NovemBer 1, 1918] 
when one attempts to define more closely the 
concept center of gravity. For the law of the 
lever then appears as implicitly assumed in 
this concept, and hence not to be demonstrated 
by its use. 
Our knowledge of Archimedes’s attainments 
is limited to the scanty remnants which gen- 
erations of militarists have allowed to survive. 
An examination of Aristotle’s “ Mechanical 
Problems ” shows that even before Archimedes 
certain phenomena of the simplest machines 
were puzzling, that the effort-demanding qual- 
ity of bodies presented itself in two aspects. 
Aristotle says (Ch. 10): 
Why is it that a balance moves more easily 
without a weight upon it than with one? So too 
with a wheel or anything of that nature, the 
smaller and lighter is easier to move than the 
heavier and larger. Is it because that which is 
heavy is difficult to move not only vertically but 
also horizontally? For one can move a weight 
_with difficulty contrary to its inclination, but 
easily in the direction of its inclination; and it 
does not incline in a horizontal direction. 
Again (Ch. 19): 
How is it that, if you place a heavy axe on a 
piece of wood and put a heavy weight on the top 
of it, it does not cleave the wood to any consider- 
able extent; whereas, if you lift the axe and 
strike the wood with it, it does split it, although 
the axe when it strikes the blow has much less 
weight upon it than when it is placed on the wood 
and pressing on it? Is it because the effect is 
produced entirely by movement, and that which is 
heavy gets more movement from its weight when 
it is in motion than when it is at rest? So, when 
it is merely pressed on the wood, it does not move 
with the movement derived from its weight; but 
when it is put into motion, it moves with the 
movement derived from its weight and also with 
that imparted by the striker. Furthermore, the 
axe works like a wedge; and a wedge, though 
small, can split large masses, because it is made 
up of two levers working in opposite directions. 
P. Duhem,!! comparing the methods of the 
two great Greeks, says: 
Admirable as a method of demonstration, the 
path followed by Archimedes in mechanics is not 
a method of invention; the certainty and the 
11 ‘‘Les Origines de la Statique,’’ p. 12 (1905). 
‘SCIENCE 
431 
clarity of his principles stick on the whole where 
they are plucked, so to speak, on the surface of 
phenomena, and are not pulled up by the roots 
from the bottom of things; according to a remark 
which Deseartes made less justly about Galileo, 
Archimedes ‘‘explains very well what is so, but 
not why it is so,’’ therefore we shall observe the 
more striking forward steps in statics to start 
rather from the doctrine of Aristotle than from 
the theories of Archimedes. 
But one should not look to the “ Mechanical 
Problems” for demonstrations by an admir- 
able method; they are but poor attempts at 
demonstration, from the hand of one of whom 
Duhem?? writes: 
Aristotle was not a geometer; from the prin- 
ciple which he had set up, he did not know how to 
draw with entire rigor all the consequences which 
can be deduced from it. 
Attempts at demonstration, moreover which 
have doubtless suffered by transcription a hun- 
dredfold repeated, and at the hands of teach- 
ers and pupils who were merely Aristotelians. 
Unable successfully to solve his problems, he 
has yet the great merit, greater than that 
of a mere problem-solver, of perceiving the 
existence of the problems, and putting for- 
ward a statement showing the difficulty. 
He for whom his most famous pupil, the 
conquering explorer Alexander, made collec- 
tions of natural history, sending them far by 
the slow transport of those days to his mas- 
ter’s school of science, was no pedant of the 
schools. He knew the mint, the market and 
the quarry; he saw the balance pans easily 
swinging when empty, but, loaded with metal 
or meat and balanced, hard to set in motion; 
he thought it odd that balanced weights, 
which, so to speak, lift each the other, 
should be hard to move; he saw the cylindrical 
column sections rolled with labor up inclined 
planes out of the quarry, but rolling down 
again at a touch; why should they be hard to 
12 Loe. cit., p. 8. 
13 **Q, M.,’’ Ch. 26. ‘‘Why is it more difficult 
to carry a long plank of wood on the shoulder if 
one holds it at the end than if it is held in the 
middle? ... The reason is, that if one lifts it in 
the middle, the two ends always lighten one 
another, and one side lifts the other up.’’ 
