Dadourian — Progressive Development of Mechanics. 165 



so that it will describe a circular path it will be observed that 

 its speed remains constant and that the spring balance registers 

 a pull. It follows from the second observation that the particle 

 exerts a force upon the string and in turn is pulled by the 

 string. Considering the particle alone, we see that it is pulled 

 towards the hole but does not approach it, and this in spite of 

 the fact that no force is acting upon the particle to counter- 

 balance that exerted by the string. In order to account for 

 this fact we must introduce, again, the concept of the kinetic 

 reaction. 



Fig. 2. 



The measure of this reaction may be obtained in a manner 

 similar to that employed in (a). When different transverse 

 accelerations are given to the particle by changing its speed, 

 the radius of its path, or both : and then these accelerations 

 are compared with the corresponding readings of the spring 

 balance, the following relations will be found : 



r 



M" 



f" 



E"' 



(4) 



where R {i) is the reading of the balance which corresponds to 

 the acceleration f ii} , while m is a constant which may be called 

 transverse mass. Therefore the transverse kinetic reaction of 

 a particle is proportional to its transverse acceleration. 



If, on the other hand, the particle is replaced by others and 

 the experiment repeated, the following relations are obtained : 



m. 





=/, 



(5) 



where m 15 m 2 , etc., denote the transverse masses of the particles, 

 while jfi? 15 i? 2 , etc., denote the readings of the spring balance 



