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, edited by J. McKeen 

 Cattell and published every Friday by 



THE SCIENCE PRESS 



I I Liberty St., Utica, N. Y. Garrison, N. Y, 



New York City: Grand Central Terminal 

 SiBsle Copies, 15 Cts. Annual Subscription, S6.00 



Entered ae second-class matter January 21, 1922, at the Poft 

 Office at Utica, N. Y., under the Act of March 3, 1879. 



Vol. LV February 24, 1922 No. 1417 



THe American Association for the Advance- 

 ment of Science: 

 A Mechanical Analogy in the Theory of 

 Equations: Peopessor D. E. Cubtiss 189 



William Bateson on Darwinism: Db. Henby 

 Faiefield Osbokn 194 



Science in the Philippines: Dr. J. C. Witt.... 197 



Charles Henry Davis Snd 200 



Scientific Events: 

 British Scientifio Instrwihents ; An English 

 Journal of Scientific Instruments; Journal 

 of the Optical Society of America and 

 Seview of Scientific Instruments; Gift of 

 Proceeds of Research for Research; Pro- 

 fessor J. W. Tourney and the Yale School 

 of Forestry 200 



Scientific Notes and News 203 



University and Educational Notes 206 



Discussion and Correspondence: 



Kilobar, Kilocal, Kilograd: Professor 

 Alexander McAdie. The Geology of 

 Western Vermont: Dr. C. E. Gordon. 

 Acute Sense of Sound Location in Birds: 

 Joseph Maillaibd 207 



Scientific BooTcs: 



Lacroix on Deodat Dolomieu: Dk. Geobge 



P. KuNZ 209 



Special Articles: 



Dissociation of Hydrogen in a Tungsten 

 Furnace and Low Voltage Arcs in the Mon- 

 atomio Gas: De. O. 8. Duffenback. A 

 Simple Method of Dealing with Electrified 

 Microsections : Dr. S. W. Geisee 210 



The American Chemical Society: Db. Charles 

 S. Parsons 212 



A MECHANICAL ANALOGY IN THE 

 THEORY OF EQUATIONS^ 



To the mathematician the solution of a prob- 

 lem is the more interesting if it utilizes meth- 

 ods and principles from fields that at first 

 glance seem foreign to the one in which the 

 problem lies. The question of whether a linear 

 differential equation has algebraic solutions is 

 sufficiently important to attract attention of 

 itself, but its answer by reference to the prop- 

 erties of regular polyhedrons has become a 

 mathematical classic. Such analogies are not, 

 however, to be regarded as mere tours de force 

 whose purpose is only to astonish, or to 

 appeal to a certain esthetic sense; the instance 

 just mentioned shows that the new point of 

 view may disclose wide vistas hitherto undis- 

 cerned. If there is a choice of terms in which 

 the analogy may be stated, the formulation 

 which is most concrete and most striking may 

 also be the most illuminating. 



Such considerations as these, doubtless, have 

 led to the description of what are essentially 

 vector methods with complex variables in 

 terms of mechanical systems. I propose here 

 to discuss the progress that has been made by 

 the aid of such an interpretation in studying 

 the distribution in the complex plane of the 

 roots of algebraic equations in one variable. 



On the algebraic side the chief purpose of 

 the investigations to be considered has been to 

 obtain what may be called theorems of separa- 

 tion, i. e., theorems which state whether roots " 

 of an equation do or do not lie in specified 

 regions of the complex plane. Such theorems 

 may also state how many roots lie in the speci- 

 fied regions, or may give limits, inferior or 

 superior, for the number of roots thus situ- 

 ated. These regions may be defined in terms 



1 Address of the vice-president and chairman 

 of Section A — Mathematiea, American Associa- 

 tion for the Advancement of Science, Toronto, 

 1921. 



