32 THE FOUNDATIONS OF SCIENCE 



the large stone is greater than that of the small stone, 

 and the mass of the iron wheel greater than that of 

 the wooden one, in the proportion of the forces needed 

 to give them the same accelerations. Hence the 

 idea of the mass of a body is reached by considering 

 the force required to give it a certain acceleration. 



It will be seen that in these relations the idea of 

 weight is not involved, and there is no reason to 

 predict that the weight of a body bears any simple 

 relation to its mass as defined above. It is a matter 

 of experiment to investigate the connection, if any, 

 between them. But the necessary experiment had 

 already been made by Galileo, before Newton placed 

 the concept of mass on a sound footing. Since 

 bodies, whether heavy or light, fall to the ground at 

 the same rate, their accelerations are the same. 

 Hence it follows that the forces acting, that is, the 

 weights of the bodies, are proportional to their 

 masses which those forces have to move. 



The mass of a body, then, is proportional to its 

 weight, and the masses of bodies are compared, 

 accurately and easily, by the familiar process of 

 weighing them. 



The unit of mass is defined, like that of length, in 

 terms of a standard. England has a standard pound 

 and France a standard kilogramme, with which other 

 pounds and kilogrammes can be compared and must 

 conform. 



When we have added the unit of mass, M, to those 



