Mr. W. J. Macquorn Rakkine oti the Science of Energetics. S97 



XVI. — Use of the Metabatic Function; Transfoematiok of 

 Energy in an aggregate. 



From the mutual proportionality of the actual energy Q, and the me- 

 tabatic function ^, it follows that the operations 



dQ dd 



are equivalent ; and that the latter may be substituted for the former in 

 all the equations expressing the laws of the transformation of energy. 

 We have therefore 



(13.) QJ^==^il=tf^ 



c?Q dB didx 



for the effort to transform actual energy of the kind Q into work of the 

 kind W, when expressed in terms of the metabatic function ; and 



(14.) dR = 6d— 



d& 



for the limit of the indefinitely small transformation produced by an in- 

 definitely small variation of the accidents on which the kind of work W 

 depends. 



There is also a form of metamorpJdc function. 



(15.) <p==^=r^=KF 



dd J 6 



suited for employment along with the metabatic function, in order to find, 

 by the integration 



(16.) K = l6d<P 



I' 



the quantity of actual energy of a given kind Q transformed to the kind 

 of work W during any finite variation of accidents. 



The advantage of the above expressions is, that they are applicable, 

 not merely to a homogeneous substance, but to any heterogeneous sub- 

 stance or aggregate, which is internally in a state of equilibrium of actual 

 and potential energy ; for throughout all the parts of an aggregate in 

 that condition, the metabatic function 6 is the same, and each of the 

 efforts X, &c., is the same, and consequently the metamorphic function 

 (p is the same. 



" CartioCs function" in thermo-dynamics is proportional to the reci- 

 procal of the metabatic function of heat. 



