Thus orange is to red what D is to C; and to resume the proportion we used before, red is to eye as C is to ear; yellow: eye: Mi: ear; and so on the proportion extends, till the analogy embraces chords, harmonies, melodies, and compositions even. We have already mentioned the chord of the tonic, and the corresponding eye-music, red, yellow, and blue; let us consider the chord of the dominant or 5th note, whose analogue is blue. This chord is constructed on the 5th of the diatonic as a fundamental note, and consists of the 5th, 7th, and 9th, or returning the 9th an octave, the 5th, 7th, and 2d. The parallel harmony among the spectral colors is blue, violet, and orange. The name 'dominant' indicates the nature of this chord; its often recurring importance in harmonic combinations of a certain key make it easily recognized, and it is even more pleasing than the tonic in its subdued character. Out of doors this chord is preeminent in the sunset key, and the western skies ever chant their evening hymn in the 5th, 7th, and 2d of the ethereal music. The correspondence of the sub-dominant would be red, green, and indigo; of the chord of the 6th, red, yellow, and indigo; and so on, the curious mind may elicit the symmetrical to any notes, half notes, or combinations of notes. It is evident that as a note may be interpolated between any two of the scale, for reach or variety, and called, _e.g._ [sharp]-F or [flat-]G, so a half tint between green and blue is a kind of analogical [sharp]green or [flat]blue. It seems to us that the elementary angles which Mr. Hay conceives to be the tonic, mediant, and dominant, in formal symmetry, will soon be proved to decompose into a scale of linear harmony, forming another beam in this glory of natural analogy. These angles are the fundamental ones of the pentagon square, and equilateral triangle--respectively 108 deg., 90 deg., and 60 deg.. Some such scale it is known existed when art was at its culmination in buried Greece, and it was less the stupendous genius of her designers than the soul of the universe which their rules taught them how to infuse into form, which rendered the marbles of Hellas synonymes for immortality. The most beautiful and conclusive, and yet most mysterious sign, that points the seeker to the prosecution of this last analogy, remains yet for us to remark, and for some investigator yet to take advantage of. It is the nodal figures which arrange themselves upon an elastic plate (as of glass), when it is made to vibrate (strewed with sand) by a fiddle bow drawn across its edge, so as to produce a pitch of some intensity. These have been investigated, and found subject to certain laws, which link into the chain of symmetry that philosophers have already grasped. Among these figures, of which the simplest arise from the deepest pitches, the angles mentioned occur.