which we see the deepest recesses of our nature find utterance. From our standpoint, therefore, at which the æsthetic effect is the criterion, we must attribute to music a far more serious and deep significance, connected with the inmost nature of the world and our own self, and in reference to which the arithmetical proportions, to which it may be reduced, are related, not as the thing signified, but merely as the sign. That in some sense music must be related to the world as the representation to the thing represented, as the copy to the original, we may conclude from the analogy of the other arts, all of which possess this character, and affect us on the whole in the same way as it does, only that the effect of music is stronger, quicker, more necessary and infallible. Further, its representative relation to the world must be very deep, absolutely true, and strikingly accurate, because it is instantly understood by every one, and has the appearance of a certain infallibility, because its form may be reduced to perfectly definite rules expressed in numbers, from which it cannot free itself without entirely ceasing to be music. Yet the point of comparison between music and the world, the respect in which it stands to the world in the relation of a copy or repetition, is very obscure. Men have practised music in all ages without being able to account for this; content to understand it directly, they renounce all claim to an abstract conception of this direct understanding itself.