Dadourian — Progressive Development of Mechanics. 159 



enough to produce the logical obscurity of which the consequences 

 are manifest in the above example." 



These remarks of Hertz apply just as well to a particle 

 which is given a longitudinal acceleration as they do to one 

 which has a transverse acceleration : to a body which has an 

 angular acceleration as to one which has a linear acceleration.* 



It must be stated that the critics of Newton's laws have had 

 greater success in their diagnoses than in their remedies. While 

 most of the criticisms have been well taken, the proposed sub- 

 stitutes for the laws of motion have been unsatisfactory. Hertz 

 proposed to replace Newton's Mechanics by another system 

 based upon the principle of straightest path. Therefore to 

 accept Hertz's proposal amounts to discarding Newton's sys- 

 tem and not to improving it. Some enthusiasts of the prin- 

 ciple of the conservation of energy have advocated to base 

 dynamics on this principle alone without realizing that it is not 

 sufficient and that the principles of the conservation of linear 

 momentum and of angular momentum are necessary to form 

 an adequate basis. Besides, a system of Mechanics based upon 

 these principles can serve the purpose of Newton's Mechanics 

 no more than Lagrange's system. Systems based upon inte- 

 gral principles can supplement but not supplant Newton's 

 Mechanics. 



Ernst Mach and Karl Pearson have each proposedf a set of 

 postulates to take the place of the laws of motion in which the 

 mutual accelerations of particles are made the central concepts. 

 Without going into a detailed discussion of these postulates it 

 may be stated that they contain too many difficult concepts 

 and are too complex to be understood by the beginner, conse- 

 quently they are not suitable bases for Newtonian Mechanics. 



While the systems of Lagrange and Hertz can not fill the 

 place of Newton's system they indicate the direction in which 

 the latter can be improved. These systems are developed in a 

 manner which may be called the unitary form of development. 

 The entire structure of each system is based upon a single 

 principle from which are derived all special laws and relations. 

 This underlying principle permeates the entire subject and 

 gives direction to its development. It makes the science a 

 closely connected and logically developed unit. 



* It is strange that many authors of Mechanics have felt a necessity for 

 "explaining centrifugal force," while no such feeling is shown with regard 

 to the analogous vector magnitude in motion of translation, which is called 

 linear kinetic reaction, in this paper. This is another indication that the 

 famous laws of motion have something vague about them even to the experts 

 on the subject. This is due to the lack of an adequate definition of the 

 term " action " used in the third law. 



f Ernst Mach, Science of Mechanics, p. 243. Karl Pearson, Grammar of 

 Science, Chapter VIII. 



