David Heydorn Ray.

A dissertation on the development of the science of mechanics : being a study of the chief contributions of its eminent masters, with a critique of the fundamental mechanical concepts, and a bibliogra online

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Online LibraryDavid Heydorn RayA dissertation on the development of the science of mechanics : being a study of the chief contributions of its eminent masters, with a critique of the fundamental mechanical concepts, and a bibliogra → online text (page 1 of 12)
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The Period of Antiquity, iogoo B. C. to 500 A. D.


1. The Science of Mechanics 8

2. Science in Antiquity 12

3. Archimedes 19

The Medieval Period, 500 A. D. to 1500 A. D.

1. The Medieval Attitude toward Science 33

2. The Influence of Arabian Culture 39

3. The Period of the Renaissance 42

4. The Contribution of Stevinus 45

5. The Contribution of Galileo 52



The Modern Period, 1500 to 1900.

1. Characteristics of the Modern Period 60

Huygens 63

2. Newton 69

3. The Contributions of Varignon, Leibnitz, the

Bernoullis, Euler and D'Alembert 77

4. The Contributions OF Lagrange AND Laplace. . . 106


iv contents.

5. Recent Contributions. The Law of Conserva-

tion 117

6. The Ether. Energy. Dissociation of Matter. 125



1. Conclusions and Critique of the Fundamental

Concepts of the Science 133

2. Tabular View of the Development of Me-

chanics 134

3. Bibliography 146


The word mechanics, though it indicated of old the study
of machines, has long since outgrown this limited meaning
and now embraces the entire study of moving bodies, both
large and small, suns and satellites, as well as atoms and mole-
cules. The phenomena of nature present to us a world of
change through ceaseless motion. Mechanics is the "Science
of Motion" as the physicist Kirchhoff has defined it, and has
all natural phenomena for its field of investigation. Why
things happen and how they happen are the questions that
here present themselves.

It was a long time before the distinction between "why"
and "how" was drawn, but when once the question "why"
was turned over to the metaphysician and the theologian,
and attention was concentrated on "Aow," then mechanics
made progress. Men then began to discover "how things
go," and to try their hand at invention.

It is not the purpose here to touch upon either the meta-
physical or the psychological aspect of phenomena, nor the
mystery of vegetable or animal activities, but to trace the
development of Mechanics as a science from the earliest records
to the present time, first analyzing the contributions made to
it, step by step, and then touching upon their use and value.

As the French philosopher Comte first noted, three stages
are apparent in the growth of human knowledge. In the
first stage, man ascribed every act to the direct interposition
of the Deity, in the second he tried to analyze the Deity's
motives and so tried to learn "why," while in the third, men
came to regard the inquiry "why" as profitless and ask "how."
In this last stage, they accept the universe and are content
with learning all they can of how it goes. With this last
attitude, called positivism, science flourishes. Out of it grew
the notion of utilitarianism, — the devotion of all energies


toward the improvement of the conditions of life on earth.
Though this later philosophy cannot entirely justify itself,
it is commonly identified with the scientific attitude of mind.

By the long road of experience, by blunder, trial and experi-
ment, men first gathered, it seems, ideas of things that appear
always to happen together as by a necessary sequence of
"cause and effect." Of the stream of appearances continu-
ously presenting themselves, some are invariably bound to-
gether, being either simultaneous or successive, the presence
or absence of the others apparently making no difference.
Those having no influence may reasonably be ignored and
eliminated as of no consequence. In this way, the method
of abstracting from the great multitude of phenomena those
that are mutually dependent seems to have been evolved.

Barbarous peoples do not possess a clear notion of sequence
or of the interdependence of things. They are prone to regard
the consequence of an action as accessory, as something done
by an invisible being or a god. An action is performed by
them, and what is commonly called by us the result is con-
ceived by them as the simultaneous act of their god. Their
medicineman is thought of, as one proficient in the art of
appealing to the moods and whims of their gods propitiously.
Even the Greeks and Romans, the founders of our European
civilization, were accustomed to be guided in affairs of state
and of the home by omens, by the flight of birds, and the
inspection of the entrails of animals, — most naive examples
of traditional error in the interdependence of simultaneous

Things which we now understand to have not the slightest
relation with each other were systematically confounded by
the ancients. For thousands of years belief in astrology was
general in Europe and the universahty of the belief is at-
tested by such words as ill-starred, disastrous, consider and
saturnine, all of which are manifestly of astrological ety-
mology. It was only very slowly and gradually, step by step,
that men came to think of phenomena quantitatively rather
than qualitatively, and to arrive at a more rational concep-
tion of nature through experience and reflection.


As the interrelation of things came to be more clearly per-
ceived, people began to say they could "explain things,"
meaning that they had arrived at a familiarity with, and had
begun to recognize certain permanent elements and sequences
in the variety of phenomena. By joining these elements, they
constructed a chain and attained to a more or less extensive
and consistent comprehension of the relations of phenomena
by a co-ordination of their permanent elements.

If these elements are linked together logically, the satis-
factoriness of "the explanation" depends upon the length of
the chain. The longer the chain, the further it reaches, and
the more satisfied one is, the more one "understands" the
matter. This is the general method of "learning things," and
the information so collected may be called, as Prof. Karl
Pearson has called it, an "intellectual resume of experience."
But it should be noted that it is rarely the simple correlation of
things that will stand the test of experiment.

There is in this method abundant chance to go wrong. It is
difficult, and especially troublesome for a beginner, untrained
in this process, to decide what things really do not have effect
and hence may be excluded from consideration. And if it is
difficult for the beginner in science to-day, surely it was im-
mensely more so for primitive men. Students are wont to
complain of the artificiality of geometry and mechanics. Fac-
tors which they feel do make a difference in reality do not
seem to them to be fully allowed for, or they are troubled by a
feeling of uncertainty as to the equity of the allowance. The
peculiar value of mathematical studies lies just here in the
rigorous training in reasoning. Whatever a student's success
with his mathematics, few make its acquaintance without
receiving wholesome lessons of patient application of the in-
tellectual method by which mankind has won its mastery
over natural forces.

We may quote here to advantage Prof. Faraday.^ "There
are multitudes who think themselves competent to decide,
after the most cursory observation, upon the cause of this or

1 Lecture delivered before Royal Institution of Great Britain, — "On Edu-
cation of the Judgment."


that event, (and they may be really very acute and correct
in things familiar to them) : — a not unusual phrase with them
is, that 'it stands to reason,' that the effect they expect should
result from the cause they assign to it, and yet it is very dif-
ficult, in numerous cases that appear plain, to show this reason,
or to deduce the true and only rational relation, of cause and

"If we are subject to mistake in the interpretation of our
mere sense impressions, we are much more liable to error
when we proceed to deduce from these impressions (as sup-
plied to us by our ordinary experience), the relation of cause
and effect; and the accuracy of our judgment, consequently,
is more endangered. Then our dependence should be upon
carefully observed facts, and the laws of nature; and I shall
proceed to a further illustration of the mental deficiency I
speak of, by a brief reference to one of these.

"The laws of nature, as we understand them, are the founda-
tion of our knowledge in natural things. So much as we
know of them has been developed by the successive energies
of the highest intellects, exerted through many ages. After
a most rigid and scrutinizing examination upon principle and
trial, a definite expression has been given to them; they have
become, as it were, our belief or trust. From day to day we
still examine and test our expression of them. We have no
interest in their retention if erroneous; on the contrary, the
greatest discovery a man could make would be to prove that
one of these accepted laws was erroneous, and his greatest
honour would be the discovery. . . .

"These laws are numerous, and are more or less compre-
hensive. 'They are also precise; for a law may present an
apparent exception, and yet not be less a law to us, when
the exception is included in the expression. Thus, that eleva-
tion of temperature expands all bodies is a well-defined law,
though there be an exception in water for a limited tempera-
ture; we are careful, whilst stating the law to state the excep-
tion and its limits. Pre-erriinent among these laws, because
of its simplicity, its universality, and its undeviating truth,
stands that enunciated by Newton (commonly called the law


of gravitation), that matter attracts matter with a force in-
versely as the square of the distance. Newton showed that,
by this law, the general condition of things on the surface of
the earth is governed; and the globe itself, with all upon it
kept together as a whole. He demonstrated that the motions
of the planets round the sun, and of the satellites about the
planets, were subject to it. During and since his time, certain
variations in the movements of the planets, which were called
irregularities, and might, for aught that was then known, be
due to some cause other than the attraction of gravitation,
were found to be its necessary consequences. By the close
and scrutinizing attention of minds the most persevering and
careful, it was ascertained that even the distant stars were
subject to this law; and, at last, to place as it were the seal
of assurance to its never-failing truth, it became, in the minds
of Leverrier and Adams (1845), the foreteller and the dis-
coverer of an orb rolling in the depths of space, so large as
to equal nearly sixty earths, yet so far away as to be invisible
to the unassisted eye. What truth, beneath that of revelation,
can have an assurance stronger than this!"

Such is the process of scientific induction. It was by linking
ideas together in an orderly way, by forming and verifying
hypotheses, that men finally came to the "principles," and
"formulae," which embody these general "truths" or "laws of
nature." In this way knowledge has been built up, chain by
chain, into a more or less complete system of the relations of
things. Without asking the "why" of it all one can see
"how" it goes together by running along the chains from link
to link. In a word this knowledge is relative, and therefore
quantitative,- and that is why numbers and mathematics play
so large a part in the exact sciences, and in mechanics.

The guiding principle in all this is the belief in the con-
stancy of the order of nature founded on the experience of
the human race. On this belief are based all scientific calcu-
lations and deductions. This is sometimes formulated as a
"Law of Causality," affirming that every effect has a sufficient
cause and that the relation of cause and effect is one of in-
variable sequence, if not interfered with by conditions or
circumstances that make the cases dissimilar.


Information thus systematized, verified and formulated into
truths or general principles is called Natural Philosophy or
Natural Science. The Science of Mechanics is the oldest and
one of the most important divisions of Natural Philosophy.
This knowledge of the interdependence and inter-relation of
phenomena makes it possible to "predict" and "control" them,
and keeps us from making hasty and erroneous inferences.
When developed with this view, applied science or applied
mechanics is the usual designation, and that such information
is power to one who has the skill to apply it, need not be dwelt
upon. As Herbert Spencer says in his volume on Education:^
"On the application of rational mechanics depends the success
of nearly all modern manufacture. The properties of the
lever, the wheel and axle, etc., are involved in every machine
— every machine is a solidified mechanical theorem; and to
machinery in these times we owe nearly all production.''
Elsewhere he says : "All Science is prevision ; and all prevision
ultimately helps us in greater or less degree to achieve the
good and to avoid the bad."^

It is not the intention here to discuss or even to enumerate
the triumphs in the practical applications of mechanics. The
utilization of power, of the strength of animals, the power
of the wind, of waterfalls, of steam and of electromagnetic
attraction, constitutes the art of machine contrivance
rather than the science of mechanics. Progress in theoretical
mechanics has always brought in its train an advance in

The innumerable engines for enlightenment and destruction,
the cylinder-printing-press and the machine-gun which have
changed and are altering the economic, social and religious
prospect of nations and tribes are the direct result of the
application of the principles of the science of mechanics. With
further advance in theory and systematic experimentation even
more revolutionizing contrivances will inevitably follow.
When invention has realized the theoretical surmise that the
"molecular energy" in a cup of tea is sufficient to tumble down

ip. 30.

2"First Principles," p. 15.


a town, we may expect an Age of Power ushering in wonders

With the philosophy that denies the existence of reaUties
outside of the mind we shall not trouble ourselves here.
Mechanics regards a "truth" or a "law" not as subjective but
as objective, holding that an external world exists and that
truth is a relation of conformity between the mental world
of perceptions and inferences, and really existing objects and
their relations. Unless this and the validity of the principle
of logical inference be conceded, our science is futile. The
mental processes by which the victories of Science are won are
in no wise different from those used by all in daily affairs. As
Huxley says : "Science is nothing but organized common sense.
The man of Science simply uses with scrupulous exactness
the methods which we all habitually and at every moment,
use carelessly. Nor does that process of induction and de-
duction by which a lady, finding a stain of a peculiar kind
on her dress, concludes that somebody has upset the inkstand
thereon, differ in any way, in kind from that by which Adams
and Leverrier discovered a new planet."

Nevertheless there will always remain certain ultimate truths
which cannot be proved and which must be consideredas axiom-
atic and intuitive. This should not invalidate our conclusions
and we will not enter upon a discussion of these questions here.

The science of mechanics has then, for its subject matter,
the motion-phenomena of the universe. Its growth is co-
extensive with that of the race, and one of its functions is the
widening of its perceptions. It is obviously a subject of
primary importance, for from apparent chaos, it evolves rules
and principles of practical utility, and so increases knowledge
and efhciency, and consequently happiness, through power
and dominion over nature.

^Suppose that a cup of tea (about lOO cubic centimeters) could be
suddenly and completely dissociated, after the manner of the radio-active
emissions of radium, into a cloud of particles with a velocity similar to
radium emanations of say 100,000 kilometers a second (about one-third
the velocity of light), then a simple calcu lation by th e theoretical formula
for energy, J^twi)^, gives 3^ X.1/9.8X 100, 000,000^ = 50,000,000,000,000
kilogramme-meters, equal to the energy of explosion of about 500,000 tons
of rifle powder, or enough energy to drive an express train around the globe
a hundred times.



The most common of all our experiences is the motion of
solid bodies. No idea is more frequently with us than the
idea of such movements. It seems to be the first experience
of the dawning intellect and it is soon fully developed by
boyhood's games of marbles and tops. Indeed, there is
nothing that our imagination pictures with greater ease and
readiness, than a moving speck or particle. There is there-
fore considerable satisfaction, and an appealing reasonableness
and inevitableness in the idea of classifying phenomena on
the basis of this familiar experience.

This idea and another, quite as familiar, namely, that com-
mon objects can be crushed and broken into many small par-
ticles and ground to dust so small as to seem indivisible, are
fundamental, and upon them the science of mechanics, as a
scheme of motions and equilibrium of particles has been built
up. Masses either change their relative position or they do
not. How they move, rather than why they move, is the
question of Mechanics. It is especially the circumstances of
motion or of rest that are the subject of investigation of the

In its formal presentation in textbooks, Mechanics is now
defined by an American Professor, Wright, as "the science
of matter, motion, and force"; by an English Professor, Ran-
kine, as the "science of rest, motion and force"; by a German
Professor, Mach, as that branch of Science which is "concerned
with the motions and equilibrium of masses." These defini-
tions do not differ essentially.

The questions at once present themselves what is force,
what is matter, what is mass? Etymology does not help us.
The further back one goes, the more indistinctive and general
is the idea corresponding to a scientific term. The terms,
matter, mass, force and weight lose precision as we trace them


back. Matter leads us back to the Latin, materia, i. e.,
substance for construction or building. Mass appears to be
derived from the Greek root (Mdaaetv), to knead. So by
derivation, matter means the substance or pith of a body,
and mass means anything kneaded together like a lump of
dough. The fundamental idea of mass is then an agglutinated
lump. Weight is of Saxon derivation from a root meaning to
bear, to carry, to lift. Force appears to come from the Latin
root, fortia, meaning muscular vigor and strength for violence.
It is an anthropomorphic concept, and is suggestive of myth-
ology in its application to inanimate things.

All these terms are derived from words expressing distinct
muscular sensations. Here in the last analysis we come back
to sense-impressions. A mass is an agglutinated lump as of
kneaded dough, weight is resistance to lifting, and force is some-
thing that produces results analogous to those produced by
muscular exertion. We cannot analyze these simple, immediate
perceptions, nor can we analyze motion. Motion is a sense of
free, unrestricted muscular action. Muscular action impeded
gives us our sense of force. Perhaps our primitive perception
of force was muscular action under restraint or not accom-
panied by motion. From these sense-impressions we attain,
by inference, the idea of space, i. e., room to move in, and the
notion of time or uniformity of sequence. Mechanics might ^;
then be crudely defined as a scheme of the relations of lumps
of matter acted upon by muscular exertion or by anything ;
that produces like effects. )

Observe that we are conscious of these sense-impressions,
comparatively only. We are aware of them only through
change in their intensity. Here in our endeavors to com-
prehend and to define the ultimate elements of mechanics we
have borne in upon us the relativity of knowledge. The con-
viction that the human intelligence is incapable of absolute
knowledge is the one idea upon which philosophers, scientists,
and theologians are in accord. It is a characteristic of con-
sciousness that it is only possible in the form of a relation.

"Thinking is relationing and no thought can express more
than relations," says Herbert Spencer in his Chapter on the


Relativity of Knowledge. And he concludes: "Deep down in
the very nature of Life, the relativity of our knowledge is dis-
cernible. The analysis of vital actions in general, leads not
only to the conclusion that things in themselves cannot be
known to us, but also to the conclusion that knowledge of
them, were it possible, would be useless."^

But though we are limited in this way we have a large field
in the building of a scheme of inter-relations of the relations
which comprise our conscious perceptions. This is the purpose
of our science of mechanics. In general it endeavors to inter-
pret for us the complex relativity of phenomena in terms of
the most common and simplest of our experiences, namely
the relativity of motion of a particle and the relativity of
the divided parts of bodies.

As science progresses the ideas, mental pictures, and terms
found serviceable in the earlier stages are bound to prove
inadequate later. The process of reorganizing these ideas,
and perfecting terminology is slow, but in it there is unmistak-
able evolutionary progress.

As the philologist Nietzsche says, "Wherever primitive man
put up a word, he believed he had made a discovery. How
utterly mistaken he really was! He had touched a problem,
and while supposing he had solved it, he had created an
obstacle to its solution. Now, with every new knowledge, we
stumble over flint-like petrified words. "^

The prehistoric races probably explained phenomena by
associating with everything that produces motion, some in-
visible god whose muscular strength was the force of wind,
wave or waterfall. We find in all languages, survivals of this
in the genders ascribed to things inanimate. Indeed, one can
dig out of philology and mythology a petrified primitive natu-
ral philosophy.

To-day we sometimes hear that all phenomena of the material
world are explainable, in terms of matter, motion, and force,
or by the whirl of molecules. One may endeavor to make
this a truism by defining matter as anything that occupies

^Spencer, "First Principles," Chapter IV.
''Nietzsche, "Morgenrote," vol. i, 47.


space, and by defining force as any agent which changes the
relative condition as to rest or motion between two bodies,
or which tends to change any physical relation between them,
whether mechanical, thermal, chemical, electrical, magnetic,
or of any other kind. But here one does not say what force
is, nor what matter is. The chain hangs in the air; it does
not begin or end anywhere, but the relation of the links is
apparent and serviceable. Indeed, the idea of force is still
fundamentally the same, it is still an agent, as was the ancient
nature-god, though much less definite, nor does it help matters
to subdivide force and mass.

The idea of force as a latent unknown cause is a historical "-^
survival of our primitive conceptions and undergoes trans-
formation with the idea of force as a "circumstance of motion," {
which was developed about the year 1700. It is now held \
by some that force is a purely subjective conception. For

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Online LibraryDavid Heydorn RayA dissertation on the development of the science of mechanics : being a study of the chief contributions of its eminent masters, with a critique of the fundamental mechanical concepts, and a bibliogra → online text (page 1 of 12)