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M E T A P
respect to A.” In a word, Mach and Kirchhoff agree that
force is not a cause, convert Newtonian reciprocal action
into mere interdependency, and, in old terminology,
reduce mechanics from a natural philosophy of causes^to
a natural history of mere facts. Now, Mach applies these
preconceived opinions to “mechanics in its development,”
with the result that, though he shows much skill in
mathematical mechanics, he misrepresents its development
precisely at the critical point of the discovery of Newton’s
third law of motion, “Actioni contrariam semper et
jequalem esse reactionem.”
The order of discovery, recorded in the Philosophical
Transactions of the Royal Society, was as follows : —
(а) Sir Christopher Wren made many experiments before
the Royal Society, which were afterwards repeated in a
corrected form by Sir Isaac Newton in the Principia,
experimentally proving that bodies of ascertained com¬
parative weights, when suspended and impelled against
one another, forced one another back by impressing on one
another opposite changes of velocity inversely as their
weights and therefore masses; that is, by impressing on
one another equal and opposite changes of momentum.
(б) Wallis showed that such bodies reduce one another
to a joint mass with a common velocity equal to their
joint momentum divided by their joint weights or masses.
This result is easily deducible also from Wren’s discovery.
If m and m are the masses, v and v their initial velocities,
and V the common velocity, then
m(v - V)=m'(V - v')
mv + m'v'= +
, mv + toV _
TO + to' —
(c) Wren and Huyghens further proved that the law of
equal action and reaction, already experimentally established
by the former, is deducible from the conservation of the
velocity of the common centre of gravity, which is the
same as the common velocity of the bodies; that is,
deducible from the fact that their common centre of
gravity does not change its state of motion or rest by
the actions of the bodies between themselves; and they
further extended the law to bodies, qua elastic.
(d) Hence, first inductively and then deductively, the
third law was originally discovered only as a law of collision
or impact between bodies of ascertained weights and
therefore masses, impressing on one another equal and
opposite changes of momentum, and always reducing one
another to a joint mass with a common velocity to begin
with, apart from the subsequent effects of elasticity.
(e) Newton in the Principia, repeating and correcting
Wren’s experiments on collision, and adding further
instances from attractive forces of magnetism and gravity,
induced the third law of motion as a general law of all
forces.
This order of discovery shows that the third law was
generalized from the experiments of Wren on bodies of
ascertained comparative weights or masses, which are not
material points or mass-points. It shows that the bodies
impress on one another opposite changes of velocity in¬
versely as their weights' or masses; and that in doing so
they always begin by reducing one another to a joint mass
with a common velocity, whatever they may do afterwards
in consequence of their elasticities. The two bodies there¬
fore do not penetrate one another, but begin by acting on
one another with a force precisely sufficient, instead of
penetrating one another, to cause them to form a joint mass
with a common velocity. Bodies then are triply extended
substances, each occupying enough sjiace to prevent mutual
penetration, and by this force of mutual impenetrability or
inter-resistance cause one another to form a joint mass
with a common velocity whenever they collide. Withdraw
H Y S I C S 667
this foundation of bodies as inter-resisting forces causing
one another in collision to form a joint mass with a common
velocity but without penetration, and the evidence of the
third law disappears; for in the case of attractive forces
we know nothing of their modus operandi except by the
analogy of the collision of inter-resisting bodies, which
makes us believe that something similar, we know not what,
takes place in gravity, magnetism, electricity, Ac. Now,
Mach, though he occasionally drops hints that the discovery
of the law of collision comes first, yet never explains the
process of development from it to the third law of motion.
On the contrary, he treats the law of collision with
other laws as an application of the third law of motion,
because it is now unfortunately so taught in books of
mechanics. He has therefore lost sight of the truths
that bodies are triply extended, mutually impenetrable
substances, and by this force causes which reduce one
another to a joint mass with a common velocity on collision,
as for instance in the ballistic pendulum ; that these forces
are the ones we best understand; and that they are reciprocal
causes of the common velocity of their joint mass, whatever
happens afterwards. In the case of this one force we know
far more than the interdependence supposed by Mach and
Kirchhoff; we know bodies with impenetrable force causing
one another to keep apart. It might have been expected
that scepticism on this subject would not have had much
effect. But the idealists are only too glad to get any
excuse for denying bodily substances and causes; and,
while Leibnitz supplied them with the fancied analysis of
material into immaterial elements, and Hume with the
reduction of bodies to assemblages of sensations, Mach
adds the additional argument that bodily forces are not
causes at all. In Great Britain, at this moment, Mach’s
scepticism is welcomed by Karl Pearson to support an
idealistic phenomenalism derived from Hume, and by Ward
to support a noumenal idealism derived from Lotze. No
real advance in metaphysics can take place, and natural
science itself is in some danger, until the true history of
the evidences of the laws of mechanical force is restored;.
and then it will soon appear that in the force of collision
what we know is not material points determining one
another’s opposite accelerations, but bodies by force of
impenetrable pressure causing one another to keep apart.
Mechanics is a natural philosophy of causes.
(3) Dualism within Experience.—As it comes to be
realized that Hume and Kant agreed more than they
differed, German philosophers tend to make new philo¬
sophies out of their common points. Hume thought that
knowledge has its origin from experience, and Kant that
d priori elements are contained in this experience; but,
in differing about the oifigin, they agreed about the limits
of knowledge, which, according to both, is a knowledge
of mental phenomena of sense, and a knowledge limited
to objects of experience, without any power of knowing
by logical inference anything existing beyond, anything
transcending, experience, actual and possible. Now,
besides philosophies which are reactions to Kant or to
Hume, there are a number of other philosophies in our
day which start with this common hypothesis as a prin¬
ciple— knowledge is experience. The consequence is
that whatever is true of experience they transfer to all
knowledge. One of the characteristics of actual experi¬
ence is that its object is, or has been, present to an
experiencing subject; and of possible experience that it
can be present. As a matter of fact, this characteristic
differentiates experience from inference By inference we
know that things, such as the farther side of the moon,
which neither are, nor have been, nor can be, present to
an experiencing subject on the earth, nevertheless exist,
and only become objects of inference. But, on the