160 Dadourian — Progressive Development of Mechanics. 



In this connection it will not be amiss to digress a little on 

 the meanings of the terms "principle" and "law." These 

 terms are often used interchangeably in scientific terminology. 

 There is, however, a wholesome tendency to limit their use to 

 convey two distinct and different ideas. A principle is a gen- 

 eralization derived from a great number of facts. A law, on 

 the other hand, is of the nature of a definition. The former 

 often has to do with an invariant of nature, while the latter 

 gives the form of dependence of one variable upon others. A 

 principle is universally true and of general applicability ; the 

 validity of a law is conditional and its domain of applicability 

 limited. Principles are intuitive, they appeal to inherited 

 instincts and acquired experience. Laws are empirical, they 

 appeal to the intellect and personal knowledge. On this view 

 the conservation of energy, the conservation of momentum and 

 Newton's third law of motion are principles, while the second 

 law of motion and the law of gravitational attraction are laws. 



The greatest field for improvement in the Newtonian system 

 of Mechanics lies in the statement of its underlying principle 

 and in the construction of the system upon this principle as 

 foundation. In Newton's laws of motion a real principle (the 

 third law), a definition (the second law), and a special law 

 (the first) are placed at parity, to say nothing of the points 

 Drought forward in the criticisms made by Hertz, Mach, and 

 others. On the other hand, the various sets of postulates which 

 have been proposed as substitutes for Newton's laws have 

 their own limitations. These postulates do not have the sim- 

 plicity and directness of the laws of motion. Besides, they 

 contain principles which are not characteristic of Dynamics. 

 For instance, the law of the parallelogram of forces, which is 

 often represented as a dynamical principle, is a purely geo- 

 metrical axiom in its general form. When applied to forces 

 it only states that forces are vector magnitudes and conse- 

 quently obey the geometrical principle of the independence of 

 mutually perpendicular directions. 



When all special laws, definitions, and non-dynamical axioms 

 are brushed aside there remains a single dynamical principle, 

 of which the principles of virtual work, of least action, of least 

 curvature, and of least constraint are different forms. The 

 form in which the principle is stated determines, in a great 

 measure, the character of the system of Mechanics which is 

 based upon it. Therefore, when the system of Mechanics is 

 given, as in the present case, the principle must be so stated as 

 to satisfy its needs. The Newtonian system of Mechanics is 

 primarily the beginner's Mechanics ; therefore the statement of 

 the principle should be adapted to the needs of the beginner 

 as well as those of the advanced student. Like the second law 



