4. In this connection it seems not out of place perhaps, 

 to make some, few remarks about the question, in how far we 

 can really speak of true "symmetry" with respect to the geome- 

 trical properties of objects observed in nature? For it is certainly 

 true that we attribute to every animal, to every flower or 

 leaf or crystal, a characteristic external form. Everyone of us 

 can at a glance tell what the difference is between an oak-\ea.i 

 and that of a poplar, or between the octahedral a/wm-crystal and 

 that of quartz. 



But detailed observation soon teaches us that two oak-leaves 

 or two poplar-leaves, two alum-, or two quartz-crystals, are never 

 absolutely identical; and that properly speaking, an undisturbed 

 and invariable regularity of form, as the result of an accurate 

 repetition of definite parts of the object, can never be met with. 

 Thus the one half of the oak-leaf appears never to be precisely 

 the same as the other half; the alum-crystal never has twelve 

 accurately equal angles, etc. Notwithstanding this variability 

 however, we never hesitate in recognising a given leaf as being 

 that of an oak-tree, nor a given alum-crystal as being an octa- 

 hedron. The reason of this is, that as a consequence of our frequent 

 observation of these objects, we have formed an ideal image of 

 the completely developed and perfect leaf or crystal, by abstraction 

 of all that is accidental; and we have learned to consider the observed 

 forms as only more or less perfect approximations to that ideal 

 form. For we are convinced, that if circumstances are more and 

 more favorable to free and undisturbed development during the 

 growth of the oak-leaf or the alum-crystal, we shall find a closer 

 approximation also to the standard-form mentioned. It is only 

 to this imaginary standard-form, that we can extend our consi- 

 derations regarding the symmetry-principle; it is again an idea- 

 listic scheme of nature only, to which these mathematical reaso- 

 nings are to be applied. In common parlance we say that 



also been, brought forward and formulated by G. Heymans: Zeits. f. Psy- 

 chologie und Physiologic der Sinnesorgane, 11. p. 333, 335, 339, 340. (1896). 

 The question is here considered from the general viewpoint of the adaptation 

 of attention to subsequent observation, as a consequence of the psychological 

 preparedness for that coming impression, when its special nature is quali- 

 tatively and quantitatively on the same level with what was expected in 

 imagination. If this.be the case, according to this author, a feeling of comfort 

 and delight will be produced,, because of the easy assimilation of the real 

 occurrence to the analogous expectation already present in our mind. 



