DEFINITIONS AND EDUCATION. 141 



aware of it, and to perform before them a small 

 number of simple and well-selected experiments. 



It is not until we have passed through all these 

 roundabout ways that we can represent forces by 

 arrows, and even then I think it would be well, from 

 time to time, as the argument develops, to come back 

 from the symbol to the reality. It would not be 

 difficult, for instance, to illustrate the parallelogram 

 of forces with the help of an apparatus composed of 

 three cords passing over pulleys, stretched by weights, 

 and producing equilibrium by pulling on the same 

 point. 



Once we know force, it is easy to define mass. 

 This time the definition must be borrowed from 

 dynamics. We cannot do otherwise, since the end 

 in view is to make clear the distinction between mass 

 and weight. Here, again, the definition must be pre- 

 pared by experiments. There is, indeed, a machine 

 that seems to be made on purpose to show what 

 mass is, and that is Atwood's machine. Besides this 

 we shall recall the laws of falling bodies, and how 

 acceleration of gravity is the same for heavy as for 

 light bodies, and varies according to latitude, etc. 



Now if you tell me that all the methods I advocate 

 have long since been applied in schools, I shall be 

 more pleased than surprised to hear it. I know that 

 on the whole our mathematical education is good ; I 

 do not wish to upset it, and should even be distressed 

 at this result ; I only desire gradual, progressive im- 

 provements. This education must not undergo sudden 

 variations at the capricious breath of ephemeral fashions. 

 In such storms its high educative value would soon 

 founder. A good and sound logic must continue to 



