HERMANN VON HELMHOLTZ 



tion than that of the law of the conservation of energy. 

 This law is not of itself sufficient to give a dynamical ex- 

 planation of the mutual actions or relations of a system. 

 The principle of least action, however, gives a dyna- 

 mical process from which, with certain assumptions, 

 those relations can be deduced. Maupertuis, who was 

 a contemporary of Voltaire, and one of the brilliant 

 group of men gathered around him by Frederick the 

 Great, saw in his principle an indubitable proof of the 

 existence of God, but he was not able to give it a 

 mathematical form, nor could he have foreseen how 

 important it was destined to become in general dyna- 

 mics. For a long period it was only a metaphysical 

 conception, even although mathematicians of the 

 first rank endeavoured to express it in the language 

 of dynamics. 



The subject has been fully treated, without the aid 

 of formulae that are bewildering to the uninitiated, 

 by Professor Leo Koenigsberger, in his admirable 

 address on the Researches of Helmholtz in Mathe- 

 matics and Mechanics, delivered in 1895, the year 

 after the decease of Helmholtz. I 



Descartes founded analytical geometry, which, by 

 determining the distances of all points by fixed lines, 

 or co-ordinates, reduced spatial relations to their arith- 

 metical expression, and by the use of algebraic 



1 Rede zum Geiurtsfeste des Kochitteligen Grossherzogs Karl Friedrich 

 und zur akademhchen Preis-vertheilung, am 22 Nov. 1895, von Dr Leo 

 Koenigsberger, Professor der Mathematik. Heidelberg, 1895. 

 2 3 6 



