To know the height of the mainmast does not suffice for calculating the age of the captain. When you have measured every bit of wood in the ship you will have many equations, but you will know his age no better. All your measurements bearing only on your bits of wood can reveal to you nothing except concerning these bits of wood. Just so your experiments, however numerous they may be, bearing only on the relations of bodies to one another, will reveal to us nothing about the mutual relations of the various parts of space. 7. Will you say that if the experiments bear on the bodies, they bear at least upon the geometric properties of the bodies? But, first, what do you understand by geometric properties of the bodies? I assume that it is a question of the relations of the bodies with space; these properties are therefore inaccessible to experiments which bear only on the relations of the bodies to one another. This alone would suffice to show that there can be no question of these properties. Still let us begin by coming to an understanding about the sense of the phrase: geometric properties of bodies. When I say a body is composed of several parts, I assume that I do not enunciate therein a geometric property, and this would remain true even if I agreed to give the improper name of points to the smallest parts I consider. When I say that such a part of such a body is in contact with such a part of such another body, I enunciate a proposition which concerns the mutual relations of these two bodies and not their relations with space. I suppose you will grant me these are not geometric properties; at least I am sure you will grant me these properties are independent of all knowledge of metric geometry. This presupposed, I imagine that we have a solid body formed of eight slender iron rods, _OA_, _OB_, _OC_, _OD_, _OE_, _OF_, _OG_, _OH_, united at one of their extremities _O_. Let us besides have a second solid body, for example a bit of wood, to be marked with three little flecks of ink which I shall call [alpha], [beta], [gamma]. I further suppose it ascertained that [alpha][beta][gamma] may be brought into contact with _AGO_ (I mean [alpha] with _A_, and at the same time [beta] with _G_ and [gamma] with _O_), then that we may bring successively into contact [alpha][beta][gamma] with _BGO_, _CGO_, _DGO_, _EGO_, _FGO_, then with _AHO_, _BHO_, _CHO_, _DHO_, _EHO_, _FHO_, then [alpha][gamma] successively with _AB_, _BC_, _CD_, _DE_, _EF_, _FA_.