are in each case caused by the action of symmetrical repetition. 

 As instances of this kind some of the highly Symmetrical vibration- 

 diagrams obtained with Goold's elliptic pendulum, when the ratio 

 of the periods of the two combined vibrations is 3 : 1 , are repro- 

 duced in figures j and 4. Indeed, the principle of form-symmetry 

 in its strict formulation has already been neglected too long in the 

 morphological and systematical description of the biological sciences; 

 or at least: its scanty applications have been too rudimentary and 

 insufficient in almost all cases. In this respect it is most necessary 

 that the obsolete and unwieldy definitions of form still in vogue 



Fig. 3. 



Vibration-figure, obtained with an elliptic pendulum. 



in these sciences, should be finally abandoned for a rational sys- 

 tem of description, in which the doctrine of symmetry is the 

 trustworthy guide. 



For our purpose it is only necessary for the moment to keep 

 in mind that the "symmetry" of a figure consists in some 

 regular repetition of definite parts of it. Thus such figures can be 

 made to coincide with themselves in several ways, either by 

 superimposing or by some other operation. 



3. With respect to the aesthetic value x ) of the symmetry- 



obtained e.g. with J. Goold's elliptic pendulum. A most remarkable and charac- 

 teristic feature of combined elliptical movements is this, that the resulting har- 

 monic motion is symmetrical, whenever the sum or difference of the ratio-numbers 

 of the composing movements is even, but unsymmetrical, when it is odd. On the 

 special symmetry of Lichtenberg's electrical figures, cf . : S.Mikola, Phys. Zeits., 

 18, 158. (1917). 



!) Cf.: H. N. Day, Aesthetics, 72, p. 76, (1872): "Akin to this beauty of 

 proportion is the beauty of symmetry", etc. Suggestive ideas of this kind are also 

 to be found in V. Goldschmidt's book: "Ueber Harmonie und Komplikation" , 



