63 
sign of an existence — a sign occurring under certain condi- 
tions ” (pp. 183, 184). He then explains the difficulty about 
the principle of activity continuing at the extremities of the 
vibration, although at those points the pendulum would offer 
no resistance to the hand, by observing that its activity is 
then latent, as proved by the fact that it forthwith begins to 
pull in the opposite direction ; and adds, “ Here, then, is the 
solution of the difficulty. The space-element of motion is not 
in itself a thing. Change of position is not an existence, 
but the manifestation of an existence. This existence may 
cease to display itself as translation ; but it can do so only by 
displaying itself as a strain. And this principle of activity, 
now shown by translation, now by strain, and often by the 
two together, is alone that which in motion we can call con- 
tinuous” (p. 187). Without further quoting Mr. Spencer's 
words, the conclusion at which he arrives at length is, that 
the continuity of motion is known to us really in terms of 
force, and that the principle of activity just described involves 
the postulate that the quantity of force is constant. This 
force, in the case of the planets, is the sun's attraction, and in 
that of the pendulum it is the earth's attraction. There is 
a very short formula to be found in elementary works on 
dynamics, occupying not so much as one line on the page, 
which, unless I greatly mistake, teaches very concisely all that 
Mr. Spencer has here said. It shows, when closely examined, 
at what parts of its path the motion of a body acted on by 
any force increases or diminishes, at what points it attains a 
maximum or a minimum, where it changes its direction, and, 
if it ever ceases, at what part of its path it does so. It also 
shows that its kinetic and potential energies are comple- 
mentary, and make up together an unvarying sum, and that 
all this can be true only on the supposition that the coefficient 
of the quantity expressing the force remains constant through- 
out.* That coefficient, in the cases brought forward as 
examples, is the gravitating force exerted by the unit of mass 
at the unit of distance, and is, in fact, that “ existence,” or 
“ principle of activity,” which, as Mr. Spencer expresses it, 
“ is alone that which, in motion, we can call continuous.” The 
upshot of it all then is, that the sun's attracting power, in the 
case of the planets, and the earth's attracting power in the 
case of the pendulum, are assumed to undergo neither increase 
nor diminution during the time that the bodies respectively 
affected by them are the subject of observation or calculation. 
The ground of this assumption has now to be considered ; 
* See Appendix. 
