Mr. W. J. ftlACQUOEN Rankine on the Science of Energetics. 391 



X. Second Axiom. 



The Total Energy of a Substance Cannot he Altered hy the Mutual Actions 

 of its Parts. 



Of the truth of this axiom there can be no doubt ; but some difference 

 of opinion may exist as to the evidence on which it rests. There is ample 

 experimental evidence from which it might be proved ; but independently 

 of such evidence, there is the argument, that the law expressed by this 

 axiom is essential to the stability of the universe, such as it exists. 



The special application of this law to mechanics is expressed in two 

 ways, which are virtually equivalent to each other ; the principle of vis- 

 viva, and that of the equality of action and reaction. The latter principle 

 is demonstrated by Newton, from considerations connected with the 

 stability of the universe {Principia, Scholium to the Laws of Motion) ; 

 for he shows, that but for the equality of action and reaction, the earth, 

 with a continually accelerated velocity, would fly away through infinite 

 space. 



It follows, from the Second Axiom, that all work consists in the transfer 

 and transformation of energy alone ; for otherwise the total amount of 

 energy would be altered. Also, that the energy of a substance can be 

 varied by external efforts alone. 



XI. External Potential Eqtjilibeitjm. 



The entire condition of a substance, so far as it is variable, as explained 

 in Article VIII., under the head of accideni, is a complex accident, which 

 may be expressed in various ways by means of different systems of 

 quantities denoting independent accidents; but the number of inde- 

 pendent accidents in each system must be the same. 



The quantity of work required to produce any change in the condition 

 of the substance, that is to say, the potential energy received by it from 

 without, during that change, may in like manner be expressed in different 

 ways by the sums of different systems of integrals of external efforts, each 

 integrated with respect to the independent accident which it tends to 

 augment ; but the number of integrals in each system, and the number 

 of efforts, like the number of independent accidents, must be the same ; 

 and so also must the sums of the integrals, each sum representing the 

 same quantity of work in a different way. 



The different systems of efforts which correspond to different systems 

 of independent accidents, each expressing the same complex accident, 

 may be called equivalent systems of efforts; and the finding of a system of 

 efforts equivalent to another may be called conversion of efforts.* 



• The conversion of efforts in PhysicB, is connected with the theory of lineal 

 tranBformatious in Algebra. 



