SCIENCE 



( JAN 19 19^ 



\. 



■<?*ic 



Fbidat, January 16, 1920 



CONTENTS 

 The American Association for the Advance- 

 ment of Science: — 



Mecent Advances in Dynamics: Propessoe 

 George D. Birkhofp 51 



Sir William Osier: Lieutenant Colonel F. 

 H. Gaerison 55 



Scientific Events: — 



A Botanic School in Regent's Farh; The 

 Attitude of German Physicians towards In- 

 human Actions; Conference on Waste of 

 Natural Gas; Scientific Lectures 58 



Scientific Notes and News 60 



University a7id Educational News 62 



Discussion and Correspondence :— 

 Musical Sands: Professor H. L. Paikchild. 

 More on Singing Sands: E. O. Pippin. The 

 Initial Course in Biology: Professor Yan- 

 DELL Henderson 62 



Scientific Boohs: — 

 Chumley on the Fauna of the Clyde Sea 

 Area: Professor Charles A. Kofoid 65 



The Ecological Society and its Opportunity : 

 Dr. Barrington Moore 66 



The Canadian Branch of the American Fhyto- 

 logical Association 68 



The American Chemical Society : Dr. Charles 

 L. Parsons 69 



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

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

 Hudaon, N. Y. 



RECENT ADVANCES IN DYNAMICS^ 



A HIGHLY important chapter in theoretical 

 dynamics began to unfold witli the appear- 

 an<je in 1878 of G. W. Hill's researches in the 

 lunar theory. 



To understand the new direction taken 

 since that date it is necessary to recall the 

 main previous developments. In doing this, 

 and throughout, we shall refer freely for 

 illustration to the problem of three bodies. 



The concept of a dynamical system did not 

 exist prior to !N"ewton's time. By use of his 

 law of gravitation IsTewton was able to deal 

 with the Earth, Sun, and Moon as essentially 

 three mutually attracting particles, and by the 

 aid of his fluxional calculus he was in a posi- 

 tion to formulate their law of motion by means 

 of differential equations. Here the independ- 

 ent variable is the time and the dependent 

 variables are the nine coordinates of the three 

 bodies. Such a set of ordinary differential 

 equations form the characteristic mathemat- 

 ical embodiment of a dynamical system, and 

 can be constructed without especial difficulty. 



The aim of ITewton and his successors was 

 to find explicit expressions for the coordinates 

 in terms of the time for various dynamical 

 systems, just as Newton was able to do in the 

 problem of two bodies. Despite notable suc- 

 cesses, the differential equations of the prob- 

 lem of three bodies and of other analogous 

 problems continued to defy " integration." 



Notwithstanding the lack of explicit ex- 

 pressions for the coordinates, Newton was 

 able to treat the lunar theory from a geo- 

 metrical point of view. Euler, Laplace, and 

 others invented more precise analytical meth- 

 ods based upon series. In both cases the 

 bodies which are disturbing the motion of the 



1 Address of tie vice-president and chairman of 

 Section A — Mathematics and Astronomy — -Ameri- 

 can Association for the Advancement of Science, 

 St. Louis, December, 1919. 



