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grand total shall actually exist. The Vis viva , or Kinetic 
Energy, does exist. Its amount is the total motion of the 
system, measured by the square of the velocity of each particle 
at any moment. But the case of the Potential Energy is just 
the reverse. It is composed, not of forces that now exist, but 
of possibilities of forces that would exist hereafter under con- 
ceivable conditions of change. The Potential Energy of a pair 
of atoms, if the force is simply repulsive, is the total of force that 
they would exert on each other in receding from the actual to 
an infinite distance. If the law is simply attractive, it is the 
like total, exerted on each other in approaching nearer to absolute 
coalescence. If the law is mixed, with repulsion for small 
distances, and attraction for the rest, then the Potential Energy 
is the total of force that may be exerted in passing from the 
actual to the neutral distance. And thus the entire Poten- 
tial Energy is not the force existing at the present moment. 
It is a total of the force that may or might be hereafter 
exercised through as many different periods of conceivable 
future time as there are pairs of atoms in the whole universe. 
To make this objection clearei’, let me adopt the same license 
in a similar case. I wish to prove that the number of persons 
in the streets of London from day to day is constant and un- 
varying. Aud I succeed in this way. First, 1 note in thought 
those actually present in the streets this day, and call it the 
kinetic street population. Next, I contemplate the vast num- 
ber who, under social laws and conditions, have been determined 
to use the streets every past day since the city was peopled, and 
call it the Past Potential of street population. Next, I form a 
Future Potential of all those who will, under the laws of London 
life, be led to walk in its streets through all the successive days 
of its future existence. I sum these three elements, and their 
total is of course invariable. Here, then, we have the a priori 
basis of a new Sociology, that the number walking in London 
streets, actual and potential, has never varied, and cannot vary 
to the remotest age. 
Fallacy the third. This total Energy, said to be invariable, 
is the sum of the actual motions, and of two potencies, measured 
from the actual to an infinite distance in repulsion, to zero or 
coalescence in attraction, but in a mixed law to the neutral 
distance, under the assumed conditions, on which the formula 
for Energy depends, that attracting points can only come 
nearer, and repelling points recede. But the real conditions are 
different, and almost opposite. Each atom, in approaching 
some, recedes from others. Forces act not only to create or 
increase velocities, but to lessen or destroy them. In moving 
