Even when the concomitant rhythms are not expressed, as in an unaccompanied solo, an accompaniment of some sort is present in the motor apparatus, and contributes its effect to the consciousness.  This regulation of the movement by the coincidence of several rhythms is the cause of the striking regularity of the temporal relations.  At some points in the musical series the several movement cycles may appear in the same phase, and at these points the same irregularities as in verse are possible, as in the case of pauses at the ends of periods and the irregularities of phrasing.  It is evident in cases of expressional variations of tempo that a single broad rhythm is dominating and serving as a cue for the other more elaborate rhythmic processes, instead of being regulated by them.

* * * * *

STUDIES IN SYMMETRY.[1]

BY ETHEL D. PUFFER.

   [1] SOURCES OF ILLUSTRATIONS.

   Fig. 1 was copied from Reiss u.  Stuebel, ‘Todtenfeld v.  Ancou,’
   Berlin, 1880-1887.

   Figs. 2, 3, 4, 5, 6, 7, 8 and 11 were copied from the
   publications of the American Bureau of Ethnology by the kind
   permission of the Direction.

   Fig. 9. was copied from A.C.  Haddon, ’The Decorative Art of
   British New Guinea,’ Cunningham Memoir, N., Royal Irish
   Academy, 1894.

   Fig. 10 was copied from Franz Boas, ’The Decorative Art of the
   Indians of the North Pacific Coast,’ Bulletin of the Am.  Mus.
   of Nat.  Hist., Vol.  IX.

I. THE PROBLEMS OF SYMMETRY.

The problem of aesthetic satisfaction in symmetrical forms is easily linked with the well-known theory of ‘sympathetic reproduction.’  If there exists an instinctive tendency to imitate visual forms by motor impulses, the impulses suggested by the symmetrical form would seem to be especially in harmony with the system of energies in our bilateral organism, and this harmony may be the basis of our pleasure.  But we should then expect that all space arrangements which deviate from complete symmetry, and thus suggest motor impulses which do not correspond to the natural bilateral type would fail to give aesthetic pleasure.  Such, however, is not the case.  Non-symmetrical arrangements of space are often extremely pleasing.

This contradiction disappears if we are able to show that the apparently non-symmetrical arrangement contains a hidden symmetry, and that all the elements of that arrangement contribute to bring about just that bilateral type of motor impulses which is characteristic of geometrical symmetry.  The question whether or not this is the fact makes the leading problem of this paper, and the answer to it must throw light on the value of the theory itself.