164: Dadourian — Progressive Development of Mechanics. 



tion, differs from forces and torques, which represent interac- 

 tions between matter and matter and not between ether and 

 matter. 



In order to obtain a quantitative definition of the kinetic 

 reaction, suppose the experiment to be continued in the follow- 

 ing manner. After the block is released one of the experi- 

 menters observes the readings of the balance, while the other 

 records the position of the block at different instants. Then a 

 comparison of the readings of the balance with the correspond- 

 ing accelerations of the block (obtained from the observations 

 of the second experimenter) gives the following result : 



R' B" B'" 



7> = T = r> = --- m > (1) 



where f {i) denotes the acceleration of the block at the instant 

 when the balance registered the pull P (i \ while on is a constant 

 which is called the mass of the block. Thus the kinetic reac- 

 tion of a body is proportional to its acceleration. 



If the blocks be replaced by other blocks and the experiment 

 repeated the same result will be obtained, with the exception 

 that the constant m will, in general, be different for different 

 blocks. If the readings of the balance are compared when 

 different blocks have equal accelerations it will be found that 



3 = x, = A. = .... f< ' m 



m 1 m 2 m 3 



where m 19 m 2 , etc., denote the masses of the blocks, determined 

 in the foregoing manner, while f denotes the common acceler- 

 ation. Therefore, the kinetic reaction of different bodies hav- 

 ing equal accelerations are proportional to their masses. 



It follows from (1) and (2) that the measure of the linear 

 kinetic reaction is given by the relation 



R V = - m T f T , (3) 



where the subscripts are introduced to emphasize the fact that 

 all three of the magnitudes involved in (3) relate to a motion 

 in which the acceleration is tangential, or, longitudinal, while 

 the negative sign is introduced to take into account the fact 

 that R r and f- are oppositely directed. 



(b) In the preceding experiment the acceleration was longi- 

 tudinal : we will now consider a case in which it is transverse. 

 Let P (fig. 2) be a particle placed upon a perfectly smooth 

 horizontal table T, and connected to a spring balance S by 

 means of an inextensible string, which passes through a smooth 

 hole in the center of the table. If the particle be set in motion 



