were no less illusory, and yet no less significant, than sensuous perceptions. They engaged man in the pursuit of the good and taught him, through disappointment, to look for it only in those satisfactions which can be permanent and perfect. Love, like intelligence, must rise from appearance to reality, and rest in that divine world which is the fulfilment of the human. [Sidenote: Equal rights of empiricism.] A geometrician does a good service when he declares and explicates the nature of the triangle, an object suggested by many casual and recurring sensations. His service is not less real, even if less obvious, when he arrests some fundamental concretion in discourse, and formulates the first principles of logic. Mastering such definitions, sinking into the dry life of such forms, he may spin out and develop indefinitely, in the freedom of his irresponsible logic, their implications and congruous extensions, opening by his demonstration a depth of knowledge which we should otherwise never have discovered in ourselves. But if the geometer had a fanatical zeal and forbade us to consider space and the triangles it contains otherwise than as his own ideal science considers them: forbade us, for instance, to inquire how we came to perceive those triangles or that space; what organs and senses conspired in furnishing the idea of them; what material objects show that character, and how they came to offer themselves to our observation—then surely the geometer would qualify his service with a distinct injury and while he opened our eyes to one fascinating vista would tend to blind them to others no less tempting and beautiful. For the naturalist and psychologist have also their rights and can tell us things well worth knowing; nor will any theory they may possibly propose concerning the origin of spatial ideas and their material embodiments ever invalidate the demonstrations of geometry. These, in their hypothetical sphere, are perfectly autonomous and self-generating, and their applicability to experience will hold so long as the initial images they are applied to continue to abound in perception. If we awoke to-morrow in a world containing nothing but music, geometry would indeed lose its relevance to our future experience; but it would keep its ideal cogency, and become again a living language if any spatial objects should ever reappear in sense.