AT THE PHYSICO-TECHNICAL INSTITUTE 401 



from the head of Jupiter. Your judgement was modified by 

 surprise, mine not: it may indeed, if anything, have been 

 depressed by the fatigue incident on work and by annoyance at 

 all the many irrational steps that I had made by the way.' 



Almost before the festivities were over, Helmholtz immersed 

 himself once more in problems of the most heterogeneous kind, 

 turning in the first place to those complex mathematical 

 problems which were to set the Principle of Least Action at 

 the head of the laws of Nature. 



On Feb. 26, 1892, he writes to Hertz: ' I too am writing another 

 little electrodynamic paper, viz. a transformation of Maxwell's 

 equations in the form of the Principle of Least Action, since, 

 as you have already remarked, the derivation of the pondero- 

 motive forces might otherwise conceivably be imperfect. But 

 it results from the above-mentioned principle in a manner 

 agreeing perfectly with the older derivation from energy.' 



Hertz replied on Feb. 28 that he was not acquainted with any 

 irreproachable connexion of the pondero-motive forces based 

 on Maxwell's equations, for the general case of any alterations 

 whatsoever. 



Helmholtz (after spending a few weeks in the North of Italy 

 and fetching his wife from her sister's home in Abbazia) 

 communicated these researches to the Academy of Berlin on 

 May 12, 1892, with the title ' The Principle of Least Action in 

 Electrodynamics'. He set himself the excessively difficult 

 problem of ascertaining whether the empirical laws of electro- 

 dynamics, as expressed in Maxwell's equations, could be 

 reduced to the form of a minimal law. 



In a system of ponderable bodies, the internal forces of which 

 are conservative, it is known, as a rule, which quantities denote 

 co-ordinates and which velocities, and it then becomes possible, 

 up to a certain point, by means of the relation which Helmholtz 

 had earlier discovered between the total energy and the kinetic 

 potential, to develop the latter from the former. There only 

 remained undetermined, as previously stated, a linear homo- 

 geneous function of momentum, which has to be added to the 

 value of the kinetic potential, because such linear terms are elimi- 

 nated from the value of the energy supply. This cannot, however, 

 be carried out, unless we are able to see which of the internal 

 changes of the system correspond to alterations in the position 





