Quantities occurring in the Mechanical Theory of Heat. 259 



an oscillation 



E = const. 



The energy of a body consists of two parts — the vis viva T ; 

 and the potential energy U ; so that 



E = T+U. 



Now since E is subject to continual alterations, T and U will 

 in general continuously vary ; their mean value, however, for 

 a complete period shall remain constant. Thus 



T = const., 



U= const., 



and E=T+U. 



The energy, dQ, received from without in the time dt is, ac- 

 cording to the principle of the conservation of energy, 



dQ=dT + dU + dW. 



Let us select any one of the material points of the body as 

 the representant of the others. Let m be the mass of this point ; 

 let its rectangular coordinates, at the time t, be x y y y z\ the 

 components of its velocity x{ y' y z 1 '; and the components of its 

 acceleration x // , y /f , z" . In the time dt the coordinates and- 

 the components of the velocity will vary with dx . . . or with 

 da/ .... And since 



T = i2,m(x /2 +y /2 + z /2 ), 

 and the total work (external and internal) performed in the 

 time dt, 



dJJ + rfW=- %m(a/ ! dx + y"dy + z"dz) 



(if the work which the forces do against the body be reckoned 

 positive). 

 Therefore 



rfQ=2m(#W4- . . . -af'da—. . . ), 

 or 



«WJ.S*(|W...-^to...)j 



hence 



From this it follows that this spontaneous periodical change 

 of the body is an adiabatic one ; the energy which comes into 

 play in this alternate performance and consumption of work 

 is exclusively borrowed from the energy of the body. 



The equation of energy for the unchanged state of the body 

 is therefore to be written as follows, 



= dT + dU + dW. 



S2 



