This curvature of space has other functions than that which it performs on the grand scale, of limiting the total volume of space. Before Einstein’s day the curvatures of the paths of planets, cricket balls and projectiles in general were all attributed to the pull of a “force” of gravitation. The theory of relativity dismisses this supposed force as a pure illusion, and attributes the curved paths of projectiles of all kinds to their efforts to keep a straight track through a curved space. This curved space is not, it is true, the ordinary space of the astronomer. It is a purely mathematical and probably wholly fictitious space, in which the astronomers’ space and the astronomers’ time are inextricably bound together and enter as equal partners. To be absolutely exact, there are four equal partners. The first three are the three dimensions of ordinary space—breadth, width, and height, or, if we prefer, north-south, east-west and up-down. The fourth is ordinary time measured in a way appropriate to the way in which we have measured our space (a year of time corresponding to a light-year of space, and so on), and then multiplied by the square-root of -1. This last multiplication by the square-root of -1 is of course the remarkable feature of the whole affair. For the square-root of -1 has no real existence; it is what the mathematician describes as an “imaginary” number. No real number can be multiplied by itself and give -1 as the product. Yet it is only when time is measured in terms of an imaginary unit of √(-1) years that there is true equal partnership between space and time. This shews that the equal partnership is purely formal—it is nothing but a convenient fiction of the mathematician. Indeed had it been anything more, our intuitive conviction that time is something essentially different from space could have had no basis in experience and so would have vanished ere now. These complications with respect to time need not concern us here; the essential point is that Einstein’s theory of relativity teaches that space ultimately bends back on itself like the earth’s surface, so that the total amount of space is finite. THE COSMOLOGY OF EINSTEIN. According to Einstein’s original theory, the dimensions of space are determined by the amount of matter it contains. The more matter there is, the smaller space must be, and conversely; space could only be of literally infinite extent if it contained no matter at all. The problem of determining the extent of space accordingly reduces to that of determining how much matter it contains. We have no means of estimating how much matter may exist outside those regions of space which are within the reach of our telescopes, but within these regions matter seems to be fairly uniformly distributed in the form of extra-galactic nebulae.