enunciating a proposition which concerns the mutual relations of the two bodies, and not their relations with space. I assume that you will agree with me that these are not geometrical properties. I am sure that at least you will grant that these properties are independent of all knowledge of metrical geometry. Admitting this, I suppose that we have a solid body formed of eight thin iron rods, oa, ob, oc, od, oe, of, og, oh, connected at one of their extremities, o. And let us take a second solid body—for example, a piece of wood, on which are marked three little spots of ink which I shall call α β γ. I now suppose that we find that we can bring into contact α β γ with ago; by that I mean α with a, and at the same time β with g, and γ with o. Then we can successively bring into contact α β γ with bgo, cgo, dgo, ego, fgo, then with aho, bho, cho, dho, eho, fho; and then α γ successively with ab, bc, cd, de, ef, fa. Now these are observations that can be made without having any idea beforehand as to the form or the metrical properties of space. They have no reference whatever to the "geometrical properties of bodies." These observations will not be possible if the bodies on which we experiment move in a group having the same structure as the Lobatschewskian group (I mean according to the same laws as solid bodies in Lobatschewsky's geometry). They therefore suffice to prove that these bodies move according to the Euclidean group; or at least that they do not move according
