PRIMARY CONCEPTS OF MODERN SCIENCE. 353 



The answer to this question will suggest itself at once to those who 

 have properly apprehended the principle of the essential relativity of 

 all material existence. A material object is, in every one of its 

 aspects, but one term of a relation ; its whole being is a presupposi- 

 tion of correlates without ; all things are, figuratively speaking (if 

 I may resort to such a figure without incurring the charge of illustrat- 

 ing obscurum per obscurius) shadows of each other. Every change 

 of a body, therefore, presupposes a corresponding change in its corre- 

 lates. If the state of any material object could be changed without 

 a corresponding change of state in other objects without, this object 

 would, to that extent, become absolute. But this is utterly unthinka- 

 ble, and therefore utterly impossible, as we have already seen. At the 

 same time it is also evident that, while every change of a body is thus 

 conditioned by changes without, these latter changes are equally con- 

 ditioned by it ; that all material action, therefore, is mutual ; that re- 

 action is invariably equal to action. A corollary from, or rather an 

 application of this is the well-known theorem that the forces within a 

 body or conservative system can alter only the positions of its con- 

 stituent parts, but cannot change the position of the body as a whole ; 

 and that, whenever such an internal change takes place, the momen- 

 tum accruing in one direction has its counterpart in an equal mo- 

 mentum accruing in the opposite direction. If we apply this theorem 

 to the universe as a whole, i. e., as a single dynamical system, and if 

 we bear in mind that, mechanically speaking, all force properly so 

 called, i. e., all potential energy, is energy of position, we see at once 

 that whatever energy is spent in actual motion is gained in position — 

 that the system, therefore, is absolutely conservative ; and we are thus 

 led, by a very simple approach, to the principle of the conservation 

 of energy. 1 



After this summary discussion of the first conceptual element of 

 matter, inertia, I proceed to the consideration of the other element, 

 force. In the canonical text-books on physics, force is defined as the 

 cause of motion. "Any cause," says Whewell (" Mechanics," p. 1), 

 " which moves or tends to move a body, or which changes or tends to 

 change its motion, is called force." Similarly Clerk Maxwell (" Theory 

 of Heat," p. 83) : " Force is whatever changes or tends to change the 

 motion of a body by altering either its direction or its magnitude." 

 Taking either of these definitions as correctly representing the re- 



1 If the term " force " is restricted, as it ought to be, to the designation of potential 

 energy, or mere tension, the expression " persistence or conservation of force " becomes 

 inaccurate ; for the sum of the forces in the universe, in this sense, is by no means 

 constant. The " persistence of force ," or, more properly, the " conservation of energy," 

 simply imports that the sum of actual or kinetic energy (energy in motion) and potential 

 energy (energy of position or energy in tension) in the material universe is invariable. 

 This, as is shown in the text, is but an amplification of the theorem that in any limited 

 conservative system the sum of the potential and kinetic energies of its parts is never 

 changed by their mutual actions. 

 vol. iv, — 23 



