Mr. W. J. ilACQUORy Rankine on the Science of Energetics. 



389 



or by the integral of the effort, with respect to the passive accident, 

 when the effort is variable. 



Let X denote a passive accident. 



X an effort tending to vary it. 



W the work performed in increasing x from x^ to x^, then, 



I ^y_ r^^ ^dx, and 

 ( W= X (k—'^o) if X 



0) 



\ — .Ty) if X is constant. 



"Work is represented geometrically by the area of a curve, whereof the 

 abscissa represents the passive accident, and the ordinate, the effort. 



Energy, Actual and Potential. 



The terra " energy " comprehends every state of a substance which 

 constitutes a capacity for performing work. Quantities of energy are 

 measured by the quantities of work which they constitute the means of 

 performing. 



" Actual energy" comprehends those kinds of capacity for performing 

 work which consist in particular states of each part of a substance, how 

 small soever ; that is, in an absolute accident, such as heat, light, electric 

 current, vis-viva. Actual energy is essentially positive, 



" Potential energy" comprehends those kinds of capacity for perform- 

 ing work which consist in relations between substances, or parts of sub- 

 stances ; that is, in relative accideiits. To constitute potential energy 

 there must be & passive accident capable of variation, and an effort tend- 

 ing to produce such variation ; the integral of this effort, with respect to 

 the possible variation of the passive accident, is potential energy, which 

 differs in work from this — that in work the change has leen effected, 

 which, in potential energy, is capable of being effected. 



Let X denote an accident, x^ its actual value ; X, an effort tending 

 to vary it; x^, the value to which the effort tends to bring the accident; 

 then 



" X</a' = U, denotes potential energy. 





Examples of potential energy are, the chemical affinity of uncombined 

 elements ; the energy of gravitation, of magnetism, of electrical attrac- 

 tion and repulsion, of electro-motive force, of that part of elasticity whicli 

 arises from actions between the parts of a body, and generally, of all 

 mutual actions of bodies, and parts of bodies. 



Potential energy may be passive or negative, according as the effort 

 in question is of the same sign with the variation of the passive accident, 



Vol. III. — No. 6. * f 



