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length of the paper, and the lateness of the hour, compel me to make my 
observations as brief as I can, and I will therefore refer, in the order in which 
they occur, to several points in the paper. I would first make a remark on 
the following observation contained in the fourth page : — 
“Force, by the usual definition, involved in Newton’s first and second 
axioms, and accepted in all works of exact science, is that which produces or 
tends to produce or destroy motion.” 
Now this is the very definition of force to which I have in my paper 
distinctly objected. If this be taken as the definition of force, then what occurs 
on the top of the next page, — 
“ A moving body does not alter, and cannot be conceived to alter, the 
state of another, except by the intervention of force,” — 
is perfectly true ; because if everything that alters the condition of a body 
with regard to its rest or motion is force, then it must be force that alters 
the condition of its rest or motion ; but if that definition be not tenable, 
then the observation which is made upon it falls to the ground. Then, 
in the fifth page, Professor Birks asks : — 
“ Is the total force, in such a universe, fixed, constant, and invariable ? 
It is one of the simplest truths of dynamics that it varies continually, 
from hour to hour, from moment to moment.” 
Now, what is here meant by the variation of a force, but the variation 
of its action ? Take one example — the force of gravitation. Does any one 
doubt that the force of gravitation is a constant, invariable force ? Is it 
not a fact that on the very invariability of the force of gravitation the accuracy 
of all the predicted results of astronomy depends : the truth of all the calcu- 
lations with regard to the movements of the heavenly bodies, — the exact 
period of an eclipse or a transit of Venus, — depends on the assumption of the 
force of gravitation being constant and invariable. How is a force to be 
measured ? I conceive that the only measure we can have of a force, or by 
which we can compare it with another, is to take its action upon a unit 
quantity of matter at a unit of distance. If the action of any force upon a 
unit of matter at a unit of distance be at all times the same, then, I say, the 
force is invariable. It acts with different degrees at different distances ; but 
that is not an increase or diminution ot the force, but of its action according 
to distance, and these appear to me to be two very different things. Pro- 
fessor Birks says : — 
'* Let us further take force in its proper sense, just defined, on which 
the Principia and all trains of abstract dynamical reasoning depend. Is the 
total of force in such a universe fixed, constant, and invariable ? ” 
The force is fixed, constant, and invariable, but the amount of its action 
will depend upon the nature of the material on which, and the amount 
of the distance at which, it acts ; and therefore Professor Birks’s subsequent 
remark that force varies continually has no real bearing upon the question. In 
the next paragraph we find the following passage : — 
“ Thus momentum, or the mass multiplied by the velocity, is viewed as a 
kind of variety of force, and Vis viva, or living force, is used to express the 
