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Progress in Science. [October 
as mathematicians, were certainly grossly ignorant of some elementary parts 
of dynamics, insomuch that Leibnitz himself was known to have considered the 
fundamental system of the “ Principia ” to be erroneous, and to have devised 
another and different system of his own. This fadt was carefully kept back 
now-a-days, but it was a fadt, and it had a great deal to do with the vague- 
ness of the terms for Force and Energy in some modern languages. In fadl, 
in their modern dress, the Vis Viva , Vis Mortna , and Vis Acceleratrix of that 
time had, in some of their Protean shapes, hooked themselves, like Entozoa, 
into the great majority of our text-books. 
The ledturer then proceeded to consider our modes of becoming acquainted 
with the physical world. In dealing with physical science it was absolutely 
necessary to keep well in view the all-important principle that — 
“ Nothing can be learned as to the physical world save by observation ar,d 
experiment , or by mathematical deductions from data so obtained .” 
The notion of force was suggested to us by the so-called muscular sense, 
which gives us a peculiar feeling of pressure when we attempt to move a piece 
of matter. The sense in which Newton used the word “ force,” and therefore 
the sense in which we must continue to use it if we desired to avoid intellectual 
confusion, would appear clearly from a brief consideration of his simple 
statement of the laws of motion. The first of these laws was — 
“ Every body continues in its state of rest or of uniform motion in a straight 
line , except in so far as it is compelled by impressed forces to change that state." 
In other words, any change, whether in the direction or in the rate of motion 
of a body, was attributed to force. Thus a stone let fall moved quicker and 
quicker, and we said that a force (viz., the weight of the stone, or the earth’s 
attraction for it) was continually acting so as to increase the rate of the motion. 
If the stone were thrown upwards the rate of its motion continually diminished, 
and we said that the same force (the stone’s weight) was continually acting so as 
to produce this diminution of speed. But this gave only half of tne informa- 
tion which Newton’s first law afforded. The moon revolved about the earth, 
and the earth and other planets revolved about the sun — approximately, at 
least, in circles. Why was this ? Their directions of motion were constantly 
changing ; in fact, a curved line was merely a fine whose direction changed 
from point to point, while a straight line was one whose direction did not 
change ; but to produce this change of direction force was required just as much 
as to produce change of speed. That was supplied by the gravitation attrac- 
tion of the central body of the system. The old notion was that a centripetal 
force was required to balance the so-called centrifugal force, it being imagined 
that a body moving in a circle had a tendency to fly outwards from the centre ! 
Newton’s simple law exposed the absurdity of this. If a body was to be made 
to move in a curved line instead of its natural straight path, we must apply 
force to compel it to do so — certainly not to prevent it from flying outwards 
from the centre, about which it was for the moment revolving. In fadt inertia 
meant not revolutionary activity, but dogged perseverance, and just as we 
must apply force in the direction of motion to change the rate of motion, so 
we must apply force perpendicular to the diredtion of motion to change that 
diredtion. Newton’s second law was ‘how required : — 
“ Change of motion is proportional to the impressed force , and takes place in 
the direction of the straight line in which the force acts." 
This one simple law held for all kinds of force alike. Change of motion 
was change of momentum, or the produdt of the mass of the moving body 
into its change of velocity. Of course the longer a given force adted the greater 
would be the change of momentum "which., it produced; so that to compare 
forces, which was the essence of the process of measuring them, we must 
give them equal times to adt, — or, in scientific language, we must measure a 
force by the rate at which it produced change of momentum. Rate of change 
of velocity was called, in kinematics; acceleration. Thus the measure of a 
force was the produdt of the mass of the body moved into the acceleration 
which the force produced in it. This was the so-called Vis motrix, or “ moving 
force” of the Cambridge text-books the so-called Vis acceleratrix , or 
“ accelerating force,” being really no force at all, but another name for the 
