$ 180] Newtorfs Laws of Motion : Mass 225 



to attribute in some way to the action of the earth on 

 the bodies. The ordinary process of weighing a body in 

 a balance shews, further, that we are accustomed to think 

 of weight as a measurable quantity. On the other hand, 

 we know from Galilei's result, which Newton tested very 

 carefully by a series of pendulum experiments, that the 

 leaden and the wooden ball, if allowed to drop, fall with 

 the same acceleration. If therefore we measure the effect 

 which the earth produces on the two balls by their 

 acceleration, then the earth affects them equally ; but if 

 we measure it by the power which they have of stretching 

 strings, or by the power which one has of supporting the 

 other in a balance, then the effect which the earth produces 

 on the leaden ball is greater than that produced on the 

 wooden ball. Taken in this way, the action of the earth 

 on either ball may be spoken of as weight, and the weight 

 of a body can be measured by comparing it in a balance 

 with standard bodies. 



The difference between two such bodies as the lea*den 

 and wooden ball may, however, be recognised in quite 

 a different way. We can easily see, for example, that a 

 greater effort is needed to set the one in motion than 

 the other; or that if each is tied to the end of a string 

 of given kind and whirled round at a given rate, the 

 one string is more tightly stretched than the other. In 

 these cases the attraction of the earth is of no importance, 

 and we recognise a distinction between the two bodies 

 which is independent of the attraction of the earth. This 

 distinction Newton regarded as due to a difference in 

 the quantity of matter or material in the two bodies, 

 and to this quantity he gave the name of mass. It may 

 fairly be doubted whether anything is gained by this par- 

 ticular definition of mass, but the really important step 

 v.as the distinct recognition of mass as a property of bodies, 

 of fundamental importance in dynamical questions, and 

 capable of measurement. 



Newton, developing Galilei's idea, gave as one measure- 

 ment of the action exerted by one body on another the pro- 

 duct of the mass by the acceleration produced a quantity 

 for which he used different names, now replaced by 

 force. The weight of a body was thus identified with the 



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