162 Dadourian — Progressive Development of Mechanics. 



are called linear action and angular action, respectively. 

 Therefore, the action principle states : 



2(A; + A.) = , (A') 



where A? denotes a linear action and k a an angular action. 

 But since A z and A a are independent of each other, the prin- 

 ciple may be stated in two parts : 



I. The sicm of all the external linear actions to which a body 

 or a part of a body is subject at any instant vanishes : 



2Az = . (A,) 



II. The sum of all the external angular actions to which a body 

 or a part of a body is subject at any instant vanishes ; 



2A a = 0. (A fl ) 



In case of equilibrium, forces are the only type of linear action 

 which come into play ; on the other hand, torques (defined as 

 that action of one body upon another which tends to pro- 

 duce a motion of rotation) are the only type of angular action. 

 Therefore, the following well-known conditions of equilibrium 

 follow, immediately, from the two sections of the action 

 principle: 



2 X = , 



(I) 



(II) 



where G denotes a torque, while G x , G v , and G s denote the 

 magnitudes of its components. 



(3) Motion of translation. Here the concept of linear 

 kinetic reaction is introduced as a linear action which is the 

 counterpart of force and which appears whenever a body is 

 given a linear acceleration. The quantitative definition, or the 

 measure, of this new form of action is illustrated by means of 

 the two following ideal experiments. 



(a) An apparatus consisting of a spring balance S (fig. 1), an 

 extensible string of great length, and a block B is set up on 

 a perfectly smooth horizontal table T. The string connects 

 the block with one end of the spring balance, the other end of 

 which is fixed on the table. Suppose, now, two persons to 

 perform the following experiment. One of the experimenters 





%X = o , 



2F = o, 



$Y=0, 





%z = o. 





2^=o, 



2G = o, 



SG v = 0, 





5G Z = 0, 



