INTRODUCTION. ii 



cases, the definitions which satisfy scientists mean 

 nothing at all to children ? Why is it necessary to 

 give them other definitions ? This is the question I 

 have set myself in the chapter which follows, and its 

 solution might, I think, suggest useful reflections to 

 philosophers interested in the logic of sciences. 



On the other hand, there are many geometricians 

 who believe that mathematics can be reduced to the 

 rules of formal logic. Untold efforts have been made 

 in this direction. To attain their object they have not 

 hesitated, for instance, to reverse the historical order of / 

 the genesis of our conceptions, and have endeavoured 

 to explain the finite by the infinite. I think I have suc- 

 ceeded in showing, for all who approach the problem 

 with an open mind, that there is in this a deceptive 

 illusion. I trust the reader will understand the im- 

 portance of the question, and will pardon the aridity 

 of the pages I have been constrained to devote to it. 



The last chapters, relating to mechanics and astron- 

 omy, will be found easier reading. 



Mechanics seem to be on the point of undergoing a 

 complete revolution. The ideas which seemed most 

 firmly established are being shattered by daring 

 innovators. It would certainly be premature to 

 decide in their favour from the start, solely because 

 they are innovators ; but it is interesting to state 

 their views, and this is what I have tried to do. As 

 far as possible I have followed the historical order, 

 for the new ideas would appear too surprising if we 

 did not see the manner in which they had come into 

 existence. 



Astronomy offers us magnificent spectacles, and 

 raises tremendous problems. We cannot dream of 



