•514 Dr. J. 11. Mayer on the Mechanical Equivalent of Heat. 



ton's law of gravitation*, the laws of the fall of bodies from cos- 

 mical elevations, and also the general laws of central motions, 

 can be developed without its being needful to employ equations 

 of more than the second degree. 



Having now become acquainted with two species of force — 

 motion and falling force — we can arrive at a conception of " a 

 force " in general, according to the well-known rule, by collect- 

 ing together the common characteristics of the two species. To 

 this end, we must consider the properties of these objects some- 

 what more closely. Their most important property 'depends on 

 their mutual relation. Whenever a given quantity of falling 

 force disappears, motion is produced ; and by the expenditure of 

 this latter, the falling force can be reproduced in its original 

 amount. 



This constant proportion which exists between falling-force 

 and motion, and is known in the higher mechanics under the 

 name of " the principle of the conservation of vis viva, 3 ' may be 

 shortly and fitly denoted by the term "transformation" (Um- 

 wandlung). For instance, we may say that a planet, in passing 

 from its aphelion to its perihelion, transforms a part of its falling 

 force into motion, and, as it moves away from the sun again, 

 changes a part of its motion into falling force. In using the 

 word " transform " in this sense, nothing else can or is intended 

 to be expressed but a constant numerical ratio. 



But it follows from the axiom mentioned at page 500, that 

 the production of a definite quantity of motion from a given 

 quantity of falling-force, and vice versa, implies that neither fall- 

 ing-force nor motion can be annihilated either totally or in part. 

 We thus obtain the following definition : — 



Forces are transformable, indestructible, and (in contradistinc- 

 tion from matter) imponderable objects. (Conf. paper already 

 quoted, p. 502.) 



It is easy to see that this definition embraces, among other 

 things, the fact that the motion which disappears in mechanical 

 processes of different kinds bears a constant relation to the heat 

 thereby produced, or that motion is convertible, as an indestruc- 

 tible magnitude, into heat. Thus heat is, like motion, a force ; 

 and motion, like heat, an imponderable. 



I have characterized the relation which various forces bear to 



* Newton's formula relates to the particular case in which the two di- 

 stances (the initial and the final distance) are equal, so that their product 

 becomes a square. In this case, however, both the space fallen through 

 and the velocity become nought ; and hence, when this expression has to 

 be taken as the starting-point for the calculation of real velocities, mathe- 

 matical artifices become necessary which are inadmissible in the elementary- 

 branches of science. 



