Dadourian — Progressive Development of Mechanics. 1 57 



Art. XI. — On a Progressive Development of Mechanics 

 oased upon a New Form of the Fundamental Principle of 

 the Science ; by H. M. Dadourian. 



There are two general types of methods which, are used in 

 developing systems of Mechanics, and which may be called the 

 differential and the integral types. Newton's method based 

 upon his laws of motion is of the first type, while methods 

 based upon the principle of least action, or upon some equiva- 

 lent integral principle, are of the second type. In order to 

 differentiate between systems of Mechanics which are based 

 upon differential principles and those based upon integral 

 principles we will call the former Newtonian systems and the 

 latter Lagrangian systems. 



In view of the fact that both of these systems are the result 

 of attempts to make a sketch of the same physical universe it 

 is natural to ask : Is the difference between the two systems 

 due to a difference in point of view or is it more intrinsic ? 

 Did Newton and Lagrange simply sketch the same dynamical 

 structure from different angles, or did they picture two dis- 

 tinct and different objects? That these masters portrayed the 

 same physical universe there is no doubt ; yet it will not be 

 correct to state that the pictures which they drew differ only 

 in perspective. There is a difference between the two systems 

 which is more fundamental than the terms "point of view" 

 and " angle of observation " imply. The relation of Newton's 

 system of Mechanics to that of Lagrange may be illustrated by 

 a comparison between an " unassembled " picture of a machine 

 with its " assembled " picture. In an unassembled picture of 

 a generator, for instance, the pictures of individual mechanisms, 

 such as the frame, the armature, the field coils, etc., are shown 

 and are so placed as to give you a clear idea as to their relative 

 positions in the assembled machine. On the other hand, only a 

 few of the mechanisms are visible in the assembled picture, 

 the rest being concealed by the frame. Newton's system 

 represents an unassembled picture of physical phenomena. It 

 aims at bringing into view the inner mechanisms of the inter- 

 actions which result in natural phenomena. Unfortunately 

 it is not always possible to reach this goal. We are very often 

 unable to apply Newton's system of Mechanics to our prob- 

 lems. In other words, it is not always possible to take the 

 machine to pieces. In such a case an assembled picture is 

 drawn by the Lagrangian method. This, however, is not 

 as satisfactory as an unassembled picture, because in the 

 former the nature of the inner mechanisms is left to the 

 imagination to unravel. Our knowledge of a physical phe- 



Am. Jour. Sci. — Fourth Series, Vol. XXXVII, No. 218. — February, 1914. 

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