]Mr. W. J. IVIacquobn Rankine on the Science of Energetics. 393 



substance independently of its relations to other parts, rather than an in- 

 dependent proposition. 



Its apjDlicability to natural phenomena arises from the fact, that there 

 are states of substances corresponding to the definition of actual energy. 



The mode of applying this third axiom is as follows : — 



Let a homogeneous substance possess a quantity Q, of a particular 

 kind of actual energy, uniformly distributed, and let it be required to 

 determine the amount of the effort arising from the actual energy, which 

 tends to perform a particular kind of work W, by the variation of a par- 

 ticular passive accident x. 



The total effort to perform this kind of work is represented by the rate 

 of its increase relatively to the passive accident, viz., — 



X= — 

 dx 



Divide the quantity of actual energy Q into an indefinite number of in- 

 definitely small parts 3Q ; the portion of the effort X due to each of those 

 parts will be 



dX 



and adding these partial efforts together, the effort caused by the whole 

 quantity of actual energy will be 



(4.) - Q^_Q^^ 



dQ~^dQdx 



If this be equal to the effective effort X, then that effort is simply pro- 

 portional to, and wholly caused by, the actual energy Q. This is the 

 case of the pressure of a perfect gas, and the centrifugal force of a moving 

 body. 



If the effort caused by the actual energy differs from the effective effor.t, 

 their difference represents, when the former is the less, an additional 

 effort 



Q4:r)x, 



d_ 



(5.) <(and when the former is the greater, a counter effort 



0^ 



Ql^-■^^. 



due to some other cause or causes. 



XIV. Rate of Tbansformation ; Metamoephic Function. 



The effort to augment a given accident x, caused by actual energy of 

 a given kind Q, may also be called the ^^ Mate of Transformation" of the 



