668 SCIENCE AND HYPOTHESIS 



one equation with several unknowns; but when I have made enough 

 experiments I shall have enough equations to calculate all my un- 

 knowns." If I know the height of the main-mast, that is not sufficient 

 to enable me to calculate the age of the captain. When you have 

 measured every fragment of wood in a ship you will have many equa- 

 tions, but you will be no nearer knowing the captain's age. All your 

 measurements bearing on your fragments of wood can tell you only 

 what concerns those fragments ; and similarly, your experiments, how- 

 ever numerous they may be, referring only to the relations of bodies 

 with one another, will tell you nothing about the mutual relations of 

 the different parts of space. 



7. Will you say that if the experiments have reference to the bodies, 

 they at least have reference to the geometrical properties of the bodies ? 

 First, what do you understand by the geometrical properties of bodies ? 

 I assume that it is a question of the relations of the bodies to space. 

 These properties therefore are not reached by experiments which only 

 have reference to the relations of bodies to one another, and that is 

 enough to show that it is not of those properties that there can be a 

 question. Let us therefore begin by making ourselves clear as to the 

 sense of the phrase: geometrical properties of bodies. Wlien I say 

 that a body is composed of several parts, I presume that I am thus 

 enunciating a geometrical property, and that will be true even if I 

 agree to give the improper name of points to the very small parts I 

 am considering. When I say that this or that part of a certain body 

 is in contact with this or that part of another bod)", I am 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 know- 

 ledge 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 a ft y. I now 

 suppose that we find that we can bring into contact a (3 y with ago; 

 by that I mean a with a, and at the same time ft with g, and y 

 with o. Then we can successively bring into contact a/3y with bgo, 

 ego, dgo, ego, fgo, then with oho, bho, cho, dho, eho, fho; and then 

 ay successively with ab, be, 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 geo- 



