Dr. J. R. Mayer on the Mechanical Equivalent of Heat. 513 



Hence, according to this definition, "motion" is always mea- 

 sured by the product of the moved mass into the square of the 

 velocity, never by the product of the mass into the velocity. 



By "falling-force" we understand a raised weight, or still 

 more generally, a distance in space between two ponderable 

 bodies. In many cases falling-force is measured with sufficient 

 accuracy by the product of the raised weight into its height ; 

 and the expressions "foot-pound," "kilogramme-metre," "horse- 

 power," and many others, are conventional units for the mea- 

 surement of this force, which have of late come into general use, 

 especially in practical mechanics. But in order to find the exact 

 quantitative expression for the magnitude in question, we must 

 consider (at least) two masses existing at a determinate distance 

 from each other, which acquire motion by mutually approaching; 

 and we must investigate the relation which exists between the 

 conditions of the motion, namely, the magnitude of the masses 

 and their original and final distance, and the amount of motion 

 produced. 



It very remarkably happens that this relation is the simplest 

 conceivable; for, according to Newton's law of gravitation, the 

 quantity of motion produced is directly proportional to the masses 

 and to the space through which they fall, but inversely propor- 

 tional to the distances of the centres of gravity of the masses 

 before and after the movement. That is, if A and B are the two 

 masses, c and d the velocities which they respectively acquire, 

 and h and U their original and final distances apart, we have 



AC +J3C - hh , , 



or in words, the falling -force is equal to the jwoduct of the masses 

 into the space fallen through divided by the two distances. 



By help of this theorem, which, as will be easily seen, is 

 nothing but a more general and convenient expression of New- 



glish expressions " dynamical energy " and "statical energy" were used bv 

 Prof. W. Thomson (Phil. Mag. S. 4. vol. iv. p. 304, 1852) in the same sense, 

 but were afterwards abandoned by him in favour of the terms "actual energy" 

 and "potential energy" introduced by Prof. Rankine. More recently 

 (' Good Words ' for October 18G2) Professors Thomson and Tait have em- 

 ployed the expression " kinetic energy " in place of " actual energy." The 

 German word Kraft in the text has been uniformly translated force, to which 

 term the ambiguity of the German original has thus been transferred. This 

 ambiguity, however, may be avoided in English by allowing the word 

 " force " to retain the meaning which it bears in common language, that is, 

 to denote all resistances which it requires the exertion of a power to over- 

 come (whence the expressions gravitating force, cohesive force, &c), and 

 by using the word " energy " to denote force as defined by Mayer.— G. C. F.] 



