June 22, 1906.] 



SCIENCE. 



933 



istics ; but it would be a less radical depart- 

 ure if such transformations or 'operations' 

 were limited to 



A. Rotation (through 180°). 



B. Reflection (in a plane). 



C. Translation (in a straight line). 



The corresponding subdivision of sym- 

 metrical forms would read: 



A. Odd symmetrical. 



B. Even symmetrical. 



C. Rhythmic. 



D. Partial. (Requiring at least two opera- 

 tions. ) 



Another modification which I should sug- 

 gest is an extension of the idea of 'radial' 

 symmetry to include forms which radiate 

 from a point not in the center of the figure. 



SYSTEMS OF STMMETBT. 



I. Radial Symmetry. 

 II. Axial Symmetry. 

 III. Plane Symmetry. 



I. Radial Symmetry. 



1. Central. (Radiant in center of figure.) 



2. Ovoid. (Radiant in axis but not central.) 

 S'. Excentric. (Radiant not in an axis.) 



II. Axial Symmetry. 



1. Circular.^ (Corresponding points on the same 



2. Elliptic. \ perpendicular through axis.) 



.3. Oval. (Corresponding points not on the 

 same perpendicular.) 



III. Plane Symmetry. 



1. Triplanar. 



2. Biplanar. 



3. Bilateral. 



Unsymmetrical forms may be regular; 

 and such may be represented by simple 

 mathematical formulae. 



The study of form relations may appro- 

 priately include the graphs of analytical 

 expressions, and the forms of physical phe- 

 nomena — such as interference patterns; 

 vortex forms of liquids, etc. These last 

 often present close and suggestive analogies 

 with biological forms. 



The various kinds of symmetry and 

 regularity were illustrated by lantern pro- 

 jections of forms selected from graphs of 

 mathematical expressions, from physics, 



from crystallography and from botany and 

 zoology. Most of these last were taken 

 from Haeckel's beautiful 'Kunst-formen 

 der Natur.' 



Before reading his paper, Sir George 

 Darwin presented to the society a medal- 

 lion of Franldin made by Josiali Wedge- 

 wood, Sir George's grandfather. 



Executive Session— 12 :30 P.M. 

 Stated Business— G&ndid&tes for mem- 

 bership were balloted for, and the follow- 

 ing were elected as members of the society : 



RESIDENTS OF THE UNITED STATES. 



Hon. Joseph Hodges Choate, LL.D., D.C.L. 

 (Oxon), New York. 



Henry Herbert Donaldson, Ph.D., Philadelphia. 



Russell Duane, Philadelphia. 



David Linn Edsall, M.D., Philadelphia. 



John W. Harshberger, Ph.D., Philadelphia. 



Charles S. Hastings, Ph.D., New Haven, Conn. 



William Francis Hillebrand, Ph.D. (Heidel- 

 berg), Washington. 



Charles Rockwell Lanman, LL.D., Cambridge, 

 Mass. 



Franklin Paine Mall, M.D., LL.D., Baltimore. 



Ernest Fox Nichols, D.Sc., New York City. 



Hon. Elihu Root, LL.D., Washington. 



Thomas Day Seymour, LL.D., New Haven, Conn. 



Edward Bradford Titchener, M.A. (Oxford), 

 Ph.D. (Leipsic), Ithaca, New York. 



Otto Hilgard Tittmann, Washington. 



Arthur Gordon Webster, Ph.D. (Berlin), 

 Worcester, Mass. 



FOBEIGN EESIDENTS. 



Adolf Engler, Ph.D., Berlin. 



Dr. Hendrik Antoon Lorentz, Leyden, Holland. 



Dmitri Ivanovitch Mendeleff, St. Petersburg. 



Theodor Noldeke, Ph.D., Strassburg. 



August Weismann, Freiburg. 



Afternoon Session — 2 o'clock. 



The Present Position of the Problem Con- 

 cerning the First Principles of Scientific 

 Theory: Professor Josiah Royce, of 

 Cambridge, Mass. 



The Human Harvest: President David 

 Starr Jordan, of Stanford University, 

 Gal. 



