THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 115 



Their configuration, therefore, is to be fixed by what Professor 

 J. iJ. Thomson has called " unconstrainable " co-ordinates, in 

 distinction from the " controllable " co-ordinates which are 

 subject to the direct control of an experimenter.* Finally, 

 by supposing the " concealed masses " to form a " cyclical 

 system," that is, to possess constantly recurrent motions, it 

 is possible to " ignore " the unconstrainable co-ordinates, and 

 deal only with their time-rates of change.! 



(A simple example of a monocyclic system in which the 

 concealed motion is determined by one " unconstrainable " 

 co-ordinate, would be a perfectly uniform rotating wheel. 

 The angular position of a point on the wheel would be the 

 " unconstrainable " co-ordinate sufficient to fix the position 

 of the wheel at a given moment, while its time-rate the 

 angular velocity of the wheel would alone affect the expres- 

 sion for the kinetic energy of the system.) 



The main features of the course of Helmholtz's somewhat 

 recondite argument are as follows : An expression is first 

 obtained for the additional energy that may be imparted to 

 a simple monocyclic systemj by means of the concealed masses 

 only. This energy corresponds to the heat given to raise the 

 temperature of a body. It is next shown that the whole 

 kinetic energy of the concealed masses is an integrating divisor 

 of the expression for this additional portion of energy. Thus it 

 appears that the kinetic energy of the concealed masses or 

 a product of this kinetic energy by any one of a certain class 

 of functions possesses the property which Clausius' theorem 

 indicates as distinctive of absolute temperature. || Helmholtz 



* Thomson, Applications of Dynamics to Physics and Chemistry, 1888, 

 p. 94. 



t Thomson, Applications, p. 14 ; Hertz, Mechanics, p. 209. 



J Le., a system containing only one set of cyclical movements, which 

 can themselves be defined by one co-ordinate. 



Functions of the "generalized momentum" of the system. 



|| Supra, p. 113. 



I 2 



