Such contrivances as we have mentioned only weary instead of aiding the conceptive faculty. If any such help is required for the mind, one of the shortest formulas of arithmetic or algebra, we contend, would be the most effective. The more we can express by the highest symbol, the less is the true grandeur of the thought impaired by any of that imitating and ever-foiled effort of the imagination which attends those longer methods that are addressed solely to it. Let us attempt such a formula by taking at once, for our unit of division, the most minute space ever brought into visibility by the highest power of the microscope. Let our dividend on the other hand, be the utmost distance within which the telescope has ever detected the existence of a material entity. Denote the quotient by the letter _x_, and let _r_ stand for the radius of the earth’s orbit. Then _rx__x_ is the formula sought; and if any one think for a moment on the immense magnitude of the latter part of the expression (_x__x_), and at what a rate the involution expands itself even when _x_ represents a moderate number,(10) he may judge how immeasurably it leaves behind it all other computations. The whole of the universe made visible by Lord Rosse’s telescope actually shrinks to the dimensions of an animalcule in the comparison. And yet, even at that distance, so utterly surpassing all conceivability, we may suppose the existence of worlds still embraced within the dominions of God, and still, in the same ratio, remote from the frontiers of his immeasurable empire.