TEE VALVE OF SCIENCE 547 



just as if I were asked if there is an analogous proportion between an 

 auditory sensation, a tactile sensation and an olfactory sensation. 



Let us now consider the internal changes, that is, those which are 

 produced by the voluntary movements of our body and which are 

 accompanied by muscular changes. They give rise to the two follow- 

 ing observations, analogous to those we have just made on the subject 

 of external changes. 



1. I may suppose that my body has moved from one point to an- 

 other but that the same attitude is retained; all the parts of the body 

 have therefore retained or resumed the same relative situation, al- 

 though their absolute situation in space may have varied. I may sup- 

 pose that not only has the position of my body changed, but that its 

 attitude is no longer the same, that, for instance, my arms which before 

 were folded are now stretched out. 



I should therefore distinguish the simple changes of position with- 

 out change of attitude, and the changes of attitude. Both would ap- 

 pear to me under form of muscular sensations. How then am I led 

 to distinguish them? It is that the first may serve to correct an 

 external change, and that the others can not, or at least can only give 

 an imperfect correction. 



This fact I proceed to explain as I would explain it to some one 

 who already knew geometry, but it need not thence be concluded that 

 it is necessary already to know geometry to make this distinction; 

 before knowing geometry I ascertain the fact (experimentally, so to 

 speak), without being able to explain it. But merely to make the dis- 

 tinction between the two kinds of change, I do not need to explain the 

 fact, it suffices me to ascertain it. 



However that may be, the explanation is easy. Suppose that an 

 exterior object is displaced; if we wish the different parts of our 

 body to resume with regard to this object their initial relative position, 

 it is necessary that these different parts should have resumed likewise 

 their initial relative position with regard to one another. Only the 

 internal changes which satisfy this latter condition will be capable of 

 correcting the external change produced by the displacement of that 

 object. If, therefore, the relative position of my eye with regard to 

 my finger has changed, I shall still be able to replace the eye in its 

 initial relative situation with regard to the object and reestablish thus 

 the primitive visual sensations, but then the relative position of the 

 finger with regard to the object will have changed and the tactile sen- 

 sations will not be reestablished. 



2. We ascertain likewise that the same external change may be cor- 

 rected by two internal changes corresponding to different muscular 

 sensations. Here again I can ascertain this without knowing geom- 

 etry : and I have no need of anything else ; but I proceed to give the 

 explanation of the fact employing geometrical language. To go from 



