HERMANN VON HELMHOLTZ 



of facts, but in the establishment of great principles, 

 which would be applicable to abstract dynamics, 

 hydrodynamics, thermodynamics, electrodynamics, 

 alike, and by which insight might be obtained into 

 hidden processes. In 1884 we find three elaborate 

 mathematical papers on what he termed monocyclic 

 systems; in 1886, a paper on the principle of least 

 action ; in 1887, another on the same subject ; and in 

 1892, a third paper on the principle of least action in 

 electrodynamics. 



Cyclic systems are those in which there are periodic 

 or circulating motions. This is a somewhat vague 

 description, but it may indicate what is meant. A 

 motion definable by a single co-ordinate, like that 

 of a circular disc spinning round its axis, he termed 

 monocyclic, but he also conceived the more com- 

 plicated case of a polycyclic system definable by 

 a large number of co-ordinates, satisfying certain 

 assumed conditions. The position of a disc in a 

 monocyclic system depends on the angle which a 

 plane containing the axis tmakes with a plane fixed 

 in space ; but the energy depends on the angular 

 velocity. The potential energy remains unaltered 

 while the disc revolves. The broad lines of the 

 methods by which such systems may be investi- 

 gated were first laid down by Thomson (Lord 

 Kelvin) and Tait. Helmholtz narrowed the dis- 

 cussion to certain types of such systems. He 

 assumes for such that neither the kinetic nor the 

 234 



