Mr. W. J. M. Rankine on the Conservation of Energy. 251 



course to be imderstood tliat the mean value of that magnitude 

 is the factor to be used iu the multipUcation ; or, what is the 

 same thing in other words, that the integral of the tendency with 

 respect to the change is the quantity in question. 



"V\Tien applied to the mechanics of bodies movmg uniformly, 

 the conservation of the quantity now described means neither 

 more nor less than the old principle of " virtual velocities." 



3. Inasmuch as the word " force " has for a long time been 

 used to denote a tendency of a pair of bodies to change of rela- 

 tive motion, a kind of magnitude to which no law of conserva- 

 tion applies, the use of the phrase " conservation of force " gives 

 rise to misapprehensions and groundless disputes, by implymg a 

 different meaning of the word "force;" and even although that 

 phrase has been sanctioned and widely spread by Mr. Grove's 

 celebrated work, it is much to be desired that a phrase should 

 be adopted in its stead about which there is no ambiguity, such 

 as " conservation of energy." The only precisely-defined mean- 

 ing which has ever been assigned to the word "energy" in 

 writings on physical science, is that which has been described in 

 Article 2 of this letter. I believe that the first definition of 

 "energy" in this sense is due to Young (Lectures on Natural 

 Philosophy, Lecture VIIL). 



4. Inasmuch as a mass moving with a given velocity must 

 have been acted upon during a certain time by a force (in the 

 sense of tendencij) represented by 



mass X velocity 

 time of action ' 

 and through a distance equal to 



half- velocity x time of action ; 

 and inasmuch the same mass in the course of having its motion 

 stopped, is capable of overcoming a resisting force as stated 

 above through a distance as stated above, the energy of a moving 

 mass is the product of its mass into the half-square of its velocity. 

 5. In order to distinguish from each other the two forms of 

 mechanical energy, as well as other forms of physical energy 

 which are analogous to them, I proposed, in 1853 (Proc. of the 

 Phil. Soc. of Glasgow, 1853, and Edinb. Phil. Journ. 1855), to 

 distinguish as potential energy that which consists in a tendency 

 towards a change capable of continuing to act throughout a 

 given change ; and as actual energy, that which consists in a 

 btate of change going on, such as the motion of a mass with 

 a given velocity. At the time, I supposed tliose terms to be 

 wholly original (as I believe tlicy were, in their appUcation to 

 forms of energy other than mechanical) ; but I have since found 

 that Caruot, in his. essay on the principles of equilibrium and 



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