But prior to objects of sense there is a third nature in which they are contained--that is to say, space, which may be explained in various ways. It is the element which surrounds them; it is the vacuum or void which they leave or occupy when passing from one portion of space to another. It might be described in the language of ancient philosophy, as 'the Not-being' of objects. It is a negative idea which in the course of ages has become positive. It is originally derived from the contemplation of the world without us--the boundless earth or sea, the vacant heaven, and is therefore acquired chiefly through the sense of sight: to the blind the conception of space is feeble and inadequate, derived for the most part from touch or from the descriptions of others. At first it appears to be continuous; afterwards we perceive it to be capable of division by lines or points, real or imaginary. By the help of mathematics we form another idea of space, which is altogether independent of experience. Geometry teaches us that the innumerable lines and figures by which space is or may be intersected are absolutely true in all their combinations and consequences. New and unchangeable properties of space are thus developed, which are proved to us in a thousand ways by mathematical reasoning as well as by common experience. Through quantity and measure we are conducted to our simplest and purest notion of matter, which is to the cube or solid what space is to the square or surface. And all our applications of mathematics are applications of our ideas of space to matter. No wonder then that they seem to have a necessary existence to us. Being the simplest of our ideas, space is also the one of which we have the most difficulty in ridding ourselves. Neither can we set a limit to it, for wherever we fix a limit, space is springing up beyond. Neither can we conceive a smallest or indivisible portion of it; for within the smallest there is a smaller still; and even these inconceivable qualities of space, whether the infinite or the infinitesimal, may be made the subject of reasoning and have a certain truth to us.