360 HERMANN VON HELMHOLTZ 



cyclic. A stationary motion is one in which (as expressly 

 pointed out by Helmholtz in reply to a criticism made by 

 Clausius, who had erroneously attempted to prove that his 

 conclusions were incorrect) the homogeneous moving particles 

 exhibit constant velocity at the same spot, as in the motion of 

 a rotating disk, or in a current of frictionless fluid in a ring- 

 shaped canal. It was further assumed that the forces that act 

 between the bodies of such a system are conservative, and that 

 the problems to be attacked are statical, in the sense that altera- 

 tions in the state of the system, while not excluded, go forward 

 so slowly that the system never perceptibly passes out of the 

 state in which it might remain : which hypotheses are also 

 tacitly accepted by Clausius as the basis of the whole system of 

 laws which he has laid down for the reversible changes of heat. 

 Helmholtz insists that heat-motion is not, strictly speaking, 

 monocyclic, since each individual atom apparently alters its mode 

 of motion perpetually ; but inasmuch as in an enormous number 

 of atoms all possible stages of motion are represented, the me- 

 chanical features of monocyclic motion obtain, even if the several 

 steps are performed now by one atom and now by another. 



He then defines as the object of his investigation the proof 

 that there is a class of motions that are perfectly intelligible 

 from the mechanical point of view, in which there are the same 

 limitations to the conversion of work-equivalents as are pre- 

 dicated by the second law for the motion of heat. Helmholtz 

 protests against Clausius's objection to the effect that he had 

 claimed to have provided an explanation of the Second Law of 

 Thermodynamics ; in choosing instances of monocyclic motion 

 he was concerned merely with their complete mechanical 

 intelligibility. 



' As a rule/ he says on a later occasion, ' I have only felt it 

 necessary to reply to a criticism of scientific laws and principles 

 when new facts could be brought forward or misunderstandings 

 cleared up, in the expectation that when all the data were given, 

 my scientific colleagues would ultimately form their judgement 

 without the discursive explanations and sophisticated arts of 

 belligerents/ 



Helmholtz in the first place developed the general equations 

 of motion of mechanics for polycyclic systems; under the 

 foregoing assumptions, and on the hypothesis that one or 



