140 SCIENCE AND METHOD. 



to learn to do this when the directions are different. 

 For this purpose we imagine a cord stretched by a 

 weight and passing over a pulley ; we say that the 

 tension of the two portions of the cord is the same, 

 and equal to the weight. 



Here is our definition. It enables us to compare 

 the tensions of our two portions, and, by using the 

 preceding definitions, to compare two forces of any 

 kind having the same direction as these two portions. 

 We have to justify it by showing that the tension of 

 the last portion remains the same for the same weight, 

 whatever be the number and the disposition of the 

 pulleys. We must then complete it by showing that 

 this is not true unless the pulleys are without friction. 



Once we have mastered these definitions we must 

 show that the point of application, the direction, and 

 the intensity are sufficient to determine a force ; that 

 two forces for which these three elements are the same 

 are always equivalent, and can always be replaced one 

 by the other, either in equilibrium or in motion, and 

 that whatever be the other forces coming into play. 



We must show that two concurrent forces can 

 always be replaced by a single resultant force, and 

 that this resultant remains the same whether the body 

 is in repose or in motion, and whatever be the other 

 forces applied to it. 



Lastly, we must show that forces defined as we have 

 defined them satisfy the principle of the equality of 

 action and reaction. 



All this we learn by experiment, and by experiment 

 alone. 



It will be sufficient to quote some common experi- 

 ments that the pupils make every day without being 



