THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 99 



so long as they remain equal the same result will follow. 

 Consequently these bodies may be thought of as possessing 

 a certain equivalence to one another which we may express 

 by saying that they have equal mass. Directly or indirectly 

 it may be shown that bodies of equal mass as thus defined 

 have also, at the same place of observation, equal weight. 

 Since we have agreed to the convention that a body whose 

 weight is equal to the weight of two other bodies of equal 

 weight shall be considered as having twice the weight of one 

 of them, it is natural to think of such a body as having at the 

 same time twice the mass of one of them. But the circum- 

 stances under which the term " equal mass " became applied 

 to the original pair of bodies do not suggest directly any sense 

 which the assertion " A's mass is twice B's " can bear ; so that 

 experiments must be instituted to discover transactions in 

 which it will be possible to find a useful meaning for the 

 assertion in question that shall be in accordance with the 

 assumption that mass is directly proportional to weight. This 

 meaning is reached when it is found that if we take two 

 inelastic bodies A and B of which A is n times as heavy as 

 B and therefore has, ex hypothesi, n times the mass, these 

 bodies will bring one another* to rest if they collide with 

 velocities inversely proportional to these masses. As the 

 result of such observations the " mass " of a body becomes 

 definitely conceived as the reciprocal of the ratio which the 

 velocity of the body in question must bear to that of a standard 

 body whose mass is taken as unity, if in inelastic collision the 

 two bodies are to bring one another to rest. 



43. 



We have now to reach the conviction that this coefficient 

 characterises the behaviour of the body in other transactions 

 besides collisions. Before this step is taken we must note that 

 the equivalence which we have described as equality of mass 

 is only a special case of the more general equivalence pre- 



H 2 



