Numerical proportions are the roots of that shaft of harmony which, springing from motion, rises and spreads into the nature around us, which the senses appreciate, the spirit feels, and the reason understands. Beauty is order, and the infinity of the law is testified in the ever-swelling proofs of an unlimited consonance in creation, of which these analogies are the smallest types. But the idea of numerical analogy is not new to our age, now that the atomic theory is established, and people are turned back to the days when the much bescouted alchemist pored with rheumy eyes over the crucible, about to be the tomb of elective affinity, and whence a golden angel was to develop from a leaden saint: when they are reminded of the Pythagorean numbers, and the arithmetic of the realists of old, they may very well imagine that the vain world, like an empty fashion, has cycled around to some primitive phase, and look for the door of that academy 'where none could enter but those who understood geometry.' But to return. When the ear accepts a tone, or the eye a single color, it is noticed that these organs, satiated finally with the sterile simplicity, echo, as it were, in a soliloquizing manner, to themselves, other notes or tints, which are the complementary or harmony-completing ones: so that if nature does not at once present a satisfaction, the organization of the senses allows them internal resources whereon to retreat. 'There is a world without, and a world within,' which may be called complementary worlds. But nature is ever liberal, and her chords are generally harmonies, or exquisite modifications of concord. The chord of the tonic, in music, is the primal type of this harmony in sound; it is perfectly satisfactory to the tympanum; and the ear, knowing no further elements (for the tonic chord combines them all), can ask for nothing more. This chord, constructed on the tonic C, or Do, as a key note, and consisting of the 1st, 3d, and 5th of the diatonic scale, or Do, Mi, Sol, is called the fundamental chord. The harmony in color which corresponds to this, and leaves nothing for the eye to desire, is, of course, the light that nature is full of--sunlight. White light is then the fundamental chord of color, and it is constructed on the red as the tonic, consisting of red, yellow, and blue, the 1st, 3d, and 5th of the solar spectrum. This little analogy is suggestive, but its development is striking. The diatonic scale in music, determined by calculation and actual experiment on vibrating chords, stands as follows. It will be easily understood by musicians, and its discussion appears in most treatises on acoustics: Do Re Mi Fa Sol La Ti Do C, D, E, F, G, A, B, C, &c. 1 9/8 5/4 4/3 3/2 5/3 15/8 2.