SCIENCE 



A WEEKLY JOURNAL DEVOTED TO THE ADVANCEMENT OF SCIENCE, PUBLISHING THE 



OFFICIAL NOTICES AND PROCEEDINGS OF THE AMERICAN ASSOCIATION 



FOR THE ADVANCEMENT OF SCIENCE. 



Friday, Jantjaet 15, 1909 



CONTENTS 



The American Association for the Advance- 

 ment of Science: — 

 The Problem of Several Bodies — Recent 

 Progress in its Solution: Pbesident Edqab 

 Odell Lovett 81 



The Phyletic Idea im Taxonomy : Fbofessob 

 Chabu:s E. Besset 91 



The Darvnn Centenary 100 



Wolcott Oibis: Peopessoe Theodoee Will- 

 iam RiCHABDS 101 



Soientiflo Notes and News 103 



University and Educational News 106 



Discussion and Correspondence: — 

 A Disclaimer: De. Fbancis G. Benedict. 

 The Late Professor Packard's " Guide to 

 the Study of Insects " : Alpheus Appleton 

 Packabd 107 



Quotations : — 

 The Administration at the University of 

 Illinois 108 



Scientifio Books: — 

 Poulton's Essays: J. P. MoM. The Cenera 

 of African Plants : W. T. Clark and Diefen- 

 dorf's Neurological and Mental Diagnosis: 

 A. M 109 



Scientifio Journals and Articles 113 



Special Articles: — 



The Texas Tertiaries — A Correction: Peo- 



FESSOB E. T. DtTMBLE 113 



The American Association for the Advance- 

 ment of Science: — 

 The Sixtieth Meeting: Db. J. Paul (Joode 114 



The American Mathematical Society 117 



Societies and Academies: — 



The Indiana Academy of Science: Pbo- 

 FESSOE J. H. Ransom. The Philosophical 

 Society of Washington: R. L. Faeis. The 

 Biological Society of Washington: M. C. 

 Mabsh. Section of Geology and Mineral- 

 ogy of the New York Academy of Sciences: 

 Db. Ohables P. Beeket. The New York 

 Section of the America/n Chemical Society: 

 C. M. Joyce 118 



MSS. intended for publication and books, etc., intended for 

 review should be sent to tbe Editor of Science, Garrison-on- 

 Hudson,,N. Y. 



THE AMERICAN ASSOCIATION FOR TEE 



ADVANCEMENT OF SCIENCE 



THE PROBLEM OF SEVERAL BODIES: 



RECENT PROGRESS IN ITS SOLUTION^ 



THE DIPFEEENTIAL EQUATIONS AND THEIR 

 TRANSFORMATIONS 



"Whittaker has formulated the classic 

 problem of three bodies as follows : Three 

 bodies attract each other according to the 

 Newtonian law so that between each pair 

 of particles there is an attractive force 

 which is proportional to the product of the 

 magses of the particles and the inverse 

 square of their distances apart: they are 

 free to move in space and are initially- 

 supposed to be moving in any given 

 manner; to determine their subsequent 

 motion. 



In mathematical phraseology the prob- 

 lem is to integrate a certain system of the 

 eighteenth order of differential equations 

 which at present are usually written in the 

 so-called canonical form 



dF 8F , 



dxi= ^ — dt, dvi= — ^r-dt, 

 dpi ' -^ Bxi ' 



in which t is the time, Xi a coordinate, pi a 

 component of momentum, and F a certain 

 function of all the xi and pi. 



In recent investigations, especially those 

 originating in the researches of Poincare, 

 the canonical equations are preferred to 

 other types because of their simplicity of 



'Abstract of the address of the vice-president 

 and chairman of Section A — ^Astronomy and 

 Mathematics — American Association for the Ad- 

 vancement of Science, Baltimore, 1908. 



