In our world of space, which includes all stars, we are the micro-inhabitants. We have been born with, or have inherited, the idea of a straight and ever-advancing path in space, and we become filled with the utmost astonishment if some one asks us to believe that if we undertake a voyage in one direction out into the universe, beyond Sirius and a million times farther, we should finally arrive at our starting-point again, although we had not changed our direction. But the macro-being, who belongs to a universe of higher dimensions and who looks on our world as we looked on the above spherical world one foot in diameter, sees the narrowness of our view. We, too, are in a position to rise above this narrow view by means of a theory founded on our experience, which will lead us to an extended world-geometry, just as the micro-professor used his experience to extend his theory of the circle to include the conception of a sphere. After these preliminary remarks we shall endeavour to get an insight into Einstein's reasoning, not in the form in which it was originally presented (in the Report of the Proceedings of the Berlin Academy of Science of 8th February 1917), but in a very easy description which was given to me during a conversation. Here, too, I shall try to preserve the sense of Einstein's remarks without binding myself strictly to his words. For although I am indebted to him for his efforts to avoid difficult points, yet the aim of this book is, if possible, to make the explanation still easier. Any lack of accuracy arising from this last simplification is to be debited to me. The new form of representing the argument, which is as important as it is fascinating, is, of course, due to Einstein. The final result stated by Einstein was: The universe, both as regards extent and mass, has finite limits and can be measured. If anyone asks whether this can be pictured, I shall not deprive him of the hope. All that is required is a power of imagination that is great enough to follow a pictorial description and that can take up the right attitude towards a sort of figurative representation. Let us again imagine a sphere of modest dimensions with its two-dimensional surface. We are concerned only with the latter, and not with the cubical content. The sphere is to be considered as resting on an absolutely plane white table of unlimited extent in all directions. The sphere touches the table at a single point which we shall call its South Pole; on the top side directly opposite, we have the North Pole. To simplify matters we may make a sketch on paper of a vertical section through the centre of the sphere. This profile-picture will show us the sphere as a circle, and the white table as a straight line; the line joining the two poles is the axis of the globe, and the sectional circle is a meridian.