HELMHOLTZ IN BERLIN 



cases on the speeds of the moving masses ; potential 

 energy by the positions of the masses in any system. 

 The discussion of the different modes of energy, and 

 the conditions of the passage of one mode of energy 

 into another, became the subject-matter of physics 

 and chemistry. Helmholtz did not, as had hitherto 

 been done, deduce the general principles of mechanics 

 from equations of motion, but he started from a more 

 general principle, that of least action. The papers on 

 this subject are, according to Hertz, the high-water 

 mark of modern physics. 



Action, according to Leibnitz, was the product of 

 the mass, the distance through which it was moved, 

 and the speed. In other words, the product of the 

 vis viva (twice the kinetic energy), and the time. 

 According to this view, when a body passed from 

 one configuration into another, the total amount of 

 the action had a limit value, while the amount of 

 the energy remained unchanged. The element of 

 time came into the statement, so that the position 

 of individual parts of the system at specific times 

 during the whole time occupied by the change of 

 configuration could also be taken into account. 

 Lagrange and Hamilton also introduced the idea, 

 that, while the relative amount of potential and 

 kinetic energy were constantly changing, the amount 

 of this change must also be considered ; while 

 Jacobi, assuming that the potential energy is inde- 

 pendent of time, gave the kinetic energy a certain 

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