Nay, since the ordinary solid bodies would continue to exist when the mechanician had constructed the strange bodies of which I have just spoken, it would be necessary to conclude that space is at the same time Euclidean and non-Euclidean. Suppose, for example, that we have a great sphere of radius _R_ and that the temperature decreases from the center to the surface of this sphere according to the law of which I have spoken in describing the non-Euclidean world. We might have bodies whose expansion would be negligible and which would act like ordinary rigid solids; and, on the other hand, bodies very dilatable and which would act like non-Euclidean solids. We might have two double pyramids _OABCDEFGH_ and _O'A'B'C'D'E'F'G'H'_ and two triangles [alpha][beta][gamma] and [alpha]'[beta]'[gamma]'. The first double pyramid might be rectilinear and the second curvilinear; the triangle [alpha][beta][gamma] might be made of inexpansible matter and the other of a very dilatable matter. It would then be possible to make the first observations with the double pyramid _OAH_ and the triangle [alpha][beta][gamma], and the second with the double pyramid _O'A'H'_ and the triangle [alpha]'[beta]'[gamma]'. And then experiment would seem to prove first that the Euclidean geometry is true and then that it is false. _Experiments therefore have a bearing, not on space, but on bodies._ SUPPLEMENT 8. To complete the matter, I ought to speak of a very delicate question, which would require long development; I shall confine myself to summarizing here what I have expounded in the _Revue de Métaphysique et de Morale_ and in _The Monist_. When we say space has three dimensions, what do we mean?