DEFINITIONS OF FORCE. 207 



In the meantime, I think the best way for us is to 

 adopt the luminous definition of the man of genius, 

 J. R. Mayer, viz., " Force is that which is expended in 

 the production of motion ; and this which is expended 

 is, as cause of the effect, equal to the motion pro- 

 duced."* The idea of expenditure is thus the cardinal 

 point in all exercise of force, and if this is constantly 

 kept before our eyes, we shall escape the difficulties 

 which are apt to entangle us in the distinction of 

 property from force. The majority now hold that 

 that which is expended is simply motion, and would 

 describe the forces as motions. The mathematicians 

 prefer to apply the word force to the dead pull or 

 pressure which is the antecedent of motion. For us it 

 is, however, far more convenient for the understanding 

 of the phenomena, to keep to the idea of expenditure and 

 of motion ; but the grand difficulty is how to conceive 

 of the passive forces as motion, i.e., those in which the 

 movements of masses or atoms of matter cannot pos- 

 sibly produce the result, e.g., the attractive forces of 

 gravitation, cohesion, chemical attraction, &c. For the 

 discovery of the mechanical equivalent of heat has 

 given the death-blow to the notion of all inherent 

 powers of attraction and repulsion as properties of 

 matter as well as all action at a distance, which were 

 till lately generally held, in spite of the strong objec- 

 tions of Newton himself. It is not necessary we should 

 have any theory of the cause of gravity, nor of the 

 nature of force, in order to accept Mayer's definition, 

 which is, indeed, framed to avoid all speculations, but 

 it clears our conceptions to have some hypothesis. 

 * " Mechanik cler Warme," p. 265. 



