In.  All tree forms lie in or between these two extremes, and leaves are susceptible of a similar classification.  It will be seen to be a classification according to time and space, for the characteristic of time is succession, and of space, simultaneousness:  the first is expressed symbolically by elements arranged with relation to axial lines; the second, by elements arranged with relation to focal points (Illustrations 6,7).

The student should train himself to recognize In and Yo in all their Protean presentments throughout nature—­in the cloud upon the mountain, the wave against the cliff, in the tracery of trees against the sky—­that he may the more readily recognize them in his chosen art, whatever that art may be.  If it happens to be painting, he will endeavor to discern this law of duality in the composition of every masterpiece, recognizing an instinctive obedience to it in that favorite device of the great Renaissance masters of making an architectural setting for their groups of figures, and he will delight to trace the law in all its ramifications of contrast between complementaries in line, color, and mass (Illustration 8).

[Illustration 8:  THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL.  BY TIEPOLO]

With reference to architecture, it is true, generally speaking, that architectural forms have been developed through necessity, the function seeking and finding its appropriate form.  For example, the buttress of a Gothic cathedral was developed by the necessity of resisting the thrust of the interior vaulting without encroaching upon the nave; the main lines of a buttress conform to the direction of the thrust, and the pinnacle with which it terminates is a logical shape for the masonry necessary to hold the top in position (Illustration 9).  Research along these lines is interesting and fruitful of result, but there remains a certain number of architectural forms whose origin cannot be explained in any such manner.  The secret of their undying charm lies in the fact that in them In and Yo stand symbolized and contrasted.  They no longer obey a law of utility, but an abstract law of beauty, for in becoming sexually expressive as it were, the construction itself is sometimes weakened or falsified.  The familiar classic console or modillion is an example:  although in general contour it is well adapted to its function as a supporting bracket, embedded in, and projecting from a wall, yet the scroll-like ornament with which its sides are embellished gives it the appearance of not entering the wall at all, but of being stuck against it in some miraculous manner.  This defect in functional expressiveness is more than compensated for by the perfection with which feminine and masculine characteristics are expressed and contrasted in the exquisite double spiral, opposed to the straight lines of the moulding which it subtends (Illustration 10).  Again, by fluting the shaft of a column its area of cross-section is diminished but the appearance of strength is enhanced because its masculine character—­as a supporting member resisting the force of gravity—­is emphasized.