MATHEMATICS 



dynamics quite simply, in the historical order of 

 its development. Beginning with Newton's simple 

 laws of motion for ' particles ' the important one 

 being the formula 



P = mf 



familiar to all elementary students the corre- 

 sponding laws for a rigid body or system of rigid 

 bodies, or for a fluid, which are in their nature a 

 kind of integration or summation of the results 

 of applying this law to all the individual particles 

 composing the body or fluid, have been built 

 up, and, naturally, ultimately take very general 

 forms such as Lagrange's equations, which can be 

 used for any possible way of specifying the positions 

 of parts of the system at any moment, or alterna- 

 tively, in the case of fluids, the Helmholtz equations. 

 But in spite of their appearance in such a general 

 shape, they contain no more than Newton's laws. 

 Hamilton reduced them to one fundamental 

 principle applicable to any system, from which 

 everything in dynamics can be deduced the Law 

 oj Least Action, In the hands of Larmor this 

 was made a foundation for the laws of electro- 

 dynamics deduced by Maxwell, and for the mathe- 

 matical side of our conception of the electron and 

 of its radiation of energy when in a state of ac- 

 celerated motion. Electromagnetic theory and 



thence, light being an electromagnetic pheno- 



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