258 M. C. Szily on the Dynamical Signification of th 

 volume during the period of a complete oscillation is 



or 



C i dv.dt_ 

 Jo i 



l{ l dv.dt = 0. 



When, therefore, it is said that the space-content of a body is 

 constant, this properly signifies only that the sum of the varia- 

 tions of volume during a complete oscillation is nil. 



If it be admitted that the body, in relation to these changes 

 of volume, can be regarded as perfectly elastic, and we assume 

 that no unparalyzed external forces alter the amplitude or the 

 period of the oscillations, then on the one hand the duration of 

 an oscillation, and on the other the mean volume for this 

 period, remain constant ; or 



i=z const., 

 and 



IC v.dt= 



?> Jo 



const. 



Therefore, if it is said the volume is constant, this by no means 

 signifies that the volume undergoes no variation, but merely that 

 the mean value of the volume remains unchanged. 



I think the justification of this conception can hardly be 

 questioned. 



But as soon as it is allowed that the space-content is subject 

 to continual alterations, it must also be admitted that the body 

 is continually performing work against the forces acting upon 

 it, now positive, now negative, although its volume is, in the 

 ordinary sense, called constant. It hence follows, not that 

 the work done, dW , in the time-element dt is nil, but merely 

 that the mean value of dW during a complete oscillation is 

 equal to nil, or 



i Jo 



dW = ^\ dW.dt=0. 



1 Jo 



But whence does the body take, and to what does it apply, 

 the energy which comes into play in this alternate performance 

 and consumption of work ? On the one hand the energy of 

 the body, and on the other the energy of the outer world, can 

 be diminished or augmented. 



Therefore the energy of the body is also subject to a con- 

 tinual variation, a continual fluctuation ; it increases and dimi- 

 nishes, even though the volume and temperature are assumed 

 to be constant. If, therefore, it is said the energy of a body is 

 constant, this properly means only that the mean value during 



