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The Conservation of Energy thus denotes the constancy of 
a total formed from three distinct elements. (1) The Kinetic 
Energy, or sum total of motion. (2) Repulsive Potential 
Energy, reckoned from the actual to an infinite distance. (3) 
Attractive Potential Energy, reckoned from the actual distance 
to zero, where its amount is infinite. But if the repulsive and 
attractive vary by a mixed law, so as to give a neutral distance, 
the Repulsive and Attractive energies must be reckoned alike 
from the actual to the neutral distance, but in opposite di- 
rections. 
Such is the exact nature of the Conservation of Energy, as a 
mathematical formula within its own proper limits. It implies 
and requires a special hypothesis as to the nature of the acting 
forces, and deduces an important and useful dynamical result. 
But when turned into an alleged discovery, the result of recent 
physical induction, or into an a priori truth, which enables 
us to explain the universe without a Divine author, it is trans- 
formed into a condensed cluster of logical fallacies and meta- 
physical contradictions. 
And first, this indestructible total, always the same, is a 
numerical and not a real total. Force, the cause, is not the same 
with motion, the effect. When a body moves uniformly in a 
right line, there is motion but not force. When two bodies 
press oppositely against a third with equal pressure, there is 
force but no motion. Take any frustum of a paraboloid with 
a circular base. Take the whole height of the paraboloid for 
the unit of height, and the circular base for the unit of surface. 
Then the sum of the height of any frustum, and of the circular 
top, measured in fractions, will always be unity. But this con- 
stant total is a mere numerical abstraction, since a height 
cannot really be added to a surface, being different and hetero- 
geneous in kind. Thus the alleged doctrine, that force is 
indestructible, because the total of two kinds of energy is 
constant, turns a numerical relation into a chimera, devoid of 
real meaning. 
Fallacy the second. Let us waive this first decisive objection, 
that force and motion are not the same, that a real total cannot 
be formed of unlike elements by any device, and least of all by 
confounding them under an ambiguous name ; that each of 
them separately is highly variable, and that what is really con- 
stant is a numerical abstraction, and nothing more. Let us 
admit the power of this name. Energy, to fuse into one total 
unchangeable and indestructible, these unlike elements, 
Potential Energy, or force, and Kinetic Energy, or motion. 
We may at least claim that both elements which compose the 
