An exhaustive treatment of our question would thus divide itself into two parts; the first dealing with real (or geometrical) symmetry, the second with apparent asymmetry; the first seeking to show that there is a real aesthetic pleasure in geometrical symmetry, and that this pleasure is indeed based on the harmony of the motor impulses suggested by symmetry, with the natural motor impulses of the human organism; the second seeking to show in what manner aesthetically pleasing but asymmetrical arrangements conform to the same principles.  Within these two groups of problems two general types of investigation are seen to be required; experiment, and the analysis of aesthetic objects.

The main question, as stated above, is of course whether the theory can explain our pleasure in arrangements which are completely or partly symmetrical.  It is, however, an indispensible preliminary to this question, to decide whether the pleasure in symmetrical arrangements of space is indeed immediate and original.  If it were shown to be a satisfaction of expectation, bred partly from the observation of symmetrical forms in nature, partly from the greater convenience of symmetrical objects in daily use, the whole question of a psychophysical explanation would have no point.  If no original aesthetic pleasure is felt, the problem would be transformed to a demand for the explanation of the various ways in which practical satisfaction is given by symmetrical objects and arrangements.  The logical order, then, for our investigation would be:  First, the appearance of symmetry in the productions of primitive life, as a (debatable) aesthetic phenomenon emerging from pre-aesthetic conditions; secondly, the experimental study of real symmetry; thirdly, the analysis of geometrical symmetry in art, especially in painting and architecture, by means of which the results of the preceding studies could be checked and confirmed.  Having once established a theory of the aesthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art—­i.e., to what extent a substitutional symmetry or balance is found in pleasing arrangements.  These investigations, again, would fall into the two groups of experiment and analysis.  The products of civilized art are too complicated to admit of the complete analysis and isolation of elements necessary to establish such a system of substitution of psychological factors as we seek.  From suggestions, however, obtained from pleasing asymmetrical arrangements, first, isolated elements may be treated experimentally, and secondly, the results checked and confirmed by works of art.