particular impression on the observer. If, however, this meaningless 

 figure is repeated several times by rotating it round an axis A 

 perpendicular to the plane of the figure, each time through an 

 angle of 72, the pattern of fig. 2 'will be produced. This pattern, 

 on the other hand, makes an undeniable "aesthetic" impression. 

 In the same way the particular effect of the patterns of wallpapers, 

 of drapery-, or dress-materials, is produced, and also that of the 

 symmetrical ornaments 

 which are met with 

 more particularly in 

 classic architecture. 



In the wellknown 

 mirror-kaleidoscopes , 

 the surprising and very 

 beautiful effects are 

 obtained by means of 

 the repeated reflection 

 in regularly arranged 

 little mirrors. A num- 

 ber of insignificant 

 pieces of coloured glass 

 which are thrown to- 

 gether by mere chance, 

 will however now seem Fig. 2. 



to be purposely arran- 

 ged and combined in beautifully shaped, coloured patterns. Here 

 also the aesthetic action is caused exclusively by the regular 

 repetition of the same arbitrary figure. The splendour and fasci- 

 nating beauty of a great number of living creatures: radiolaries, 

 medusae, diatomeae, corals, starfishes, of innumerable flowers', that 

 of the splendid forms of many crystals and of the figures produced in 

 Lissajous' wellknown experiments with combined harmonic vibra- 

 tions, in vibrating membranes (eidophone) or metalplates (Chladni's 

 sand-figures), especially the splendid diagrams obtained by means 

 of the modern elliptic and twin-pendulums or harmonographes *), - 



1 ) D. Brewster, Treatise on the Kaleidoscope, Edinburgh, (1819). 



2 ) J. Goold, Ch. E. Benham, R. Kerr, and L. R. Wilberforce; Edid. H. C. 

 Newton, Harmonic Vibrations and Vibration Figures, London; Th. Bazley, 

 Index to the Geometrical Chuck, (1875). Remarkable symmetrical figures can be 



