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Energy is no sum of motions. My own opinion on the “fourth fallacy” 
is that the author has confounded motions with forces, and I think that will 
explain a great deal of what he has stated in the course of his paper. Then 
he says : — 
“ By the laws of force, however, so far as science has detected or conjectured 
them, the force depends on the inverse distance, and will be infinite when 
two particles touch or coalesce ” ; 
and some subsequent argument is founded on the summation of these 
infinities. But so far as we know, it is impossible for two particles to touch 
or coalesce. The opinion of Newton was that the distance between con- 
tinuous particles is indefinitely great compared with the magnitude of the 
particles themselves. We know there is no limit to the contraction of most 
bodies by cold, and we can only suppose the particles come into actual 
contact when we reach absolute zero of temperature — a degree of cold or 
negation of heat which is utterly unattainable, and which probably never 
did or will exist in nature. It therefore appears to me that any argu- 
ment founded on the introduction of infinite qualities, 'which must neces- 
sarily be introduced if the particles touch, falls to the ground, because it 
cannot possibly be assumed. Then Professor Birks says : — 
“ Contradiction the second. The doctrine assumes that motion or Kinetic 
Energy is the same identical thing or quality with Potential Energy, because 
of a numerical equivalence, when reckoned in one especial way. But this is 
wholly untrue. A rectangle, when its breadth is the unit of distance, has 
its length and its area or surface expressed by the same number. But a 
length and a surface are not on that account the same.” 
In the first place I maintain that motion and kinetic energy are two totally 
different things, and any contradiction founded on the assumption that they 
are identical falls to the ground, because they are not synonymous terms. 
Of course, as the author says, a length and a surface are not the same ; but 
that has nothing to do with the question— -with a rectangle, the width of 
which is the unit of length, the length of the rectangle will be the length 
of the other side, whether it be longer or shorter. But what does that mean ? 
It only means that there are as many units of length on the other side of 
the rectangle, as there are units of area in its surface. In a rectangle which 
is one inch wide and five inches long, the length of the rectangle will be five 
inches and the area five square inches. These are merely the numerical 
equivalents or the co-efficients in the two cases, but no one would infer from 
that that length and surface mean the same thing, or can be added to- 
gether. Then again Professor Birks says : — 
“ A cannon-ball is shot upward at the rate of a thousand feet a second. 
The doctrine affirms this speed of motion to be the very same thing with the 
place of that ball on the top of a mountain three miles high.” 
This is certainly not affirmed by any doctrine with which I am 
acquainted. I do not know where Professor Birks will find any such 
argument used by any writer on the subject : they arc two totally different 
th'ffitfs, having no relation to each other. The doctrine, as I and its sup- 
porters understand it, is that if a ball is shot up at the rate of 1,000 feet in a 
