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are equal and opposite. A pulls B, and B pulls A, to the same 
amount, but in opposite directions. And the result is not the 
constancy either of force or motion, but their continual increase 
from zero to an infinite value. 
In short, the Persistence of Force, in Mr. Spencer’s treatise, 
means four or five different things, one wholly irrelevant, the 
rest inconsistent, untrue, and even absurd. First, it is Newton’s 
third law, or the equality of action and reaction. “ To assert 
that action and reaction are equal and opposite is to assert that 
Force is persistent” (p. 188). This is a truth, but one wholly 
distinct from the one with which it is confounded. Next, it is 
the same with the non-annihilation of matter, which means 
that “ the force a given quantity of matter exercises, remains 
always the same” (p. 177, § 54). Thirdly, it is the constancy 
of each force in any system of forces ; for “ to conceive one or 
more of the forces to have increased or diminished is conceiving 
that force is not persistent ” (p. 193, § 53). Fourthly, it is the 
constant variation of all forces, attractive or repulsive, by the 
law of the inverse square. For this law, we are told, is no 
discovery of Newton, but the inalienable possession of every 
thinker from the beginning. It is not simply empirical, but 
is deducible mathematically from the relations of space, and 
one of which the negation is inconceivable. We are thus 
taught the double a priori truth, that forces cannot be thought 
of as varying at all, and must be thought of as always varying 
in one particular way. Lastly by the persistence of Force “ we 
really mean the persistence of some Power which transcends 
our knowledge and conception. In other words, asserting the 
persistence of Force is but another mode of asserting an 
unconditioned Reality, without beginning or end” (p. 189). 
Thus its final sense is the known and certain continuance, 
through all time, of some Being or Power wholly unknown, or the 
constant invariable sameness, in quantity, of some Power wholly 
inscrutable, and thus incapable of any measurement whatever. 
To find what we seek, we must escape from this quagmire 
of contradictions, and turn to the mathematicians. Their phrase 
is different, not the Persistence of Force, but the Conservation of 
Energy. Let us try to learn what it really means. 
Force, in dynamics, is the cause of motion, and distinct from 
the motion it causes. Suppose the force to cease, and the 
motion caused by it will continue. Let the force still act, and 
the velocity or motion is increased. Let some opposite force 
act, and the motion is diminished. Now let two bodies act on 
each other by a law of force, which depends on the inverse dis- 
tance, and their motion be measured by the square of the 
