Dadourian — Progressive Development of Mechanics. 161 



of Thermodynamics it should be simple and direct, yet capable 

 of broad interpretation. It should convey to the student a 

 depth of meaning and a breadth of applicability commensurate 

 with his knowledge and ability. 



In a recent book the present author has based the subject 

 upon a single principle and developed it in a manner which, he 

 believes, deserves the attention of all interested in the science 

 of Mechanics. The principle which is made the foundation of 

 the subject states : 



The sum of all the external actions to which a body {system) or 

 a part of a body [system) is subject at any instant vanishes. 



SA = o* (A) 



The significance of this principle, which may be called the 

 action principle^ is gradually broadened as the needs of the 

 student require it. This is done at four different stages and in 

 connection with four different classes of problems, namely, the 

 equilibrium and motion of a particle and of a rigid body. The 

 following statement gives the salient points in the develop- 

 ment and the line of reasoning used. 



(1) Equilibrium of a particle. A particle which is in 

 equilibrium is subject to only one type of action, namely, the 

 actions of other particles which tend to set it in motion. The 

 vector magnitude which represents the action of one particle 

 upon another is called a force • consequently all actions 

 which come into play in this particular class of problems are 

 forces. Therefore the action principle states that the sum of 

 all the forces to which a particle in the state of equilibrium is 

 subject at any instant vanishes. Hence the following relations 

 form the conditions of equilibrium of a particle : 



ir='o, 



2F = o, sr=o, (I) 



where F denotes a force, while X, Y, and Z denote the magni- 

 tudes of its components. 



(2) Equilibrium of a rigid body. It is shown that a rigid 

 body is capable of having two distinct and independent types 

 of motion, namely, a motion of translation and a motion of 

 rotation. Consequently, a rigid body is capable of being sub- 

 jected to two distinct types of action, one of which relates to 

 translation, while the other is connected with rotation. These 



* Letters in black type denote vector magnitudes. 



+ In the Newtonian system of Mechanics the term action is used in a sense 

 different from that in advanced Dynamics, therefore there is no danger of 

 confounding this principle with the principle of least action. 



