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Walter H. Snell, formerly of the Office of Investigations in Forest Pathology of the Department of Agriculture, has accepted an instructorship in the same department.

PROFESSOR A. K. PEITERSEN, who for the past seven years has been assistant professor of botany and assistant botanist of the experiment station, of the University of Vermont, has gone to Fort Collins, Colorado, where he has been elected professor of botany.

PROFESSOR SWALE VINCENT, who has occupied the chair of physiology at the University of Manitoba (Winnipeg) since 1904, has been appointed professor of physiology in the University of London (Middlesex Hospital). He will probably take up his duties in London at the beginning of May.

DR. HAROLD PRINGLE, lecturer on histology and assistant in physiology in the University

of Edinburgh, has been appointed professor of physiology in Trinity College, Dublin, succeeding the late Sir Henry Thompson.

DISCUSSION AND CORRESPONDENCE

FURTHER HISTORY OF THE CALCULUS TO THE EDITOR OF SCIENCE: Please make a correction of my college address to Rose Polytechnic Institute, in the paper on "The Early History of Calculus," in SCIENCE for July 11. The error is due perhaps to the fact that only my name was signed to the article. The quotation from the "Encyclopedia Britannica" should be stated as from the ninth edition, since it has been omitted in the eleventh. The historical part of the article "Inf. Cal." is entirely changed in the last edition to one of still stronger German bias. It makes the statement, for example, that Leibniz did not meet Collins, nor see the tract "De analysi per aequationen . . ." on his first visit to London in 1673. No verification of this statement is offered. English histories and documents have it the other way with regard to Collins.

Evidence of the possible duplicity of Collins which indicates that he was an agent under Oldenberg as early as 1669, appears in the rewritten history. To quote:

The tract "De analysi per aequationen . . was sent by Newton to Barrow, who sent it to John Collins with a request that it might be made known. One way of making it known would have been to print it in the Philosophical Transactions of the Royal Society, but this course was not adopted. Collins made a copy of the tract and sent it to Lord Brouncker, but neither of them brought it before the Royal Society. . . . In 1680 Collins sought the assistance of the Royal Society for the publication of the tract and this was granted in 1682, yet it remained unpublished. The reason is unknown. . . .

The usual history is that Collins was the active agent in soliciting the tract "to make it known." Also, Oldenberg was secretary of the Royal Society, and published the Transactions for his private profit, without supervision from the society. The relations of these two men were intimate. The tract was prob

ably brought directly to Oldenberg—he has

shown that he had knowledge of it-and that he did not act upon it in his official capacity is evidence of conspiracy to suppress it. When both were urging Newton, as already cited, to undertake "for the honor of England," a correspondence which Leibnitz had planned, it was at that time within their power to promote greater honor to England by publishing the tract in the Transactions. In reference to the threatened publication in 1680, the death of Oldenberg about two years before, had left Collins without his principal, if Oldenberg were such, and that transaction might have been a shrewd move on Collins' part to retain his honorariums through Leibniz. At least some cause delayed Leibniz seven years in the publication of his calculus, already prepared, while it was put in in the hands of the printer immediately after the death of Collins.

There is reason to believe that Leibniz had information of matters transpiring in England before he left Germany. It is difficult to explain otherwise the grandiloquent announcement of wonderful discoveries of new methods in mathematics, which heralded his visit to Paris in 1672, with no work to show, and with admittedly inferior mathematical knowledge for such work. The London exposure by

Pell, in 1673, is clarifying. Leibniz was a politician, not a mathematician, and worked and wrote for the power and prestige of Germany. To this end he founded the Berlin Academy of Science, and was perhaps the first to inaugurate that system of espionage on scientific work in foreign countries by which the usefulness and credit of as much of that work as possible might be transferred to Germany.

It may be urged that calculus has been benefited by the interference of Leibniz. This is true as to notation, but it has been harmful as to the theory and understanding of the subject. On the one hand we have an illogical infinitesimal method, on the other an incomplete derivative one in protest of the first, whose rival expounders reason along different lines, and hardly understand each other. Newton substitutes one rigorous rigorous theory, broader than either of these, neglecting no

=

Starting from given corresponding values, x, y, z, the actual variables are corresponding increments to these with a common first value, 0; and starting with any corresponding increments, Ax, Ay, Az, we form an ideal variation in the same ratio, A'x= NAx, A'y=NAY, A'z NAz, where the common multiplier N, varies. This is the familiar law of uniform variation between two sets of values of the variables, and the symbols A'x, etc., are not limited to small values but vary from 0 to co, as N so varies, however small Ax, etc., may be.

Such A'x, A'y, A'z are approximate fluxions; and the exact fluxions dx, dy, dz, are limits of these for lim. Ax=0, lim. Ay = 0, lim. Az=0. For example, let z=xy, then Az=yAx+ (x+Ax)Ay, and multiply both members by N. A'z=yA'x+(x+Ax)A'y,

whence by limits, dz=ydx+xdy.

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A's shaded area. variations geometrically:

dz shaded area.

(2) In the Same Ratio. (3) In the First Ratio.

A shaded area, We may illustrate the three (1) Actual. quantity, however small, leaving no unexplained symbol, and yet of an arithmetical character of the utmost simplicity. A free translation of his definition in "Quadrature of Curves," is as follows:

In their highest possible approximation, fluxions are quantities in the same ratio as the smallest possible corresponding increments of variables, or, in a form of exact statement, they are in the first ratio of nascent increments.

Thus fluxions, or differentials, are interpreted as ordinary arithmetical increments, but in a variation defined as in the first ratio, or, as the variables begin to increase, or, in the instantaneous state, which are all one.

ARTHUR S. HATHAWAY ROSE POLYTECHNIC INSTITUTE

SCIENTIFIC BOOKS

REPORT OF THE CANADIAN ARCTIC EXPEDITION, 1913-18

SHORTLY after the return of the Southern Party of the Canadian Arctic Expedition with their collections in the fall of 1916, steps were taken to arrange for the publication of the scientific results of the expedition. Although the general direction of the operations of the expedition had been under the Department of the Naval Service, most of the scientific men on the expedition were under the Geological Survey, of the Department of Mines, the col

lections were destined for the Victoria Memorial Museum, of Ottawa, and interdepartmental cooperation was desirable in publishing the results. An Arctic Biological Committee was appointed jointly by the two services, to select specialists to report on the various groups of specimens represented in the collections of the expedition, to distribute the specimens, and arrange for the final publication of the reports. This committee consisted of: Chairman, Professor E. E. Prince, commissioner of Dominion Fisheries; secretary, Mr. James M. Macoun, C.M.G., botanist and chief of the biological division of the Geological Survey; Professor A. B. Macallum, chairman of the Commission for Scientific and Industrial Research; Dr. C. Gordon Hewitt, Dominion Entomologist, of the Department of Agriculture, and Dr. R. M. Anderson, zoologist of the Geological Survey and lately chief of the Southern Party of the expedition, representing the expedition. Each member of the committee was made responsible for the editing of reports in his own section, and Dr. R. M. Anderson was appointed general editor of the reports. This committee has been at work for nearly three years, but owing to the difficulty of securing the services of the fifty or more competent specialists needed to work up the reports, on account of the exigencies of war and other reasons, the first of the technical reports was not issued from the press until July 10, 1919.

These biological reports, and to a large extent the geological and ethnological reports which it is hoped will follow them, were mainly the results of the work of the scientists of the Southern Party of the expedition, owing to the unfortunate death or elimination from work of most of the scientific staff of the Northern Party of the expedition and the total loss of their collections with the Karluk in 1914. As a result the later activities of the remainder of that party were practically all geographical and other work and collections merely incidental. The small amount of fragmentary material which was brought back in 1918 has in most cases been included in the reports issued, but in some cases a separate paper will be issued.

The plan adopted by the committee is to issue the report on each group or subject as a separate paper, of the regular octavo size which has been found to be the most convenient and popular for modern scientific papers. Most of the papers are illustrated by line drawings or half-tone engravings from photographs, and in some cases by heliotype or colored plates, illustrating many new species and a few new genera. These papers are mostly too technical to be of interest to the general reader, and the separates are intended to be distributed at time of issue to specialists interested in the particular branch covered, and 1,000 copies of each paper are to be kept by the government and bound into volumes for distribution to public libraries, universities, colleges and other scientific institutions. Eight volumes have been arranged for the biological series, including reports on mammalogy, ornithology, ichthyology and invertebrate marine biology, entomology and botany, and the parts as issued are numbered as parts of these volumes. They are not issued in consecutive order, but each part is printed as it is ready, in order to avoid delay in making the knowledge available to the scientific world and to the public. The amount of specimens and data available and the character and scientific reputation of the specialists engaged in the work promise to make this the most extensive and comprehensive publication on Canadian and western Arctic biology since Richardson and Swainson's "Fauna Boreali-Americana" (1829-31) and Hooker's "Flora Boreali-Americana" (1840).

The volumes in preparation are as follows: Volume I: General Introduction and Narrative. A. Northern Party.

B. Southern Party. Volume II: A. Mammals. B. Birds. Volume III: Insects. (10 parts.) Volume IV: Botany. (Cryptogams) (5 parts). Volume V: Botany. (Phanerogams.) Volume VI: Fishes, Tunicates, etc. (2 parts.) Volume VII: Crustacea. (12 parts.) Volume VIII: Mollusks, Echinoderms, Coelenterates, etc. (9 parts.)

Volume IX: Annelids, Parasitic Worms, Protozoans, etc. (12 parts.)

Volume X: Plankton, Hydrography, Tides, etc.

Eleven of the separate parts of the different volumes have been issued: Volume III-Insects:

Part A-Collembola, by Justus W. Folsom. July 10, 1919.

Part B-Neuropteroid Insects, by Nathan Banks. July 11, 1919.

Part C-Diptera. July 14, 1919.

Crane-flies, by Charles P. Alexander.
Mosquitoes, by Harrison G. Dyar.

Diptera (excluding Tipulidae and Culicidae),
by J. R. Malloch.

Part D-Mallophaga and Anoplura. September 12, 1919.

Mallophaga, by A. W. Baker.

Anoplura, by G. F. Ferris and G. H. F. Nut-
tall.

Part E-Coleoptera. December 12, 1919.
Forest Insects, including Ipidae, Cerambycidæ,
and Buprestidæ, by J. M. Swaine.
Carabidae and Silphide, by H. C. Fall.
Coccinnellidæ, Elateraidæ, Clerysomelida and
Rhynchophora, by C. W. Leng.
Dystiscidæ, by J. D. Sherman, Jr.

Part F-Hemiptera, by E. P. Van Duzee. July 11, 1919.

Sawflies, by Alex. D. MacGillivray.

Parasitic Hymenoptera, by Charles T. Brues.
Wasps and Bees, by F. W. L. Sladen.
Plant Galls, by E. Porter Felt.

Part G-Hymenoptera and Plant Galls, November 3, 1919.

Sawflies, by Alex. D. MacGillivray.

Parasitic Hymenoptera, by Chas. T. Brues.
Wasps and Bees, by F. W. Sladen.

Plant Jalls, by E. P. Felt.

Part H-Spiders, Mites and Myriapods. July 14, 1919.

Spiders, by J. H. Emerton.

Acarina, by Nathan Banks.

Chilopoda, by Ralph V. Chamberlin.

Volume VII.-Crustacea.

Part A-Decapod Crustaceans, by Miss Mary J. Rathbun. August 18, 1919.

Part B-Schizopod Crustaceans, by Waldo L. Schmitt. September 22, 1919.

Volume VIII-Mollusks, Echinoderms, Coelenterates, etc.

Part A-Mollusks, Recent and Pleistocene, by Wm. Healey Dall. September 24, 1919. Volume IX.-Annelids, Parasitic Worms, Protozoans, etc.

Part A-Oligochaeta, by Frank Smith and Paul S. Welch. September 29, 1919.

THE AMERICAN SOCIETY OF NATURALISTS

THE thirty-seventh annual meeting of the American Society of Naturalists was held in Guyot Hall, Princeton University, on December 30 and 31, 1919.

The report of the treasurer showing a balance on hand of $327.33 was accepted.

The following changes in the constitution, recommended by the executive committee, were authorized.

Article III., Section 1, to read: The officers of the society shall be a president, a vice-president, a secretary and a treasurer. These, together with three past-presidents and the retiring vice-president, shall constitute the executive committee of the society.

Article III., Section 2, to read: The president and vice-president shall be elected for a term of one year, the secretary and treasurer for a term of three years. Each president on retirement shall serve on the executive committee for three years. Each vice-president on retirement shall serve on the executive committee for one year. The election of officers shall take place at the annual meeting of the society, and their official term shall commence at the close of the meeting at which they are elected.

On recommendation of the executive committee the society accepted an invitation from the National Research Council to appoint an advisory committee to act with the Division of Biology and Agriculture. The following were elected to this committee: Herbert S. Jennings, Alfred G. Mayor, George H. Shull, Ross G. Harrison, Bradley M. Davis.

A request for financial support from the management of Botanical Abstracts was discussed by the society with the result that a motion was carried to the effect that such appropriations were against the general policy of the American Society of Naturalists.

On motion the society approved of the appointment by the chair of a committee to consider and report on genetic form and nomenclature. This committee consists of Clarence C. Little, Donald F. Jones, Sewall Wright, Alfred H. Sturtevant and George H. Shull.

The following resolution presented by Charles B. Davenport and strongly supported from the floor was adopted.

WHEREAS, A current index of scientific publications is necessary to the progress of science and

can be conducted properly only by bibliographers of experience, and at great expense; and

WHEREAS, The Concilium Bibliographicum of Zurich has for a quarter of a century maintained a valuable and unique service in international bibliography, especially in the fields of zoology, physiology, vertebrate anatomy and general biology; has continued the bibliography of Engelmann and Carus which covers the period from 1700 to the present; and has maintained a service of general bibliographic information; and

WHEREAS, the sciences named are the pure sciences upon which the science of medicine rests;

Therefore resolved, that the American Society of Naturalists (which has in the past made such subsidies to the Concilium as it could afford) cordially endorses the effort of the Concilium Bibliographicum to secure adequate financial support in this country.

There was elected to honorary membership in the society, William Bateson, John Innes Hortioultural Institute, England.

The following were elected to membership: Joseph C. Arthur, Purdue University; Henry C. Cowles, University of Chicago; William Crocker, University of Chicago; Herbert M. Evans, University of California; Edward M. Freeman, University of Minnesota; Aleš Hrdlička, United States National Museum; Clarence M. Jackson, University of Minnesota; Warren H. Lewis, Johns Hopkins Medical School; Ann H. Morgan, Mount Holyoke College; John T. Patterson, University of Texas; Everett F. Phillips, United States Department of Agriculture; Donald Reddick, New York State College of Agriculture; Jacob R. Schramm, New York State College of Agriculture; Homer L. Shantz, United States Department of Agriculture; Henry B. Ward, University of Illinois.

The following program was presented at the morning session of December 30:

Causes of variation in sex ratio of the wasp, Hadrobracon: P. W. WHITING.

Population and race in the Pacific area: W. E. RITTER.

The evolution of Pacific coral reefs: A. G. MAYOR. The relative importance of heredity and environment in determining the piebald pattern of guinea pigs: Sewall Wright,

Relations between nuclear number, chromatin mass, cytoplasmic mass and shell characteristics in Arcella: R. W. HEGNER.

The function of the striae in the rotation of the Euglenoids and the problem of evolution: L. B. WALTON.

Iodine and the thyroid: W. W. SWINGLE.

Selective fertilization in pollen mixtures: D. F. JONES.

Changing by castration the hen-feathered into the cock-feathered condition: T. H. MORGAN. Application of the chromosome theory to embryonic differentiation: E. G. CONKLIN.

The session of the afternoon of December 30 consisted of a symposium on Some relations of biology to human welfare.

The theoretical problems of forestry: RAPHAEL
ZON.

Biology in relation to ethics: W. E. RITTER.
Biology and society: W. M. WHEELER.
The significance of some general biological prin-
ciples in public health problems: RAYMOND

PEARL.

General biology in its relation to medicine: H. E. JORDAN (read by title.)

The program of December 31 consisted of the following papers:

A type of primary non-disjunction in Drosophila melanogaster: A. H. STURTEVANT.

A sex-linked recessive linkage variation in Drosophila melanogaster: C. B. Bridges.

A race of Drosophila willistoni giving a shortage of females: D. E. LANCEFIELD AND C. W. METZ. Mutants and mutability in different species of Drosophila: C. W. METZ.

Two hereditary tumors in Drosophila: MARY B. STARK.

Inheritance of the rubricalyx character in Enothera: G. H. SHULL.

An analysis of an intergrading sex character: A. M. BANTA AND MARY GOVER. Precocious development in Salpa: a biological not a utilitarian phenomenon: M. M. METCALF (read by title.)

Ontogeny versus phylogeny in the development of the sensory apparatus in mammalian embryos: H. H. LANE.

The influence of alcoholized grandparents upon the behavior of white rats: E. C. MACDOWELL AND E. M. VICARI.

Evidence of specific evolution in the genus Partula in the Society Islands: H. E. CRAMPTON. Inheritance of flower form in Phlox Drummondii: J. P. KELLY.

An extra chromosome in Camnula pellucida; variations in the number of chromosomes within the testis: MITCHEL CARROLL.

Inheritance of milk production and butter-fat percentage as shown by first generation hybrids between the dairy and beef breeds of cattle: J. W. GOWEN.

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