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amount of motion, as measured by the product of the mass and the square of 
the velocity.” 
Novvforce and momentum appear to me, if they mean anythingat all, to mean 
two totally different things, and therefore I cannot conceive how momentum 
can be viewed as a kind of force. The latter part of the passage, referring to 
Vis viva, appears to me to be giving a meaning to the word “ motion ” which 
it does not bear. As I understand it, motion is nothing more than the act 
of moving or changing place. If you say a body is in motion, you mean it 
is changing its position in space ; if you say it is not in motion, you mean 
that it is in the same position that it occupied before, that is relatively ; for, 
of course, everything on the surface of the earth is moving in common with 
the earth ; but we mean motion in relation to the earth. If we say a body 
is at rest, we mean at rest with regard to the mass of the earth. Therefore we 
must all bear in mind what is the real distinction between actual and relative 
motion, and that we are constantly inclined to speak of relative motion, and to 
give it the name of actual motion. We are inclined to say that any object upon 
a table is at rest, whereas we know that it is moving round the axis of the earth, 
and moving together with the earth on its orbit ; and if the sun is progressing 
through space, it is also partaking of that motion. Therefore, to say a body 
is at rest does not mean that it is occupying the same absolute point of 
space, but relatively at rest with regard to the objects by which it is sur- 
rounded. Then Professor Birks says : — 
“ Thirdly, it is the constancy of each force in any system of forces ; for 
‘ to conceive one or more of the forces to have increased or diminished is 
conceiving that force is not persistent’ (F.P., p. 193, § 53). Fourthly, it is 
the constant variation of all forces, attractive or repulsive, by the law of 
the inverse square.” 
A force does vary. The force of gravitation is a constant force : its action 
depends on the inverse square of the distance of the body acted upon by it ; 
but the force itself does not vary. Here, I think, is an instance of a l'orco 
being confounded with its action. Then Professor Birks says : — 
“Now let two bodies act on each other by a law of force, which depends 
on the inverse distance, and their motion be measured by the square of the 
velocity.” 
But is their motion to be measured by the square of the velocity ? Supposing 
one body moving at the rate of one foot per second, and another at the 
rate of two feet per second, if I ask what is the relation between their 
motions, any one will tell me the motion in one case is double that of the 
other ; but according to this we should say one is four times the other. 
If motion be a change of place, it can only be measured by the amount of 
that change ; and if one body travels at the rate of one foot in a second, and 
the other at the rate of two feet in the same time, it is quite clear that the 
motion of the one body is double the motion of the other. But in this case 
I think motion is confused with energy. Then, again, Professor Birks 
says 
“ The old name of the motion, thus increased or diminished, is Vis viva, 
and the new one ; not at all clearer, Kinetic Energy.” 
