Mr. R. F. Muirhead on the Laws of Motion. 483 



measured, should we hesitate between rejecting the law or 

 rejecting the method of force-measurement ? And it is certain 

 that we cannot find a spring-balance which would render this 

 event unlikely to happen. 



A more promising method would be the definition of unit 

 of force as the weight of a certain piece of matter at a certain 

 place on the Earth's surface. The force F would then be de- 

 fined as being equal to the weight of a body whose mass was 

 F times the standard mass. This would involve an inde- 

 pendent method of mass-measurement, which we shall con- 

 sider later. In treating questions of the secular changes of 

 the Earth such a definition would be useless, unless we were 

 also to specify the date as well as the place of the weighing 

 supposed to be at the base of force-measurement ; and this 

 could not be brought into connexion with measurements at 

 any other date without employing the whole science of Dyna- 

 mics, which would thus involve reasoning in a circle. 



A modification of this method would be one in which force- 

 measurement would be made to depend on the gravitational 

 or astronomical unit of mass, as well as the theory of the 

 force of gravitation. But this also would be a system of 

 force-measurement, involving for its conception the whole 

 science of Dynamics, of which it would not be independent. 



When Statics is treated as a science, independent of Kine- 

 tics, force is sometimes left undefined at first, while the mode 

 of procedure is as follows : — We are supposed to have a 

 certain idea of the nature of force, partly based on the sensa- 

 tions we experience when our body forms one of the two 

 bodies which exert force on one another*, and starting from 

 this, by the aid of a priori reasoning the idea of the measure- 

 ment of force is evolved. Then, with the help of certain 

 physical axioms and constructions (" transmissibility of force/' 

 " superposition of forces in equilibrium," &c), the parallelo- 

 gram of forces is proved. 



All this has a very artificial character, and would lead us 

 to prefer the simpler kinetic conception of force; but still 

 further argument is required before we get to Kinetics. The 

 " Second Law of Motion " is proved by means of experiments 

 which could not be accurately performed, and whose inter- 

 pretation generally involves a knowledge of the science whose 

 foundations we are laying. Then the proportionality of force 

 to mass is thus proved: — 



Suppose two equal masses acted on by equal and parallel 



* The so-called u sense of force" should be called "sense of stress." 

 Our bodies subjected to forces, however great, if the force on each part is 

 proportional to its mass and in a common direction, feel nothing. 



