289 
velocity. Then a certain amount of motion is produced, when 
they pass from one given distance to another. In repulsive 
forces, the motion ^increased when they recede, and in attractive 
forces, when they approach nearer. The change in the total 
motion Avhen so measured, does not depend on the path, but on 
the initial and final distances alone. The old name of the 
motion, thus increased or diminished, is Vis viva , and the new 
one, not at all clearer. Kinetic Energy. 
In the same case, we may calculate, or express by algebraic 
symbols, the total amount of force which is exercised in passing 
from any one distance to another. Such a total, when 
reckoned .from the actual distance to some natural limit, if 
such can be found, may be called by the new name, Potential 
Energy. 
The result, in the case of repulsive forces, takes a simple form. 
The motion increases as the system dilates, and the bodies or 
particles recede from each other. But the Potential Energy, in 
repulsive force, has for its natural limits the actual distance and 
infinity. For then the force of repulsion would vanish, and it 
becomes less and less, as the distances increase. Thus, the 
motion or Kinetic Energy increases, and the Potential Energy, 
a right unit being assumed, decreases by a like amount. Their 
sum, thei’efore, or the Potential plus the Kinetic Energy, will 
be constant and invariable. 
But in all cases of mutual attraction there is a serious diffi- 
culty. For by such force bodies do not pass from a finite to an 
infinite distance, but from a greater to a less, from a finite dis- 
tance to coincidence. Thus the Potential Energy, if reckoned 
as before, between the actual distance and infinity, where the 
force vanishes, has a wrong sign. It increases with the increase 
of the acquired motion, and not their sum, but their difference, 
will be constant. As a mere matter of calculation, the case is 
easy. The Potential of an attractive force, if reckoned from 
zero to its value at any finite distance, must have a negative 
sign. The total Energy, if the system has started from rest at 
any finite distance, will be negative also. But if this Energy be 
taken for the supreme and ultimate power of the universe, a 
kind of Divinity, to make it an algebraic quantity with a negative 
sign is too ridiculous. Also to assume an arbitrary distance, 
within which no attraction can be exercised, contradicts the 
law, which recognizes no limiting distance. Thus, to save the 
theory, the Potential Energy, in attractive powers, must be 
reckoned from the actual distance to coalescence. But then the 
force, and its total sum, the Energy, become infinite and im- 
measurable. 
