The fact that the spectra of the most distant nebulae shew these large displacements provides a certain presumption in favour of the truth of de Sitter’s cosmology; this at least explains them twice over, while no other cosmology explains them at all. If we tentatively accept this cosmology, then each observed spectral shift must be regarded as the sum of two parts, one arising in the ordinary way from a recession of the nebula, and the other arising merely from its distance. A preliminary study by Dr Hubble has shewn that on the whole the spectral displacements are largest for the most distant nebulae, and that their amounts are roughly proportional to the distances of the nebulae from us. If we interpret the whole of the observed displacements purely as evidence of recession, we can calculate that the radius of the universe is about 2000 million light-years, or some fourteen times the distance of the furthest visible nebula. With so large a radius of the universe, the further displacement resulting from the mere distance of even remote nebulae is negligible, so that our assumption that the displacements arise almost entirely from velocities of recession receives _à posteriori_ vindication. If the observed displacements of the nebular spectra had been strictly proportional to their distances from us, we should have obtained a consistent explanation of the observed facts by assuming that we lived in a de Sitter universe having a radius of about 2000 million light-years. THE EXPANDING UNIVERSE. It used to be thought that the cosmologies of Einstein and de Sitter were antagonistic to one another, since obviously no one universe could be an Einstein universe and a de Sitter universe at the same time. A recent investigation by a Belgian mathematician, the Abbé G. Lemaître, has put a different complexion on the problem. In brief Lemaître has shewn that no universe could stay permanently in the state considered by Einstein. A universe in this state is an unstable structure; immediately it came into being it would start to expand, and would not cease from expanding until it had become a de Sitter universe. Even after this the expansion would continue, but it would now become merged in the normal expansion of the de Sitter universe, such as we have already considered.