394 Mr. W. J. Macquobn Raskine on the Science of Energetics. 



given kind of actual energy with increase of the given accident ; for the 

 limit of the amount of actual energy which disappears in performing 

 work by an indefinitely small augmentation dx, of the accident, is 



,„ ,. dH = Q — t-dx 



(6-) aQ 



= Q dx = Qd 



dQdx dq 



The last form of the above expression is obviously applicable when the 

 work W is the result of the variation of any number of independent acci- 

 dents, each by the corresponding elFort. For example, let x, y, z, &c., 

 be any number of independent accidents, and X, Y, Z, &c., the efforts to 

 augment them ; so that 



dW = Xdx + Ydy + Zdz + &c. 

 Then 



= Qd as before. 



dQ 



The function of actual energy, efforts, and passive accidents, denoted 



by 



^ ^ dQ J Q ' 



whose variation, multiplied by the actual energy, gives the amount of 

 actual energy transformed in performing the work dW, may be called 

 the " Metamoephic Function" of the kind of actual energy Q relatively 

 to the kind of work W. 



"When this metamorphic function is known for a given homogeneous 

 substance, the quantity H of actual energy of the kind Q transformed to 

 the kind of work W, during a given operation, is found by taking the 

 integral 



(9.) H= /^QrfF. 



The transformation of actual energy into work by the variation of 

 passive accidents is a reversible operation ; that is to say, if the passive 

 accidents be made to vary to an equal extent in an opposite direction, 

 potential energy will be exerted upon the substance, and transformed 

 into actual energy: a case represented by the expression (9.) becoming 

 negative. 



The metamorphic function of heat relatively to expansive power, was 

 first employed in a paper on the Economy of Heat in Expansive Ma- 



