It is here virtually--perhaps I may say expressly--conceded that if the matter and energy of the universe be finite and located in infinite space, the reasoning by which the theorists of thermodynamics maintain that perpetual motion is incompatible with the transformation and dissipation of energy, cannot be resisted. Unless matter and energy be infinite or space finite, the known laws of nature must eventually abolish all differences of temperature and destroy all life--this is what is admitted. To me it seems to amount to yielding all that is demanded; because whoever seriously considers the difficulties involved in believing either matter infinite or space finite must, I am persuaded, come to regard it as equivalent to an acknowledgment that the world will have an end and must have had a beginning. Zoellner, in his ingenious work on the nature of comets, endeavours to avoid this inference by recourse to the hypotheses of Riemann and others as to a space of _n_ dimensions. In such a space the shortest line would be a circle, and a body might move for ever, yet describe a limited course. Matter, space, and inferentially time, would, in fact, according to this hypothesis, be both finite and infinite. It is to be hoped that few persons in the full possession of their intellects will ever accept a view like this. The imaginary geometry may be thoroughly sound reasoning, but it is reasoning from erroneous premises, and it can only be useful so long as it is remembered that its premises are erroneous. They have only to be assumed to be true to experience and reality, and all science must be set aside in favour of nonsense. Logic ought not, however, to be confounded with truth. Caspari fancies that by representing the universe as not a mechanism but an organism, he preserves the right to believe it eternal. But surely the laws of heat apply to organisms no less than to mechanisms.