington, D. C., and Secretary-Treasurer, Professor W. H. Chase, University of North Carolina. The newly elected members of the council are: Dr. Tom A. Williams, Washington, D. C., Professor E. B. Crooks, Randolph-Macon, Lynchburg, Va., and Professor Knight Dunlap, of Johns Hopkins University.

Ar the annual meeting of the American Association of Immunologists, held in New York, April 6 and 7, Dr. John A Kolmer, Philadelphia, was elected president; Dr. Martin J. Synnott, Montclair, N. J., secretary, and Dr. Willard J. Stone, Toledo, Ohio, treasurer. The new council is composed of the officers and Drs. Richard Weil, Arthur F. Coca and William H. Park, New York, and Dr. A. Parker

will be held in Minneapolis in April, 1918.

A SCIENCE Faculty Club has been organized at the University of Southern California, Los Angeles, Calif. The purpose of the club is to promote research and cooperation between the departments of science in the university. A meeting is held each month. The officers are Professor Albert B. Ulrey, president; Professor Arthur W. Nye, vice-president, and Miss Catherine V. Beers, secretary.

THE Oklahoma State Bureau of Standards, which was organized by act of the legislature of 1915 secured an appropriation of $8,500 with which to purchase equipment. It is the purpose of the bureau to secure primary and secondary standards of weights and measures and for testing gas, water and electric meters. The bureau is also planning the equipment of a laboratory for the measuring and testing of the best values of fuels as coal and petroleum products. The bureau is situated at the State University and with the equipment planned will be able to provide the people of the state a place where they may have their weights and meters, etc., calibrated.

UNIVERSITY AND EDUCATIONAL

NEWS

THE president of the Republic of Panama has signed a decree establishing a Pan-American University in accordance with a law passed by the legislature on January 27. The trustees are to consist of the secretary of public instruction of Panama and the diplomatic representatives of the American republics or their representatives. Diplomatic representatives of other countries maintaining chairs in the university are also to have representatives on the board. It is believed that the university may be of international value to the American republics, especially in subjects such as medicine, law and agriculture.

THE legislature of the state of Oklahoma at its recent session made provision for the following buildings for the State University at Norman: Auditorium, $150,000; wing to library, $75,000; geology building, $100,000; hospital at Oklahoma City in connection with

the medical school, $200,000. At the same time the Agricultural and Mechanical Arts College at Stillwater was granted: Science hall, $100,000; gymnasium, $100,000.

THE residue of the estate of James Buchanan Brady, which is estimated as more than four million dollars, is bequeathed to the New York Hospital on West Sixteenth Street, New York City, to establish the James Buchanan Brady Foundation for a urological institute, similar to that at Johns Hopkins Hospital at Baltimore, which Mr. Brady had endowed during his life with $200,000. An additional $300,000 is left in trust to the Johns Hopkins Hospital for the maintenance of the institute.

THE Harvard Medical School will provide instruction for the senior class during the summer, with two weeks holiday. It is optional with students whether they will begin their fourth year's work on June 4 or September 24.

OWING to the national emergency, the Cornell University Medical College announces that it will continue instruction for members of its senior class throughout the summer so that they may be graduated with the degree of M.D. on or about January 1, 1917.

PROFESSOR C. R. RICHARDS, professor of mechanical engineering and head of the department since 1911, has been appointed dean of the College of Engineering and director of the Engineering Experiment Station of the University of Illinois to succeed Dr. W. F. M. Goss who has resigned to become president of the Railway Car Manufacturers' Association of New York.

DR. CHAS. BROOKOVER, of the University of Kansas, has been elected professor of anatomy and director of the department at the University of Louisville.

DISCUSSION AND CORRESPONDENCE A VIABLE TEN-YEAR-OLD CULTURE OF BACILLUS PARATYPHOSUS BETA

As the usual text-books, manuals and current literature make but little or no mention of the length of life of individual bacteria the following record may not be without interest.

In 1909, when I began teaching bacteriology at Howard University, among the stock cultures of organisms in the laboratory was one labeled "Paratyphoid Schottmüller 1-1406." It was a deep agar stab made in a narrow test tube and the tube instead of being closed in the usual manner by a cotton plug had been sealed off in the flame. Hermetically sealed, the agar culture had been prevented from drying. The culture had been prepared three years previously by Dr. W. W. Alleger.

On January 17, 1916, ten years and three days after the culture had been made, the tube was broken open and the organisms transferred to Russell double sugar. The characteristic red color and gas did not appear in the butt of the tube on the first transfer. Transfers were then made from this tube to other double sugar tubes at irregular intervals during a couple of months. At about the fifth transfer the organism showed its characteristic reaction on the double sugar. Its fermentation of separate sugars was tried, as well as other cultural tests, and the agglutination test with paratyphoid beta immune serum was done. All these indicated that the organism was Bacillus paratyphosus beta.

kept in a closet away from the light, along During the ten years it had always been with the other stock cultures. The temperature in closet varied during the first five years from as high as 32° C. in summer to nearly as low as 0° C. in winter. During the last five years the temperature was never lower than 15° C.

M. W. LYON, JR.

GEORGE WASHINGTON UNIVERSITY

A METHOD FOR KILLING TURTLES

KILLING turtles for class purposes is more or less of a task depending upon the equipment at hand. Even though a closed tank is available for administering gas, thirty minutes to an hour is required for anesthetizing these reptiles and then they may revive during dissection. Another expedient sometimes resorted to is to place the specimens in boiling water for a few minutes. This has its objections. I have observed attempts to

give an anesthetic or a poison by way of the mouth which is almost impossible. However, substances can be introduced into the alimentary tract through the anus and the desired results obtained.

Such is the method used in this laboratory. Chloroform is injected into the cloaca and a string tied in front of the anus to prevent the ejection of the liquid. Five c.c. of chloroform thus given will anesthetize an eight-inch turtle sufficiently for dissection in thirty to forty-five minutes.

The value of this method is threefold. First, a string and a pipette constitute the necessary equipment; second, the ease with which the anesthetic can be given is evident; and third, there is no danger of the specimens coming out from under the chloroform.

UNIVERSITY OF UTAH

NEWTON MILLER

SCIENTIFIC BOOKS Combinatory Analysis. By MAJOR PERCY A. MACMAHON. Cambridge University Press. 1915, Vol. 1, xix + 300 pp., and 1916, Vol. 2, ix + 340 pp.

One of the four grand divisions of what may be called properly static mathematics is the theory of configurations. It includes the construction out of given elements of compound forms under certain given conditions or restrictions; together with the characters possessed by such constructions when they are varied under given laws, such as, for instance, the character of transitivity, or that of primitivity; and the laws of dependence of such constructions upon each other; as well as finally the invention of new or ideal elements of mathematics that enable the solution of problems of construction to be effected. These constructions vary from the mere permutation of a linear series of elements up to the comof chemical combinations plicated trees studied by Cayley, and in general to all sorts of problems in what has been happily denominated tactics by Cayley, or syntactics by Cournot. We find in its field the construction of magic squares, of Latin squares, of LatinGreek squares, of triangles, stars, polygons,

chess problems, routes over net works, problems of topography, and without much stretch of imagination we might now include the disposition of the elements of war. The field is obviously large in extent, and in a wide variety of aspects fascinating. From certain points of view one might be tempted to conclude that we could include in it all mathematics, for the definition given by C. S. Peirce made mathematics the science of ideal constructions and their applicability to the world as it is.

The study of configurations usually begins with combinatory analysis. By this is usually meant the study of the arrangements along a line of a collection of objects, either as individuals or in groups; arrangements at the nodes of a lattice; combinations of arrangements. Such problems arise not only as matters of tactic, curious problems or puzzles, but in the determination of the number of such arrangements needed in solving problems in the theory of probabilities.

The treatise of Professor MacMahon undertakes to present some very general methods of handling such studies. These methods consist for a large part in the construction of enumerating generating functions, and involve considerable study of symmetric functions and certain differentiating operators. In the course of this study he arrives at some very elegant theorems. These methods not only enumerate the possible forms, but in many cases afford methods of actual construction of the entire list of such possible forms. They are very powerful and have enabled the author to solve problems that were considered for a long time to be beyond the reach of mathematical analysis. His success and presentation in complete form may induce others to study this important branch of mathematics.

There are eleven sections, and the topics under consideration will give some idea of the character of the treatise. Section one considers ordinary symmetric functions and their connection with the theory of distribution of objects into parcels. The operators which are useful for these purposes are developed, and their algebra considered, turning out to be quite analogous to the algebra of symmetric

functions. A distinction is drawn between the parcel of objects, in which the order of arrangement in the parcel is immaterial, and the group of objects, in which the order of arrangement in the group is material. For instance if we sort 3 a's 2 B's, 1 1 8 into seven boxes of which four boxes are exactly alike, and three boxes alike but different from the first four, we find that we have a problem of distribution of objects of type (3212) into parcels of type (43), which can be done in 11 ways. This number 11 may be found by a distribution function, derived from the theory of symmetric functions. This function gives, for instance, for the various types of 4 objects distributed into parcels of type (2) these results: for type (4), 2 ways, for type (31) 3 ways, for type (22) 4 ways, for type (211) 5 ways, for type (1111) 7 ways. If, however, the distribution is into groups rather than into parcels, we have for type (4) 2 ways, for type (31) 6 ways, for type (22) 10 ways, for type (211) 18 ways, and for type (1111) 36 ways. The determination by the function consists in finding the coefficients in formula that arise from the theory of symmetric functions. These coefficients may be found directly for the individual terms by using the operators referred to.

Section two considers the theory of separations, a separation being a distribution of the numbers constituting a partition of some integer into parcels, or groups. Extensive generalizations are possible from the formulæ and the operators produced. The application to sets of objects of given types and their distributions resolves more complicated problems than those given before. For instance, with a set of four threefold objects, a,a,a,, a,a,a, bbb, c,b,c, can be formed 38 cases of distribution into the types (211), (22), (211), namely the objects a,a,b,c,, aabb, a,a,b,c,, and the different permutations of these arrangements.

Section three deals with permutations, particularly with points useful in the general theory of combinations and distributions. A certain master theorem is deduced which has great resolving power. In particular it solves

the problem of ascertaining the number of permutations in which every letter occupies a new place, and in expressing sums of powers of binomial coefficients. The notion of lattice permutation is introduced, by which is meant that if any permutation be made of a a's, b B's, cy's, etc., to be a lattice permutation it must be such that reading it from left to right, at no point of it will the number of a's so far written be less than the number of B's, nor number of p's less than the number of y's, etc. For instance, for 2 a's and 2 B's the lattice permutations are aαββ, and αβαβ. The permutation aßßa is not a lattice permutation because when we arrive at the third letter, we shall have 2 B's and only 1 These are called lattice permutations because they serve to handle arrangements of integers at the nodes of a rectangular lattice in a plane,. or in space.

a.

Section four considers compositions of integers, by which is meant the permutations of the partitions of the integer. In connection with these some new symmetric functions are introduced. An application to Newcomb's problem is made. It is this: given p cards marked 1, q marked 2, r marked 3, etc., which are shuffled and dealt in such wise, that as long as a card is not of lower number than the preceding it is placed upon the preceding, but if lower it must start a new pile; what is the probability that there are at most m piles when all have been dealt?

Section five introduces the notion of perfect partition, that is partitions such that each contains only one partition of each lower number. For instance, for 7, a perfect partition is (4111), since we have only one partition of 1, 2, 3, 4, 5, 6. These are then applied to distributions upon a chess board. A connection is thus arrived at between magic squares and the general theory. The enumeration of Latin squares is effected by generating functions, thus solving a long-standing problem. For instance, the number of reduced Latin squares of order 1, is 1, of order 2, is 1, of order 3, is 1, of order 4, is 4, and of order 5, is 52.

Section six enumerates the partitions of multipartite numbers. multipartite numbers. A multipartite num