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ceding popular editions. There is a modicum of descriptive text to enable the investigator to proceed with intelligent appreciation in the application of the methods described to practical problems of diagnosis. The book is somewhat unique in respect to the systematic manner in which the uses of laboratory clinical diagnosis are presented and also in the large number of data on "normals" which serve as a basis for comparison. Perhaps the book can best be described as a compact, compendious well illustrated vade mecum for those who have occasion to apply either chemical, bacteriological or microscopic technique as diagnostic aids.

L. B. M.

9. Memoirs of the Bernice Pauchi Bishop Museum of Polynesian Ethnology and Natural History. Volume VI, No. 3. 4to, pp. 359-546.-Fornander collection of Hawaiian antiquities and folklore; by ABRAHAM FORNANDER, with translations by THOMAS G. THRUM.

10. New Geography, Book 1; by ALEXIS EVERETT FRYE. Pp. viii, 264. Boston, 1920 (Ginn & Co.).-This publication, from the Frye Atwood Geographical Series, is much to be commended for the variety and attractive character of the subject matter as well as for its ample illustrations which include 539 text figures as also a series of geographic and other plates. It differs from the dry publications of an earlier period in style as well as in subject matter and cannot fail to be interesting and instructive to the youthful generation for which it is prepared. Dr. Atwood of Harvard University has lent his assistance and many of the excellent pictures included have already appeared in the National Geographic Magazine. There is also a supplement giving the population of the principal cities, relief maps and other matters of interest.

11. Memoirs of the Queenland Museum, HEBER A. LONGMAN, Director, Volume 7, Part I, Brisbane.-This issue contains papers on several natural history subjects. One of these is a continuation of the edible Fishes of Queensland by J. DOUGLAS OGILBY. Two papers are devoted to Queensland flies, one by T. H. JOHNSTON and M. J. BANCROFT; another by C. P. ALEXANDER. occurrence of the little Penquin is noted by the Director, H. A. LONGMAN.

The

12, Transactions and Proceedings of the New Zealand Institute, Wellington, N. Z. Volume 52 (new series).-This embraces 544 pages with a large number of plates and text figures. The field covered includes anthropology, botany, chemistry, geology, and zoology, and many of the papers merit an individual notice which is here impossible.

13. The National Academy of Sciences.-The Annual Meeting of the National Academy of Sciences will be held at the United States National Museum, Natural History Building, April 25 to 27, 1921. Several features of unusual interest are promised. The Prince of Monaco, who is to receive the Agassiz Medal, will give an address on Monday evening, April 25, on his long continued and highly valued researches in oceanography.

another occasion Dr. W. S. Adams, of Pasadena, will speak of

his many years of investigation whereby for the first time the spectrum classification, distances, absolute magnitudes, velocities, and directions of motion in space of nearly 2,000 stars are fully known, so that a new far-reaching view of the arrangement of the stellar system appears.

A large attendance is anticipated and the Home Secretary, Dr. C. G. Abbot, has already called for a list of papers, from those of 10 minutes in length to others embracing 15 to 30 minutes.

14. Observatory Publications.-Recent acquisitions include the following:

The Annual Report of the Naval Observatory for the fiscal year 1920.-This forms appendix No. II to the annual report of the Chief of the Bureau of Navigation.

Washburn Observatory of the University of Wisconsin, volume 13, part 1; by ALBERT S. FLINT, Astronomer.-This important work contains meridian observations for stellar parallax, from 1898 to 1905. These were conducted by the method of meridian transits similar to those of volume 11 of the observatory, with some minor changes in conditions. Twelve students were employed in the computations, chiefly graduates and undergraduates. The list of stars observed extends from -35 degrees in declination to the Pole.

Leander McCormick Observatory of the University of Virginia, volume III-Parallaxes of 260 Stars, by S. A. MITCHELL. Publications of the Yerkes Observatory, volume IV, part III.— Parallaxes of fifty-two stars; by GEORGES VAN BIESBROECK and Mrs. HANNAH STEELE PETTIT.

Contributions from the Princeton University Observatory, No. 5.-Photometric researches: the eclipsing variable, U Cephei; by RAYMOND SMITH DUGAN.

15. A Laboratory Manual of Anthropometry; by HARRIS H. WILDER, professor of zoology at Smith College, Northampton, Mass. Pp. 200, 43 illustrations. Philadelphia, 1920 (P. Blakiston's Sons & Co.).-In order that the records of each observer may be readily made use of by every other observer, it is imperative that series of measures be uniform and be taken in uniform ways. The matter of unification was first placed upon an international basis by the International Congress of Anthropologists held at Monaco in 1906. The unification process was carried still further at the Geneva Congress in 1912. There remain for consideration at some future Congress the general skeletal measures, exclusive of the cranium and lower jaw.

The work of the special International Commissions of the two Congresses rightly forms the basis of Wilder's Laboratory Manual. However his statement on page vi of the preface, that the periodicals in which the reports of the labors of the two Commissions "appeared were exclusively European" is incorrect; for report from the reviewer's pen of the work accomplished at Geneva appeared both in the American Anthropologist and in Science for the year 1912.

To the measures accepted by international agreement, the author adds a convenient and useful list of general skeletal measures, as well as angles and indices. No mention is made of the spheno-maxillary angle, which might well find a place even in an abridged manual. His enumeration of instruments and description of the manner in which they are employed are done with a thorough knowledge of the difficulties which beset the beginner. The pages devoted to simple biometric methods were written for the benefit of the student, whose chief interest is in morphological relations, and whose mathematical ability and training are not sufficient to enable him to follow abstruse biometric methods.

To the laboratory student of the subject, Wilder's Manual is recommended for its lucidity and conciseness, as well as for the author's ability to transmit a maximum amount of his own pervading enthusiasm for the subject by means of the printed page. For good measure, two instructive appendices are added: A, Measures of Skulls of 93 Indians from Southern New England; 'B, Bodily Measures of 100 Female College Students. Yale University.

GEORGE GRANT MACCURDY.

OBITUARY.

DR. WILLIAM T. SEDGWICK, professor of biology and public health at the Massachusetts Institute of Technology, authority on biology and sanitation, and for a time president of the American Health Association, died suddenly on January 26. He was born in West Hartford, Conn., in 1855, was graduated from Sheffield Scientific School in 1877, and received the degree of Ph.D. from Johns Hopkins in 1881. Among his many activities he was curator of the Lowell Institute, Boston, 1897; he was also a member of the advisory board Hygienic Laboratory, United States Public Health Service, 1902, and at one time president of the Boston Civil Service Reform Association.

He was a man of charming personality and the value of his services to this country from east to west, particularly in biology and sanitation, can hardly be overestimated.

SIR LAZARUS FLETCHER, the distinguished English mineralogist, died in January in his sixty-seventh year. In addition to his many and important contributions to his department of science he was the keeper of the mineral department of the British Museum for some forty years; in this connection he had the responsibility for the removal and installation of the collections from their early home at Bloomsbury to the new Museum of Natural History in South Kensington.

DR. LINCOLN WARE RIDDLE, assistant professor of cryptogamic botany and associate curator of the Farlow Herbarium, died at Cambridge on January 16 in his forty-first year.

DR. ALEXANDER MUIRHEAD, the British physicist, died on December 13 at the age of seventy-two years.

FRÉDÉRIC HOUSSAY, professor of zoology at the Sorbonne since 1904, and dean in 1919, died recently in Paris.

THE

AMERICAN JOURNAL OF SCIENCE

[FIFTH SERIES.]

ART. XVIII.—Determinate Orbital Stability: its Mechanism and some of its Functions in Celestial Mechanics; by FRANK BURSLEY TAYLOR.

CONTENTS.

Introduction.

The three kinds of equilibrium.

Equilibrium and orbital stability.

The mechanism of determinate orbital stability.

Some functions of determinate orbital stability in celestial mechanics.

Introduction.

The subject to be considered in this paper is the stability of the Moon's revolution around the Earth, with special reference to the quality of that stability, whether it be determinate or indeterminate in a sense defined below. I have not as yet seen any writing in which the quality of the stability of the Moon's revolution is considered from the point of view here presented. Present and recent textbooks and treatises discuss the motion of the Moon and the perturbing action of the Sun's attraction, but they seldom mention stability as such, and do . not discuss its quality.

The Three Kinds of Equilibrium.

Before beginning the discussion of the quality of the Moon's stability, it is necessary to take note of certain theoretical considerations which have an important bearing on this subject.

The general definition of the word "equilibrium” is given as "equipoise; the state of being equally balanced; a situation of a body in which the forces acting on it AM. JOUR. SCI.-FIFTH SERIES, VOL. I, Nɔ. 4.—APRIL, 1921.

balance one another." Then continuing by way of elaboration and further definition, three kinds of equilibrium are defined as follows:

"When a body, being slightly moved out of its position, always tends to return to its position, the latter is said to be one of stable equilibrium; when a body, on the contrary, once moved, however slightly, from the position of equilibrium, tends to depart from it more and more, like a needle balanced on its point, its position is said to be one of unstable equilibrium; and when a body, being moved more or less from its position of equilibrium, will rest in any of the positions in which it is placed, and is indifferent to any particular position, its equilibrium is said to be neutral or indifferent."

A needle balanced on its point is a typical illustration of an unstable equilibrium. A billiard ball of homogeneous composition and density, resting on the smooth surface of a billiard table, is in equilibrium. If it be moved to any other place on the table it will rest there in its new position just as well as in its first position, and it has no tendency to return to its first position. This is a typical illustration of neutral or indifferent equilibrium. A weight freely suspended by a cord from a fixed point hangs toward the center of the Earth, and is in equilibrium. If it be pushed aside in any direction it will oscillate for a time, but will always return at last to its original position as the only place where it can find equilibrium. Thus, every force or impulse which disturbs the suspended weight from its original position brings into action another force which causes it to return to that position. This device is called a pendulum, and is a typical illustration of stable equilibrium.

The distinctions between these three kinds or qualities of equilibrium are useful in connection with the present paper, because, theoretically, they may be taken to represent corresponding types of stability in orbital revolution, and hence furnish a convenient basis for a determination of the quality of the stability of the Moon's revolution around the Earth.

1 From the Century Dictionary. This definition was chosen rather than one from a textbook of physics or dynamics mainly because it suited the present purpose better than any found in such sources. In his "Physics,'' (advanced course), 1892, page 79. Prof. G. F. Barker defines Staties as "that branch of Dynamics which investigates the action of force in maintaining bodies in equilibrium.' "Matter in motion is in equilibrium when its acceleration is zero. Referring to the equilibrium of floating bodies on pages 160 and 161, Barker defines the three kinds and gives them the same meanings as are given above.

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