508 K68m
68-14243
of science, digest of 13
great classics
1 1 d
Kansas city public library
Books will be issued only
Please report lost cards and
change of residence promptly.
Card holders are resf
all books, records, films, pictures
or other library materials
checked out on their cards.
HOV I7 1375;
00118 950E
DA'I'fc. DUE
APR 1 2 197|
14JSBL
4 <989
%AY 2 .0 1981
TFT9ST
irnssr
A
MM ^PB 3 1986 |
MM
? ; MU
; « < /' vi
MASTERWORKS OF SCIENCE
MASTERWORKS SERIES
Editorial Board
Alvm Johnson, LL.D,
PRESIDENT EMERITUS, THE NEW SCHOOL
FOR SOCIAL RESEARCH
Robert Andrews Million, Sc.D.
CHAIRMAN OF THE EXECUTIVE COUNCIL,
CALIFORNIA INSTITUTE OF TECHNOLOGY
Alexander Madaren Witherspoon, PhD.
ASSOCIATE PROFESSOR OF ENGLISH,
YALE UNIVERSITY
MASTERWORKS
Sci
OF
aerice
DIGESTS OF 13 GREAT CLASSICS
Edited by
John Warren Knedler, Jr.
DOUBLEDAY & COMPANY, INC., GARDEN ClTY, N. Y., 1947
COPYRIGHT, X947
BY DOUBLEDAY & COMPANY, INC.
ALL RIGHTS RESERVED
PRINTED IN THE UNITED STATES
AT
THE COUNTRY LIFE PRESS, GARDEN CITY, N. Y.
FIRST EDITION
CONTENTS
INTRODUCTION . 3
THE ELEMENTS
by Euclid . 13^
ON FLOATING BODIES, AND OTHER PROPOSITIONS
by Archimedes . r. , ... 27
,'ON THE REVOLUTIONS OF THE HEAVENLY SPHERES *
by Nifolaus Copernicus . 4^
DIALOGUES CONCERNING Two NEW SCIENCES
by Galileo . * . 75
PRINCIPIA
by Isaac Newton 171
THE ATOMIC THEORY
by John Dalton . 247
PRINCIPLES OF GEOLOGY
by Charles Lyell 275,
THE ORIGIN OF SPECIES
by Charles Darwin . 331^
EXPERIMENTAL RESEARCHES IN ELECTRICITY
by Michael Faraday . 447
EXPERIMENTS IN PLANT-HYBRIDIZATION
by Gregor Johann Mendel , 505
THE PERIODIC LAW
by Dmitri Ivanovich Mendeleyev , 535
RADIOACTIVITY
by Marie Curie 571
RELATIVITY: THE SPECIAL AND GENERAL THEORY
by Albert Einstein . 599
KANSAS CITY fMO.}
6814243
ACKNOWLEDGMENTS
THE EDITOR wishes to thank Peter Smith, Publisher, for permission to
include our condensation of Relativity; The Special and General Theory,
by Albert Einstein.
J.W.K.JR.
PREFACE BY THE EDITORS
THIS VOLUME is one of a series of books which will make available to the
modern reader the key classics in each of the principal fields of knowl-
edge.
The plan of this series is to devote one volume to each subject, such
as Philosophy, Economics, Science, History, Government, and Autobiog-
raphy, and to have each volume represent its field by authoritative con-
densations of ten to twelve famous books universally recognized as mas-
terworks of human thought and knowledge. The names of the authors
and the books have long been household words, but the books themselves
are not generally known, and many of them are quite inaccessible to the
public. With respect to each subject represented, one may say that seldom
before have so many original documents of vital importance been brought
together in a single volume. Many readers will welcome the opportunity
of coming to know these masterworks at first hand through these compre-
hensive and carefully prepared condensations, which include the most sig-
nificant and influential portion of each book — in the author's own words.
Furthermore, the bringing together in one volume of the great classics
in individual fields of knowledge will give the reader a broad view and
a historical perspective of each subject.
Each volume of this series has a general introduction to the field with
which it deals, and in addition each of the classics is preceded by a bio-
graphical introduction.
The plan and scope of the Masterworks Series are indicated by the
classics selected for the present volume, "Masterworks of Science," and
for the five other volumes in the series:
MASTERWORKS OF PHILOSOPHY
«/ Plato — Dialogues
v Aristotle — '-Nicomachean Ethics
%/Bacon — Novum Organum
/ Descartes — Principles of Philosophy
«/" Spinoza — Ethics
Locke — Concerning Human Understanding
PREFACE BY THE EDITORS
Kant — The Critique of Pure Reason
Schopenhauer — The World as Will and Idea
""' Nietzsche — Beyond Good and Evil
- William James — Pragmatism
* Henri Bergson — Creative Evolution
:'' MASTER WORKS OF ECONOMICS
Thomas Mun — England's Treasure by Foreign Trade
Turgot — Reflections on the Formation and Distribution of Wealth
v Adam Smith — The Wealth of Nations
*<' Malthus — An Essay on the Principle of Population
Ricardo — Political Economy and Taxation
Robert Owen — A New Vieiu of Society
John Stuart Mill — Principles of Political Economy
>^ftarl Marx — Capital
Henry George — Progress and Poverty
Thorstein Veblen — The Theory of the Leisure Class
MASTERWORKS OF AUTOBIOGRAPHY
Augustine — Confessions
Benvenuto Cellini — Autobiography
Pepys — Diary
Benjamin Franklin — Autobiography
x Rousseau — Confessions
^ Goethe — Truth and Poetry
Hans Christian Andersen — The True Story of My Life
Newman — Apologia pro Vita Sua
Tolstoy — Childhood, Boyhood, Youth
'Henry Adams — The Education of Henry Adams
* MASTERWORKS OF GOVERNMENT
• Plato— The Republic
"'Aristo tie — Politics
*<Machiavelli — The Prince
XGrotius — The Rights of War and Peace
, •liobbes — Leviathan
vLocke — Of Civil Government
% Montesquieu — The Spirit of Laws
vRousseau — The Social Contract
•^Hamilton — from The Federalist
^Jefferson — on Democracy
Kropotkin — The State: Its Historic Role
i Lenin — The State and Revolution
Wilson — on The League of Nations
PREFACE BY THE EDITORS ix
MASTERWORKS OF HISTORY
/Herodotus — History
^Thucydides — The Peloponnesian War
Caesar — The Gallic Wars
^ Tacitus — The Annals
Bede — Ecclesiastical History of the English Nation
Gibbon — The Decline and Fall of the Roman Empire
Symonds-r-Renaissance in Italy
xMacaulay— The History of England
t Carlyle — The French Revolution
> George Bancroft — The History of the United States
Charles A. and Mary R. Beard — The Rise of American Civilization
All these books have had a profound effect upon the thinking and
activities of mankind. To know them is to partake of the world's great
heritage of wisdom and achievement. Here, in the Masterworks Series,
epoch-making ideas of past and present stand forth freshly and vividly — a
modern presentation of the classics to the modern reader.
ALVIN JOHNSON, LLD.
President Emeritus, The New School
for Social Research
ROBERT ANDREWS MILLIKAN, Sc.D.
Chairman of the Executive Council,
California Institute of Technology
ALEXANDER MACLAREN WITHERSPOON, PH.D.
Associate Professor of English,
Yale University
MASTERWORKS OF SCIENCE
INTRODUCTION
MAN lives in a puzzling physical environment. Since long before the time
of recorded history, he has busied himself to explain the phenomena of
his world. All his theories and guesses properly belong to the history of
science, even such as primitively construed the thunderbolt as a weapon in
the hands of an angry, anthropomorphic god. Generally, however, only
those portions of his explanations which can be organized into a coherent,
self-consistent picture of his universe, and which endure the tests of ob-
servational and experimental trial, are admitted as elements in the history
of science.
In this narrowed sense, science begins with the ancient Chaldeans and
Egyptians. They patiently observed the changing appearance of the
heavens and developed theories to account for the changes. Despite the
crudity of their instruments, they made observations of astonishing acute-
ness. But their conclusions have not uniformly withstood the questioning
of later generations. The ancient Greeks also theorized and observed.
Their method — in the most general terms — was to start from certain
assumptions concerning origins, and to deduce therefrom, in the most
rigorously logical way, those ideas which combined to form their, science.
If the assumptions were successfully challenged, the whole system col-
lapsed. Much of Greek science has from this cause been a casualty of the
ages. But in geometry, an area in which deductive reasoning requires no
aid, the Greek discoveries and methods have lasted. The geometers started
with a few simple postulates, such as the axioms of Euclid, and deduced
from them the properties of lines and points, of plane and of solid figures.
Euclid (£L 300 B.C.) combined his own geometrical work with that of his
predecessors into one great edition, the Elements, He gave to investigators
of the next two thousand years a model in the use of deductive reasoning
and a form in which to present their conclusions. His is the first great
name in the history of science.
About one hundred years after Euclid's death, Archimedes of Syracuse
(287-212 B.C.) applied the Euclidean method to the study of levers and
of hydrostatics. From a few simple axioms, always using a geometer's
method, he deduced his laws. Actually it was the mathematical beauty of
his problems and solutions which delighted him. The correspondence
MASTERWORKS OF SCIENCE
between his conclusions and observed physical fact he considered almost
incidental and immaterial. Yet his familiar laws of the lever and those of
the floating body still express the world as it appears to our senses. In
formulating these laws, Archimedes founded the exact science of me-
chanics.
Other Greek philosophers advanced larger theories to explain the
universe. One of them — without convincing many of his contemporaries —
arrived at what we know as the heliocentric theory; another deduced
something very like the modern nebular hypothesis; another developed an
idea of matter which (incidentally, Aristotle rejected it) strikingly antici-
pates the modern atomic theory. None of these theories won general
acceptance, partly, at least, because the theorists had no means to demon-
strate the validity of their ideas. The ideas themselves, even those which
later investigators have revived, therefore were lost in the mass of similar
notions which the Greek thinkers produced. Indeed, outside mechanics
and pure mathematics, the direct debt of modern science to the Greek
world is small. But modern science owes everything to the Greek idea
that man can attain a generalized, rational, comprehensible explanation
of the physical world. During the Middle Ages this idea lay dormant;
with the Renaissance it revived. Leonardo da Vinci began freshly to
observe the physical world, to question the phenomena of the world, and
to experiment. So did other Italians, his contemporaries. From them
Copernicus (1473-1543) caught method and enthusiasm. When he re-
turned from Italy to Poland, principally interested in astronomy, he used
the new methods of the Italian investigators. He observed, measured,
theorized; then he observed and measured again to test his theories. Un-
able to accept the current geocentric theory, and aided by the mere,st hint
of such a thing which had survived from the Greeks, he framed a helio-
centric theory. Then, almost singlehanded, he wrought for this theory the
stamp of truth.
The invention of the telescope gave Galileo (1564-1642) the oppor-
tunity to supplement the observations and measurements of Copernicus
and to add to the Copernican theory the weight of evidence. He grasped
even more surely than Copernicus the true method of science. Whereas
his predecessors from Aristotle on had been busy, for example, with the
problem of why bodies fall, Galileo set himself the more compact problem:
How do bodies fall? Facing this problem, he first framed a hypothetical
answer. When he found it not self-consistent, he rejected it and formed
another. This process he repeated until he had a theory satisfactory to
himself: that the space traversed by a falling body is proportional to the
square of the time of fall. Next he devised experiments to test his theory.
They confirmed it. Galileo had, partly by his discoveries, more by his
methodology — theory confirmed by experiment — founded the science of
dynamics.
Galileo understood and used what are now known as the first two laws
of motion. The first of these is the law of inertia: a body remains in its
original state of rest or of motion along a straight line unless it is acted
INTRODUCTION
upon by an outside force. This law is the very foundation of dynamics.
From it grows the second: the change in the velocity of a motion is
proportional to the force which causes the change. Upon these two laws,
the laws of inertia and of acceleration, much of later physical investigation
has been based. They remain the foundation of dynamics in the gross
world. Fame acknowledges Galileo for his early recognition of these laws.
He deserves his niche in the history of science even more because he
first saw the possibility of verifying hypotheses by experiments expressly
designed for that purpose.
Born in the year of Galileo's death, Newton (1642-1727) early devoted
himself to inquiries similar to those which had attracted Galileo. As a
young man, he invented a method of mathematical investigation which
he called "fluxions," and which modern students know as the calculus.
Using it, and applying the principle of inverse squares, he extended the
work of his predecessor. First he gave definitive statement to the two
laws of motion already recognized, and then he added a third: to every
action there is an equal and opposite reaction. He considered the problem
of the universe to be a problem of matter and force — in this following
Galileo — and he chose, in the manner of his predecessors, to express his
findings in the form of Euclidean propositions and demonstrations. That
force which causes a body to fall in the neighborhood of the earth Newton
thought might operate throughout the universe. By means of the calculus
— but always giving his results in the geometer's form — he satisfied him-
self that his idea was valid. To this force he gave the name gravitation;
then he wrote mathematical equations to express gravitation and its
effects. He succeeded in showing that all the motions of the heavenly
bodies can be described by one simple physical law. He welded together
the data of astronomy, physics, and mathematics into one great physical
synthesis, one coherent system. He had done more even than Copernicus,
and historians call his the greatest single achievement in the history of
science.
Though physics is the aspect of science most enhanced by the labors of
Euclid, Archimedes, Galileo, Copernicus, and Newton, other branches of
science were not neglected during the centuries covered by the careers of
these men. During the Middle Ages the alchemists strove gallantly to dis-
cover the elixir, stone, or process which would transmute one metal into
another. For they were the heirs of a Greek theory that all matter is ulti-
mately composed of one common element, and that differing substances
owe their peculiar qualities to differences in the shape*, size, or state of
motion of particles in themselves indistinguishable from one another, of
which these substances are constructed. Really the alchemists were trying
to solve the problems of chemistry. Chemistry became a real science, how-
ever, only after Lavoisier, in the eighteenth century, rediscovered oxygen,
produced a reasonable explanation of combustion, and by the use of the
balance showed that in the course of a chemical reaction the total mass
remains the same.
In the eighteenth century, geology also finally emerged from the theo-
MASTERWORKS OF SCIENCE
logical bogs of the Middle Ages. When Hutton announced his uniform!-
tarian theories, he weakened the old catastrophic theories which had been
depended upon to explain the changes observable in the history of the
organic and inorganic worlds. Much earlier, medicine had moved beyond
the bounds of ancient knowledge. In sixteenth-century Italy, Vcsalius had
shown how anatomy should be studied; in seventeenth-century England,
Harvey had discovered the circulation of the blood. Other physicians and
surgeons in various countries o£ Europe had learned about the mechanisms
of respiration and digestion. They had concluded that physical and chemi-
cal principles^ could be applied in physiology.
Considering the enormous preparatory accomplishments of these
scientists — from Copernicus and Galileo to Harvey and Hutton — it is
possibly not surprising that the nineteenth century surpassed all preced-
ing centuries^in the variety and magnitude of its scientific investigations
and discoveries. Sir Charles Lyell (1797-1875) revolutionized geology,
partly, at least, because he could take advantage of the labors of his prede-
cessors. He exhaustively reviewed their theories, co-ordinated their dozens
of studies, familiarized himself with the enormous mass of data they had
accumulated on geological change. Then he threw the weight of his great
learning into support of a theory largely Hutton's — that past geological
changes have been brought about by natural forces still operative. Indus-
triously, patiently, wisely, he studied subjects allied to geology, such as
archeology and conchology, in order to adjust to the recognized data of
observation and experiment the facets of his theory. The results convinced
all geologists. By his labors Lyell immensely increased the concept of
geological time. Whereas earlier commentators on the past changes in the
earth's crust had imagined forces and cataclysms which might have made
these changes in the course of some hundreds of years, Lyell read the
geological record as the tale of millions of years. The earth, geologists
and then Daymen began to believe, has existed for eons, The prodigious
modifications which have taken place in its crust have occurred in slow
sequence.
Charles Darwin (1809-1882) could scarcely have built his theories had
LyeU's concept of the extent of geological time not been previously devel-
oped. Puzzled by the variety of species, concerned over the problem of the
origin of species, he saw that his problem, like Ly ell's, could be solved
only by one who had assembled and mastered vast bodies of information.
Unlike the theorists of the earlier centuries, he found this information
available. Generations of travelers and students and trained observers had
bequeathed to him a volume of data which it was a life's work to assimi-
late. Tirelessly he labored at the task. In the quiet of a retired country life
he not only experimented constantly but also read endlessly. With La-
marck's ideas and Malthus's theories as a point of departure, he had hit
upon the notion that the problem of adaptation was central in the great
biological puzzle of origins. So he indefatigably collected and classified
data until in 1859 ne was able to announce to the world, persuasively, that
.sexual selection, acting under the pressure of the struggle for life, ex-
INTRODUCTION
plained the survival o£ those species favored by adaptation to their en-
vironments and the disappearance of those less fortunate. The terms of
this theory, if debatable, were comprehensible; and the immense length
of geological time envisaged by Lyell stretched far enough to accommo-
date the slow changes Darwin predicated. Within a generation the old
explanations of origins, partly theological, partly folklore, had lost their
standing. Darwinism was triumphant.
Scientific inquiry of all sorts might well have thrived in the nineteenth
century had Darwin's ideas never been published. No doubt can exist,
however, that they turned the attention of physiologists^ comparative
anatomists, medical scientists into those channels where industry and
scientific honesty have earned the rewards the contemporary world enjoys.
In Darwin's theories themselves criticism found one great flaw: if new
organs and new species evolve over long spans of time, being perfect
examples of adaptation only when the evolution is complete, why did they
survive the earlier stages of their development when their usefulness was
slight or even nonexistent? One answer to this question Mendel (1822-
1884) found in his experimental work on the hybridizing of peas. He
showed that discontinuous variations may arise suddenly. His results sug-
gest that in nature sudden jumps are the normal mechanism of evolu-
tionary development. Subsequent investigations have thrown new light
upon the theories of Darwin and those of Mendel, sometimes even modi-
fying them. There remain yet some vexed questions about heredity, en-
vironment, evolution; and vast areas interesting to the naturalist and the
biologist are still unexplored. No biological scientist in recent years has
been able, however, to neglect Darwin and Mendel, and their influence
seems likely to last.
In its medical aspects, biological science developed gradually during
the nineteenth century and more rapidly in the twentieth. Meantime,
chemistry grew from almost nothing to the giant it is in the contemporary
world. Lavoisier had prepared the way by showing the need for accurate
measurement in all chemical experiment. But the real foundation was laid
in the first decade of the nineteenth century by John Dalton (1766-1844),
Considering the combinations of reagents which chemists produce in the
laboratory, he observed that the proportions in these combinations are
always the same. This invariability led him to his atomic theory—the idea
that an element is divisible not indefinitely, but only into particles of a
given size. Out of this concept came the possibility of explaining in under-
standable terms the recognized facts of chemical combinations. Similarly,
it provided the basis for solving the riddles of gaseous volumes. Twentieth-
century physics and chemistry have far outdistanced Dalton in apprecia-
tion and understanding of the almost infinitely small particles out of
which matter is built. They could never have journeyed so easily and far
had not Dalton paved the first street. He identified the atom as the in-
divisible particle of an element which cannot be modified without chang-
ing the element of which it is the constituent part. Thus he indicated to
MASTERWORKS OF SCIENCE
his successors a method of defining elements in terms of their atomic
properties.
A full generation after Dalton's death, Mendeleyev (1834-1907) noted
that when the elements are listed in a given order, the atomic properties
of these elements recur periodically. He was carrying Dalton's work a step
farther. Since the older man's time the number of recognized elements
had greatly increased, and as each new one was discovered, chemists had
hastened to measure and record its atomic properties. Now Mendeleyev,
a synthesizer, devised his great Periodic Tables. In these he showed that
the known elements demand grouping in accord with their common
atomic properties. His work led chemists to see greater necessity than
before for the accurate determination of such properties as atomic weight.
More, these Tables made .possible a prophecy of then undiscovered ele-
ments, for there were blanks in the Tables. In the years since Mendeleyev
first published his Tables, the blanks have gradually been filled by the
discovery of elements not before known. Our own day bears witness to
the excitement attending such discoveries; for plutonium and neptunium,
terms easy to our lips, were strangers to yesterday's chemical vocabulary.
Concerning the phenomena of electricity, a little, but only a little, in-
formation had been collected by the end of the eighteenth century. A little
• — but only a little — experimental work had been done with this myste-
rious form of energy. Franklin's experiments with a kite, a silk string, and
a door key typify at once the curiosity of his generation, the crudity of
their instruments, and the state of their knowledge. Scarcely had the new
century opened when imaginative experiments and startling discoveries
widened the possible areas of inquiry. Volta, Ampere, Ohni are merely
the better known among the many men whose labors have influenced
every dweller in the twentieth century. Very great among these scien-
tists of electricity, half chemists and half physicists, was Faraday. He is
often called the "prince of experimenters," and for ingenuity in devising
experiments, patience in repeating them, industry in recording them, he
well deserves the title. Like Lyell and Darwin, he considered no exertion
too great in the collecting of data, and like the great scientists named
earlier in this essay, he recognized the value of accurate measurements.
When he began his experimental labors, various electrical phenomena
were already well known. He first exhaustively studied these to show that
all of them witness the presence of the same energy, electricity. Then he
investigated and satisfactorily explained the passage of electricity through
liquids. He studied the battery and worked out a reasonable explanation
of its behavior; devised means to measure electrical quantities; showed
the equality between the quantity of electricity employed and the chemical
action provoked in any electro-chemical process. He discovered the mag-
netization of light and diamagnetisni; investigated magneto-crystallic
action and electro-magnetic rotation; he studied the lines of magnetic
force and the annual and daily variations of the magnetic needle. From
among such monumental works, it is hard to choose that one which
specifically marks Faraday as one of the greatest of scientists. Yet perhaps
INTRODUCTION
his most important discovery was magneto-electric induction. For upon
this discovery depends the operation of the dynamo, and upon the dynamo
to no mean degree depends contemporary civilization.
Though his experimental work belongs almost equally to chemistry
and to physics, Faraday called himself a chemist. To him physics was still
the science of statics and of dynamics, founded by Galileo, brought to its
peak by Newton. In the closing hours of the nineteenth century, physics and
chemistry moved so close to one another that a student of one had per-
force to be a student of the other. Marie Curie (1867-1934) once won the
Nobel Prize as a chemist and once as a physicist. All her life long her
scientific interest centered in radioactivity. In her student days the
discoveries of Roentgen and Becquerel were new and exciting. She under-
took to learn more about the rays they had first observed. Before her death
she had almost singlehanded founded the branch of science called radio-
activity, and she had herself carried far the investigations she had initi-
ated. The discoveries she and her husband made of polonium and radium
filled two of the blank spaces in Mendeleyev's tables. Her students and
followers have filled many more. But it is not merely the knowledge of
new elements which the scientific world owes to Marie Curie. The fruits
of her studies we are only beginning to be aware of in these days of
cyclotrons, atomic fission, and nuclear power.
No one needs to be reminded that the new science of radioactivity has
not only wedded chemistry to physics and mathematics, but has aided
medicine and biology powerfully. The twentieth century has accomplished
an even more remarkable synthesis. Albert Einstein (1879- ) has used
the data of physics, chemistry, astronomy, and mathematics to found a,
new cosmogony. Trained as a mathematician and physicist, he has been
able to divorce his mind from the rigid concepts of the Newtonian world
and to apply freshly to the riddle of time and space the ideas available
in non-Euclidean geometry, the mathematics of Minkowski, and the
quantum theory of Planck. He takes neither time nor space nor motion
as an absolute quantity, but maintains that all time and space and motion
is relative. There is, nevertheless, in his concept a time-space continuum
which has an absolute value governed by the velocity of light. In this
time-space continuum bodies move along straight lines in empty space,
along curved lines as they approach matter. Space-time itself curves. The
General Theory of Relativity supersedes the Newtonian theory of gravita-
tion and relegates Galileo's laws of motion to a definitive position only
in special cases. When Einstein propounded his theory, many scientists
hesitated long in accepting it. It was, after all, a mathematical theory,
seemingly not subject to confirmation in the gross physical world. But
within a few years the observations of astronomers had confirmed the
new theory, and the labors of nuclear physicists had been so aided by it
that it began to enjoy universal esteem. Einstein, like Copernicus and
Newton, stands as the founder of a new method of approach to the prob-
lems of the physical universe. His ideas have already largely influenced
the physical ideas of the twentieth century, and they will doubtless color
10 MASTERWORKS OF SCIENCE
the philosophy the century makes its own. For like the great theories
of the past, this one too is comprehensible, and it affirms once more
man's inexhaustible ability to frame for himself explanations of the physi-
cal world.
When Darwin's theories had been debated and finally accepted, for a
full generation biologists neglected the problems of genetics. Then the
rediscovery of Mendel's work revealed to them that there were vast areas
unexplored, vast empires of knowledge to be gained. After Newton's
theories had won the agreement of his fellow physicists and astronomers,
they so dominated physical research for two centuries that physics became
practically the property of the engineer, busy solving practical problems in
terms of force and matter. The general acceptance of Einstein's theory has
produced no such doldrums. Rather, Einstein has reconvinced the scien-
tific world that science is not a mere collection of laws, a series of facts,
but a creation of the human mind eager to present to itself a comprehen-
sible picture of the puzzling physical world. So long as the human mind
endures, therefore, so long the scientific world will expand its boundaries.
As the nineteenth century used the richly accumulated resources of pre-
ceding centuries to build a scientific structure more imposing than all pre-
ceding centuries had erected, the twentieth century bids fair to use the
accomplishments of the nineteenth as the firm foundation upon which
to construct a grander edifice. However daring and adventurous and suc-
cessful this our century may be, it will in turn be outdone by the next.
THE ELEMENTS
by
EUCLID
CONTENTS
The Elements
Definitions
Postulates
Axioms
Proposition i. Problem
Proposition 2. Problem
Proposition 3. Problem
Proposition 4. Theorem
Proposition 5. Theorem
Proposition 47. Theorem
EUCLID
ft. ^OO B.C.
ONE FACT is known with certainty about the Greek mathema-
tician Euclid: he taught in Alexandria in the time of Ptolemy
I and founded a school there. All other biographical details
must be prefixed with a "probably." Probably he learned
mathematics in Athens, probably from pupils of Plato. Several
anecdotes told concerning him come from very early com-
mentators and probably contain reflections of truth. When
King Ptolemy asked him if there were no shorter way in
geometry than that of the Elements, he replied: "There is no
royal road to geometry." And when a pupil who had mastered
the first proposition in the Elements inquired what he would
get by learning such things, Euclid called a slave and in-
structed him to give the pupil threepence, "since he must
needs make gain by what he learns."
From such biographical bits a reader may piece together
a notion of Euclid as a severe but not humorless teacher, a
stern, bold seeker after mathematical truth. But details about
his personal and family life, about his appearance and habits,
about his non-mathematical occupations and ideas, did not
interest his early biographers. To learn something about
Euclid, modern students must go straight to the task of study-
ing his writings.
These writings, edited in a definitive edition in eight
volumes (Heiberg and Menge, Eudidis opera omnia, Leipzig,
1883-1916), include the Data, On Divisions (of figures),
Optics, Phaenomena, and the Elements. (At least four other
treatises, three of them on higher geometry, have been lost.)
All of these discuss. problems in geometry. The Elements has
been the standard textbook in geometry for more than two
thousand years — a record unequaled by any other treatise on
any subject whatsoever — and surely qualifies therefore as a
Masterwork.
14 MASTERWOR K S OF _S C I E N C E
The Elements is divided into thirteen books. The first six
and the last three are^ devoted to geometry, plane and solid;
three others are devoted to arithmetic, and one is devoted to
irrationals. It is the first six books which have been the study
o£ generation after generation of schoolboys, with whom
Euclid and geometry have become synonymous. But geometry
is really much older than Euclid.
Geometry means "earth measurement." In the ancient
world the need for earth measurements appeared acutely in
Egypt because the annual floods of the Nile made surveying
constantly necessary for the re-establishment of boundaries.
In Egypt, therefore, a practical, applied geometry developed.
It consisted of a number of crude rules for the measurement
of various simple geometric figures, for laying out angles,,
particularly right angles, and so on. The Greeks developed
this crude beginning into demonstrative geometry. That is>
various mathematicians among the Greeks worked out a series
of propositions so logically interrelated that if the proof of
one is granted or assumed, later ones, based on it, can be
proved logically from the assumptions therein demonstrated.
As early as 500 B.C,, Hippocrates of Chios compiled a
series of such propositions. Succeeding geometers did the
same thing. Euclid analyzed the work of his predecessors,
arranged the various propositions in an order of his own,
introduced new proofs of some propositions, and thus com-
posed his masterwork, the Elements. In the first six books
about 170 geometrical propositions arc presented and proved.
Of these only one is certainly original with Euclid — the proof
of the Pythagorean theorem, that in any right-angled triangle
the square on the hypotenuse is equal to the sum of the
squares on the other two sides. Yet so much needed was
Euclid's editorial work that from the time of the first appear-
ance of the Elements, all earlier compilations were neglected.
If geometrical propositions be arranged — as Euclid's are —
in such an order that each one depends for its proof upon the
acceptance of propositions earlier proved, it is evident that,,
proceeding backwards, one comes to an early proposition, per-
haps several of them, which cannot be logical consequences of
preceding ones. The logical status of these early propositions
rests upon various definitions which must be precedent, and
upon various assumptions or postulates or axioms the truth of
which must be granted before any logical structure can be
erected upon them. The first book of the Elements is therefore
preceded by a set of definitions and a set of assumptions; and
later books have, when it is necessary, similar prefaces.
The definitions seem to modern readers elementary. The
axioms seem self-evident to the point that statements of them
EUCLID — THE ELEMENTS 15
are needless. That they are thus acceptable to us merely shows
how completely our common geometric ideas stem from
Euclid. For the postulates in particular, being undemonstrable,
can be abandoned, and alternate or contrary postulates set up.
Upon these a new geometry can be based. Several modern
mathematicians have done exactly this, and from their work —
notably Riemann's — comes what is known as non-Euclidean
geometry.
The design of any systematic geometer must be to reduce
the number of definitions and postulates to a minimum. That
is, he will wish to assume as little as possible, and to force
the truth of his propositions upon the reader by the might of
his logic. Euclid may have originated the definitions and
axioms with which his treatise begins. Possibly he rather
selected from similar lists prepared by earlier geometers. Of
the origin of the definitions with which the following selec-
tion begins, nothing is certainly known. Of the axioms,
number 12 is acknowledged to be Euclid's.
A proposition consists of various parts. There is first the
general statement of the problem or theorem, then the con-
struction— which states the necessary straight lines and circles
which must be drawn to assist in the demonstration of the
theorem — and last the demonstration itself, closing Q.E.F. —
quod erat faciendum — "which was to be constructed" — or
Q.E.D. — quod erat demonstrandum — "which was to be
proved."
The portion of the Elements which follows is verbatim
from the edition of Euclid prepared by Isaac Todhunter in
1862. It includes a number of the definitions and all the pos-
tulates and axioms which precede Book I; the first five propo-
sitions with their full Euclidean construction and demonstra-
tion, of which number 5 is the notorious pans asinorum, or
bridge of asses, so called because it has ever been an obstacle
to schoolboys; and number 47 from the first book, the famous
Pythagorean theorem.
THE ELEMENTS
DEFINITIONS
1. A point is that which has no parts, or which has no magnitude.
2. A line is length without breadth.
3. The extremities of a line are points,
4. A straight line is that which lies evenly between its extreme points.
5. A superficies is that which has only length and breadth.
6. The extremities of a superficies are lines.
7. A plane superficies is that in which any two points being taken,
the straight line between them lies wholly in that superficies.
8. A plane angle is the inclination of two lines to one another in
a plane, which meet together, but are not in the same direction.
9. A plane rectilineal angle is the inclination of two straight lines
to one another, which meet together, but are not in the same straight line.
10. When a straight line standing on another
straight line makes the adjacent angles equal to
one another, each of the angles is called a right
angle; and the straight line which stands on the
other is called a perpendicular to it.
11. A term or boundary is the extremity of any thing.
12. A figure is that which is enclosed by one or more boundaries.
13. A circle is a plane figure contained by one
line, which is called the circumference, and is such
that all straight lines drawn from a certain point
within the figure to the circumference are equal
to one another:
14. And this point is called the centre of the circle.
EUCLID — THE ELEMENTS
17
15. A diameter of a circle is a straight line drawn through the centre,
and terminated both ways by the circumference.
[A radius of a circle is a straight line drawn from the centre to the
circumference.]
1 6. Rectilineal figures are those which are contained by straight lines:
17. Trilateral figures, or triangles, by three straight lines:
18. Quadrilateral figures by four straight lines:
19. Multilateral figures, or polygons, by more than four straight lines.
20. Of three-sided figures,
An equilateral triangle is that which has three
equal sides:
21. An isosceles triangle is that which has two
sides equal:
22. A scalene triangle is that which has three
unequal sides:
23. A right-angled triangle is that which has
a right angle:
Of four-sided figures,
24. A square is that which has all its sides
equal, and all its angles right angles:
25. An oblong is that which has all its angles
right angles, but not all its sides equal:
26. A rhombus is that which has all its sides
equal, but its angles are not right angles:
27. A rhomboid is that which has its opposite
sides equal to one another, but all its sides are not
equal, nor; its angles right angles:
18 MASTERWORK S Q F SO I E N C E
28. All other four-sided figures besides these are called trapeziums.
29. Parallel straight lines are such as are in
the same plane, and which being produced ever so
far both ways do not meet.
[Some writers propose to restrict the word trapezium to a quadri-
lateral which has two of its sides parallel; and it would certainly be con-
venient if this restriction were universally adopted,]
POSTULATES
Let it be granted,
r. That a straight line may be drawn from any one point to any other
point:
2. That a terminated straight line may be produced to any length
in a straight line:
3. And that a circle may be described from any centre, at any dis-
tance from that centre.
AXIOMS
1. Things which are equal to the same thing are equal to one another.
2. If equals be added to equals the wholes are equal,
3. If equals be taken from equals the remainders are equal,
4. If equals be added to unequals the wholes are unequal.
5. If equals be taken from unequals the remainders are unequal
6. Things which are double of the same thing are equal to one an-
other.
7. Things which are halves of the same thing are equal to one an-
other,
8. Magnitudes which coincide with one another that is, which ex-
acdy fill the same space, are equal to one another,
9. The whole is greater than its part.
10. Two straight lines cannot enclose a space.
it. All right angles are equal to one another.
12. If a straight line meet two straight lines, so as to make the two
interior angles on the same side of it taken together less than two right
angles, these straight lines, being continually produced, shall at length
meet on that side on which are the angles which are less than two right
angles.
EUCLID — THE ELEMENTS 19
PROPOSITION i. PROBLEM
To describe an equilateral triangle on a given finite straight line.
Let AB be the given straight line: it is required to describe an equi-
lateral triangle on AB.
From the centre A, at the distance AB, describe the circle BCD.
[Postulate 3,
From the centre B, at the distance BAf describe the circle ACE. [Post. 3.
From the point C, at which the circles cut one another, draw the straight
lines CA and CB to the points A and B. [Postulate i.
ABC shall be an equilateral triangle.
Because the point A is the centre of the circle BCD, AC is equal to
AB. [Definition 13.
And because the point B is the centre of the circle ACEf BC is equal to
BA. [Definition 13,
But it has been shewn that CA is equal to AB;
therefore CA and CB are each of them equal to AB.
But things which are equal to the same thing are equal to one another.
[Axiom i.
Therefore CA is equal to CB.
[Therefore CA, AB, BC are equai to one another.
Wherefore the triangle ABC is equilateral, [Definition 20.
and it is described on the given straight line AB. Q.E.F.
PROPOSITION 2. PROBLEM
From a git/en point to draw a straight line equal to a given straight
line.
Let A be the given point, and BC the given straight line: it is re-
quired to draw from the point A a straight line equal to BC.
From the point A to B draw the straight line AB; [Postulate i.
and on it describe the equilateral triangle DAB> [L i.
and produce the straight lines DAr DB to E and F. [Postulate 2.
From the centre B, at the distance BCf describe the circle CGH, meeting
DP at G. [Postulate 3.
20
MASTERWORKS OF SCIENCE
From the centre D, at the distance DGf describe the circle GKL, meeting
DE at L. [Postulate 3.
AL shall be equal to BC.
Because the point B is the centre of the circle CGH, BC is equal to
BG. „ [Definition 13.
And because the point D is the centre of the circle GKL, DL is equal to
DG; [Definition 13.
and DA, DB parts of them are equal; [Definition 20.
therefore the remainder AL is equal to the remainder BG. [Axiom 3.
But it has been shewn that BC is equal to BG;
therefore AL and BC are each of them equal to BG.
But things which are equal to the same thing are equal to one another.
[Axiom i.
Therefore AL is equal to BC.
Wherefore from the given point A a straight line AL has been drawn
equal to the given straight line BC. Q.E.F,
PROPOSITION 3. PROBLEM
From the greater of two given straight lines to cut off a part equal
to the less.
Let AB and C be the two given straight lines, of which AB is the
greater: it is required to cut off from AB, the greater, a part equal to C
the less.
From the point A draw the straight line AD equal to C; [I. 2*
and from the centre A, at the distance AD, describe the circle DEF meet-
ing AB at E. [Postulate 3.
AE shall be equal to C.
EUCLID — THE ELEMENTS 21
Because the point A is the centre of the circle DEF, AE is equal to
AD. [Definition 13.
But C is equal to AD. [Construction.
Therefore AE and C are each of them equal to AD.
Therefore AE is equal to C. [Axiom i.
Wherefore from AB the greater of two given straight lines a fart AE
has been cut off equal to C the less. Q.E.F.
PROPOSITION 4. THEOREM
If two triangles have two sides of the one equal to two sides of the
other, each to each, and have also the angles contained by those sides
e^qual to one another, they shall also have their bases or third sides equal;
and the two triangles shall be equal, and their other angles shall be equal,
each to each, namely those to which the equal sides are opposite.
Let ABC, DEF be two triangles which have the two sides AB, AC
equal to the two sides DE, DP, each to each, namely, AB to DE, and AC
to DP, and the angle BAC equal to the angle EDF: the base BC shall be
equal to the base EF, and the triangle ABC to the triangle DEF, and the
other angles shall be equal, each to each, to which the equal sides are
opposite, namely, the angle ABC to the angle DEF, and the angle ACB
to the angle DFE.
For if the triangle ABC be applied to the triangle DEF, so that the
point A may be on the point D, and the straight line AB on the straight
line DE, the point B will coincide with the point E, because AB is equal
to DE. [Hypothesis.
And, AB coinciding with DE, AC will fall on DF, because the angle BAC
is equal to the angle EDF. [Hypothesis.
Therefore also the point C will coincide with the point F, because AC is
equal to DF. [Hypothesis.
A D
22 MAST E R W OR K S OF SCIENCE _
But the point B was shewn to coincide with the point E, therefore the
base EC will coincide with the base EF;
because, B coinciding with E and C with Ff if the base EC does not coin-
cide with the base EF, two straight lines will enclose a space; which is
impossible. [Axiom 10.
Therefore the base BC coincides with the base EFf and is equal to it,
[Axiom 8.
Therefore the whole triangle ABC coincides with the whole triangle
DEF, and is equal to it. [Axiom 8.
And the other angles of the one coincide with the other angles of the
other, and are equal to them, namely, the angle ABC to the angle BEF,
and the angle ACE to the angle DFE.
Wherefore, if two triangles &c. Q.E.D.
PROPOSITION 5. THEOREM
The angles at the base of an isosceles triangle are equal to one another;
and if the equal sides be produced the angles on the other side of the base
shall be equal to one another.
Let ABC be an isosceles triangle, having the side AB equal to the side
ACf and let the straight lines ABf AC be produced to D and E: the angle
ABC shall be equal to the angle ACBf and the angle CBD to the angle
BCE.
In BD take any point F,
and from AE the greater cut off AG equal to AF the less, [1. 3.
and join FCf GB.
A
D
Because AF is equal to AG, [Construction,
and AB to AC, , [Hypothesis.
the two sides FA, AC are equal to the two sides GA, ABt each to each;
and they contain the angle FAG common to the two triangles AFCf AGB;
therefore the base FC is equal to the base GB, and the triangle AFC to
the triangle AGBf and the regaining angles of the one to the remaining
angles of the other, each to each, to which the equal sides are opposite,
namely the angle ACF to the angle ABGf and the angle AFC to the angle
AGB. 11*4.
EUCLID — THE ELEMENTS
23
And because the whole AF is equal to the whole AGf of which the
parts ABf AC are equal, [Hypothesis.
the remainder BF is equal to the remainder CG. . [Axiom 3.
And FC was shewn to be equal to GB;
therefore the two sides BF, FC are equal to the two sides CGf GB, each
to each;
and -the angle BFC was shewn to be equal to the angle CGB; therefore
the triangles BFC, CGB are equal, and their other angles are equal, each
to each, to which the equal sides are opposite, namely the angle FBC to
the angle GCB, and the angle BCF to the angle CBG. [1.4.
And since it has been shewn that the whole angle AEG is equal to
the whole angle ACF,
and that the parts of these, the angles CBG, BCF are also equal;
therefore the remaining angle ABC is equal to the remaining angle ACE,
which are the angles at the base of the triangle ABC. [Axiom 3.
And it has also been shewn that the angle FBC is equal to the angle
GCB, which are the angles on the other side of the base.
Wherefore, the angles &c. Q.E.D.
Corollary. Hence every equilateral triangle is also equiangular.
PROPOSITION 47. THEOREM
In any right-angled triangle, the square which is described on the
side subtending the right angle is equal to the squares described on the
sides which contain the right angle.
Let ABC be a right-angled triangle, having the right angle BAC: the
square described on the side BC shall be equal to the squares described
on the sides BA, AC.
H
On BC describe the square BDEC/and on BA, AC describe the
squares GBt HC;
through A draw AL parallel to BD or CE;
and join AD, FC.
Then, because the angle BAC is a right angle, [Hypothesis.
and that the angle BAG is also a right angle, [Definition 24.
24 MASTERWORKS OF SCIENCE
the two straight lines AC, AG, on the opposite sides of AB, make with it
at the point A the adjacent angles equal to two right angles;
therefore CA is in the same straight line with AG.
For the same reason, AB and AH are in the same straight line.
Now the angle DEC is equal to the angle FBA, for each of them is
a right angle. [Axiom n.
Add to each the angle ABC.
Therefore the whole angle DBA is equal to the whole angle FBC.
[Axiom 2.
And because the two sides AB, BD are equal to the two sides FB, BCf
each to each; [ Definition 24.
and the angle DBA is equal to the angle FBC;
therefore the triangle ABD is equal to the triangle FBC. [1. 4.
Now the parallelogram BL is double of the triangle ABD, because
they are on the same base BDt and between the same parallels BDf AL.
[i. 4i.
And the square GB is double of the triangle FBC, because they are on the
same base FBf and between the same parallels FB, GC. [I. 41. ,
But the doubles of equals are equal to one another, [Axiom 6.
Therefore the parallelogram BL is equal to the square GB.
In the same manner, by joining AE, BK, it can be shewn, that the
parallelogram CL is equal to the square CM. Therefore* the whole square
BDEC is equal to the two squares GB, HC. [Axiom 2.
And the square BDEC is described on BC, and the squares GB, HC on
BAf AC.
Therefore the square described on the side BC is equal to the squares de-
scribed on the sides BAf AC.
Wherefore, in any right-angled triangle &c. Q.E.D,
ON FLOATING BODIES, AND
OTHER PROPOSITIONS
by
ARCHIMEDES
CONTENTS
On Floating Bodies, and Other Propositions
On the Sphere and Cylinder
Assumptions
Proposition i
Proposition 2— Measurement of a Circle
On the Equilibrium of Planes, or The Centres of Gravity of Planes
Postulates
Proposition i
Proposition 2
Proposition 3
Proposition 4
Proposition 5
Proposition 6
On Floating Bodies
" Postulate
Proposition i
Proposition 2
Proposition 3
Proposition 4
Proposition 5
Proposition 6
Proposition 7
ARCHIMEDES
2<§7-2/2 B.C.
ARCHIMEDES was born too late to study under Euclid. But
when, as a young man, he went to Alexandria to study, his
instructors in mathematics there were students and successors
of Euclid. Ever afterward he considered himself a geometer.
Physicists remember him for his investigations into the be-
havior of floating bodies and for his studies of the lever. His-
torians mention his invention of military engines used by
his kinsman, Hieron of Syracuse, to stave off the besieging
Romans. He himself regarded his practical inventions and
his mechanical inquiries as the "diversions of geometry at
play." Plutarch reports of him that he "possessed so lofty a
spirit, so profound a soul, and such a wealth of scientific
knowledge that ... he would not consent to leave behind
him any written work on such subjects, but, regarding as
ignoble and sordid the business of mechanics and every sort
of art which is directed to practical utility, he placed his
whole ambition in those speculations in the beauty and sub-
tlety of which there is no admixture of the common needs
of life." It is recorded that he wished to have placed on his
tomb a representation of a cylinder circumscribing a sphere
within it, together with an inscription giving the ratio 3/2-
which the cylinder's volume bears to the sphere's. Apparently
he considered the discovery of this mathematical relationship
to be his great claim upon posterity's regard.
The episodes of Archimedes* life cannot clearly be read
in the conflicting accounts which give any information about
him. After the years of study in Egypt he returned to the
Greek city of Syracuse in Sicily, his birthplace, there to spend
his days in studying geometry save when, at the command
of the king, he did occasionally apply himself to mechanics.
He was killed when the Romans finally took Syracuse and
sacked it. A picturesque version of his death says that while
28 M AS T E R W O R K S O F S C I E N C E
he was working over an intricate geometrical diagram, a
Roman soldier came too close. Archimedes ordered: "Stand
aside, fellow, from my diagram!" Immediately the conquer-
ing soldier, in a rage, killed him. If the story is not true, it
at least underlines the notion elsewhere derived that Archime-
des died, as he had lived, in the midst of mathematical specu-
lation.
Unlike Euclid, Archimedes was not a compiler of geomet-
rical propositions and an editor of the work of others. Rather,
taking the work of others as completed, he embarked on new
inquiries based on what they had accomplished. He remarks
in one of his letters that, in connection with the attempts of
earlier geometers to square the circle, he noticed that no one
had tried to square a parabolic segment. Taking the problem
for his own, he eventually solved it. In the preface to one of
his works he reviews the theorems of a predecessor, Eudoxus,
about the pyramid, cone, and cylinder, and approves them.
Then he offers, as supplements to the work of Eucioxus, his
own greater discoveries about the relative surfaces and vol-
umes of cylinders and spheres.
The works of Archimedes — so far as they remain to us —
include two books on the sphere and cylinder, two on plane
equilibriums, two on floating bodies, one each on spirals, on
conoids and spheroids, on the parabola, and on the measure-
ment of the circle. There is a work called Method in which
he tells, in the form of a letter to a friend, how he generally
conceived of a theorem by means of mechanics and then pro-
ceeded to a rigorous geometrical proof of it. And another
work, The Sand Reckoner, is a curiosity of mathematics, in-
valuable to our knowledge of Greek astronomy by reason of
the materials it uses, and fascinating because it reveals the
versatility and ingenuity of Archimedes. It begins with the
observation that the sands have been called innumerable
chiefly because sufficiently large numbers do not exist to re-
cord their numbers. Then, assuming that the whole universe
is compact of sand, Archimedes shows that a system of num-
bers can readily be formed to express the total. His method
amounts to our modern one of expressing large numbers as
powers of ten. But the Greeks used letters and words, not
numerals, to express numbers. Archimedes had, therefore, to
invent a method of "orders" and "periods" so that he could
write the higher powers of numbers. He thus succeeds in
expressing in a few words any number up to that which in
modern notation would be written as i followed by 80,000
billion ciphers.
Various references, many of them Arabian, indicate that
Archimedes composed other works than those listed. Though
ARCHIMEDES — ON FLOATING BODIES 29
he did live a long span, it is hard to understand where, in a
lifetime so productive of mathematical masterpieces, he found
time and energy to perfect also the mechanical devices, meth-
ods, and principles for which the non-mathematical world
reveres him. Historians of science call him the greatest mathe-
matician of antiquity, perhaps the greatest mathematical
genius of all time. They admire him for his application of
the principle of exhaustion to geometrical measurement, a
practice in which he anticipates the calculus of Leibnitz and
Newton. Less specialized historians remember his work on
levers, his invention of war machines for hurling missiles, his
experiments to discover whether the king's crown were pure
gold or a mixture of gold and silver — an experiment in which
he evolved a method for measuring specific gravity. Every
schoolboy knows the story, possibly true, of how, in his excite-
ment over solving a problem which he had been pondering
while he bathed, he ran naked through the streets shouting
"Eureka" — that is, "I've got it."
Of the mechanical appliances which Archimedes in-
vented, there is no record in his own words. Of his work
on levers, floating bodies, and so on, there remains a series
of theorems and demonstrations which constantly indicate
that he had learned his method of rigorous mathematical
proof from Euclid's Elements. In fact, so precisely does he
apply the Euclidean method that frequently a reader does not
understand as he reads an initial theorem whither it will lead,
For example, the second theorem on Floating Bodies proves
that the surface of any fluid at rest is the surface of a sphere
the center of which is the center of the earth. Then in logi-
cal order follow four theorems devoted to the behavior of
solids placed in liquids. Finally, at Proposition 7, occurs the
statement now known to us as Archimedes' principle — that a
solid immersed in a fluid is buoyed up by, a force equal to
the weight of the fluid displaced. Plutarch remarks that it is
not possible "to find in geometry more difficult and trouble-
some questions, or more simple and more lucid explanations."
The lucidity and simplicity, all editors agree, is a real miracle
of workmanship.
In geometry, Archimedes built upon the work of his pred-
ecessors. In mechanics, and particularly in hydrostatics, he
was a wholly original workman. He had the ability to see a
problem in all its difficulties, to plan an attack upon it, and
— so far as records show — always to conquer the obstacles
in the way of a solution. Yet he was honest and modest enough
to make a great point in one of his prefaces of confessing that
certain views he had previously held were in error. He thus
presents to posterity the picture of the perfect scientist — one
30 MASTERWORKSO F S C I E N Cj_
original, rigorous, pertinacious, and, equally important, mod-
est and honest. It is no wonder that his name lives.
The passages from Archimedes' works which follow are
from the translation of T. L. Heath.
ON FLOATING BODIES, AND OTHER
PROPOSITIONS
ON THE SPHERE AND CYLINDER
"ARCHIMEDES to Dositheus greeting.
On a former occasion I sent you the investigations which I had up to
that time completed, including the proofs, showing that any segment
bounded by a straight line and a section of a right-angled cone [a parabola]
is four-thirds of the triangle which has the same base with the segment
and equal height. Since then^certain theorems not hitherto demonstrated
(av€\6yKTUv) have occurred to me, and I have worked out the proofs of
them. They are these: first, that the surface of any sphere is four times
its greatest circle (rou jnejicrrov /okAou); next, that the surface of any seg-
ment of a sphere is equal to a circle whose radius (97 k rou xevrpov) is
equal to the straight line drawn from the vertex (/copu^) of the segment
to the circumference of the circle which is the base of the segment; and,
further, that any cylinder having its base equal to the greatest circle of
those in the sphere, and height equal to the diameter of the sphere, is
itself [i.e. in content] half as large again as the sphere, and its surface
also [including its bases] is half as large again as the surface of the
sphere. Now these properties were all along naturally inherent in the
figures referred to (avry r# tfrvcrei, TpovTrrjpxev irepl ra etprjjjikva vxywra),
but remained unknown to those who were before my time engaged in
the study of geometry. Having, however, now discovered that the proper-
ties are true of these figures, I cannot feel any hesitation in setting them
side by side both with my former investigations and with those of the
theorems of Eudoxus on solids which are held to be most irrefragably
established, namely, that any pyramid is one third part of the prism
which has the same base with the pyramid and equal height, and that
any cone is one third part of the cylinder which has the same base with
the cone and equal height. For, though these properties also were natu-
rally inherent in the figures all along, yet they were in fact unknown to
all the many able geometers who lived before Eudoxus, and had not been
observed by any one. Now, however, it will be open to those who possess,
the requisite ability to examine these discoveries of mine. They ought
to have been published while Conon was still alive, for I should conceive
MASTERWORKS OF SCIENCE
that he would best have been able to grasp them and to pronounce upon
1 them the appropriate verdict; but, as I judge it well to communicate
them to those who are conversant with mathematics, I send them to you
with the proofs written out, which it will be open to mathematicians to
examine. Farewell.
I first set out the assumptions which I have used for the proofs
of my proposition.
Assumptions
1. Of all lines which have the same extremities the straight line is
the least.
2. Of other lines in a plane and having the same extremities, [any
two] such are unequal whenever both are concave in the same direction
and one of them is either wholly included between the other and the
straight line which has the same extremities with it, or is partly included
by, and is partly common with, the other; and that [line] which is in-
cluded is the lesser [of the two].
3. Similarly, of surfaces which have the same extremities, if those
extremities are in a plane, the plane is the least [in area].
4. Of other surfaces with the same extremities, the extremities being
In a plane, [any two] such are unequal whenever both are concave in the
same direction and one surface is either wholly included between the
other and the plane which has the same extremities with it, or is partly
included by, and partly common with, the other; and that [surface] which
is included is the lesser [of the two in area],
5. Further, of unequal lines, unequal surfaces, and unequal solids,
the greater exceeds the less by such a magnitude as, when added to itself,
can be made to exceed any assigned magnitude among those which are
comparable with [it and with] one another.
These things being premised, // a polygon be inscribed in a circle,
it is plain that the perimeter of the inscribed polygon is less than the
circumference of the circle; for each of the sides of the polygon is less
than that part of the circumference of the circle which is cut off by it.
Proposition
If a polygon be circumscribed about a circle, the perimeter of the
circumscribed polygon is greater than the perimeter of the circle.
Let any two adjacent sides, meeting in At touch the circle at P, Q
respectively.
Then [Assumptions, 2]
PA+AQ>(*rc PQ).
ARCHIMEDES — ON FLOATING BODIES 33
A similar inequality holds for each angle of the polygon; and, by addi-
tion, the required result follows.
MEASUREMENT OF A CIRCLE
Proposition i
The area of any circle is equal to a right-angled triangle in which one
of the sides about the right angle is equal to the radius, and the other to
the circumference, of the circle.
Proposition 2
The area of a circle is to the square on its diameter as u to 14.
Proposition 3
The ratio of the circumference of any circle to its diameter is less
than 3% but greater than 31%i.
I. Let AB be the diameter of any circle, 0 its centre, AC the tangent
,at A; and let the angle AOC be one-third of a right angle.
Then 0^:^0265:153 (i),
and , OC:CA=$o6: 153 (2).
First, draw OD bisecting the angle AOC and meeting AC in D.«
Now CO:OA=CD:DAf [Eucl. VI. 3]
so that [CO+OA:OAs=CA:DA*, or]
CO+OA:CA=OA;AD.
34 _ MASTERWQRK S_ OF SCI E N C E _
Therefore by (i) and (2)
OA:AD>s7i:i53 .................... (3).
Hence OD*;AD2^(OA2+AD*) :AB*
> 349450 123409,
so that OD:D^>59i%:i53 ..................... (4),
0 '£
Secondly, let OE bisect the angle AODt meeting AD in E,
Then DO:OA*=DE:EA,
so that DO+OA:DA^OA:AE.
Therefore OA:AE> 1162% 1153 (5).
It follows that
123409
> 1373943 a% 4 :23409-
Thus OE:E^>ii72%:i53 ..................... (6).
Thirdly, let OF bisect the angle AOE and meet AE in JP.
We thus obtain the result corresponding to (3) and (5) above that
Therefore OF2 *':FA*> {(2334^)^+15 32}:i$f
>5472i32yl6 123409.
Thus OF:F^>2339%:i53 ................ , , , , ,(8).
_ ARCHIMEDES — ON FLOATING BODIES 35
Fourthly, let OG bisect the angle AQF, meeting AF in G.
We have then
0^:^G>(2334%4-2339%):i53, by means of (7) and (8)
> 4673% :*53-
Now the angle AOC, which is one-third of a right angle, has been
bisected four times, and it follows that
£AOG=y48 (a right angle).
Make the angle AOH on the other side of OA equal to the angle
AOG, and let GA produced meet OH in H.
Then ZGOH=%4 (a right angle).
Thus GH is one side of a regular polygon of 96 sides circumscribed
to the given circle. ^
And, since OA:AG^>^6^Y2:i53y
while AB=2,oA, GH=2AG,
it follows that
AB: (perimeter of polygon of 96 sides) [> 4673% -.153X96]
>4673% 114688.
But 14688 667%
Therefore the circumference of the circle (being less than the perime-
ter of the polygon) is a joniori less than 3% times the diameter AB.
II. Next let AB be the diameter of a circle, and let AC, meeting the
circle in C, make the angle CAB equal to one-third of a right angle.
Join BC.
Then AC:CB< 1351 1780.
First, let AD bisect the angle BAC and meet BC in d and the circle
in D. Join BD.
Then Z.BAD=Z.dAC
and the angles at D, C are both right angles.
It follows that the triangles ADB, [ACd], BDd are similar,
Therefore AD:DB=*BD:Dd
=AB:Bd [Eucl. VI. 3]
36
MASTERWORKS OF SCIENCE
= 1560:780,
Therefore AD\DB< 29 11:780 (i).
Hence Aff :BD'2 < (291 i*+j^) 780^
<9o8232i:6o8400*
Thus /fB:BD<30i3%:78o (2).
Secondly, let AE bisect the angle BAD, meeting the circle in E; and
let BE be joined.
Then we prove, in the same way as before, that
)78o, by (i) and (2)
(3)-
Hence AB2:BE2<(i^+2^o2):2^2
<338o929:576oo,
Therefore ^B:BB<i838%1:240 , (4).
Thirdly, let AF bisect the angle BAE, meeting the circle in F,
Thus AF:FB^BA+AE:BE
i%!:240, by (3) and (4)
i%iX11/40^4oX11/40
(5).
It follows that
AB2:BF2< ( ioo72+662) :662
< 1018405:4356.
_ ARCHIMEDES — ON FLOATING BODIES 37
Therefore ^B:BF<ioo9%:66 ..................... (6).
Fourthly, let the angle BAF be bisected by AG meeting the circle
in G.
Then AG:GB=*BA+AF:BF
<20i6%:66, by (5) and (6).
And AB*:BG*< {(2016% )2+662} :662
Therefore ABiBG < 2017^:66,
whence BG:AB> 66:2017% .................... (7).
Now the angle BAG which is the result of the fourth bisection of the
angle BACf or of one-third of a right angle, is equal to one-forty-eighth
of a right angle.
Thus the angle subtended by BG at the centre is
%4 (a right angle).
Therefore BG is a side of a regular inscribed polygon of 96 sides.
It follows from (7) that
(perimeter of polygon) :AB[> 96X66:2017%]
Much more then is the circumference of the circle greater than
times the diameter.
Thus the ratio of the circumference to the diameter
but >310/7i.
ON THE EQUILIBRIUM OF PLANES
OR
THE CENTRES OF GRAVITY OF PLANES
I POSTULATE the following:
1. Equal weights at equal distances are in equilibrium, and equal
weights at unequal distances are not in equilibrium but incline towards
the weight which is at the greater distance.
2. If, when weights at certain distances are in equilibrium, something
be added to one of the weights, they are not in equilibrium but incline
towards that weight to which the addition was made.
3. Similarly, if anything be taken away from one of the weights, they
are not in equilibrium but incline towards the weight from which nothing
was taken. •
38
MASTERWORKS OF SCIENCE
4. When equal and similar plane figures coincide i£ applied to one
another, their centres of gravity similarly coincide,
5. In figures which are unequal but similar the centres of gravity will
be similarly situated. By points similarly situated in relation to similar
figures I mean points such that, it straight lines be drawn from them to
the equal angles, they make equal angles with the corresponding sides.
6. If magnitudes at certain distances be in equilibrium, (other) mag-
nitudes equal to them will also be in equilibrium at the same distances,
7. In any figure whose perimeter is concave in (one and) the same
direction the centre of gravity must be within the figure,
Proposition i
Weights which balance at equal distances are equaL
For, if they are unequal, take away from the greater the difference
between the two. The remainders will then not balance [Post, 3]; which
is absurd.
Therefore the weights cannot be unequal
Proposition 2
Unequal weights at equal distances will not balance but will incline
towards the greater weight.
For take away from the greater the difference between the two. The
equal remainders will therefore balance [Post. i]. Hence, if we add the
difference again, the weights will not balance but incline towards the
greater [Post, 2].
Proposition 3
Unequal weights will balance at unequal distances, the greater weight
being at the lesser distance,
Let A, B be two unequal weights (of which A is the greater) baL
ancing about C at distances AC, EC respectively.
Then shall AC be less than BC, For, if not, take away from A the
weight (A — B). The remainders will then incline towards B [Post. 3], But
ARCHIMEDES — ON FLOATING BODIES
39
this is impossible, for (i) if AC=CBf the equal remainders will balance,
or (2) if AC>CB, they will incline towards A at the greater distance
[Post. i].
Hence AC<CB.
Conversely, if the weights balance, and AC<CBf then A>B.
Proposition 4
If two equal weights have not the same centre Oj gravity, the centre
of gravity of both ta\en together is at the middle point of the line joining
their centres of gravity.
Proposition 5
// three equal magnitudes have their centres of gravity on a straight
line at equal distances, the centre of gravity of the system will coincide
with that of the middle magnitude.
COR. i. The same is true of any odd number of magnitudes if those
which are at equal distances -from the middle one are equal, while the
distances between their centres of gravity are equal.
COR. 2. // there be an even number of magnitudes with their centres
of gravity situated at equal distances on one straight line, and if the two
middle ones be equal, while those which are equidistant from them (on
each side) are equal respectively, the centre of gravity of the system is the
middle point of the line joining the centres of gravity of the two middle
ones.
Proposition 6
Two magnitudes balance at distances reciprocally proportional to the
magnitudes.
I. Suppose the magnitudes A, B to be commensurable, and the points
A, B to be their centres of gravity. Let DE be a straight line so divided at
C that
We have then to prove that, if A be placed at E and B at D, C is the
centre of gravity of the two taken together.
A
B
[}°
EC £>
i i , . . t » i i i 1 1
H
40 _ MAS T E R W O R K S OF SCIENCE ___
Since A, B are commensurable, so are DC, CE. Let N be a common
measure of DC, CE. Make DH, DK each equal to CE, and EL (on CE
produced) equal to CD. Then EH^CD, since DH=CE. Therefore LH
is bisected at E, as JfJ^ is bisected at D,
Thus LH, HK must each contain N an even number of times.
Take a magnitude 0 such that 0 is contained as many times in A as N
is contained in LH, whence
But B:A^CE:DC
Hence, ex ae quail, B:0~HK:N, or 0 is contained in B as many times as
N is contained in HK.
Thus 0 is a common measure of A, B.
Divide LH, HK into parts each equal to N, and At B into parts each
equal to 0, The parts of A will therefore be equal in number to those of
LH, and the parts of B equal in number to those of HK. Place one of the
parts of A at the middle point of each of the parts N of LH, and one of
the parts of B at the middle point of each of the parts N of HK.
Then the centre of gravity of the parts of A placed at equal distances
on LH will be at E, the middle point of LH [Prop. 5, Cor. 2], and the
centre of gravity of the parts of B placed at equal distances along HK
will be at Df the middle point of HK.
Thus we may suppose A itself applied at E, and B itself applied at D.
But the system formed by the parts 0 of A and B together is a system
of equal magnitudes even in number and placed at equal distances along
LK. And, since LE=CD, and EC=DK, LC**CK, so that C is the middle
point of LK. Therefore C is the centre of gravity of the system ranged
along LK.
Therefore A acting at E and B acting at D balance about the point C.
ON FLOATING BODIES
Postulate
"Let it be supposed that a fluid is of such a character that, its parts
lying evenly and being continuous, that part which is thrust the less is
driven along by that which is thrust the more; and that each of its parts
is thrust by the fluid which is above it in a perpendicular direction if the
fluid be sunk in anything and compressed by anything else,"
Proposition I
If a surface be cut by a plane always passing through a certain point,
and if the section be always a circumference of a circle whose centre is
the aforesaid point, the surface is that of a sphere.
ARCHIMEDES — ON FLOATING BODIES 41
For, if not, there will be some two lines drawn from the point to the
surface which are not equal.
Suppose O to be the fixed point, and A, B to be two points on the
surface such that OA, OB are unequal. Let the surface be cut by a plane
passing through OAf OB. Then the section is, by hypothesis, a circle
whose centre is Q.
Thus OA = OB; which is contrary to the assumption. Therefore the
surface cannot but be a sphere.
Proposition 2
The surface of any fluid at rest is the surface of a sphere whose centre
is the same as that of the earth.
Suppose the surface of the fluid cut by a plane through O, the centre
of the earth, in the curve ABCD.
ABCD shall be the circumference of a circle.
For, if not, some of the lines drawn from 0 to the curve will be un-
equal. Take one of them, OB, such that OB is greater than some of the
lines from 0 to the curve and less than others. Draw a circle with OB as
radius. Let it be EBF, which will therefore fall partly within and partly
without the surface of the fluid.
EA P O DF
Draw OGH making with OB an angle equal to the angle EOBf and
meeting the surface in H and the circle in G. Draw also in the plane an
arc of a circle PQR with centre 0 and within the fluid.
* Then the parts of the fluid along PQR are uniform and continuous,
and the part PQ is compressed by the part between it and ABf while the
part QR is compressed by the part between QR and BH. Therefore the
parts along PQ, QR will be unequally compressed, and the part which is
compressed the less will be set in motion by that which is compressed the
more.
Therefore there will not be rest; which is contrary to the hypothesis.
Hence the section of the surface will be the circumference of a circle
whose centre is 0; and so will all other sections by planes through 0.
Therefore the surface is that of a sphere with centre 0.
Proposition 3
Of solids those which, size for size, are of equal weight with a fluid
will, if let down into the fluid, be immersed so that they do not project-
above the surface but do not sin\ lower.
42 MAS TE R WO R K S OF SCIENCE
If possible, let a certain solid EFHG of equal weight, volume for
volume, with the fluid remain immersed in it so that part of it, EBCF,
projects above the surface.
Draw through 0, the centre of the earth, and through the solid a
plane cutting the surface of the fluid in the circle ABCD.
Conceive a pyramid with vertex 0 and base a parallelogram at the
surface of the fluid, such that it includes the immersed portion of the
solid. Let this pyramid be cut by the plane of ABCD in OLf OM. Also let
a sphere within the fluid and below GH be described with centre 0, and
let the plane of ABCD cut this sphere in FOR.
Conceive also another pyramid in the fluid with vertex 0} continuous
with the former pyramid and equal and similar to it. Let the pyramid so
described be cut in OM, ON by the plane of ABCD,
Lastly, let STUV be a part of the fluid within the second pyramid
equal and similar to the part BGHC of "the solid, and let SV be at the
surface of the fluid.
Then the pressures on PQ, QR arc unequal, that on PQ being the
greater. Hence the part at QR will be set in motion by that at PQ, and
the fluid will not be at rest; which is contrary to the hypothesis.
Therefore the solid will not stand out above the surface.
Nor will it sink further, because all the parts of the fluid will be under
the same pressure.
Proposition 4
A solid lighter than a fluid will, if immersed in it, not be completely
submerged, but part of it -will project above the surface,
In this case, after the manner of the previous proposition, we assume
the solid, if possible, to be completely submerged and the fluid to be at
rest in that position, and we conceive (i) a pyramid with its vertex at 0,
the centre of the earth, including the solid, (2) another pyramid continu-
ous with the former and equal and similar to it, with the same vertex
0, (3) a portion of the fluid within this latter pyramid equal to the im-
mersed solid in the other pyramid, (4) a sphere with centre 0 whose
surface is below the immersed solid and the part of the fluid in the second
pyramid corresponding thereto. We suppose a plane to be drawn through
ARCHIMEDES — ON FLOATING BODIES
43
the centre O cutting the surface of the fluid in the circle ABC, the solid
in S, the first pyramid in OA, OB, the second pyramid in OB, OCf the
portion of the fluid in the second pyramid in K, and the inner sphere
in PQR.
Then the pressures on the parts of the fluid at PQ, QR are unequal,
since S is lighter than K. Hence there will not be rest; which is contrary
to the hypothesis.
Therefore the solid S cannot, in a condition of rest, be completely
submerged.
Proposition 5
Any solid lighter than a fluid will, if placed in the fluid, be so far
immersed that the weight of the solid will be equal to the weight of the
fluid displaced.
For let the solid be EGHF, and let BGHC be the portion of it im-
mersed when the fluid is at rest. As in Prop. 3, conceive a pyramid with
vertex 0 including the solid, and another pyramid with the same vertex
continuous with the former and equal and similar to it. Suppose a portion
of the fluid STUV at the base of the second pyramid to be equal and
similar to the immersed portion of the solid; and let the construction be
the same as in Prop. 3.
N
Then, since the pressure on the parts of the fluid at PQ, QR must be
equal in order that the fluid may be at rest, it follows that the weight of
the portion STUV of the fluid must be equal to the weight of the solid
EGHF. And the former is equal to the weight of the fluid displaced by
the immersed portion of the solid BGHC.
44
MASTERWORKS OF SCIENCE
Proposition 6
If a solid lighter than a fluid be forcibly immersed in it, the solid will
be driven upwards .by a force equal to the difference between its weight
and the weight of the fluid displaced.
For let A be completely immersed in the fluid, and let G represent
the weight of A, and (G~\-H) the weight of an equal volume of the fluid.
Take a solid D, whose weight is H, and add it to A. Then the weight of
(A~\-D) is less than that of an equal volume of the fluid; and, if (A-{-D)
is immersed in the fluid, it will project so that its weight will be equal
to the weight of the fluid displaced. But its weight is (G-J-/TT).
H
Therefore the weight of the fluid displaced is (G-f-H), and hence the
volume of the fluid displaced is the volume of the solid A, There will
accordingly be rest with A immersed and D projecting.
Thus the weight of D balances the upward force exerted by the fluid
on A, and therefore the latter force is equal to H, which is the difference
between the weight of A and the weight of the fluid which A, displaces.
Proposition 7
A solid heavier than a fluid will, if placed in it, descend to the bottom
of the fluid, and the solid will, when weighed in the fluid, be lighter than
its true weight by the weight of the fluid displaced,
(1) The first part of the proposition is obvious, since the part of the
fluid under the solid will be under greater pressure, and therefore the
other parts will give way until the solid reaches the bottom,
(2) Let A be a solid heavier than the same volume of the fluid, and
let (G+H) represent its weight, while G represents the weight of the
same volume of the fluid.
Take a solid B lighter than the same volume of the fluid, and such
that the weight of B is G, while the weight of the same volume of the
fluid is (G+H).
Let A and B be now combined into one solid and immersed. Then,
since (/4+B) will be of the same weight as the same volume of fluid,
ARCHIMEDES — ON FLOATING BODIES
45
both weights being equal to (G+H)+G, it follows that (A+B) will
remain stationary in the fluid.
A
H
Therefore the force which causes A by itself to sink must be equal
to the upward force exerted by the fluid on B by itself. This latter is equal
to the difference between (G+H) and G [Prop. 6]. Hence A is depressed
by a force equal to H, i.e. its weight in the fluid is Ht or the difference
between (G+H) and G.
ON THE REVOLUTIONS OF
THE HEAVENLY SPHERES
h
NIKOLA US COPERNICUS
CONTENTS
On the Revolutions of the Heavenly Spheres
I. That the World is Spherical
II. That the Earth also is Spherical
III. How the Land and Sea Form but One Globe
IV. That the Motion of the Heavenly Bodies is Uniform, Perpetual,
and Circular or Composed of Circular Motions
V. Is a Circular Movement Suitable to the Earth?
VI. Concerning the Immensity of the Heavens Compared to the Dimen-
sions of the Earth
VII. Why the Ancients Believed that the Earth is Motionless at the
Middle of the World as its Center
VIII. A Refutation of the Arguments Quoted, and Their Insufficiency
IX. Whether Several Motions may be Attributed to the Earth; and of
the Center of the World
X. Of the Order of the Heavenly Bodies
XL Demonstration of the Threefold Motion of the Earth
NIKOLA US COPERNICUS
1475-1543
NIKOLAUS COPERNICUS was born in Thorn, in East Prussia, in
1473, the son o£ a prosperous copper dealer who had married
the daughter o£ a well-to-do merchant and landowner o£ that
city. An orphan at ten, he came into the care o£ his mother's
brother, a rising churchman named Lucas Watzelrode. When
he was nineteen his uncle, now Bishop of Varmia, sent him
to the University of Cracow; a few years later this uncle had
him appointed a canon of Frauenberg cathedral. Thenceforth
Copernicus held always a church office or two; he never ex-
perienced poverty.
At Cracow, Copernicus studied mathematics and astron-
omy, the use of astronomical instruments, and Aristotle. He
was in Italy, apparently for the second time, in 1498, and he
seems to have gone there to study medicine. He stayed for
three years. During this time, probably, he learned Greek
and developed a taste for humanistic studies. Certainly he
studied astronomy at Bologna, and certainly he lectured on
mathematics in Rome in 1500. At one time he registered at
Bologna as a student of canon law. Subsequently he went to
Padua to study medicine, then to Ferrara to study law, then
back to Padua to study medicine again. In 1503 he returned to
Varmia to live in close association with his uncle for almost
a decade. A trained physician, he served as his uncle's secre-
tary and companion, supervised the diet o£ the whole elabo-
rately organized episcopal household, bought medical books
for the bishop's library — many of which he annotated — and
cared for the health of the bishop. He was constantly active
in administrative matters as the agent of his uncle or of the
cathedral chapter, constantly in contact in the great cities of
East Prussia and Poland with powerful church and secular
lords. Yet he found time for other activities. He translated
the Epistles of Simocatta — a second-rate bit of late Greek
50 MASTERWO R K S_QJF^S_CjJEN^jE
literature — into Latin and published his translation in 1509. It
was the first original print of a Greek author in Poland. In the
same year he observed a lunar eclipse, one of a large number
on which during his long life he made extended notes. More
important, he proceeded far enough with his theorizings and
speculations to plan his book De Rcvolutionibus Orbium
Cade st mm (On the Revolutions of the Heavenly Spheres).
Though thirty years lapsed before his book was printed, he
may already have completed a draft of it when, at forty, he
removed from Varmia to Frauenbcrg. He lived in Fraucnberg
almost continuously for the next thirty years, until his death
in 1543.
During these long years, affairs of the church, of the
cathedral chapter, of the secular world, intruded upon the
scholar. In 1514 the Pope invited him to Rome to assist in the
revision of the calendar. He refused, long afterward explain-
ing that he could not accept because he had not then the
accurate knowledge about the courses of the sun and moon
which the revisionary task demanded. From 1515 to 1521 he
was the administrator of Allenstein and Mehlsack, two tiny
provinces in Ermland, and, after a war between the King of
Poland and the Prussian Order — during which he defended
the castle of Allenstein against the Prussians — he became
administrator of all Ermland. In 1519? by invitation, he drew
up a memorandum on the need and the means for stabilizing
and improving the currency. This he presented to the Diets of
Poland, Lithuania, and Prussia several times between 1519
and 1527. Unfortunately, though his ideas were sound, they
were not adopted.
Meantime, the greatest tumult of the times, the revolt of
Luther from the Church, apparently left Copernicus in re-
mote Ermland quite unperturbed and untouched. A physician
of some fame, an astronomer recognized in his own time, an
able administrator in public affairs, an architect, a diplomat,
a map maker, a warrior, a painter, an economist; indeed a
man of almost universal abilities, he was yet a churchman but
no theologian. While the storms of controversy roared over
Europe, echoing even in Varmia, he continued quietly, per-
sistently, to study the stars from his observatory higher than
the cathedral roof in Frauenberg, to collect the data with
which to support his theories, and to write and revise the
book which eventually overthrew the accepted hypotheses of
medieval astronomy.
The astronomical ideas of the Middle Ages all derived
from Ptolemy, a second-century Alexandrian. He had left to
his successors not only an admirable body of observations and
computations, but also five hypotheses: (i) The World is a
REVOLUTIONS OF HEAVENLY SPHERES 51
sphere and revolves as a sphere; (2) The Earth is also a
sphere; (3) The Earth is the center of the World; (4) In size,
the Earth compared to the World is a mere point; (5) The
Earth is motionless. No one had seriously doubted Ptolemy
for fifteen hundred years; nor had anyone questioned his
views, inherited from the Greek Hipparchus (160-125 B.C),
that the planetary motions followed an intricate system of
epicycles and eccentrics.
Copernicus particularly queried the fifth hypothesis.
Others had done the same: Macrobius, John Scotus Erigena,
Averroes, Maimonides, Nicolas of Cusa. But none had carried
his queries very far. Copernicus convinced himself that this
hypothesis was wholly untenable; then he discovered that
number three similarly lacked validity.
In 1514, in a brief work called Commentariolus, Coperni-
cus summed up his ideas in seven hypotheses: (i) There is no
one center of all the celestial spheres; (2) The center of the
Earth, though the center of gravity, is not the center of the
World; (3) The planetary spheres revolve round the Sun as
their center; (4) The distance of the' Earth from the Sun is
incommensurable with the dimensions of the firmament; (5)
The Earth daily rotates on its axis; (6) The Earth performs
more than one motion; (7) The motions of the Earth explain
the apparent motions of the heavenly bodies. These proposi-
tions sharply modify those of Ptolemy. They are the essential
propositions of the De Revolutionibus.
For full fifteen years after the composition of the brief
Commentariolus, Copernicus busied himself in collecting data
to substantiate his propositions. He came to believe that the
older observations of astronomers were too inaccurate to be
dependable, and he substituted for them his own more care-
ful— though still faulty — observations and computations.
Probably he constantly revised his book. When in 1539 a
young Lutheran scholar from Wittenberg, Rheticus, sought
out the famous astronomer in distant Frauenberg, the great
work was apparently complete. Rheticus studied it enthusi-
astically, gave an account of it in a long formal letter to one
of his scientific friends (printed as Narratio Prima in 1540),
and two years later persuaded Copernicus to let him have
the whole work printed. The first copy came into the old
man's hands on the very day of his death in 1543.
Copernicus had originally planned his work in eight
books; later he replanned it in six, of which the first is here
translated. It presents the propositions of the Commentariolus
together with the reasons, astronomical and geometrical, for
accepting them. Book II is devoted to spherical astronomy;
Book III, to the length of the year and the orbit of the earth;
52 MASTERWORKS OF SCIENCE
Book IV, to the moon and its eclipses; Books V and VI, to
the planetary motions. The work did not immediately win
readers. Twenty years passed before there was a second print-
ing (Basel, 1566), and another fifty before there was a third
(1617). Even today it is not available in English. Yet in this
long-neglected book Copernicus, almost singlchanded, over-
threw the old geocentric theory and established the current
heliocentric. Some of his "proofs" are now outmoded, chiefly
because Copernicus had to rely upon observations and meas-
urements made with the crudest of instruments. Some of his
hypotheses later generations of astronomers have refused, nota-
bly the one concerning that motion of the earth which, ac-
cording to him, explains the precession of the equinoxes.
Nevertheless, this book, the lifework of one of the world's
great men, is one of the world's greatest.
ON THE REVOLUTIONS OF THE
HEAVENLY SPHERES
/. That the World is Spherical
FIRST, it must be recognized that the world is spherical. For the spherical
is the form of all forms most perfect, having need of no articulation; and
the spherical is the form of greatest volumetric capacity, best able to con-
tain and circumscribe all else; and all the separated parts of the world — I
mean the sun, the moon, and the stars — are observed to have spherical
form; and -all things tend to limit themselves under this form — as appears
in drops of water and other liquids — whenever of themselves they tend
to limit themselves. So no one may doubt that the spherical is the form
of the world, the divine body.
//. That the Earth also is Spherical
SIMILARLY, the earth is spherical, all its sides resting upon its center. Of
course, its perfect sphericity is not immediately seen because of the great
height of the mountains and the great depth of the valleys. But these
scarcely modify the total rotundity of the earth. Its sphericity is manifest.
Indeed, for those who, from any part of the earth, journey towards the
north, the pole of diurnal revolution little by little rises and the opposite
pole declines, and many stars in the northern region seem never to set,
whereas others in the southern regions seem never to rise. Thus Italy
never sees Canopus, which is visible in Egypt. And Italy sees the last star
of Fluvius, which our country, in a colder zone, knows naught of. Con-
trarily, for those who journey southward, these constellations rise whereas
others, high for us, set. Nevertheless, the inclination of the poles has
everywhere the same relation to any portion of the earth — which could
not be true if the figure were not spherical. Hence it is clear that the
earth is itself limited by poles and is consequently spherical. We may add
that dwellers in the East do not see the eclipses of the sun and moon
which chance to occur during the night, and that those of the West do
not see those occurring by day; those between see these phenomena, some
earlier and some later.
54 MASTERWORKS OF SCIENCE
That the seas take a spherical form is perceived by navigators. For
when land is still not discernible from a vessel's deck, it is from the mast-
head. And if, when a ship sails from land, a torch be fastened from the
masthead, it appears to watchers on the land to go downward little by
little until it entirely disappears, like a heavenly body setting. Yet it is
certain that water, because of its fluidity, tends downward and does not
rise above its container more than its convexity permits. That is why the
land is so much the higher, why it rises from the ocean.
///. How the Land and Sea Form but One Globe
THE OCEAN which surrounds the land, pouring its waters every way, fills
therewith the deepest depths. There is necessarily, therefore, less water
in total than land — granted that both, because of their weight, tend
toward the center; otherwise, the waters would cover the land. But for
the safety of living creatures, the waters leave free some portions of land
such as the numerous islands which are found here and there. As to the
continent itself and the whole terrestrial world, is it not merely an island
larger than the others?
It is unnecessary to heed those peripatetics who have affirmed that
the quantity of water must be ten times that of the land because, as is
notorious in the transmutation of elements, one part of land in lique-
faction produces ten parts of water. Accepting that idea, they say that
the land emerges just to a certain point because, possessing interior cavi-
ties, it is not in equilibrium with respect to gravity, and that the center
of gravity is different from the center of volume. These men deceive
themselves through their ignorance of geometry. They do not understand
that even if there were seven times as much water as land, and if any part
of the land remained dry, the land would have to withdraw wholly from
the center of gravity, yielding place to the water as if it were the heavier
element. For spheres arc among themselves in the ratio of the cubes of
their diameters. If, then, to seven parts of water the land were an eighth,
its diameter could not be greater than the distance from the center to the
circumference of the water. It is then still less possible that there should
be ten times as much water as land. And that there is no dillerence be-
tween the center of gravity of the earth and its center of volume is proved
by the fact that the convexity of the land which rises above the waters is
not swollen in one smooth abscess; if it were, it would have thrust back
the waters wholly and would not, in any manner, be subject to the in-
roads of interior seas and deep gulfs. Further, the greater the distance
from the shore, the greater would be the ocean depths; and sailors depart-
ing from land would never encounter an island or a rock or any kind
of land.
Now it is well known that between the Egyptian Sea and the Arabian
Gulf, almost at the middle of the terrestrial world, the distance is scarcely
fifteen stadii. Yet Ptolemy taught that the habitable earth extends to the
REVOLUTIONS OF HEAVENLY SPHERES 55
median circle; beyond that, he indicates unexplored land where moderns
have identified Cathay and other vast areas reaching even to 60° of longi-
tude. Thus the habitable land stretches through a greater longitude than
is left for the ocean. And if thereto be added the islands discovered in our
time under the Spanish and Portuguese princes, and especially all America
— thus named by the ship's captain who discovered it — which from its
dimensions (so far ill-known) appears to be a second continent, and
numerous other islands hitherto unknown, one would not be greatly as-
tonished to learn that there are antipodes and antichthones.
Indeed, geometric reasons force us to believe that America occupies
a position diametrically opposite Gangean India. Hence, I think it clear
that the land and the water alike tend toward a common center of gravity
which is no other than the center of volume of the land, because it is the
heavier. It is clear that the partly open portions of the land are filled with
water, and that consequently, in comparison to the land, there is not
much water even though,* at the surface, there appears to be more water
than land.
The land together with the water which encompasses it necessarily
has the figure which its shadow reveals. Now, during eclipse, the shadow
of the earth projected on the moon has the circumference of a perfect
circle. In conclusion, then, the earth is not flat, even though Empedocles
and Anaximenes thought so; nor is it drum-shaped, as Leucippus thought;
nor is it boat-shaped, as Heraclitus thought; nor is it hollowed out in
some other form, as Democritus believed; nor is it cylindrical, as Anaxi-
mander taught; no more is it infinitely extended downward, growing
larger towards its base, as Xenophanes thought; but, as the philosophers
thought, it is perfectly spherical.
IV. That the Movement of the Heavenly Bodies is Uniform, Perpetual,
and Circular or Composed of Circular Movements
WE SHALL NOW remind ourselves that the motion of the heavenly bodies
is circular. Indeed, for a sphere, the appropriate motion is rotation: by
that very act, while it moves uniformly in itself, it expresses its form —
that of the simplest of bodies in which can be distinguished neither be-
ginning nor end, nor distinction between the one and the other.
Now because there are many spheres, there are varying motions. The
most observable of these is the daily revolution which the Greeks called
nychthemeron, that is, "the space of one day and one night." In that time,
the whole of creation except the earth—so they believed — is borne from
the east to the west. This motion has been accepted as the common
measure for all other motions: we measure time itself usually by number
of days. Then we see also other revolutions — some of which are retro-
grade, that is, going from west to east — notably those of the sun, the
moon, and the five planets.
Thus the sun gives us the year and the moon the month, common
56 MASTERWORKS OF SCIENCE
divisions of time; similarly, each of the five planets travels its own proper
course. These motions, however, differ very strongly. First, they arc not
based on the same poles as the first revolution, but follow the slant of the
zodiacal circle (the ecliptic). Then, in their individual circuits, they do
not move in uniform fashion. The sun and the moon are discovered to
be moving at one time more slowly, at another more rapidly. As for the
five wandering stars, we see them sometimes even retrograding, and actu-
ally halting between their forward and backward motions. And though
the sun ever travels along its route, these five wander in diverse fashions,
now towards the south, now towards the north. This is, indeed, the
reason for calling them wandering stars (planets). Further, sometimes
they approach near to the earth — when they are said to be at the perigee
— and at other times they proceed far from the earth — when they are said
to be at the apogee. Nevertheless, it must be acknowledged that their
paths are circular or composed of circles, for they execute their unequal
motions in conformity with a certain law, and repeat the same motions
periodically — a phenomenon impossible if their paths were not circular.
Only the circle can bring back the past, as, for example, the sun by its
motion composed of circular motions brings again to us the inequality
of days and nights and of the four seasons.
Several different motions arc recognized, for the heavenly bodies can
not possibly be moved in an unequal fashion by a single sphere. Indeed,
such inequality could occur only through the inconstancy of the moving
power, which might conceivably arise from an external or an internal cause
or by a modification in the revolving body. Now, since the intellect re-
coils with horror from these two suppositions, and since it would be
unworthy to suppose such a thing in a creation constituted in the best
way, it must be admitted that the equal movement of these bodies ap-
pears to us unequal either because the various spheres have not the same
poles or because the earth is not the center of the circles round which
they move. For us who from the earth view the movements of the
heayenly bodies, they appear to be larger when they are near us than
when they are more distant — an effect explained in optics. Thus the equal
movements of the spheres may appear unequal motions in equal times to
us, viewing them from different distances. This is the reason that I believe
it first of all necessary for us to examine attentively the relation of the
earth to the sky, so that, though we desire to study the highest things,
we shall not be ignorant of those near at hand, and shall not, by similar
error, attribute to heavenly bodies that which appertains to the earth.
V. Is a Circular Movement Suitable to the Earth?
IT HAS BEEN already demonstrated that the earth has the form of a globe,
and I think it needful now to examine whether it follows a motion like
to its form, and what is the place which it occupies in the universe.
Without these bits of knowledge, it will not be possible to explain cer-
REVOLUTIONS OF HEAVENLY SPHERES 57
tain of the phenomena of the heavens. Certainly it is ordinarily so agreed
among authors that the earth is at rest at the center of the world that
they think it unreasonable and even ridiculous to maintain the contrary.
If, however, we examine the question with great attention, it will emerge
as not wholly solved, and not beneath inquiry. For all apparent local
movement arises either from the motion of the thing observed, or from
that of the observer, or from the simultaneous motions — of course unequal
— of the two. If two bodies — I have in mind an observer and an object
observed — move with equal motion, the motion is not perceived. Now
it is from the earth that we observe the motions of the heavenly bodies.
If, then, the earth did have some motion, we would observe it in the
apparent motion of bodies external to the earth, as if they were swept
along at an equal speed, but in an opposite sense; and such, in the first
place, is the diurnal revolution. That seems, truly, to carry round the
whole world except the earth and objects near it. If it were granted that
the heavens have no motion but that the earth rotates from west to east,
and if the result of such an assumed motion upon the apparent rising
and setting of the sun were seriously examined, it would be found to be
precisely as it now appears. And since the heavens embrace and contain
all else, and are the common place of all things, it is not immediately
clear why motion should be attributed rather to the containing body than
to the body contained.
The Pythagoreans Heraclides and Ecphantus thought as much, and
so, according to Cicero, did the Syracusan Nicetus. They conceived the
earth to be turning at the center of the world. They considered that the
stars "set" because the earth moved in front of them, and rose when the
earth moved away. But if these views be accepted, there arises another
problem no less important: What is the place of the earth? It is agreed
by almost everyone that the earth is the center of the world. Yet if any-
one were to deny this belief and should grant that the distance from the
earth to the center of the world is by no means so great as to be com-
parable with the dimensions of the sphere of the fixed stars, yet still very
great and, from the relations to the spheres of the suns and the other
planets, quite obvious; if he should note that the motions of these later
bodies appear irregular because they are controlled with relation to an-
other center than the center of the earth; he might perhaps be able to
offer an explanation not superficially absurd of the apparent irregularity
in the motions of the heavenly bodies. For example: as the wandering
stars are observed now nearer to the earth, now farther away, it necessar-
ily follows that the earth is not the center o£ their circular paths. And it
is not clear whether it is the earth which varies its distance from them
or they which approach to and retreat from the earth.
It would be scarcely surprising if someone were to attribute to the
earth another motion besides the diurnal revolution. Indeed, Philolaus the
Pythagorean, a remarkable mathematician, believed, they say, that the
earth really moves circularly and at the same time executes several other
motions. He considered the earth itself merely one of the stars. It was
58 _MAj>^^ F SCIENCE
to see him that Plato did not hesitate to travel to Italy, as those record
who have narrated the life o£ Plato.
On the other hand, a number of philosophers have convinced them-
selves by geometric arguments that the earth is the center of: the world.
Indeed, only if it occupies the central position — being like a point in com-
parison to the immensity of the heavens — can it be, from that fact, motion-
less, For when the whole universe turns, its center remains still, and
those things move slowest which are nearest to the center.
VI. Concerning the Immensity of the Heavens Compared
to the Dimensions oj the Earth
THAT the size of the earth, though huge, is yet not commensurable with
that of the sky can be comprehended from what follows, The limiting
circle (thus the Greek term horizon is interpreted) cuts the whole celes-
tial sphere into two halves, and it could not were the earth's size great
compared to that of the sky or to its distance from the center of the
world. As is well known, the circle which cuts a sphere into two halves
is the greatest circle of the sphere which can be circumscribed upon the
sphere's center. Let the circle a b c d be the horizon and let e be the earth
from which we view the horizon, and itself the central point of the hori-
zon which separates the visible from the non-visible stars. Now if, by
means of a theodolite, a zodiacal chart, and a level placed at e, the begin-
ning of Cancer is identified rising at cf at the same instant the beginning
of Capricorn will be setting at a. But since the points ef af and c are on a
straight line running across the theodolite, clearly this line is the diameter
of the zodiacal circle; for six signs of the zodiac circumscribe the visible
stars, and the line center c is also the center of the horizon. Now, when
a revolution has occurred and the beginning of Capricorn rises at bf then
the beginning of Cancer is setting at d. Then bed is a straight line and
is a diameter of the zodiacal circle. But it has already been shown that
a c c is similarly the diameter of the same circle. Clearly, the center of
the circle is at the intersection of these two diameters. Thus, then, the
horizon always cuts the circle of the zodiac, which is itself the greatest
REVOLUTIONS OF HEAVENLY SPHERES 59
possible circle of the sphere. And as, on a sphere, any circle which bisects
a great circle is itself a great circle, it follows that the horizon is itself
a great circle and that its center is the center of the ecliptic. Hence it is
obvious that though the line passing across the earth's surface is different
from the one passing through its center, yet because of the immensity
of their lengths compared to the dimensions of the earth, they are like
parallels which seem to form a single line. For because of the very huge-
ness of their length the distance between them becomes negligible in
comparison — as is demonstrated in optics.
Thanks to this reasoning, it seems to be clear that the sky in com-
parison to the earth is immense, and may almost be considered infinite;
and as reckoned by our senses, the earth compared to the sky is as a point
to a body, or as the finite to the infinite. Precisely so much is demon-
strated.
Now it does not follow from this concept that the earth must be
motionless at the center of the world. Indeed, it would be more astonish-
ing that the whole immense world should turn in twenty-four hours than
that a little part of it, the earth, should. If it is claimed that a center is
motionless and that those things nearest the center move most slowly,
this does not prove that the earth remains motionless at the center of the
world. It is easily said that the sky turns on unmoving poles, and that
that which is nearest the poles is moved the least. Thus the Little Bear
appears to us to move much more slowly than the Eagle or Sirius, for,
close to the pole, it describes a very small circle; and since all these belong
to one sphere, this sphere's motion being less near the pole of the axis
does not allow that all its parts shall have motions equal the one to the
other. The motion of the whole sweeps along the parts in their respective
paths in equal time, but not through equal distances.
Observe now the consequence of the argument that the earth, being
a part of the celestial sphere, participating in its nature and its motion,
would be little moved because close to the center. It would be moved,
it too, existing as a body not the geometric center of the sphere, and
would describe in the same time circumferences like the celestial circles,
but smaller. Now how false such a motion is, is clearer than day. Were
it true, some part of the earth would be ever at high noon, and some other,
ever at midnight. At no place would sunrise or sunset ever occur. For the
motion of the whole and of the part would be one and inseparable.
Between things separated by a diversity of natures, the relation is
wholly different, and such that those which travel a smaller circuit trace
it more rapidly than those which travel a longer path. Saturn, for example,
the most distant of the planets, moves round its circuit once in thirty
years; whereas the moon, which is doubtless of all the planets the closest
to the earth, accomplishes its whole journey in a month; and the earth
itself turns in the space of a day and a night. Observe that the problem
of the diurnal revolution recurs. So does that of the earth's place, not
determined by what has preceded. For the earlier demonstration proves
only the undefined immensity of the sky as compared to the size of the
60 MASTER WORKS OF
earth. Yet how far that immensity extends is not at all clear, As with
those tiny and indivisible bodies called atoms which, though they are not
perceivable by themselves and do not when taken two or several together
immediately form a visible body, yet may be multiplied until they join
to form finally a great mass; just so it is with the place of the earth:
although it is not itself at the center of the world, its distance from the
center is not comparable with the immense dimensions of the sphere of
the fixed stars.
V1L Why the Ancients Believed that the Earth is Motionless
at the Middle of the World as its Center
FOR a variety of reasons the ancient philosophers asserted that the earth
must be the center of the world. They adduced as a principal argument
the matter of relative heaviness and lightness. Of the elements, earth is
the heaviest; and all heavy objects move towards the earth, plunging
towards its interior. Since the earth — towards which heavy things are
borne from all sides and perpendicularly to the surface — is round, these
heavy things would, if not restrained at the earth's surface, meet at the
earth's center. For a straight line perpendicular to a surface tangential to
a sphere leads to the sphere's center. Now objects which of themselves
move towards a center seek to repose in the center. Surely, then, the earth
must be in repose at its center. It receives in itself everything which falls,
and must from its weight remain motionless.
These ancients sought to support the same belief by reasoning based
on, motion and its nature. Aristotle said that the motion of a single, simple
body is simple; that of simple motions, one is circular, the other recti-
linear; that of rectilinear motions, one is up and the other down. Conse-
quently, every simple motion is directed toward the center — that is, down
— or away from the center — that is, up — -or around the center-— that is,
in a circle. To move downward — that is, toward the center — is proper only
to the elements earth and water, regarded as the elements which have
weight. To move up — that is, away from the center — is proper only to
the elements air and fire, regarded as the elements which have lightness.
These four elements are limited, therefore, to rectilinear motions; but the
heavenly bodies turn round a center. Thus said Aristotle.
Ptolemy of Alexandria argued that if the earth turns, making even
a daily revolution, the opposite of what has been said would occur. He
shows that the motion which in twenty-four hours would turn the earth
would be extremely violent and of an unsurpassable velocity. But things
moved with a violent rotational motion are quite unlikely to cohere, but
will rather disperse in fragments — unless they are held together by a
superior force. And long ago, he says, a whirling earth would have been
scattered beyond the sky itself (which is wholly ridiculous), and much
more so all animate beings and other separate masses, none of which
could have remained stable. Furthermore, were the earth turning, freely
REVOLUTIONS OF HEAVENLY SPHERES 61
falling bodies would never arrive perpendicularly at the points destined
for them. And we would always see the clouds and other objects floating
on the air moving towards the west.
VIII. A Refutation of the Arguments Quoted, and Their Insufficiency
FOR such reasons and others like them, the ancient philosophers affirmed
that the earth stays always immobile at the center of the world, and that
thereof there can be no doubt. But if anyone were to claim that the earth
moves, he would surely say that this motion is natural and not violent,
Now events occurring in conformity with nature produce results opposite
to those caused by violence. Those things, indeed, to which are applied
force and violence cannot long subsist and must needs soon be destroyed;
but those which are in accord with nature exist in a proper way and in
the best possible way.
Ptolemy therefore had no need to fear that the earth and all terres-
trial beings would be destroyed by a rotation resulting from natural
causes. Such a rotation wholly differs from one caused by art or by human-
enterprise. Why, indeed, on this head, did he not fear even more for the
whole world, the motion of which would have to be as much more rapid
as the heavens are greater in size than the earth? Have the heavens ac-
quired their immensity because their motion, of an inexpressible magni-
tude, pulls them away from the earth? and would they fall if that motion
ceased? Surely, if this reasoning were valid, the heavens would be infinite
in extent. The more they are extended by the force of their motion, the
more rapid would the motion become, for the distance to be traversed
in twenty-four hours would be always increasing; and conversely, the im-
mensity of the heavens would ever augrnent with the increase of the
motion. Thus to very infinity the velocity would increase the magnitude
of the motion, and the magnitude of the motion, the velocity. Then in
agreement with this axiom of physics, "What is infinite cannot be trav-
ersed and cannot be moved," the heavens would necessarily halt.
It is alleged that beyond the heavens there is no body, no place, no-
void — nothing. Then there is only nothing into which the heavens could
expand. Surely, too, it is astonishing that something should be stopped
by nothing. And if the heavens are considered infinite and bounded only
by an interior concavity, it is the more true that there is nothing beyond
them, for everything must be within, whatever its dimensions may be.
But from this argument, the heavens if infinite must be motionless; for
the principal argument depended upon to show the world finite is its
assumed motion.
Let us leave the philosophers to decide whether the world is finite
or infinite. We are sure, in any event, that the earth between its poles is
bounded by a spherical surface. Why then should we hesitate to attribute
to it a motion properly according in nature with its form, rather than to
disturb ourselves about the whole world, the limits of which we do not
MASTERWORKS OF SCIENCE
and cannot know? Shall we not therefore admit that the daily revolution
belongs in reality to the earth and its appearance only to the heavens? As
Virgil's Aeneas said: "We depart from the port, and the cities and lands
recede."
When a ship sails along without tossing, the sailors see all things
exterior to the ship moving; they sec, as it were, the image of their own
motion; and they think themselves and all with them to be at rest. Pos-
sibly, in the same manner, we have believed the earth to be without
motion and the whole world to move round it. What then about the
clouds and all other bodies floating on the air, both those which fall and
those which tend to rise? Very simply, we may think that not only the
earth and the aqueous element which is a part of it move thus, but also
the portion — not negligible — of the air and all its contents which have a
relation to the earth. Either the air neighboring the earth, mixed with
aqueous and earthy materials, shares in the nature of the earth, or the
motion of the air is an acquired motion in which it participates because
of the contiguity of the earth and its perpetual motion. As a contrary
view, it is alleged — which is astounding — that the uppermost portion
of the air shares in the motions of the heavens, and thus reveals those
abruptly appearing stars which the Greeks called comets or "long-haired
stars" (Lat., pogontae), to the formation of which this uppermost air is
assigned as place, and which, like other stars, rise and set. We can reply
merely that if that part of the air, because of its great distance from the
-earth, is freed from the aforesaid terrestrial motion, the air nearest the
earth and those things suspended in it will appear to be at rest until by
the wind or some other force it is buileted hither and yon. Is not a wind
in the air like a current in the water?
As to things which by their nature rise or by their nature fall, we
may affirm that in relation to the world their motions may be double and
are generally composed of straight lines and circles. That things earthy
in their nature are drawn downward by their weight is understandable,
for indubitably the parts retain the nature of the whole. For no unlike
reason are fiery things drawn upwards. Consider that terrestrial fire feeds
on terrestrial matter; it is even said that flame is merely glowing smoke.
Now the nature of fire is to distend that of which it takes possession,
and it accomplishes this expansion with such force that it cannot in any
manner or by any device be prevented from performing its work once it
has shattered the imprisoning bonds. But an expanding motion is directed
away from the center towards the circumference. Thus if any earthy por-
tion be kindled, it must be borne away from the center, upwards. As has
been said before, for a simple body the proper motion is simple (a fact
verified particularly for circular motion) as long as that body retains its
individuality and rests in its natural place. In that natural place, there-
fore, the motion is none other than circular, the motion which is self-
contained, and likest to repose. Contrarily, motion in a straight line is
the act of those things which move out of their proper places, which are
forced from it, or for some other reason are outside it. Now nothing is
REVOLUTIONS OF HEAVENLY SPHERES 63
more repugnant to the form and order of the world than that something
be out of its place. Therefore motion in a straight line is proper only to
things which are not in order and which are not conforming to their
nature — to things which are separated from their natural entities or have
lost their essential individualities.
What is more, things which are impelled up or down, even neglect-
ing their possible circular motion, do not execute a simple movement,,
uniform and equal. They conform consistently neither to their native
lightness nor to the impulse of their weight. Those which fall execute
first a slow motion which augments in velocity as they fall. Similarly, we
see that terrestrial fire (and we see no other kind) as it rises simulta-
neously slows down, as if manifesting the force of the earthy materiaL
Circular motion, however, always progresses in a uniform way, for it
results from a constant cause. And again, things which move in straight
lines soon put an end to their accelerated motion, because when they
reach their destinations, they cease to be either light or heavy, and their
motion stops. As, therefore, circular motion is proper to all complete,
individual things, straight motion to partial things only, we may con-
clude that the circular motion stands toward the straight as the whole
animal nature toward the sick member.
The fact that Aristotle divided simple motion into three kinds — away
from the center, towards the center, and around the center — may be dis-
missed as merely an act of intellect. Just so, we distinguish the point,,
the line, and the surface, even though no one of them can exist without
the others, and none of them without a body.
To all that precedes may be added that the state of immobility is
usually considered more noble and more nearly divine than that of change
and instability. For which is the state of rest more appropriate then, for
the earth or for the world? It seems absurd to me to attribute motion to
the containing and localizing rather than to the contained and localized
— which is the earth.
Finally, since the planets clearly now approach and now recede from
the earth, their movements being motions of single, self-contained bodies
round a center, if the center of their revolutions is the center of the earth,
their motion must be at one and the same time centripetal and centrifu-
gal. Properly, one must conceive of the circular motion round a center
in a more general fashion, and must be satisfied that the movement o£
each planet is related to its own true center.
For all the reasons given, then, motion for the earth is more probable
than immobility; and especially is this true of the daily revolution, in as
much as this motion is most proper for the earth. And I think that this
discussion will suffice for the first part of the question.
64 MASTERWORKS OF SCIENCE
IX. Whether Several Motions may be Attributed to the Earth;
and of the Center of the World
SINCE then there are no reasons for our believing that the earth does not
move, I think it proper now to question whether we may attribute to it
several motions, whether it may not be thought of as one of the wander-
ing stars (planets). That it is not the center of the motions of all the other
heavenly bodies, their apparently unequal motions and varying distances
from the earth demonstrate. For these variations cannot be explained for
circular paths homocentric with the earth. But if there are several centers
for these motions, it is not overbold to query whether the center of the
world is the center of terrestrial gravity or some other center. For myself, I
think that gravity is nothing other than a certain natural tendency given by
the divine providence of the Architect of the World to the various parts so
that they might assemble themselves into the one of which they arc a part,
coming together in the form of a globe. And it is credible that the same
property belongs equally to the sun, to the moon, and to the other wander-
Ing stars. If it docs, it might be thanks to its efficacy that although they
travel their circuits in divers ways, they uniformly retain the roundness
in which they appear.
If the earth docs, execute motions other than that around its center,
they must be such, obviously, as will evidence themselves in many phe-
nomena. Such a motion might be an annual progress round a circuit. If
this annual motion be attributed to the earth, and if immobility be con-
ceded to the sun, ,the rising and setting of the zodiacal signs and other
fixed stars, thanks to which they are overhead in daytime as well as at
night, will occur just as they do now. Then the progressions, halts, and
retrogressions of the planets will be seen to be caused not by their mo-
tions, but by those of the earth which' lends to the planets misleading
appearances. Then, finally, it will have to be acknowledged that the sun
occupies the center of the world.
These things both the law of the order in which they follow one
after another and the harmony of the world combine to teach us, pro-
vided only that we look upon things themselves with, as it were, two eyes.
X. Of the Order of the Heavenly Bodies
I OBSERVE that no one questions that the heaven of the fixed stars is the
highest of all which is visible. As to the order of the, planets, we note that
the ancient philosophers preferred to determine it according to the mag-
nitudes of their respective revolutions. They reasoned that of bodies car-
ried at equal speed, those which are more distant appear to be borne
more slowly; this principle Euclid established in The Optics, They
thought that as the moon completed its course in the briefest time, it
REVOLUTIONS OF HEAVENLY SPHERES 65
was borne round the smallest circle and was therefore closest to the earth.
Saturn, which in the longest time travels the greatest circuit, they consid-
ered to be the highest or most distant. Nearer than Saturn they placed
Jupiter; nearer than Jupiter, Mars. About Mercury and Venus, opinions
varied; for these two never, like the others, proceed far from the sun.
Some thinkers, therefore, like the Timaeus of Plato, placed them beyond
the sun. Others, such as Ptolemy and a number of more recent scholars,
place them this side of the sun. Alpetragius places Venus beyond the sun
and Mercury on this side the sun.
Now those who agree with Plato in thinking that all the stars (other-
wise dark bodies) shine only by light reflected from the sun argue that be-
cause the distance of these two planets from the sun is small, if they were
below the sun they would be visible to us only in part, and never entirely
round. Ordinarily, they would reflect the light they receive upwards — that
is, towards the sun — as we see in the new and in the waning moon. They
say, too, that sometimes the sun would necessarily be hidden from us by
the interposition of these planets and that its light would for us be dimin-
ished in proportion to their size as they interposed. Since such a dimming
never occurs, they conclude that these planets can in no fashion ever come
this side the sun.
Those who place Mercury and Venus this side the sun base their
argument on the vastness of the space which they discover between the
sun and the moon. They have found that the greatest distance between
the earth and the moon is sixty-four and one sixtieth times the distance
from the center of the earth to its surface; and that the smallest distance
between the earth and the sun is almost eighteen times the greatest dis-
tance between the earth and the moon. The distance between the earth
and the sun is to the distance between the rnoon and the sun as 1160
is to 1096. In order, therefore, that so great a space need not be consid-
ered empty and void, and judging from the distances between the plane-
tary orbits by which they calculate the depth of these orbits, they affirm
that the space would be almost filled up if the distance between Mercury
and the sun were less than that between the moon and the sun, and if the
distance of Venus from the sun were less than that between Mercury and
the sun, each of these distances being progressively smaller. Further, in
this arrangement, the highest part of the orbit of Venus would approach
very close to the sun. They calculate that between the aphelion and peri-
helion of Mercury there would be 177 times the distance between the
earth and the moon, and that the remaining distance, 910 times that
between the earth and the moon, v^ould be almost filled by the apsidal
dimensions of Venus. They also do not admit that there is any opacity
in the stars, asserting that these shine either by their own light or by that
of the sun impregnated in their entire bodies. These planets never darken
because they only very rarely interpose between us and the sun; generally,
they merely skirt the sun. And because these two are small bodies — Venus
is larger than Mercury, but can yet hide not a hundredth part of the sun,
according to Al Bategui the Aratonian who estimates the diameter of
66 MASTERWORKS OF SCIENCE ^
the sun as ten times that of Venus — they believe that if either of them
Interposes between us and the sun, we would hardly see so small a speck
in the sun's most resplendent light. Moreover, Averroes, in his paraphrase
of Ptolemy, reports that he did see something blackish when he was
observing the conjunction of Mercury and the sun which he had foretold
by computations. Yet some persons judge that these two planets move
wholly beyond the solar path.
How feeble ancl unsure is this reasoning becomes clear when we con-
sider the fact that the least distance between the earth and the moon is,
according to Ptolemy, thirty-eight times the distance from the earth's
center to its surface (according to a better calculation, as will be shown
later, more than forty -nine), yet we do not know that there is in all that
space anything but air and, if it pleases us to think so, a certain fiery
element. Furthermore, the diameter of the orbit of Venus, thanks to which
it moves away from the sun by 45°, would have to be six times as great
as the distance between the center of the earth and its perihelion, as will
be demonstrated in the proper place. What do these reasoners maintain
is contained in all that space, all the more that it would compass the earth,
the air, the ether, the moon, and Mercury? So much must the huge epi-
cycle of Venus embrace if that planet revolves round the motionless
earth. How empty is Ptolemy's argument that the sun must occupy the
micl-point between the planets moving away in all directions and those
which do not depart is made clear by the moon which, itself moving
away in every direction, exposes the falsity of the idea,
As to those who place Venus, then Mercury, on this side the sun,
or arrange them in some other order, what reason can they allege that
these do not effect the independent ancl different orbit of the sun, even
as the other planets, unless the ratio of rapidity and slowness prevents
any warping of the orbit?
It seenis almost necessary to admit that the earth is not the center
to which is referred the order of the stars and the orbits, even that there
can be no reason for their order, and that one cannot know why the
higher place belongs to Saturn rather than to Jupiter or some other planet.
Perhaps that scheme is not despicable which was imagined by Martianus
'Capella (who wrote an encyclopedia) as well as by some other Latins,
They held that Mercury and Venus revolve around the sun, which is at
the center, and are unable to move further away from the sun than the
convexities of their spheres permit. They thought that these two planets
do not revolve round the earth, like the other planets, but have converse
orbits. What can they wish to imply &save that the center of these spheres
is near the sun? If they are right, the sphere of Mercury is contained
within that of Venus — which must be two or more times greater — and
finds sufficient space within that amplitude.
Now if one should opportunely ascribe to that same center Saturn,
Jupiter, and Mars — remembering that the dimensions of these spheres are
such that within them they contain and embrace the earth also — he would
not be far wrong; the canonic order of their motions declares it. Certainly,
REVOLUTIONS OF HEAVENLY SPHERES 67
these planets always approach nearest to the earth when they rise at eve-
ning; that is, when they are opposite the sun, the earth being between
them and the sun. Contrarily, they are most distant when they set at even;
that is, when they are hidden in the sunlight, when observably the sun is
between them and the earth. This phenomenon shows adequately that the
center of their circuits is associated with the sun and is, in fact, the same
as that round which Mercury and Venus circle in their revolutions. If the
spheres of these planets have all the same center, the space which remains
between the convex side of the sphere of Venus and the concave side o£
the sphere of Mars must form another orb or sphere homocentric with
those at its two surfaces. This sphere contains the earth with its com-
panion the moon and with all that belongs within the lunar globe. For
indeed we can in no fashion separate the moon from the earth to which it
is, of heavenly bodies, incontestably the nearest, and the less need we to>
in that the space left for it is sufficiently vast.
Therefore we need feel no shame in affirming that all which the moon's
sphere embraces, even to the center of the earth, is drawn along by the
motion of the greatest sphere, first as are the spheres of the other planets,
in an annual revolution round the sun. Similarly, we dare assert that the
sun is the center of the world, and that the sun remains motionless, all the
motion which it appears to have being truly only an image of the earth's
movement. And further, we may assert that the dimensions of the world
are so vast that though the distance from the sun to the earth appears very
large as compared with the size of the spheres of some planets, yet com-
pared with the dimensions of the sphere of the fixed stars, it is as.
nothing.
All these assertions I find it easier to admit than to shatter reason by
accepting the almost infinite number of spheres which those are forced to
suppose who insist that the earth is the center of the world. It surely is.
better to conform to the wisdom of nature. Even as she dreads producing
anything superfluous or useless, she often endows one causation with
several effects.
The ideas here stated are difficult, even almost impossible, to accept;
they are quite contrary to popular notions. Yet with the help of God, we
will make everything as clear as day in what follows, at least for those
who are not ignorant of mathematics. The first law being admitted — no
one can propose one more suitable — that the size of the spheres is meas-
ured by the time of their revolutions, the order of the spheres imme-
diately results therefrom, commencing with the highest, in the following;
way:
The first and highest of all the spheres is the sphere of the fixed stars~
It encloses all the other spheres and is itself self-contained; it is immobile;
it is certainly the portion of the universe with reference to which the
movement and positions of all the other heavenly bodies must be con-
sidered. If some people are yet of the opinion that this sphere moves, we
are of a contrary mind; and after deducing the motion of the earth, we
shall show why we so conclude. Saturn, first of the planets, which accom-
68
MASTERWORKS OF SCIENCE
plishes its revolution in thirty years, is nearest to the first sphere. Jupiter,
making its revolution in twelve years, is next. Then comes Mars, revolving
once in two years. The fourth place in the series is occupied by the sphere
which contains the earth and the sphere of the moon, and which performs
an annual revolution. The fifth place is that of Venus, revolving in nine
months. Finally, the sixth place is occupied by Mercury, revolving in
eighty days.
In the midst of all, the sun reposes, unmoving. Who, indeed, in this
most beautiful temple would place the light-giver in any other part than
that whence it can illumine all other parts? Not ineptly do some call the
sun the lamp of the world, or the spirit of the world, or even the world's
governor. Trismegistus calls it God visible; Sophocles* Electra, the all-
seeing. Indeed, the sun, reposing as it were on a royal throne, controls the
family of wandering stars which surrounds him. The earth will surely
never be deprived of the ministry o£ the moon; as Aristotle says in De
dnimalibus, the earth and the moon enjoy the closest possible kinship.
Meantime, the earth conceives by the sun and each year becomes great,
In this ordering there appears a wonderful symmetry in the world and
REVOLUTIONS OF HEAVENLY SPHERES 69
a precise relation between the motions and sizes of the spheres which no
other arrangement offers. Herein the attentive observer can see why the
progress and regress of Jupiter appear greater than Saturn's and less than
Mars's; why also the progress and regress of VCQUS appear greater than
Mercury's; why Saturn appears less often in reciprocation than Jupiter,
and Mercury more often than Mars and Venus; why Saturn, Jupiter, and
Mars are nearer to the earth when they rise at eventide than at the time
of their occultation and apparition; why Mars when it becomes pernoctur-
nal seems to equal Jupiter in size and can be distinguished from the latter"
only by its reddish color, and yet at other times is scarcely discoverable
among stars of the second order unless by a careful observer working with
a sextant. All these phenomena arise from the same cause: the movement
of the earth.
That nothing similar can be discovered among the fixed stars proves
their immense distance from us, a distance so immense as to render im-
perceptible to us even their apparent annual motion, the image of the
earth's true motion. For every visible object or event there is a distance
beyond which it cannot be seen, as is proven in optics. The glitter of the
fixed stars' light shows that between the highest of the planetary spheres,
Saturn's, and the sphere of the fixed stars, there is still an enormous space.
It is by this glitter that the fixed stars are especially distinguishable from
the planets; and it is proper that between the moving and the non-moving
there should be a great difference. Thus perfect, truly, are the divine
works of the best and supreme Architect.
XL Demonstration of the Threefold Motion of the Earth
SINCE the numerous and important evidences from the planets support
the hypothesis that the earth moves, we shall now expound that motion
completely and shall show how far the motion hypothesized explains the
phenomena. The motion is threefold. First there is the motion which the
Greeks called nychthemeron, as we have said, which causes the sequence
of day and night. This motion is executed from west to east — as it has
been believed that the world moves in a contrary sense — and is a rotation
of the earth on its axis. The motion traces the equinoctial circle which
some, imitating the Greek expression, name the equidiurnal.
The second motion is the annual progress of the earth's center which,
with all that is attached to it, travels round the sun on the circle of the
zodiac. This motion is also from west to east, and it takes place, as we
have said, between the spheres of Venus and Mars. Seemingly, it is the sun
which executes a similar motion. Thus, when the center of the earth passes
across Capricorn, Aquarius, and so forth, the sun seems to pass Cancer,
Leo, and so on.
Next it must be recognized that the equator and the axis of the earth
have a variable inclination with respect to the circle of the earth's path
and the plane of this circle. Were the inclination fixed, there would be no
70
MASTERWORKS OF SCIENCE
shifting inequality between days and nights; rather, at all times, there
would exist the conditions of the equinox, or of the solstice, or of the
shortest day, or of winter, or of summer, or of some other season. There
must therefore be a ttpird motion of the earth, varying the declination.
This motion also is annual, but proceeds in a sense opposite to the motion
of the center. Because these two motions are almost equal to one another
But in opposite senses, the axis of the earth and the greatest of the parallel
circles, the equator, face ever toward the same part of the world, as if
they were motionless. Yet because of this motion of the earth, the sun
appears to move obliquely on the ecliptic exactly as if the earth were the
center of the world. The fact offers no difficulty provided one remembers
that the distance from the earth to the sun is, compared to that from the
sphere of the fixed stars, almost imperceptible.
There are matters better presented to the eye than expressed in
words. I shall therefore trace the accompanying circle abed which may
represent the annual motion of the earth's center in the plane of the
ecliptic. In the center of the circle, E may represent the sun. I now cut the
circle into four equal parts by means of the diameters a E c and b E d
subtending equal arcs. Let us suppose that the point a is occupied by the
beginning of Cancer, b by that of Libra, c by Capricorn, and d by Aries.
REVOLUTIONS OF HEAVENLY SPHERES 71
Let us also suppose that the center of the earth is, to begin with, at a, and
let us trace the terrestrial equator / g h i, but not in the same plane, so
that the diameter g a i may be common to both planes, that o£ the equator
and that of the ecliptic. Then we shall trace similarly the diameter / a h
at right angles to g a i, so that / shall be the limit of the greatest declina-
tion toward the south, and h, toward the north.
All these conditions being granted, the observer on the earth will see
the sun — which is at the center E — in the position of the winter solstice,
in Capricorn. This result arises from the greatest northern declination
with respect to the sun. Conformably to the distance comprehended by
the angle E a ht the inclination of the equator describes during the diurnal
revolution the winter tropic.
Let the center of the earth now advance until it reaches the point k,
while at the same time /, the limit of the greatest declination, advances in
a contrary sense. Each will now have described a quarter circle. During
this time, because of the equality of the two motions, the angle E a i will
always remain equal to the angle a E bf and the diameters / a h and g a i
will remain parallel to the diameters / b h and g b i, as will the equator.
Because of the immensity of the sky, often mentioned before, they will
appear the same.
Now, from the point b — the beginning of Libra — E will appear to be
in Aries, and the common sections of the two circles will coincide in a
single line, g b i E. In relation to this line, all declination is lateral, and
the daily revolution reveals no decimation. The sun appears to be in the
position right for the spring equinox.
Let the earth continue its journey under the conditions specified
until, having traveled half its route, it has reached c. The sun is now
apparently entering Cancer. Since the southern declination of the equator,
/, is now turned toward the sun, it will during the diurnal revolution
move along the summer tropic, as measured by the angle E c f.
When / has moved through the third quadrant of the circle, the com-
mon section g i will coincide again with the line E d, and the sun will be
observed in Libra; that is, the sun is at the position for the autumn
equinox. Then, the same motion continuing, and h f turning little by
little again toward the sun, there will result the original situation, that
with which we started.
Another explanation. In the accompanying diagram, let a e c be the
diameter of the ecliptic and represent the line common to the circle a b c
and the circle of the ecliptic in the preceding diagram; this diagram is at
right angles to the preceding one. In this new diagram, at a and at c, that
is, in Cancer and in Capricorn, let us draw d g f i, which will represent a
meridian of the earth, and d /, which will represent its axis. The north
pole is at d; the south at /; and g i the equatorial diameter. As before, the
sun is at e. When / turns toward the sun and the inclination of the equator
is north by the angle i a e, as the earth rotates on its axis, the chord c I at
the distance / / from the equator will describe the southern circle parallel
to the equator. This circle appears in the sun as the tropic of Capricorn.
72 MASTER WORKS OF SCIENCE
Norih
South
To speak more exactly, as the earth rotates on its axis, the line a e de-
scribes a conic section of which the apex is the center o£ the earth, and of
which the base is parallel to the equator.
In the opposite sign of the zodiac, at cf precisely the same things will
be true — but in the inverse sense.
It is clear, therefore, how the two mutually opposed motions — I mean
those of the center and of the inclination — compel the axis of the earth to
remain ever at the same inclination and in the same position, Equally
clear is it that these motions appear to be motions of the sun.
We have said that the annual revolution of the center and of the in-
clination are almost equal. Were they precisely equal, the equinoctial and
solstitial points, and the obliquity of the ecliptic with respect to the fixed
stars, ought never to change. They are not precisely equal, and hence a
change occurs, but so small that it is revealed only over a long period of
time. For example, from Ptolemy's time to ours, the solstitial and equinoc-
tial points have executed a precession of twenty-one degrees. From this
observation, some men have argued that the sphere of the fixed stars also
moves. Some talk of a ninth sphere; and as that does not suffice to explain
everything, the moderns now add a tenth. They still do not attain their
end. But using the movements of the earth as a principle and as a hypothe-
sis, we hope to explain even more phenomena* If anyone maintains that
the motions of the sun and of the moon can be explained on the hypothe-
sis that the earth is immobile, the explanation oflcred does not accord
with the motions of the other planets. Probably it was for this reason or
some other similar reason — and not for the reasons alleged and refuted by
Aristotle — that Philolaus admitted that it is the earth which moves. Ac-
cording to some authorities, Aristarchus held the same opinion.
These are matters which can, indeed, be understood only by a pene-
trating spirit and after long study. Knowledge of them was consequently
rare among the philosophers. True, the number of those who studied the
motions of the stars was very small; and it did not include Plato. And
even if these matters were understood by Philolaus and some other
Pythagoreans, it is not strange that their knowledge did not survive
among their4 successors. For the Pythagoreans were not accustomed to
entrust their secrets to books, or to initiate the whole world into the
mysteries of philosophy. They rather confided only in their friends and
kinsmen, passing their secrets on only, as it were, from hand to hand. Of
this fact, the letter of Lysis to Hipparchus gives evidence. With a refer-
ence to its sentiments on secrecy, worthy to be remembered, it pleases me
to end this first book.
DIALOGUES CONCERNING
TWO NEW SCIENCES
GALILEO
CONTENTS
Dialogues Concerning Two New Sciences
First Day
Second Day
Third Day
Fourth Day
GALILEO GALILEI
1564-1642
VINCENZIO GALILEI, a poor nobleman of Florence, early recog-
nized the talents o£ his son Galileo. An able musician and a
good mathematician, he sent the boy, born in Pisa in 1564,
first to study Greek, Latin, and logic at the monastery of Val-
lombrosa, near Florence, and, in 1581, to the University of
Pisa to study medicine. The boy had already shown aptitude
in music and in painting, and a small talent in literature —
eventually visible in an inconsiderable comedy, in a few minor
poems, in some critical remarks on Ariosto, and in a volumi-
nous and eloquent correspondence. Vincenzio had, however,
decided on medicine as his son's profession. He had, indeed,
allowed the boy training in the recognized arts; but he had
kept him wholly from any study in mathematics.
Quite by accident, Galileo overheard at the university a
lecture on geometry. His interest flared so high that he per-
suaded his father to let him have mathematical instruction.
From this time on, though he stayed at the university until he
was twenty-one, he read medicine no more. Instead he de-
voted himself to mathematics and mechanics, and continued
the study of these sciences for the remainder of a long, fruit-
ful life. In 1585, apparently for want of funds, Vincenzio with-
drew his son from the University of Pisa. The young man re-
turned to Florence and secured an appointment as lecturer in
mathematics at the Academy there/
Already, during his years in Pisa, Galileo had made the
first of those observations in mechanics which were to bring
him fame. He had watched the swaying of a lamp suspended
on a long chain in the Cathedral of Pisa sharply enough to
discover that whatever the range of the oscillations, they were
executed in the same time. He conducted some verifying ex-
periments, discovered the isochronism of the pendulum, and,
oerhaps because he had somewhat studied medicine, applied
76 MASTER WORKS OF SCIENCE
the newly discovered principle to the timing of the human
pulse. In 1586 he published an account of a hydrostatic bal-
ance which he had invented, and his name began to be widely
known in Italy. Two years later he wrote a treatise on the
center of gravity in solids. As a result, he was recalled to Pisa
as a professor of mathematics in the university. The young
medical matriculant of seven years before had wholly shitted
his ground. Yet old Vinccnzio was not denied matter for
pride in his son.
Once more in Pisa, Galileo made the observations in me-
chanics which, confirmed according to his usual method by
experiments, led him to the discovery that bodies of differing
masses fall with equal acceleration from rest, and to the
discovery that the path of a projectile is a parabola. That he
demonstrated his discoveries by dropping and tossing objects
from the top of the Leaning Tower of Pisa is an often re-
peated story which has no foundation in fact. It is a fiction of
his later biographers, supported by imaginative illustrators of
"great moments in the history of science," But if not in the
Leaning Tower, at least in Pisa, he made these discoveries,
fundamental to the whole theory of dynamics.
Galileo's discovery about velocity and acceleration in free
fall contradicted the views his contemporaries held, views for
which they thought they had the authority of Aristotle. They
attacked Galileo, pooh-poohed his theories, and provoked him
to sarcastic replies. Thus he entered into the first of the con-
troversies which enlivened his public life. He also earned such
unpopularity that he had to resign his university appoint-
ment and return to Florence. He lived in that city quietly for
a year, and was then called to Padua to become professor of
mathematics in the university there. He continued to live in
Paclua for the next twenty years. Even when, in 1610, he left
Padua permanently, he retained his professorship in the uni-
versity, for it had been granted for life. The stipend from this
appointment, together with the income from some sinecures
which came to him as the rewards of increasing age and fame,
enabled him to continue his studies, his theorizing, his experi-
ments— and his controversies — without recourse to any activity
o£ which the end would have been merely economic inde-
pendence.
In 1609, during a visit to Venice, Galileo heard a rumor
that a telescope had been invented by a lens maker in the Low
Countries. He returned to Padua, busied himself with experi-
ment, and in a few days hastened to Venice to present to the
Doge the first telescope known to Venice. It magnified three
diameters. Galileo patiently learned the technique of grinding
and polishing lenses; he experimented with arrangements of
GALILEO — DIALOGUES 77
lenses. Eventually he constructed an instrument which mag-
nified thirty-three diameters. Meantime he had begun a series
of astronomical observations with his telescopes. He observed
the mountains of the moon, the satellites of Jupiter, sun spots,
the constituent stars of the Milky Way. He manufactured tele-
scopes in sufficient numbers to supply a great part of Europe,
and so firmly was his name attached to the device that to this
day the telescope he used — of which the modern opera glass is
a type — though he was not its real inventor, is called the
•Galilean telescope.
The astronomical observations which Galileo made con-
tributed a great deal to the stock of information of astrono-
mers. Most particularly, it provided evidence for the validity
of the Copernican theories — as against the Ptolemaic — explain-
ing the motion of heavenly bodies. Galileo had accepted the
Copernican ideas as early as 1597, but a fear of ridicule had
restrained him from a public avowal of his opinion. In 1613,
after he had demonstrated his telescope to an .acclaiming
public in Rome, he published Letters on the Solar Spots in
which he argued for the Copernican views. His great reputa-
tion provoked ecclesiastical authorities to examine this work,
and they found that the new views ran counter to conventional
interpretation of Biblical texts. Immediately a controversy of
large dimensions arose. Galileo threw himself into it avidly.
He lectured and demonstrated and wrote. He sought out Bib-
lical texts to support his position. The consequence was that
in 1616 the theologians of the Holy Office decided that the
Copernican theories were heretical, and Pope Paul V admon-
ished Galileo not "to hold, teach, or defend" the condemned
doctrine. He was, in short, advised to avoid theology and to
restrict himself to physical reasoning; and he promised to
heed the advice.
Galileo retired once more to Florence, to seven years of
studious quiet. Then he published a work on comets, dedi-
cated to Urban VIII, the new pope. The intellectual atmos-
phere seemed less suffocating than some years earlier. Mean-
time he had become ever more convinced of the truth of the
Copernican theories. He now, in the freer air, reweighed all
the arguments, discussed them with friends, and finally, in
1630, completed Dialogo del due massimi sistemi del mondo
{Dialogue Concerning the Two Chief Systems of the World),
a work which really demolished the Ptolemaic doctrine and
established that of Copernicus. When he published the work
in 1632, Europe applauded. But the Inquisition at Rome had
not forgotten that Galileo had promised sixteen years before
not to "hold, teach, or defend" the forbidden doctrine. Sale
of the book was banned; Galileo was cited to Rome for trial.
78 M^ASTER WORKS OF SCIENCE
Eventually he did stand trial in Rome, recanted, and was con-
demned to recite the seven penitential psalms once a week for
three years.
There is a tale that Galileo, rising from the kneeling posi-
tion in which, before the trial, officers, he had agreed that the
earth stands stationary while the sun moves round it, stamped
on the earth and muttered, "It does move, anyway." The story
is pure fiction. But whatever the words he muttered, if he
muttered any, it is reasonable to believe that he privately held
to his published ideas. For his intellectual vigor had not de-
clined. He had yet eight years to live, and even after he had
become blind in 1637, he continued his speculations on physi-
cal subjects. Indeed, he was dictating to his pupils, Torricelli
and Viviani, his latest ideas on impact when he was seized by
the slow fever of which, in 1642, he died.
The later years of Galileo's life were notable not for new
discoveries, but for the composition and publication of his
Dialoghi dclle nuove scienzc (Dialogues Concerning New
Sciences). In these he recounted the bulk of his experimental
and theoretical work, and literally laid the foundations for the
science of mechanics. Though some isolated notions had been
grasped by his predecessors, Galileo first clearly understood
and presented the idea of force as a mechanical agent. He
further showed how a combination of experiment with calcu-
lation, the perpetual comparison of results, the translation of
the concrete into the abstract, provide a method for investi-
gating natural laws. Of such laws he stated many, and his
work implies the knowledge and understanding of others.
The science of mechanics rests upon the three Laws o£ Mo-
tion which Newton, not many years after Galileo's death,
enunciated in their final form. Galileo never stated these
Laws; yet his work suggests that he was aware of the princi-
ples they codify. In the Dialogues, his last work, he explored
the territory which Newton was later to survey and measure.
And these Dialogues, better than any notes on Galileo, illus-
trate his methods and reveal his discoveries.
(In the Dialogues, Galileo presents his own arguments as
the words of Salviati. He also refers occasionally to himself
as "Author" or as "Academician,")
DIALOGUES CONCERNING TWO
NEW SCIENCES
FIRST DAY
Interlocutors: Salviati, Sagredo and Simplicio
SALVIATI. The constant activity which you Venetians display in your fa-
mous arsenal suggests to the studious mind a large field for investigation,
especially that part of the work which involves mechanics; for in this de-
partment all types of instruments and machines are constantly being con-
structed by many artisans, among whom there must be some who, partly
by inherited experience and partly by their own observations, have be-
come highly expert and clever in explanation,
SAGREDO. You are quite right. Indeed, I myself, being curious by na-
ture, frequently visit this place for the mere pleasure of observing the
work of those who, on account of their superiority over other artisans, we
call "first rank men." Conference with them has often helped me in the
investigation of certain effects including not only those which are striking,
but also those which are recondite and almost incredible. At times also I
have been put to confusion and driven to despair of ever explaining some-
thing for which I could not account, but which my senses told me to be
true. And notwithstanding the fact that what the old man told us a little
while ago is proverbial and commonly accepted, yet it seemed to me alto-
gether false, like many another saying which is current among the igno-
rant; for I think they introduce these expressions in order to give the
appearance of knowing something about matters which they do not under-
stand,
SALVIATI. You refer, perhaps, to that last remark of his when we asked
the reason why they employed stocks, scaffolding and bracing of larger
dimensions for launching a big vessel than they do for a small one; and he
answered that they did this in order to avoid the danger of the ship part-
ing under its own heavy weight, a danger to which small boats are not
subject?
SAGREDO. Yes, that is what I mean; and I refer especially to his last
assertion which I have always regarded as a false, though current, opinion;
namely, that in speaking of these and other similar machines one cannot
argue from the small to the large, because many devices which succeed on
80 MASTERWORKS OF SCIENCE
a small scale do not work on a large scale. Now, since mechanics has its
foundation in geometry, where mere size cuts no figure, I do not see that
the properties of circles, triangles, cylinders, cones and other solid figures
will change with their size. If, therefore, a large machine be constructed in
such a way that its parts bear to one another the same ratio as in a smaller
one, and if the smaller is sufficiently strong for the purpose for which it
was designed, I do not see why the larger also should not be able to with-
stand any severe and destructive tests to which it may be subjected.
SALVIATI. The common opinion is here absolutely wrong. Indeed, it is
so far wrong that precisely the opposite is true, namely, that many ma-
chines can be constructed even more perfectly on a large scale than on a
small; thus, for instance, a clock which indicates and strikes the hour can
be made more accurate on a large scale than on a small. There are some
intelligent people who maintain this same opinion, but on more reason-
able grounds, when they cut loose from geometry and argue that the
better performance of the large machine is owing to the imperfections
and variations of the material. Here I trust you will not charge me with
arrogance if I say that imperfections in the material, even those which are
great enough to invalidate the clearest mathematical proof, are not suffi-
cient to explain the deviations observed between machines in the concrete
and in the abstract. Yet I shall say it and will affirm that, even if the
imperfections did not exist and matter were absolutely perfect, unalterable
and free from all accidental variations, still the mere fact that it is matter
makes the larger machine, built of the same material and in the same
proportion as the smaller, correspond with exactness to the smaller in
every respect except that it will not be so strong or so resistant against
violent treatment; the larger the machine, the greater its weakness. Since
I assume matter to be unchangeable and always the same, it is clear that
we are no less able to treat this constant and invariable property in a rigid
manner than if it belonged to simple and pure mathematics. Therefore,
Sagredo, you would do well to change the opinion which you, and per-
haps also many other students of mechanics, have entertained concerning
the ability of machines and structures to resisc external disturbances,
thinking that when they are built of the same material and maintain the
same ratio between parts, they are able equally, or rather proportionally,
to resist or yield to such external disturbances and blows. For we can
demonstrate by geometry that the large machine is not proportionately
stronger than the small Finally, we may say that, for every machine and
structure, whether artificial or natural, there is set a necessary limit be-
yond which neither art nor nature can pass; it is here understood, of
course, that the material is the same and the proportion preserved.
SAGREDO. My brain already reels. My mind, like a cloud momentarily
illuminated by a lightning flash, is for an instant filled with an unusual
light, which now beckons to me and which now suddenly mingles and
obscures strange, crude ideas. From what you have said it appears to me
impossible to build two similar structures of the same material, but of
different sizes and have them proportionately strong; and if this were so,
GALILEO — DIALOGUES 81
it would not be possible to find two single poles made of the same wood
which shall be alike in strength and resistance but unlike in size.
SALVIATI. So it is, Sagredo. And to make sure that we understand each
other, I say that if we take a wooden rod of a certain length and size,
fitted, say, into a wall at right angles, i. e., parallel to the horizon, it may
be reduced to such a length that it will just support itself; so that if a
hair's breadth be added to its length it will break under its own weight
and will be the only rod of the kind in the world. Thus if, for instance,
its length be a hundred times its breadth, you will not be able to find
another rod whose length is also a hundred times its breadth and~*which,
like the former, is just able to sustain its own weight and no more: all the
larger ones will break while all the shorter ones will be strong enough to
support something more than their own weight. And this which I have
said about the ability to support itself must be understood to apply also
to other tests; so that if a piece of scantling will carry the weight of ten
similar to itself, a beam having the same proportions will not be able to
support ten similar beams.
Please observe, gentlemen, how facts which at first seem improbable
will, even on scant explanation, drop the cloak which has hidden them
and stand forth in naked and simple beauty. Who does not know that a
horse falling from a height of three or four cubits will break his bones,
while a dog falling from the same height or a cat from a height of eight or
ten cubits will suffer no injury? Equally harmless would be the fall of a
grasshopper from a tower or the fall of an ant from the distance of the
moon. Do not children fall with impunity from heights which would cost
their elders a broken leg or perhaps a fractured skull? And just as smaller
animals are proportionately stronger and more robust than the larger, so
also smaller plants are able to stand up better than larger. I am certain
you both know that an oak two hundred cubits high would not be able to
sustain its own branches if they were distributed as in a tree of ordinary
size; and that nature cannot produce a horse as large as twenty ordinary
horses or a giant ten times taller than an ordinary man unless by miracle
or by greatly altering the proportions of his limbs and especially of his
bones, which would have to be considerably enlarged over the ordinary.
Likewise the current belief that, in the case of artificial machines the very
large and the small are equally feasible and lasting is a manifest error.
Thus, for example, a small obelisk or column or other solid figure can
certainly be laid down or set up without danger of breaking, while the
very large ones will go to pieces under the slightest provocation, and that
purely on account of their own weight. And here I must relate a circum-
stance which is worthy of your attention as indeed are all events which
happen contrary to expectation, especially when a precautionary measure
turns out to be a cause of disaster. A large marble column was laid out so
that its two ends rested each upon a piece of beam; a little later it oc-
curred to a mechanic that, in order to be doubly sure of its not breaking
in the middle by its own weight, it would be wise to lay a third support
midway; this seemed to all an excellent idea; but the sequel showed that
it was quite the opposite, for not many months passed before the column
was found cracked and broken exactly above the new middle support.
SIMPLICIO. A very remarkable and thoroughly unexpected accident,
especially if caused by placing that new support in the middle.
SALVIATI. Surely this is the explanation, and the moment the cause is
known our surprise vanishes; for when the two pieces of the column were
placed on level ground it was observed that one of the end beams had,
after a long while, become decayed and sunken, but that the middle one
remained hard and strong, thus causing one half of the column to project
in the air without any support. Under these circumstances the body there-
fore behaved differently from what it would have done if supported only
upon the first beams; because no matter how much they might have
sunken the column would have gone with them. This is an accident
which could not possibly have happened to a small column, even though
made of the same stone and having a length corresponding to its thick-
ness, i. e., preserving the ratio between thickness and length found in the
large pillar.
SAGREDO. I am quite convinced of the facts of the case, but I clo not
understand why the strength and resistance are not multiplied in the
same proportion as the material; and I am the more puzzled because, on
the contrary, I have noticed in other cases that the strength and resistance
against breaking increase in a larger ratio than the amount of material.
Thus, for instance, if two nails be driven into a wall, the one which is
twice as big as the other will support not only twice as much weight as
the other, but three or four times as much,
SALVIATI. Indeed you will not be far wrong if you say eight times as
much; nor does this phenomenon contradict the other even though in
appearance they seem so different. %
SAGREDO, Will you not then, Salviati, remove these difficulties and
clear away these obscurities if possible: for I imagine that this problem
of resistance opens up a field of beautiful and useful ideas; and if you are
pleased to make this the subject of today's discourse you will place Sim-
plicio and me under many obligations,
SALVIATI. I am at your service if only I can call to mind what I learned
from our Academician [Galileo] who had thought much upon this sub-
ject and according to his custom had demonstrated everything by geomet-
rical methods so that one might fairly call this a new science. For, al-
though some of his conclusions had been reached by others, first of all by
Aristotle, these are not the most beautiful and, what is more important,
they had not been proven in a rigid manner from fundamental principles.
Now, since I wish to convince you by demonstrative reasoning rather than
to persuade you by mere probabilities, I shall suppose that you are familiar
with present-day mechanics so far as it is needed in our discussion. First
of all it is necessary to consider what happens when a piece of wood or
any other solid which coheres firmly is broken; for this is the fundamental
fact, involving the first and simple principle which we must take for
granted as well known.
GALILEO — DIALOGUES
83
To grasp this more clearly, imagine a cylinder
or prism, AB, made of wood or other solid co-
herent material. Fasten the upper end, A, so that
the cylinder hangs vertically. To the lower end,
B, attach the weight C. It is clear that however
great they may be, the tenacity and coherence be-
tween the parts of this solid, so long as they are
not infinite, can be overcome by the pull of the
weight C, a weight which can be increased indefi-
nitely until finally the solid breaks like a rope.
And as in the case of the rope whose strength we
know to be derived from a multitude of hemp
threads which compose it, so in the case of the
wood, we observe its fibres and filaments run
lengthwise and render it much stronger than a
hemp rope of the same thickness. But in the case
of a stone or metallic cylinder where the coherence
seems to be still greater the cement which holds
the parts together must be something other than
filaments and fibres; and yet even this can be
broken by a strong pull.
SIMPLICIO. If this matter be as you say I can well understand that the
fibres of the wood, being as long as the piece of wood itself, render it
strong and resistant against large forces tending to break it. But how can
one make a rope one hundred cubits long out of hempen fibres which are
not more than two or three cubits long, and still give it so much strength?
Besides, I should be glad to hear your opinion as to the manner in which
the parts of metal, stone, and other materials not showing a filamentous
structure are put together; for, if I mistake not, they exhibit even greater
tenacity.
SALVIATI. To solve the problems which you raise it will be necessary
to make a digression into subjects which have little bearing upon our
present purpose.
SAGREDO. But if, by digressions, we can reach new truth, what harm is
there in making one now, so that we may not lose this knowledge, re-
membering that such an opportunity, once omitted, may not return; re-
membering also that we are not tied down to a fixed and brief method
but that we meet solely for our own entertainment? Indeed, who knows
but that we may thus frequently discover something more interesting and
beautiful than the solution originally sought? I beg of you, therefore, to
grant the request of Simplicio, which is also mine; for I am no less curious
and desirous than he to learn what is the binding material which holds
together the parts of solids so that they can scarcely be separated. This
information is also needed to understand the coherence of the parts of
fibres themselves of which some solids are built up.
SALVIATI. I am at your service, since you desire it. The first question
is, How are fibres, each not more than two or three cubits in length, so
84
MASTERWORKS OF SCIENCE
tightly bound together in the case of a rope one hundred cubits long that
great force is required to break it?
Now tell me, Simplicio, can you not hold a hempen fibre so tightly
between your fingers that I, pulling by the other end, would break it
before -drawing it away from you? Certainly you can. And now when the
fibres of hemp are held not only at the ends, but are grasped by the sur-
rounding medium throughout their entire length is it not manifestly
more difficult to tear them loose from what holds them than to break
them? But in the case of the rope the very act of twisting causes the
threads to bind one another in such a way that when the rope is stretched
with a great force the fibres break rather than separate from each other.
At the point where a rope parts the fibres are, as everyone knows,
very short, nothing like a cubit long, as they would be if the parting of
the rope occurred, not by the breaking of the filaments, but by their
slipping one over the other.
SAGREDO. In confirmation of this it may be remarked that ropes some-
times break not by a lengthwise pull but by excessive twisting. This, it
seems to me, is a conclusive argument because the threads bind one an-
other so tightly that the compressing fibres do not permit those which are
compressed to lengthen the spirals even that little bit by which it is neces-
sary for them to lengthen in order to surround the rope which, on twist-
ing, grows shorter and thicker.
SALVIATJ. You are quite right. Now sec how one fact suggests another.
The thread held between the fingers does not yield to one who wishes to
draw it away even when pulled with considerable force, but resists be-
cause it is held back by a double compression,
seeing that the upper finger presses against the
lower as hard as the lower against the upper.
Now, if we could retain only one of these pres-
sures there is no doubt that only half the
original resistance would remain; but since we
are not able, by lifting, say, the upper finger,
to remove one of these pressures without also
removing the other, it becomes necessary to pre-
serve one of them by means of a new device
which causes the thread to press itself against
the finger or against some other solid body
upon which it rests; and thus it is brought
about that the very force which pulls it in order
to snatch it away compresses it more and more
as the pull increases. This is accomplished by
wrapping the thread around the solid in the
manner of a spiral; and will be better under-
stood by means of a figure. Let AB and CD be
two cylinders between which is stretched the
thread EF: and for the sake of greater clearness
we will imagine it to be a small cord. If these
GALILEO — DIALOGUES
85
two cylinders be pressed strongly together, the cord EF, when drawn* by
the end F, will undoubtedly stand a considerable pull before it slips
between the two compressing solids. But if we remove one of these
cylinders the cord, though remaining in contact with the other, will not
thereby be prevented from slipping freely. On the other hand, if one
holds the cord loosely against the top of the cylinder A, winds it in the
spiral form AFLOTR, and then pulls it by the end R, it is evident that the
cord will begin to bind the cylinder; the greater the number of spirals the
more tightly will the cord be pressed against the cylinder by any given
pull. Thus as the number of turns increases, the line of contact becomes
longer and in consequence more resistant; so that the cord slips and
yields to the tractive force with increasing difficulty.
Is it not clear that this is precisely the kind of resistance which one
meets in the case of a thick hemp rope where the fibres form thousands
and thousands of similar spirals? And, indeed, the binding effect of these
turns is so great that a few short rushes woven together into a few inter-
lacing spirals form one of the strongest of ropes which I believe they call
pack rope.
SAGREDO. What you say has cleared up two points which I did not
previously understand. One fact is how two, or at most three, turns of a
rope around the axle of a windlass cannot only hold it fast, but can also
prevent it from slipping when pulled by the immense force of the weight
which it sustains; and moreover how, by turning the windlass, this same
axle, by mere friction of the rope around it, can wind up and lift huge
stones while a mere boy is able to handle the slack of the rope. The other
fact has to do with a simple but clever device, invented by a young kins-
man of mine, for the purpose of descending from a window by means of
a rope without lacerating the palms, of his hands, as had happened to him
shortly before and greatly to his discomfort. A
small sketch will make this clear. He took a
wooden cylinder, AB, about as thick as a walking
stick and about one span long: on this he cut a
spiral channel of about one turn and a half, and
large enough to just receive the rope which he
wished to use. Having introduced the rope at the
end A and led it out again at the end B, he en-
closed both the cylinder and the rope in a case of
wood or tin, hinged along the side so that it could
be easily opened and closed. After he had fastened
the rope to a firm support above, he could, on
grasping and squeezing the case with both hands,
hang by his arms. The pressure on the rope, lying
between the case and the cylinder, was such that
he could, at will, either grasp the case more tightly
and hold himself from slipping, or slacken his
hold and descend as slowly as he wished.
-x.
86 MASTERWORKS OF SCIE NCE _
SALVIATI. A truly ingenious device! I feel, however, that for a com-
plete explanation other considerations might well enter; yet I must not
now digress upon this particular topic since you are waiting to hear what
I think about the breaking strength of other materials which, unlike ropes
and most woods, do not show a filamentous structure. The coherence of
these bodies is, in my estimation, produced by other causes which may be
grouped under two heads. One is that much-talked-of repugnance which
nature exhibits towards a vacuum; but this horror of a vacuum not being
sufficient, it is necessary to introduce another cause in the form of a gluey
or viscous substance which binds firmly together the component parts of
the body.
First I shall speak of the vacuum, demonstrating by definite experi-
ment the quality and quantity of its force. If you take two highly polished
and smooth plates of marble, metal, or glass and place them face to face,
one will slide over the other with the greatest ease, showing conclusively
that, there is nothing of a viscous nature between them. But when you
attempt to separate them and keep them at a constant distance apart, you
find the plates exhibit such a repugnance to separation that the upper one
will carry the lower one with it and keep it lifted indefinitely, even when
the latter is big and heavy.
This experiment shows the aversion of nature for empty space, even
during the brief moment required for the outside air to rush in and fill
up the region between the two plates. It is also observed that if two plates
are not thoroughly polished, their contact is imperfect so that when you
attempt to separate them slowly the only resistance oflerecl is that of
weight; "if, however, the pull be sudden, then the lower plate rises, but
quickly falls back, having followed the upper plate only for that very
short interval of time required for the expansion of the small amount of
air remaining between the plates, in consequence of their not fitting, and
for the entrance of the surrounding air. This resistance which is exhibited
between the two plates is doubtless likewise present between the parts of
a solid, and enters, at least in part, as a concomitant cause of their co-
herence.
SAGREDO. Allow me to interrupt you for a moment, please; for I want
to speak of something which just occurs to me, namely, when I see how
the lower plate follows the tipper one and how rapidly it is lifted, I feel
sure that, contrary to the opinion of many philosophers, including per-
haps even Aristotle himself, motion in a vacuum is not instantaneous. If
this were so the two plates mentioned above would separate without any
resistance whatever, seeing that the same instant of time would suffice for
their separation and for the surrounding medium to rush in and fill the
vacuum between them. The fact that the lower plate follows the upper
one allows us to infer, not only that motion in a vacuum is not instantane-
ous, but also that, between the two plates, a vacuum really exists, at least
for a very short time, sufficient to allow the surrounding medium to rush
in and fill the vacuum; for if there were no vacuum there would be no
need of any motion in the medium. One must admit then that a vacuum
GALILEO — DIALOGUES 87
is sometimes produced by violent motion or contrary to the laws of na-
ture (although in my opinion nothing occurs contrary to nature except
the impossible, and that never occurs).
But here another difficulty arises. While experiment convinces me of
the correctness of this conclusion, my mind is not entirely satisfied as to
the cause to which this effect is to be attributed. For the separation of the
plates precedes the formation of the vacuum which is produced as a con-
sequence of this separation; and since it appears to me that, in the order
of nature, the cause must precede the effect, even though it appears to
follow in point of time, and since every positive effect must have a posi-
tive cause, I do not see how the adhesion of two plates and their resist-
ance to separation — actual facts — can be referred to a vacuum as cause
when this vacuum is yet to follow. According to the infallible maxim of
the Philosopher, the non-existent can produce no effect.
SIMPLICIO. Seeing that you accept this axiom of Aristotle, I hardly think
you will reject another excellent and reliable maxim of his, namely, Na-
ture undertakes only that which happens without resistance; and in this
saying, it appears to me, you will find the solution of your difficulty. Since
nature abhors a vacuum, she prevents that from which a vacuum would
follow as a necessary consequence. Thus it happens that nature prevents
the separation of the two plates.
SAGREDO. Now admitting that what Simplicio says is an adequate solu-
tion of my difficulty, it seems to me, if I may be allowed to resume my
former argument, that this very resistance to a vacuum ought to be suffi-
cient to hold together the parts either of stone or of metal or the parts of
any other solid which is knit together more strongly and which is more
resistant to separation. If for one effect there be only one cause, or if, more
being assigned, they can be reduced to one, then why is not this vacuum
which really exists a^sufficient cause for all kinds of resistance?
SALVIATI. I do not wish just now to enter this discussion as to whether
the vacuum alone is sufficient to hold together the separate parts of a solid
body; but I assure you that the vacuum which acts as a sufficient cause in
the case of the two plates is not alone sufficient to bind together the parts
of a solid cylinder of marble or metal which, when pulled violently, sepa-
rates and divides. And now if I find a method of distinguishing this well
known resistance, depending upon the vacuum, from every other kind
which might increase the coherence, and if I show you that the aforesaid
resistance alone is not nearly sufficient for such an effect, will you not
grant that we are bound to introduce another cause? Help him, Simplicio,
since he does not know what reply to make.
SIMPLICIO. Surely, Sagredo's hesitation must be owing to another
reason, for there can be no doubt concerning a conclusion which is at
once so clear and logical.
SAGREDO. You have guessed rightly, Simplicio. I was wondering
whether, if a million of gold each year from Spain were not sufficient to
pay the army, it might not be necessary to make provision other than
small coin for the pay of the soldiers.
MASTERWORKS OF SCIENCE
But go ahead, Satviati; assume that I admit your conclusion and show
us your method of separating the action of the vacuum from other causes;
and by measuring it show us how it is not sufficient to produce the effect
in question.
SALVIATI. Your good angel assist you. I will tell you how to separate
the force of the vacuum from the others, and afterwards how to measure
it. For this purpose let us consider a continuous substance whose parts
lack all resistance to separation except that derived from a vacuum, such
as is the case with water, a fact fully demonstrated by our Academician in
one of his treatises. Whenever a cylinder of water is subjected to a pull
and offers a resistance to the separation of its parts this can be attributed
to no other cause than the resistance of the vacuum. In order to try such
an experiment I have invented a device which I
can better explain by means of a sketch than by
mere words. Let CABD represent the cross sec-
tion of a cylinder either of metal or, preferably,
of glass, hollow inside and accurately turned. Into
this is introduced a perfectly fitting cylinder of
wood, represented in cross section by EGHF, and
capable of up-and-down motion. Through the
.middle of this cylinder is bored a hole to receive
an iron wire, carrying a hook at the end K, while
the upper end of the wire, I, is provided with a
conical head. The wooden cylinder is counter-
sunk at the top so as to receive, with a perfect fit,
the conical head I of the wire, IK, when pulled
down by the end K.
Now insert the wooden cylinder EH in the
hollow cylinder AD, so as not to touch the upper
end of the latter but to leave free a space of two
or three fingcrbreadths; this space is to be filled with water by holding
the vessel with the mouth CD upwards, pushing down on the stopper
EH, and at the same time keeping the conical head of the wire, I, away
from the hollow portion of the wooden cylinder* The air is thus allowed
to escape alongside the iron wire (which does not make a close fit) as
soon as one presses clown on the wooden stopper, The air having been
allowed to escape and the iron wire having been drawn back so that it
fits snugly against the conical depression in the wood, invert the vessel,
bringing it mouth downwards, and hang on the hook K a vessel which
can be filled with sand or any heavy material in quantity sufficient to
finally separate the upper surface of the stopper, EF, from the lower
surface of the water to which it was attached only by the resistance of
the vacuum. Next weigh the stopper and wire together with the attached
vessel and its contents; we shall then have the force of the vacuum, If one
attaches to a cylinder of marble or gl&ss a weight which, together with
the weight of the marble or glass itself, is just equal to the sum of the
weights before mentioned, and if breaking occurs we shall then be justi-
GALILEO — DIALOGUES 89
fied in saying that the vacuum alone holds the parts of the marble and
glass together; but if this weight does not suffice and if breaking occurs
only after adding, say, four times this weight, we shall then be compelled
to say that the vacuum furnishes only one fifth of the total resistance.
SIMPLICIO. No one can doubt the cleverness of the device; yet it pre-
sents many difficulties which make me doubt its reliability. For who will
assure us that the air does not creep in between the glass and stopper
even if it is well packed with tow or other yielding material? I question
also whether oiling with wax or turpentine will suffice to make the cone,
I, fit snugly on its seat. Besides, may not the parts of the water expand
and dilate? Why may not the air or exhalations or some other more
subtile substances penetrate the pores of the wood, or even of the glass
itself?
SALVIATI. With great skill indeed has Simplicio laid before us the
difficulties; and he has even partly suggested how to prevent the air from
penetrating the wood or passing between the wood and the glass. But
now let me point out that, as our experience increases, we shall learn
whether or not these alleged difficulties really exist. For if, as is the case
with air, water is by nature expansible, although only under severe treat-
ment, we shall see the stopper descend; and if we put a small excavation
in the upper part of the glass vessel, such as indicated by V, then the air
or any other tenuous and gaseous substance, which might penetrate the
pores of glass or wood, would pass through the water and collect in this
receptacle V. But if these things do not happen we may rest assured that
our experiment has been performed with proper caution; and we shall
discover that water does not dilate and that glass does not allow any
material, however tenuous, to penetrate it.
SAGREDO. Thanks to this discussion, I have learned the cause of a
certain effect which I have long wondered at and despaired of under-
standing. I once saw a cistern which had been provided with a pump
under the mistaken impression that the water might thus be drawn with
less effort or in greater quantity than by means of the -ordinary bucket.
The stock of the pump carried its sucker and valve in the upper part so
that the water was lifted by attraction and not by a push as is the case
with pumps in which the sucker is placed lower down. This pump worked
perfectly so long as the water in the cistern stood above a certain level;
but below this level the pump failed to work. When I first noticed this
phenomenon I thought the machine was out of order; but the workman
whom I called in to repair it told me the defect was not in the pump but
in the water which had fallen too low to be raised through such a height;
and he added that it was not possible, either by a pump or by any other
machine working on the principle of attraction, to lift water a hair's
breadth above eighteen cubits; whether the pump be large or small this
is the extreme limit of the lift. Up to this time I had been so thoughtless
that, although I knew a rope, or rod of wood, or of iron, if sufficiently"
long, would break by its own weight when held by the upper end, it
never occurred to me that the same thing would happen, only much more
90 MASTERWORKS OF SCIENCE
easily, to a column of water. And really is not that thing which is attracted
in the pump a column of water attached at the upper end and stretched
more and more until finally a point is reached where it breaks, like a rope,
on account of its excessive weight?
SALVIATI. That is precisely the way it works; this fixed elevation of
eighteen cubits is true for any quantity of water whatever, be the pump
large or small or even as fine as a straw. We may therefore say that, on
weighing the water contained in a tube eighteen cubits long, no matter
what the diameter, we shall obtain the value of the resistance of the
vacuum in a cylinder of any solid material having a bore of this same
diameter. And having gone so far, let us see how easy it is to find to what
length cylinders of metal, stone, wood, glass, etc., of any diameter can be
elongated without breaking by their own weight.
Take for instance a copper wire of any length and thickness; fix the
upper end and to the other end attach a greater and greater load until
finally the wire breaks; let the maximum load be, say, fifty pounds. Then
it is clear that if fifty pounds of copper, in addition to the weight of the
wire itself which may be, say, % ounce, is drawn out into wire of this
same size we shall have the greatest length of this kind of wire which can
sustain its own weight. Suppose the wire which breaks to be one cubit
in length and % ounce in weight; then since it supports 50 Ibs. in addition
to its own weight, i. e., 4800 eighths-of-an-ounce, it follows that all copper
wires, independent of size, can sustain themselves up to a length of 4801
cubits and no more. Since then a copper rod can sustain its own weight
up to a length of 4801 cubits it follows that that part of the breaking
strength which depends upon the vacuum, comparing it with the remain-
ing factors of resistance, is equal to the weight of a rod of water, eighteen
cubits long and as thick as the copper rod. If, for example, copper is nine
times as heavy as water, the breaking strength of any copper rod, in so
far as it depends upon the vacuum, is equal to the weight of two cubits
of this same rod. By a similar method one can find the maximum length
of wire or rod o£ any material which will just sustain its own weight,
and can at the same time discovet the part which the vacuum plays in
its breaking strength,
SAGREDO. It still remains for you to tell us upon what depends the
resistance to breaking, other than that of the vacuum; what is the gluey
or viscous substance which cements together the parts of: the solid? For
I cannot imagine a glue that will not bura tip in a highly heated furnace
in two or three months, or certainly within ten or a hundred. For if gold,"
silver and glass are kept for a long while in the moltea state and are
removed from the furnace, their parts, on cooling, immediately reunite
and bind themselves together as before. Not only so, but whatever diffi-
culty arises with respect to the cementation of the parts of the glass arises
. also with regard to the parts of the glue; in other words, what is that
which holds these parts together so firmly?
SALVIATI. A little while ago, I expressed the hope that your good
GALILEO — DIALOGUES 91
angel might assist you. I now find myself in the same straits. Experiment
leaves no doubt that the reason why two plates cannot be separated,
except with violent effort, is that they are held together by the resistance
of the vacuum; and the same can be said of two large pieces of a marble
or bronze column. This being so, I do not see why this same cause may
not explain the coherence of smaller parts and indeed of the very smallest
particles of these materials. Now, since each effect must have one true and
sufficient cause and since I find no other cement, am I not justified in
trying to discover whether the vacuum is not a sufficient cause?
SIMPLICIO. But seeing that you have already proved that the resistance
which the large vacuum offers to the separation of two large parts of a
solid is really very small in comparison with that cohesive force which
binds together the most minute parts, why do you hesitate to regard this
latter as something very different from the former?
SALVIATI. Sagredo has already answered this question when he re-
marked that each individual soldier was being paid from coin collected
by a general tax of pennies and farthings, while even a million of gold
would not suffice to pay the entire army. And who knows but that there
may be other extremely minute vacua which affect the smallest particles
so that that which binds together the contiguous parts is throughout of
the same mintage?
In reply to the question raised by Simplicio, one may say that al-
though each particular vacuum is exceedingly minute and therefore easily
overcome, yet their number is so extraordinarily great that their com-
bined resistance is, so to speak, multipled almost without limit. The
nature and the amount of force which results from adding together an
immense number of small forces is clearly illustrated by the fact that a
weight of millions of pounds, suspended by great cables, is overcome and
lifted, when the south wind carries innumerable atoms of , water, sus-
pended in thin mist, which moving through the air penetrate between
the fibres of the tense ropes in spite of the tremendous force of the hang-
ing weight. When these particles enter the narrow pores they swell the
ropes, thereby shorten them, and perforce lift the heavy mass.
SAGREDO. There can be no doubt that any resistance, so long as it is
not infinite, may be overcome by a multitude of minute forces. Thus a
vast number of ants might carry ashore a ship laden with grain. And since
experience shows us daily that one ant can easily carry one grain, it is
clear that the number of grains in the ship is not infinite, but falls below
a certain limit. If you take another number four or six times as great, and
if you set to work a corresponding number of ants they will carry the
grain ashore and the boat also. It is true that this will call for a prodigious
number of ants, but in my opinion this is precisely the case with the vacua
which bind together the least particles of a metal.
SALVIATI. But even if this demanded an infinite number would you
still think it impossible?
SAGREDO. Not if the mass of metal were infinite.
92 M A S T E R WORKS OF SCI E N C E
SAGREDQ. The phenomenon of light is one which I have many times
remarked with astonishment. I have, for instance, seen lead melted in-
stantly by means of a concave mirror only three hands in diameter. Hence
I think that if the mirror were very large, well polished and of a para-
bolic figure, it would just as readily and quickly melt any other metal,
seeing that the small mirror, which was not well polished and had only
a spherical shape, was able so energetically to melt lead and burn every
combustible substance. Such effects as these render credible to me the
marvels accomplished by the mirrors of Archimedes.
SALVIATI. Speaking of the effects produced by the mirrors of Archi-
medes, it was his own books (which I had already read and studied with
infinite astonishment) that rendered credible to me all the miracles de-
scribed by various writers. And if any doubt had remained the book
which Father Buenaventura Cavalieri has recently published on the sub-
ject of the burning glass and "which I have read with admiration would
have removed the last difficulty.
SAGREDO. I also have seen this treatise and have read it with pleasure
and astonishment; and knowing the author I was confirmed in the opinion
which I had already formed of him that he was destined to become one
of the leading mathematicians of our age. But now, with regard to the
surprising effect of solar rays in melting metals, must we believe that
such a furious action is devoid of motion or that it is accompanied by
the most rapid of motions?
SALVTATI. We observe that other combustions and resolutions are
accompanied by motion, and that, the most rapid; note the action of
lightning and of powder as used in mines and petards; note also how
the charcoal flame, mixed as it is with heavy and impure vapors, increases
its power to liquefy metals whenever quickened by a pair of bellows.
Hence I do not understand how the action of light, although very pure,
can be devoid of motion and that of the swiftest type.
SAGREDO. But of what kind and how great must we consider this
speed of light to be? Is it instantaneous or momentary or does it like
other motions require time? Can we not decide this by experiment?
SIMPLICIO. Everyday experience shows that the propagation of light
is instantaneous; for when we see a piece of artillery fired, at great dis-
tance, the flash reaches our eyes without lapse of time; but me sound
reaches the ear only after a noticeable interval.
SAGREDO. Well, Simplicio, the only thing I am able to infer from this
familiar bit of experience is that sound, in reaching our ear, travels more
slowly than light; it does not inform me whether the coming of the light
is instantaneous or whether, although extremely rapid, it still occupies
time. An observation of this kind tells us nothing more than one in which
it is claimed that "As soon as the sun reaches the horizon its light reaches
our eyes"; but who will assure me that these rays had not reached this
limit earlier than they reached our vision?
SALVIATI. The small conclusiveness of these and other similar obser-
vations once led me to devise a method by which one might accurately
GALILEO — DIALOGUES 93
ascertain whether illumination, i. e., the propagation of light, is really
instantaneous. The fact that the speed of sound is as high as it is, assures
us that the motion of light cannot fail to be extraordinarily swift. The
experiment which I devised was as follows:
Let each of two persons take a light contained in a lantern, or other
receptacle, such that by the interposition of the hand, the one can shut
of! or admit the light to the vision of the other. Next let them stand
opposite each other at a distance of a few cubits and practice until they
acquire such skill in uncovering and occulting their lights that the instant
one sees the light of his companion he will uncover his own. After a few
trials the response will be so prompt that without sensible error the
uncovering of one light is immediately followed by the uncovering of the
other, so that as soon as one exposes his light he will instantly see that of
the other. Having acquired skill at this short distance let the two experi-
menters, equipped as before, take up positions separated by a distance
of two or three miles and let them perform the same experiment at night,
noting carefully whether the exposures and occultations occur in the same
manner as at short distances; if they do, we may safely conclude that
the propagation of light is instantaneous; but if time is required at a
distance of three miles which, considering the going of one light and the
coming of the other, really amounts to six, then the delay ought to be
easily observable. If the experiment is to be made at still greater distances,
say eight or ten miles, telescopes may be employed, each observer adjust-
ing one for himself at the place where he is to make the experiment at
night; then although the lights are not large and are therefore invisible
to the naked eye at so great a distance, they can readily be covered and
uncovered since by aid of the telescopes, once adjusted and fixed, they
will become easily visible.
SAGREDO. This experiment strikes me as a clever and reliable invention.
But tell us what you conclude from the results.
SALVIATI. In fact I have tried the experiment only at a short distance,
less than a mile, from which I have not been able to ascertain with
certainty whether the appearance of the opposite light was instantaneous
or not; but if not instantaneous it is extraordinarily rapid — I should call
it momentary; and for the present I should compare it to motion which
we see in the lightning flash between "clouds eight or ten miles distant
from us. We see the beginning of this light — I might say its head and
source — located at a particular place among the clouds; but it immediately
spreads to the surrounding -ones, which seems to be an argument that
at least some time is required for propagation; for if the illumination were
instantaneous and not gradual, we should not be able to distinguish its
origin — its center, so to speak — from its outlying portions.
SAGREDO. I quite agree with the peripatetic philosophers in denying
the penetrability of matter. As to the vacua I should like to hear a
thorough discussion of Aristotle's demonstration in which he opposes
them, and what you, Salviati, have to say in reply. I beg of you, Simplicio,
94 MASTERWORKS OF SCIENCE
that you give us the precise proof of the Philosopher and that you, Salviati,
give us the reply.
SIMPLICIO. So far as I remember, Aristotle inveighs against the ancient
view that a vacuum is a necessary prerequisite for motion and that the
latter could not occur without the former. In opposition to this view
Aristotle shows that it is precisely the phenomenon of motion, as we
shall see, which renders untenable the idea of a vacuum. His method is
to divide the argument into two parts. He first supposes bodies of dif-
ferent weight to move in the same medium; then supposes, one and
the same body to move in different media. In the first case, he supposes
bodies of different weight to move in one and the same medium with
different speeds which stand to one another in the same ratio as the
weights; so that, for example, a body which is ten times as heavy as
another will move ten times as rapidly as the other. In the second case
he assumes that the speeds of one and the same body moving in different
media are in inverse ratio to the densities of these media; thus, for in-
stance, if the density of water were ten times that of air, the speed in
air would be ten times greater than in water. From this second suppo-
sition, he shows that, since the tenuity of a vacuum differs infinitely from
diat of any medium filled with matter however rare, any body which
moves in a plenum through a certain space in a certain time ought to
move through a vacuum instantaneously; but instantaneous motion is an
impossibility; it is therefore impossible that a vacuum should be produced
by motion.
SALVIATI. The argument is, as you see, ad homincm, that is, it is
directed against those who thought the vacuum a prerequisite for motion,
Now if I admit the argument to be conclusive and concede also that
motion cannot take place in a vacuum, the assumption of a vacuum con-
sidered absolutely and not with reference to motion, is not thereby invali-
dated. But to tell you what the ancients might possibly have replied and
in order to better understand just how conclusive Aristotle's demonstra-
tion is, we may, in my opinion, deny both of his assumptions. And as to
the first, I greatly doubt that Aristotle ever tested by experiment whether
it be true that two stones, one weighing ten times as much as the other,
if allowed to fall, at the same instant, from a height of, say, 100 cubits,
would so differ in speed that when the heavier had reached the ground,
the other would not have fallen more than 10 cubits.
SIMPLICIO. His language would seem to indicate that he had tried
the experiment, because he says: We see the heavier; now the word sec
shows that he had made the experiment.
SAGREDO. But I, Simplicio, who have made the test can assure you
that a cannon ball weighing one or two hundred pounds, or even more,
will not reach the ground by as much as a span ahead of a musket ball
weighing only half a pound, provided both are dropped from a height
of 200 cubits.
SALVIATI. But, even without further experiment, it is possible to prove
GALILEO — DIALOGUES 95
clearly, by means of a short and conclusive argument, that a heavier body
does not move more rapidly than a lighter one provided both bodies are
of the same material and in short such as those mentioned by Aristotle.
But tell me, Simpliciq, whether you admit that each falling body acquires
a definite speed fixed by nature, a velocity which cannot be increased or
diminished except by the use of force or resistance.
SIMPLICIO. There can be no doubt but that one and the same body
moving in a single medium has a fixed velocity which is determined by
nature and which cannot be increased except by the addition of momen-
tum or diminished except by some resistance which retards it.
SALVTATI. If then we take two bodies whose natural speeds are dif-
ferent, it is clear that on uniting the two, the more rapid one will be
partly retarded by the slower, and the slower will be somewhat hastened
by the swifter. Do you not agree with me in this opinion?
SIMPLICIO. You are unquestionably right.
SALVIATI. But if this is true, and if a large stone moves with a speed
of, say, eight while a smaller moves with a speed of four, then when they
are united, the system will move with a speed less than eight; but the
two stones when tied together make a stone larger than that which before
moved with a speed of eight. Hence the heavier body moves with less
speed than the lighter; an effect which is contrary to your supposition.
Thus you see how, from your assumption that the heavier body moves
more rapidly than the lighter one. I infer that the heavier body moves
more slowly.
SIMPLICIO. I am all at sea because it appears to me that the smaller
stone when added to the larger increases its weight and by adding weight
I do not see how it can fail to increase its speed or, at least, not to
diminish it.
SALVIATI. Here again you are in error, Simplicio, because it is not true
that the smaller stone adds weight to tne larger.
SIMPLICIO. This is, indeed, quite beyond my comprehension.
SALVIATI. It will not be beyond you when I have once shown you the
mistake under which you are laboring. Note that it is necessary to dis-
tinguish between heavy bodies in motion and the same bodies at rest. A
large stone placed in a balance not only acquires additional weight by
having another stone placed upon it, but even by the addition of a handful
of hemp its weight is augmented six to ten ounces according to the
quantity of hemp. But if you tie the hemp to the stone and allow them
to fall freely from some height, do you believe that the hemp will press
down upon the stone and thus accelerate its motion or do you think the
motion will be retarded by a partial upward pressure? One always feels
the pressure upon his shoulders when he prevents the motion of a load
resting upon him; but if one descends just as rapidly as the load would fall
how can it gravitate or press upon him? Do you not see that this would
be the same as trying to strike a man with a lance when he is running
away from you with a speed which is equal to, or even greater, than that
with which you are following him? You must therefore conclude that,
96 MT
during free and natural fall, the small stone does not press upon the larger
and consequently does not increase its weight as it does when at rest.
SIMPLICIO. But what if we should place the larger stone upon the
smaller?
SALVIATI. Its weight would be increased if the larger stone moved
more rapidly; but we have already concluded that when the small stone
moves more slowly it retards to some extent the speed of the larger, so
that the combination of the two, which is a heavier body than^the larger
of the two stones, would move less rapidly, a conclusion which is contrary
to your hypothesis. We infer therefore that large and small bodies move
with the same speed provided they are of the same specific gravity.
SIMPLICIO. Your discussion is really admirable; yet I do not find it
easy to believe that a bird shot falls as swiftly as a cannon ball.
SALVIATI. Why not say a grain of sand as rapidly as a grindstone?
But, Simplicio, I trust you will not follow the example of many others
who divert the discussion from its main intent and fasten upon some
statement of mine which lacks a hairsbreadth of the truth and, under this
hair, hide the fault of another which is as big as a ship's cable, Aristotle
says' that "an iron ball of one hundred pounds falling from a height of
one hundred cubits reaches the ground before a one-pound ball has fallen
a single cubit." I say that they arrive at the same time. You find, on
making the experiment, that the larger outstrips the smaller by two finger-
breadths, that is, when the larger has reached the ground, the other is
short of it by two fingcrbrcadths; now you would not hide behind these
two fingers the ninety-nine cubits of Aristotle, nor would you mention
my small error and at the same time pass over in silence his very large
one. Aristotle declares that bodies of different weights, in the same
medium, travel (in so far as their motion depends upon gravity) with
speeds which are proportional to their weights; this he illustrates by use
of bodies in which it is possible to perceive the pure and unadulterated
effect of gravity, eliminating other considerations, for example, figure, as
being of small importance, influences which arc greatly dependent upon
the medium which modifies the single effect of gravity alone. Thus we
observe that gold, the densest of all substances, when beaten out into a
very thin leaf, goes floating through the air; the same thing happens with
stone when ground into a very fine powder. But if you wisjh to maintain
the general proposition you will have to show that the same ratio of
speeds is preserved in the case of all heavy bodies, and that a stone of
twenty pounds moves ten times as rapidly as one of two; but I claim that
this is false and that, if they fall from a height of fifty or a hundred cubits,
they will reach the earth at the same moment.
SIMPLICIO. Perhaps the result would be different if the fall took place
not from a few cubits but from some thousands of cubits.
SALVIATI. If this were what Aristotle meant you would burden him
with another error which would amount to a falsehood; because, since
there is no such sheer height available on earth, it is clear that Aristotle
could not have made the experiment; yet he wishes to give us the impres-
GALILEO — DIALOGUES 97
sion of his having performed it when he speaks of such an effect as one
which we see.
SIMPLICIO. In fact, Aristotle does not employ this principle, but uses
the other one which is not, I believe, subject to these same difficulties.
SALVIATI. But the one is as false as the other; and I am surprised that
you yourself do not see the fallacy and that you do not perceive that if it
were true that, in media of different densities and different resistancesy
such as water and air, one and the same body moved in air more rapidly
than in water, in proportion as the density of water is greater than that
of air, then it would follow that any body which falls through air ought
also to fall through water. But this conclusion is false inasmuch as many
bodies which descend in air not only do not descend in water, but actually
rise.
SIMPLICIO. I do not understand the necessity of your inference; and
in addition I will say that Aristotle discusses only those bodies which
fall in both media, not those which fall in air but rise in water.
SALVIATI. The arguments which you advance for the Philosopher are
such as he himself would have certainly avoided so as not to aggravate
his first mistake. But tell me now whether the density of the water, or
whatever it may be that retards the motion, bears a definite ratio to the
density of air which is less retardative; and if so fix a value for it at your
pleasure. *
SIMPLICIO. Such a ratio does exist; let us assume it to be ten; then,
for a body which falls in both these media, the speed in water will be
ten times slower than in air.
SALVIATI, I shall now take one of those bodies which fall in air but
not in water, say a wooden ball, and I shall ask you to assign to it any
speed you please for its descent through air.
SIMPLICIO. Let us suppose it moves with a speed of twenty.
SALVIATI. Very well. Then it is clear that this speed bears to some
smaller speed the same ratio as the density of water bears to that of air;,
and the value of this smaller speed is two. So that really if we follow
exactly the assumption of Aristotle we ought to infer that the wooden
ball which falls in air, a substance ten times less-resisting than water, with
a speed of twenty would fall in water with a speed of two, instead of
coming to the surface from the bottom as it does; unless perhaps you wish
to reply, which I do not believe you will, that the rising of the wood
through the water is the same as its falling with a speed of two. But
since the wooden ball does not go to the bottom, I think you will agree
with me that we can find a ball of another material, not wood, which
does fall in water with a speed of two.
SIMPLICIO. Undoubtedly we can; but it must be of a substance con-
siderably heavier than wood.
SALVIATI. That is it exactly. But if this second ball falls in water with
a speed of two, what will be its speed of descent in air? If you hold to
the rule of Aristotle you must reply that it will move at the rate o£
twenty; but twenty is the speed which you yourself have already assigned
98 MASTERWORKS OF SCIENCE ______
to the wooden ball; hence this and the other heavier ball will each move
through air with the same speed. But now how does the Philosopher
harmonize this result with his other, namely, that bodies of different
weight move through the same medium with different speeds — speeds
which are proportional to their weights? But without going into the
matter more deeply, how have these common and obvious properties
escaped your notice? Have you not observed that two bodies which fall
in water, one with a speed a hundred times as great as that of the other,
will fall in air with speeds so nearly equal that one will not surpass the
other by as much as one hundredth part? Thus, for example, an egg made
of marble will descend in water one hundred times more rapidly than a
hen's egg, while in air falling from a height of twenty cubits the one will
fall short of the other by less than four fingerbreadths. In short, a heavy
body which sinks through ten cubits of water in three hours will traverse
ten cubits of air in one or two pulse beats; and if the heavy body be a ball
of lead it will easily traverse the ten cubits of: water in less than double
the time required for ten cubits of air. And here, I am sure, Simplicio,
you find no ground for difference or objection. We conclude, therefore,
that the argument does not bear against the existence of a vacuum; but
if it did, it would only do away with vacua of considerable size which
neither I nor, in my opinion, the ancients ever believed to exist in nature,,
although they might possibly be produced by force as may be gathered
from various experiments whose description would here occupy too much
time.
SAGREDO. Seeing that Simplicio is silent, I will take the opportunity
of saying something. Since you have clearly demonstrated that bodies of
different weights do not move in one and the same medium with veloci-
ties proportional to their weights, but that they all move with the same
speed, understanding of course that they are of the same substance or at
least of the same specific gravity; certainly not of different specific gravi-
ties, for I hardly think you would have us believe a ball of cork moves
with the same speed as one of lead; and again since you have clearly
demonstrated that one and the same body moving through differently
resisting media does not acquire speeds which are inversely proportional
to the resistances, I am curious to learn what are the ratios actually ob-
served in these cases.
SALVIATI. These are interesting questions and I have thought much
concerning them, I will give you the method of approach and the result
which I finally reached. Having once established the falsity of the propo-
sition that one and the same body moving through differently resisting
media acquires speeds which arc inversely proportional to the resistances
of these media, and having also disproved the statement that in the same
medium bodies of different weight acquire velocities proportional to their
weights (understanding that this applies also to bodies which differ
merely in specific gravity), I then began to combine these two facts and
to consider what would happen if bodies of different weight were placed
in media of different resistances; and I found that the differences m speed
GALILEO — DIALOGUES 99
were greater in those media which were more resistant, that is, less yield-
ing. This difference was such that two bodies which differed scarcely at
all in their speed through air would, in water, fall the one with a speed
ten times as great as that of the other. Further, there are bodies which
will fall rapidly in air, whereas if placed in water not only will not sink
but will remain at rest or will even rise to the top: for it is possible to find
some kinds of wood, such as knots and roots, which remain at rest in
water but fall rapidly in air.
SAGREDO. I have often tried with the utmost patience to add grains
of sand to a ball of wax until it should acquire the same specific gravity
as water and would therefore remain at rest in this medium. But with all
my care I was never able to accomplish this. Indeed, I do not know
whether there is any solid substance whose specific gravity is, by nature,,
so nearly equal to that of water that if placed anywhere in water it will
remain at rest.
SALVIATI. In this, as in a thousand other operations, men are surpassed
by animals. In this problem of yours one may learn much from the fish
which are very skillful in maintaining their equilibrium not only in one
kind of water, but also in waters which are notably different either by
their own nature or by some accidental muddiness or through salinity ,
each of which produces a marked change. So perfectly indeed can fish
keep their equilibrium that they are able to remain motionless in any
position. This they accomplish, I believe, by means of an apparatus espe-
cially provided by nature, namely, a bladder located in the body and com-
municating with the mouth by means of a narrow tube through which
they are able, at will, to expel a portion of the air contained in the bladder:
by rising to the surface they can take in more air; thus they make them-
selves heavier or lighter than water at will and maintain equilibrium.
SAGREDO. By means of another device I was able to deceive some
friends to whom I had boasted that I could make up a ball of wax that
would be in equilibrium in water. In the bottom of a vessel I placed some
salt water and upon this some fresh water; then I showed them that the
ball stopped in the middle of the water, and that, when pushed to the
bottom or lifted to the top, it would not remain in either of these places
but would return to the middle.
SALVIATI. This experiment is not without usefulness. For when phy-
sicians are testing the various qualities of waters, especially their specific
gravities, they employ a ball of this kind so adjusted that, in certain water,
it will neither rise nor fall. Then in testing another water, differing ever
so slightly in specific gravity, the ball will sink if this water be lighter
and rise if it be heavier. And so exact is this experiment that the addition
of two grains of salt to six pounds of water is sufficient to make the ball
rise to the surface from the bottom to which it had fallen. To illustrate
the precision of this experiment and also to clearly demonstrate the non-
resistance of water to division, I wish to add that this notable difference
in specific gravity can be produced not only by solution of some heavier
substance, but also by merely heating or cooling; and so sensitive is water
to this process that by simply adding four drops of another water which
is slightly warmer or cooler than the six pounds one can cause the ball to
•sink or rise; it will sink when the warm water is poured in and will rise
upon the addition of cold water. Now you can see how mistaken are those
philosophers who ascribe to water viscosity or some other coherence of
parts which oilers resistance to separation of parts and to penetration.
SAGREDO. With regard to this question I have found many convincing
arguments in a treatise by our Academician; but there is one great diffi-
culty of which I have not been able to rid myself, namely, if there be no
tenacity or coherence between the particles of water how is it possible for
those large drops of water to stand out in relief upon cabbage leaves with-
out scattering or spreading out?
SALVIATI. Although those who are in possession of the truth are able
to solve all objections raised, I would not arrogate to myself such power;
nevertheless my inability should not be allowed to becloud the truth. To
begin with let me confess that I do not understand how these large
globules of water stand out and hold themselves up, although I know for
a certainty that it is not owing to any internal tenacity acting between
the particles of water; whence it must follow that the cause of this effect
is external Beside the experiments already shown to prove that the cause
is not internal, I can offer another which is very convincing. If the
particles of water which sustain themselves in a heap, while surrounded
by air, did so in virtue of an internal cause then they would sustain
themselves much more easily when surrounded by a medium in which
they exhibit less tendency to fall than they clo in air; such a medium
would be any fluid heavier than air, as, for instance, wine: and therefore if
some wine be poured about such a drop of water, the wine might rise
until the drop was entirely covered, without the particles of water, held
together by this internal coherence, ever parting company. But this is
not the fact; for as soon as the wine touches the water, the latter without
waiting to be covered scatters and spreads out underneath the wine if it
be red. The cause of this effect is therefore external and is possibly to be
found in the surrounding air. Indeed there appears to be a considerable
antagonism between air and water as I have observed in the following
experiment. liaving taken a glass globe which had a mouth of about the
same diameter as a straw, I filled it with water and turned it mouth down-
wards; nevertheless, the water, although quite heavy and prone to descend,
and the air, which is very light and disposed to rise through the water,
refused, the one to descend and the other to ascend through the opening,
but both remained stubborn and defiant- On the other hand, as soon as
I apply to this opening a glass of red wine, which is almost inappreciably
lighter than water, red streaks are immediately observed to ascend slowly
through the water while the water with equal slowness descends through.
the wine without mixing, until finally the globe is completely filled with
wine and the water has all gone down into the vessel below. What thea
can we say except that there exists, between water and air, a certain in-
compatibility which I do not understand, but perhaps * . »
GALILEO — DIALOGUES 101
SIMPLICIO. I feel almost like laughing at the great antipathy which
Salviati exhibits against the use of the word antipathy; and yet it is
excellently adapted to explain the difficulty.
SALVIATI. All right, if it please Simplicio, let this word antipathy be
the solution of our difficulty. Returning from this digression, let us again
take up our problem. We have already seen that the difference of speed
between bodies of different specific gravities is most marked in those
media which are the most resistant: thus, in a medium of quicksilver,
gold not merely sinks to the bottom more rapidly than lead but it is the
only substance that will descend at all; all other metals and stones rise
to the surface and float. On the other hand the variation of speed in air
between balls of gold, lead, copper, porphyry, and other heavy materials
is so slight that in a fall of 100 cubits a ball of gold would surely not out-
strip one of copper by as much as four fingers. Having observed this I
came to the conclusion that in a medium totally devoid of resistance all
bodies would fall with the same speed.
SIMPLICIO. This is a remarkable statement, Salviati. But I shall never
believe that even in a vacuum, if motion in such a place were possible,
a lock of wool and a bit of lead can fall with the same velocity.
SALVIATI. A little more slowly, Simplicio. Your difficulty is not so
recondite nor am I so imprudent as to warrant you in believing that I
have not already considered this matter and found the proper solution.
Hence for my justification and for your enlightenment hear what I have
to say. Our problem is to find out what happens to bodies of different
weight moving in a medium devoid of resistance, so that the only differ-
ence in speed is that which arises from inequality of weight. Since no
medium except one entirely free from air and other bodies, be it ever so
tenuous and yielding, can furnish our senses with the evidence we are
looking for, and since such a medium is not available, we shall observe
what happens in the rarest and least resistant media as compared with
what happens in denser and more resistant media. Because if we find as
a fact that the variation 'of speed among bodies of different specific gravi-
ties is less and less according as the medium becomes more and more
yielding, and if finally in a medium of extreme tenuity, though not a per-
fect vacuum, we find that, in spite of great diversity of specific gravity,
the difference in speed is very small and almost inappreciable, then we are
justified in believing it highly probable that in a vacuum all bodies would
fall with the same speed. Let us, in view of this, consider what takes
place in air, where for the sake of a definite figure and light material
imagine an inflated bladder. The air in this bladder when surrounded
by air will weigh little or nothing, since it can be only slightly com-
pressed; its weight then is small being merely that of the skin which does
not amount to the thousandth part of a mass of lead having the same size
as the inflated bladder. Now, Simplicio, if we allow these two bodies to
fall from a height of four or six cubits, by what distance do you imagine
the lead will anticipate the bladder? You may be sure that the lead will
102 MAS ^ gJRW^RK S O F S C I E N C E
not travel three times, or even twice, as swiftly as the bladder, although
you would have made it move a thousand times as rapidly.
SIMPLICIO. It may be as you say during the first four or six cubits of
the fall; but after the motion has continued a long while, I believe that
the lead will have left the bladder behind not only six out of twelve parts
of the distance but even eight or ten.
SALVIATI. I quite agree with you and doubt not that, in very long dis-
tances, the lead might cover one hundred miles while the bladder was
traversing one; but, my clear Simplicio, this phenomenon which you
adduce against my proposition is precisely the one which confirms it
Let me once more explain that the variation of speed observed in bodies
of different specific gravities is not caused by the difference of specific
gravity but depends upon external circumstances and, in particular, upon
the resistance of the medium, so that if this is removed all bodies would
fall with the same velocity; and this result I deduce mainly from the fact
which you have just admitted and which Is very true, namely, that, in the
case of bodies which differ widely in weight, their velocities differ more
and more as the spaces traversed increase, something which would not
occur if the effect depended upon differences of specific gravity. For since
these specific gravities remain constant, the ratio between the distances
traversed ought to remain constant whereas the fact is that this ratio keeps
on increasing as the motion continues. Thus a very heavy body in a fall
of one cubit will not anticipate a very light one by so much as the tenth
part of this space; but in a fall of twelve cubits the heavy body would
outstrip the other by one-third, and in a fall of one hundred cubits by
90/100, etc.
SIMPLICIO. Very well: but, following your own line of argument, if
differences of weight in bodies of different specific gravities cannot pro-
duce a change in the ratio of their speeds, on the ground that their specific
gravities do not change, how is it possible for the medium, which also we
suppose to remain constant, to bring about any change in the ratio of
these velocities?
SALVIATL This objection with which you oppose my statement is
clever; and I must meet it. I begin by saying that a heavy body has an
inherent tendency to move with a constantly and uniformly accelerated
motion toward the common center of gravity, that is, toward the center
of our earth, so that during equal intervals of time it receives equal incre-
ments of momentum and velocity. This, you must understand, holds
whenever all external and accidental hindrances have been removed; but
of these there is one which we can never remove, namely, the medium
which must be penetrated and thrust* aside by the falling body. This
quiet, yielding, fluid medium opposes motion through it with a resistance
which is proportional to the rapidity with which the medium must give
way to the pasi>age of the body; which body, as I have said, is by nature
continuously accelerated so that it meets with more and more resistance
in the medium and hence a diminution in its rate of gain of speed until
finally the speed reaches such a point and the resistance of the medium
GALILEO — DIALOGUES 103
becomes so great that, balancing each other, they prevent any further
acceleration and reduce the motion of the body to one which is uniform
and which will thereafter maintain a constant value. There is, therefore,
an increase in the resistance of the medium, not on account of any change
in its essential properties, but on account of the change in rapidity with
which it must yield and give way laterally to the passage of the falling
body which is being constantly accelerated.
Now seeing how great is the resistance which the air offers to the
slight momentum of the bladder and how small that which it offers to
the large weight of the lead, I am convinced that, if the medium were
entirely removed, the advantage received by the bladder would be so
great and that coming to the lead so small that their speeds would be
equalized. Assuming this principle, that all falling bodies acquire equal
speeds in a medium which, on account of a vacuum or something else,
offers no resistance to the speed of the motion, we shall be able accord-
ingly to determine the ratios of the speeds of both similar and dissimilar
bodies moving either through one and the same medium or through dif-
ferent space-filling, and therefore resistant, media. This result we may
obtain by observing how much the weight of the medium detracts from
the weight of the moving body, which weight is the means employed by
the falling body to open a path for itself and to push aside the parts of
the medium, something which does not happen in a vacuum where,
therefore, no difference [of speed] is to be expected from a difference
of specific gravity. And since it "is known that the effect of the medium
is to diminish the weight of the body by the weight of the medium dis-
placed, we may accomplish our purpose by diminishing in just this pro-
portion the speeds of the falling bodies, which in a non-resisting medium
we have assumed to be equal.
Thus, for example, imagine lead to be ten thousand times as heavy
as air while ebony is only one thousand times as heavy. Here we have two
substances whose speeds of fall in a medium devoid of resistance are
equal: but, when air is the medium, it will subtract from the speed of the
lead one part in ten thousand, and from the speed of the ebony one part
in one thousand, i. e. ten parts in ten thousand. While therefore lead
and ebony would fall from any given height in the same interval of time,
provided the retarding effect of the air were removed, the lead will, in
air, lose in speed one part in ten thousand; and the ebony, ten parts in
ten thousand. In other words, if the elevation from which the bodies
start be divided into ten thousand parts, the lead will reach the ground
leaving the ebony behind by as much as ten, or at least nine, of these
parts. Is it not clear then that a leaden ball allowed to fall from a tower
two hundred cubits high will outstrip an ebony ball by less than four
inches? Now ebony weighs a thousand times as much as air but this
inflated bladder only four times as much; therefore air diminishes the
inherent and natural speed of ebony by one part in a thousand; while
that" of the bladder which, if free from hindrance, would be the same,
experiences a diminution in air amounting to one part in four. So that
104 MASTERWORKS OF SCIENCE
when the ebony ball, falling from the tower, has reached the earth, the
bladder will have traversed only three-quarters of this distance. Lead is
twelve times as heavy as water; but ivory is only twice as heavy. The
speeds of these two substances which, when entirely unhindered, are
equal will be diminished in water, that of lead by one part in twelve, that
of ivory by half. Accordingly when the lead has fallen through eleven
cubits of water the ivory will have fallen through only six. Employing
this principle we shall, I believe, find a much closer agreement of experi-
ment with our computation than with that of Aristotle.
In a similar manner we may find the ratio of the speeds of one and
the same body in different fluid media, not by comparing the different
resistances of the media, but by considering the excess of the specific
gravity of the body above those of the media. Thus., for example, tin is
one thousand times heavier than air and ten times heavier than water;
hence, if we divide its unhindered speed into 1000 parts, air will rob it
of one of these parts so that it will fall with a speed of 999, while in
water its speed will be 900, seeing that water diminishes its weight by
one part in ten while air by only one part in a thousand.
Again take a solid a little heavier than water, such as oak, a ball of
which will weigh let us say 1000 drachms; suppose an equal volume of
water to weigh 950, and an equal volume of air, 2; then it is clear that
if the unhindered speed of the ball is 1000, its speed in air will be 998,
but in water only 50, seeing that the water removes 950 of the 1000 parts
which the body weighs, leaving only 50.
Such a solid would therefore move almost twenty times as fast in air
as in water, since its specific gravity exceeds that of water by one part in
twenty. And here we must consider the fact that only those substances
which have a specific gravity greater than water can fall through it — sub-
stances which must, therefore, be hundreds of times heavier than air;
hence when we try to obtain the ratio of the speed in air to that in water,
we may, without appreciable error, assume that air does not, to any con-
siderable extent, diminish the free weight and consequently the unhin-
dered speed of such substances, Having thus easily found the excess of
the weight of these substances over that of water, we can say that their
speed in air is to their speed in water as their free weight is to the excess
of this weight over that of water. For example, a ball of ivory weighs 20
ounces; an equal volume of water weighs 17 ounces; hence the speed of
ivory in air bears to its speed in water the approximate ratio of 20:3.
SAGREDQ. I have made a great step forward in this truly interesting
subject upon which I have long labored in vain. In order to put these
theories into practice we need only discover a method of determining
the specific gravity of air with reference to water and hence with reference
to other heavy substances.
SIMPLICIO. But if we find that air has levity instead of gravity what
then shall we say of the foregoing discussion which, in other respects, is
very clever?
SALVIATI. I should say that it was empty, vain, and trifling. But can
GALILEO — DIALOGUES 105
you doubt that air has weight when you have the clear testimony of
Aristotle^ affirming that all the elements have weight including air, and
excepting only fire? As evidence of this he cites the fact that a leather
bottle weighs more when inflated than when collapsed.
SIMPLICIO. I am inclined to believe that the increase of weight ob-
served in the inflated leather bottle or bladder arises, not from the gravity
of the air, but from the many thick vapors mingled with it in these lower
regions. To this I would attribute the increase of weight in the leather
bottle.
SALVIATI. I would not have you say this, ,and much less attribute it
to Aristotle; because, if speaking of the elements, he wished to persuade
me by experiment that air has weight and were to say to me: "Take a
leather bottle, fill it with heavy vapors and observe how its weight in-
creases/- I would reply that the bottle would weigh still more if filled
with -bran; and would then add that this merely proves that bran and
thick vapors are heavy, but in regard to air I should still remain in the
same doubt as before. However, the experiment of Aristotle is good and
the proposition is true. But I cannot say as much of a certain other con-
sideration, taken at face value; this consideration was offered by a philoso-
pher whose name slips me; but I know I have read his argument which
is that air exhibits greater gravity than levity, because it carries heavy
bodies downward more easily than it does light ones upward.
SAGREDO. Fine indeed! So according to this theory air is much heavier
than water, since all heavy bodies are carried downward more easily
through air than through water, and all light bodies buoyed up more
easily through water than through air; further there is an infinite number
of heavy bodies which fall through air but ascend in water and there is
an infinite number of substances which rise in water and fall in air. But,
Simplicio, the question as to whether the weight of the leather bottle is
owing to thick vapors or to pure air does not affect our problem which
is to discover how bodies move through this vapor-laden atmosphere of
ours. Returning now to the question which interests me more, I should
like, for the sake of more complete and thorough knowledge of this mat-
ter, not only to be strengthened in my belief that air has weight but also
to learn, if possible, how great its specific gravity is. Therefore, Salviati,
if you can satisfy my curiosity on this point pray do so.
SALVIATI. The experiment with the inflated leather bottle of Aristotle
proves conclusively that air possesses positive gravity and not, as some
have believed, levity, a property possessed possibly by no substance what-
ever; for if air did possess this quality of absolute and positive levity, it
should on compression exhibit greater levity and, hence, a greater tend-
ency to rise; but experiment shows precisely the opposite.
As to the other question, namely, how to determine the specific
gravity of air, I have employed the following method. I took a rather
large glass bottle with a narrow neck and attached to it a leather cover,
binding it tightly about the neck of the bottle: in the top of this cover
I inserted and firmly fastened the valve of a leather bottle, through which
106 MASTERWORKS OF SCIENCE
I forced into the glass bottle, by means of a syringe, a large quantity of
air. And since air is easily condensed one can pump into the bottle two
or three times its own volume of air. After this I took an accurate balance
and weighed this bottle of compressed air with the utmost precision,
adjusting the weight with fine sand. I next opened the valve and allowed
the compressed air to escape; then replaced the flask upon the balance
and found it perceptibly lighter: from the sand which had been used as
a counterweight I now removed and laid aside as much as was necessary
to again secure balance. Under these conditions there can be no doubt
but that the weight of the sand thus laid aside represents the weight of
the air which had been forced into the flask and had afterwards escaped.
But after all this experiment tells me merely that the weight of the com-
pressed air is the same as that of the sand removed from the balance;
when however it comes to knowing certainly and definitely the weight of
air as compared with that of water or any other heavy substance this I
cannot hope to do without first measuring the volume of compressed air;
for this measurement 1 have devised the two following methods.
According to the first method one takes a bottle with a narrow neck
similar to the previous one; over the mouth of this bottle is slipped a
leather tube which is bound tightly about the neck of the ila.sk; the other
end of this tube embraces the valve attached to the first flask and is
tightly bound about it. This second flask is provided with a hole in the
bottom through which an iron rod can be placed so as to open, at will,
the valve above mentioned and thus permit the surplus air of the first
to escape after it has once been weighed: but this second bottle must be
filled with water. Having prepared everything in the manner above de-
scribed, open the valve with the rod; the air will rush into the flask con-
taining the water and will drive it through the hole at the bottom, it
being clear that the volume of water thus displaced is equal to the volume
of air escaped from the other vessel. Having set aside this displaced
water, weigh the vessel from which the air has escaped (which is sup-
posed to have been weighed previously while containing the compressed
air), and remove the surplus of sand as described above; it is then mani-
fest that the weight of this sand is precisely the weight of a volume of air
equal to the volume of water displaced and set aside; this water we can
weigh and find how many times its weight contains the weight of the
removed sand, thus determining definitely how many times heavier water
is than air; and we shall find, contrary to the opinion of Aristotle, that
this is not 10 times, but, as our experiment shows, more nearly 400 times*
The second method is more expeditious and can be carried out with
a single vessel fitted up as the first was. Here no air is added to that
which the vessel naturally contains but water is forced into it without
allowing any^ air to escape; the water thus introduced necessarily com-
presses the air. Having forced into the vessel as much water as possible,
filling it, say, three-fourths full, which does not require any extraordinary
effort, place it upon the balance and weigh it accurately; next hold the
vessel mouth up, open the valve, and allow the air to escape; the volume
GALILEO — DIALOGUES 107
of the air thus escaping is precisely equal to the volume of water con-
tained in the flask. Again weigh the vessel which will have diminished
in weight on account of the escaped air; this loss in weight represents
the weight of a volume of air equal to the volume of water contained
in the vessel.
SIMPLICIO. No one can deny the cleverness and ingenuity of your
devices; but while they appear to give complete intellectual satisfaction
they confuse me in another direction. For since it is undoubtedly true
that the elements when in their proper places have neither weight nor
levity, I cannot understand how it is possible for that portion of air,
which appeared to weigh, say, 4 drachms of sand, should really have such
a weight in air as the sand which counterbalances it. It seems to me,
therefore, that the experiment should be carried out, not in air, but in a
medium in which the air could exhibit its property of weight if such it
really has.
SALVIATI. The objection of Simplicio is certainly to the point and
must therefore either be unanswerable or demand an equally clear solu-
tion. It is perfectly evident that that air which, under compression,
weighed as much as the sand, loses this weight when once allowed to
escape into its own element, while, indeed, the sand retains its weight.
Hence for this experiment it becomes necessary to select a place where
air as well as sand can gravitate; because, as has been often remarked, the
medium diminishes the weight of any substance immersed in it by an
amount equal to the weight of the displaced medium; so that air in air
loses all its weight. If therefore this experiment is to be made with accu-
racy it should be performed in a vacuum where every heavy body exhibits
its momentum without the slightest diminution. If then, Simplicio, we
were to weigh a portion of air in a vacuum would you then be satisfied
and assured of the fact?
SIMPLICIO. Yes truly: but this is to wish or ask the impossible.
SALVIATI. Your obligation will then be very great if, for your sake,
I accomplish the impossible. But I do not want to sell you something
which I have already given you; for in the previous experiment we
weighed the air in vacuum and not in air or other medium. The fact that
any fluid medium diminishes the weight of the mass immersed in it is
due, Simplicio, to the resistance which this medium offers to its being
opened up, driven aside, and finally lifted up. The evidence for this is
seen in the readiness with which the fluid rushes to fill up any space
formerly occupied by the mass; if the medium were not affected by such
an immersion then it would not react against the immersed body. Tell
me now, when you have a flask, in air, filled with its natural amount of
air and then proceed to pump into the vessel more air, does this extra
charge in any way separate or divide or change the circumambient air?
Does the vessel perhaps expand so that the surrounding medium is dis-
placed in order to give more room? Certainly not. Therefore one is able
to say that this extra charge of air is not immersed in the surrounding
medium for it occupies no space in it, but is, as it were, in a vacuum.
108 MASTERWQRKS OF SCIENCE
Indeed, it is really in a vacuum; for it diffuses into the vacuities which
are not completely filled by the original and uncondensed air. In fact I
do not see any difference between the enclosed and the surrounding
media: for the surrounding medium does not press upon the enclosed
medium and, vice versa, the enclosed medium exerts no pressure against
the surrounding one; this same relationship exists in the case of any
matter in a vacuum, as well as in the case of the extra charge of air com-
pressed into the flask. The weight of this condensed air is therefore the
same as that which it would have set free in a vacuum. It is true oi course
that the weight of the sancl used as a counterpoise would be a little
greater in vacua than in free air. We must, then, say that the air is slightly
lighter than the sancl required to counterbalance it, that is to say, by an
amount equal to the weight in vacuo of a volume of air equal to the
volume of the sand.
SIMFLICIO. The previous experiments, in my opinion, left something
to be desired: but now I am fully satisfied.
SALVIATI. The facts set forth by me up to this point and, in particu-
lar, the one which shows that difference of weight, even when very great,
is without eflect in changing the speed of falling bodies, so that as far
as weight is concerned they all fall with equal speed: this idea is, I say,
so new, and at first glance so remote from fact, that if we do not have
the means of making it just as clear as sunlight, it had better not be
mentioned; but having once allowed it to pass my lips I must neglect no
experiment or argument to establish it.
SAGREDO, Not only this but also many other of your views are so far
removed from the commonly accepted opinions and doctrines that if you
were to publish them you would stir up a large number of antagonists;
for human nature is such that men do not look with favor upon discov-
eries— either of truth or fallacy — in their own field, when made by others
than themselves. They call him an innovator of doctrine, an unpleasant
title, by which they hope to cut those knots which they cannot untie,
and by subterranean mines they seek to destroy structures which patient
artisans have built with customary tools. But as for ourselves who have
no such thoughts, the experiments and arguments which you have thus
far adduced are fully satisfactory; however if you have any experiments
which are more direct or any arguments which are more convincing we
will hear them with pleasure.
SALVIATI. The experiment made to ascertain whether two bodies,
differing greatly in weight, will fall from a given height with the same
speed offers some difficulty; because, if the height is considerable, the
retarding effect of the medium, which must be penetrated and thrust
aside by the falling body, will be greater in the case of the small momen-
tum of the very light body than in the case of the great force of the
heavy body; so that, in a long distance, the light body will be left behind;
if the height be small, one may well doubt whether there is any differ-
ence; and if there be a difference it will be inappreciable.
It occurred to me therefore to repeat many times the fall through
GALILEO — DIALOGUES 109
a small height in such a way that I might accumulate all those small inter-
vals of time that elapse between the arrival of the heavy and light bodies
respectively at their common terminus, so that this sum makes an inter-
val of time which is not only observable, but easily observable. In order
to employ the slowest speeds possible and thus reduce the change which
the resisting medium produces upon the simple effect of gravity it oc-
curred to me to allow the bodies to fall along a plane slightly inclined
to the horizontal. For in such a plane, just as well as in a vertical plane,
one may discover how bodies of different weight behave: and besides
this, I also wished to rid myself of the resistance which might arise from
contact of the moving body with the aforesaid inclined plane. Accord-
ingly I took two balls, one of lead and one of cork, the former more than
a hundred times heavier than the latter, and suspended them by means
of two equal fine threads, each four or five cubits long. Pulling each ball
aside from the perpendicular, I let them go at the same instant, and they,
falling along the circumferences of circles having these equal strings for
semi-diameters, passed beyond the perpendicular and returned along the
same path. This free vibration repeated a hundred times showed clearly
that the heavy body maintains so nearly the period of the light body that
neither in a hundred swings nor even in a thousand will the former
anticipate the latter by as much as a single moment, so perfectly do they
keep step. We can also observe the effect of the medium which, by the
resistance which it offers to motion, diminishes the vibration of the cork
more than that of the lead, but without altering the frequency of either;
even when the arc traversed by the cork did not exceed five or six degrees
while that of the lead was fifty or sixty, the swings were performed in
equal times.
SIMPLICIO. If this be so, why is not the*speed of the lead greater than
that of the cork, seeing that the former traverses sixty degrees in the
same interval in which the latter covers scarcely six?
SALVIATI. But what would you say, Simplicio, if both covered their
paths in the same time when the cork, drawn aside through thirty de-
grees, traverses an arc of sixty, while the lead .pulled aside only two
degrees traverses an arc of four? Would not then the cork be proportion-
ately swifter? And yet such is the experimental fact. But observe this:
having pulled aside the pendulum o£ lead, say through an arc of fifty
degrees, and set it free, it swings beyond the perpendicular almost fifty
degrees, thus describing an arc of nearly one hundred degrees; on the
return swing it describes a little smaller arc; and after a large number
of such vibrations it finally comes to rest. Each vibration, whether of
ninety, fifty, twenty, ten, or four degrees, occupies the same time: accord-
ingly the speed of the moving body keeps on diminishing since in equal
intervals of time it traverses arcs which grow smaller and smaller.
Precisely the same things happen with the pendulum of cork, sus-
pended by a string of equal length, except that a smaller number of vibra-
tions is required to bring it to rest, since on account of its lightness it is
less able to overcome the resistance of the air; nevertheless the vibra-
HO MASTERWORKS OF SCIENCE
tions, whether large or small, are all performed In time-intervals which
are not only equal among themselves, but also equal to the period of the
lead pendulum. Hence it is true that, if while the lead is traversing an
arc of fifty degrees the cork covers one of only ten, the cork moves more
slowly than the lead; but on the other hand it is also true that the cork
may cover an arc of fifty while the lead passes over one of only ten^ or
six; thus, at different times, we have now the cork, now the lead, moving
more rapidly. But if these same bodies traverse equal arcs in equal times
we may rest assured that their speeds are equal.^
SIMPLICIO. I hesitate to admit the conclusiveness of this argument
because of the confusion which arises from your making both bodies
move now rapidly, now slowly and now very slowly, which leaves me in
doubt as to whether their velocities are always equal.
SAGREDO. Allow me, if you please, Salviati, to say just a few words.
Now tell me, Simplicio, whether you admit that one can say with cer-
tainty that the speeds of the cork and the lead are equal whenever both,
starting from rest at the same moment and descending the same slopes,
always traverse equal spaces in equal times?
SIMPLICIO. This can neither be doubted nor gainsaid.
SAGREDO. Now it happens, in the case of the pendulums, that each
o£ them traverses now an arc of sixty degrees, now one of fifty, or thirty
or ten or eight or four or two, etc.; and when they both swing through
an arc of sixty degrees they do so in equal intervals of time; the same
thing happens when the arc is fifty degrees or thirty or ten or any other
number; and therefore we conclude that the speed of the lead in an arc
of sixty degrees is equal to the speed of the cork when the latter also
swings through an arc of sixty degrees; in the case of a fifty-degree arc
these speeds are also equal to %ach other; so also in the case of other arcs.
But this is not saying that the speed which occurs in an arc of sixty is
the same as that which occurs in an arc of fifty; nor is the speed in an
arc of fifty equal to that in one of thirty, etc.; but the smaller the arcs,
the smaller the speeds; the fact observed is that one and the same moving
body requires the same time for traversing a large arc of sixty degrees
as for a small arc of fifty or even a very small arc of ten; all these arcs,
indeed, are covered in the same interval of time. It is true therefore that
the lead and the cork each dimmish their speed in proportion as their
arcs diminish; but this does not contradict the fact that they maintain
equal speeds in equal arcs. *
My reason for saying these things has been rather because I wanted
to learn whether I had correctly understood Salviati, than because I
thought Simplicio had any need of a clearer explanation than that given
by Salviati which like everything else of his is extremely lucid, so lucid,
indeed, that when he solves questions which are difficult not merely in
appearance, but in reality and in fact, he does so with reasons, observa-
tions and experiments which are common and familiar to everyone.
In this manner he has, as I have learned from various sources, given
occasion to a highly esteemed professor for undervaluing his discoveries
GALILEO — DIALOGUES 1H
on the ground that they are commonplace, and established upon a mean
and vulgar basis; as if it were not a most admirable and praiseworthy
feature of demonstrative science that it springs from and grows out of
principles well-known, understood and conceded by all.
But let us continue with this light diet; and if Simplicio is satisfied
to understand and admit that the gravity inherent in various falling
bodies has nothing to do with the difference of speed observed among
them, and that all bodies, in so far as their speeds depend upon it, would
move with the same velocity, pray tell us, Salviati, how you explain the
appreciable and evident inequality of motion; please reply also to the
objection urged by Simplicio — an objection in which I concur — namely,
that a cannon ball falls more rapidly than a bird shot. From my point
of view, one might expect the difference of speed to be small in the case
of bodies of the same substance moving through any single medium,
whereas the larger ones will descend, during a single pulse beat, a dis-
tance which the smaller ones will not traverse in an hour, or in four, or
even in twenty hours; as for instance in the case of stones and fine sand
and especially that very fine sand which produces muddy water and
which in many hours will not fall through as much as two cubits, a dis-
tance which stones not much larger will traverse in a single pulse beat.
SALVIATI. The action of the medium in producing a greater retarda-
tion upon those bodies which have a less specific gravity has already been
explained by showing that they experience a diminution of weight. But
to explain how one and the same medium produces such different retarda-
tions in bodies which are made of the same material and have the same
shape, but differ only in size, requires a discussion more clever than that
by which one explains how a more expanded shape or an opposing motion
of the medium retards the speed of the moving body. The solution of the
present problem lies, I think, in the roughness and porosity which are
generally and almost necessarily found in the surfaces of solid bodies.
When the body is in motion these rough places strike the air or other
ambient medium. The evidence for this is found in the humming which
accompanies the rapid motion of a body through air, even when that
body is as round as possible. One hears not only humming, but also hiss-
ing and whistling, whenever there is any appreciable cavity or elevation
upon the body. We observe also that a round solid body rotating in a
lathe produces a current of air. But what more do we need? When a top
spins on the ground at its greatest speed do we not hear a distinct buzz-
ing of high pitch? This sibilant note diminishes in pitch as the speed of
rotation slackens, which is evidence that these small rugosities on the
surface meet resistance in the air. There can be no doubt, therefore, that
in the motion of falling bodies these rugosities strike" the surrounding
fluid and retard the speed; and this they do so much the more in propor-
tion as the surface is larger, which is the case of small bodies as compared
with greater.
SIMPLICIO. Stop a moment please, I am getting confused. For al-
though I understand and admit that friction of the medium upon the
112 MASTERWQRKS OF SCIENCE
surface of the body retards its motion and that, if other things are the
same, the larger surface suffers greater retardation, I do not see on what
ground you say that the surface of the smaller body is larger. Besides if,
as you say, the larger surface suffers greater retardation the larger solid
should move more slowly, which is not the fact. But this objection can
be easily met by saying that, although the larger body has a larger sur-
face, it has also a greater weight, in comparison with which the resistance
of the larger surface is no more than the resistance of the small surface
in comparison with its smaller weight; so that the speed of the larger
solid does not become less. I therefore see no reason for expecting any
difference of speed so long as the driving weight diminishes in the same
„ proportion as the retarding power of the surface.
SALVIATI. I shall answer all your objections at once. ^ You will admit,
of course, Simplicio, that if one takes two equal bodies, of the same
material and same figure, bodies which would therefore fall with equal
speeds, and if he diminishes the weight of one of them in the same pro-
portion as its surface (maintaining the similarity of shape) he would not
thereby diminish the speed of this body.
SIMPLICIO. This inference seems to be in harmony with your theory
which states that the weight of a body has no effect in cither accelerating
or retarding its motion.
SALVIATI. I quite agree with you in this opinion from which it
appears to- follow that, if the weight of a body is diminished in greater
proportion than its surface, the motion is retarded to a certain extent;
and this retardation is greater and greater in proportion as the diminution
of weight exceeds that of the surface.
SIMPLICIO. This I admit without hesitation.
SALVIATI. Now you must know, Simplicio, that it is not possible to
diminish the surface of a solid body in the same ratio as the weight, and
at the same time maintain similarity of figure. For since it is clear that
in the case of a diminishing solid the weight grows less in proportion
to the volume, and since the volume always diminishes more rapidly than
the surface, when the same shape is maintained, the weight must there-
fore diminish more rapidly than the surface. But geometry teaches us
that, in the case of similar solids, the ratio of two volumes is greater than
the ratio of their surfaces; which, for the sake of better understanding,
I shall illustrate by a particular case.
Take, for example, a cube two inches on a side so that each face has
an area of four square inches and the total area, i. e., the sum of the six
faces, amounts to twenty-four square inches; now imagine this cube to be
sawed through three times so as to divide it into eight smaller cubes,
each one inch on the side, each face one inch square, and the total sur-
face of each cube six square inches instead of twenty-four as in the case
of the larger cube, It is evident therefore that the surface of the little cube
is only one-fourth that of the larger, namely, the ratio of six to twenty-
four; but the volume of the solid cube itself is only one-eighth; the vol-
ume, and hence also the weight, diminishes therefore much more rapidly
GALILEO — DIALOGUES 113
than the surface. If we again divide the little cube into eight others we
shall have, for the total surface of one of these, one and one-half square
inches, which is one-sixteenth of the surface of the original cube; but its
volume is only one-sixty-fourth part. Thus, by two divisions, you see that
the volume is diminished four times as much as the surface. And, if the
subdivision be continued until the original solid be reduced to a fine
powder, we shall find that the weight of one of these smallest particles
has diminished hundreds and hundreds of times as much as its surface.
And this which I have illustrated in the case of cubes holds also in the
case of all similar solids. Observe then how much greater the resistance,
arising from contact of the surface of the moving body with the medium,
in the case of small bodies than in the case of large; and when one con-
siders that the rugosities on the very small surfaces of fine dust particles
are perhaps no smaller than those on the surfaces of larger solids which
have been carefully polished, he will see how important it is that the
medium should be very fluid and offer no resistance to being thrust aside,
easily yielding to a small force. You see, therefore, Simplicio, that I was
not mistaken when, not long ago, I said that the surface of a small solid
is comparatively greater than that of a large one.
SIMPLICIO. I am quite convinced; and, believe me, if I were again
beginning my studies, I should follow the advice of Plato and start with
mathematics, a science which proceeds very cautiously and admits noth-
ing as established until it has been rigidly demonstrated.
SAGREDO, This discussion has afforded me great pleasure. And now
although there are still some details, in connection with the subject under
discussion, concerning which I might ask questions yet, if we keep
making one digression after another, it will be long before we reach the
main topic which has to do with the variety of properties found in the
resistance which solid bodies offer to fracture; and, therefore, if you
please, let us return to the subject which we originally proposed to dis-
cuss.
SALVIATI. Very well; but the questions which we have already con-
sidered are so numerous and so varied, and have taken up so much time,
that there is not much of this day left to spend upon our main topic
which abounds in geometrical demonstrations calling for careful consid-
eration. May I, therefore, suggest that we postpone the meeting until
tomorrow, not only for the reason just mentioned but also in order that
I may bring with me some papers in which I have set down in an orderly
way the theorems and propositions dealing with the various phases of
this subject, matters which, from memory alone, I could not present in
the proper order.
SAGREDO. I fully concur in your opinion and all the more willingly
because this will leave time today to take up some of my difficulties with
the subject which we have just been discussing/One question is whether
we are to consider the resistance of the medium as sufficient to destroy
the acceleration of a body of very heavy material, very large volume, and
spherical figure. I say spherical in order to select a volume which is con-
114 MASTERWORKS OF SCIENCE
tained within a minimum surface and therefore less subject to retarda-
tion.
Another question deals with the vibrations of pendulums which may
be regarded from several viewpoints; the first is whether all vibrations,
large, medium, and small, are performed in exactly and precisely equal
times: another is to find the ratio of the times of vibration of pendulums
supported by threads of unequal length.
SALVIATI. These are interesting questions: but I fear that here, as
in the case of all other facts, if we take up for discussion any one of
them, it will carry in its wake so many other facts and curious conse-
quences that time will not remain today for the discussion of all.
SAGE.EDO. If these arc as full of interest as the foregoing, I would
gladly spend as many clays as there remain hours between now and night-
fall; and I dare say that Simplicio would not be wearied by these discus-
sions,
SIMPLICIO, Certainly not; especially when the questions pertain to
natural science and have not been treated by other philosophers.
SALVIATL Now taking up the first question, I can assert without hesi-
tation that there is no sphere so large, or composed of material so dense,
but that the resistance of the medium, although very slight, would check
its acceleration and would, in time, reduce its motion to uniformity; a
statement which is strongly supported by experiment. For if a falling
body, as time goes on, were to acquire a speed as great as you please, no
such speed, impressed by external forces, can be so great but that the
body will first acquire it and then, owing to the resisting medium, lose
it. Thus, for instance, if a cannon ball, having fallen a distance of four
cubits through the air and having acquired a speed of, say, ten units
were to strike the surface of the water, and if the resistance of the water
were not able to check the momentum of the shot, it would either increase
in speed or maintain a uniform motion until the bottom were reached:
but such is not the observed fact; on the contrary, the water when only
a few cubits deep hinders and diminishes the motion in such a way that
the shot delivers to the bed of the river or lake a very slight impulse.
Clearly then if a short fall through the water is sufficient to deprive a
cannon ball of its speed, this speed cannot be regained by a fall of even
a thousand cubits. How could a body acquire, in a fall of a thousand
cubits, that which it loses in a fall of four? But what more is needed?
Do we not observe that the enormous momentum, delivered to a shot
by a cannon, is so deadened by passing through a few cubits of water that
the ball, so far from injuring the ship, barely strikes it? Even the air,
although a very yielding medium, can also diminish the speed of a falling
body, as may be easily understood from similar experiments. For if a gun
be fired downwards from the top of a very high tower the shot will make
a smaller impression upon the ground than if the gun had been fired
from an elevation of only four or six cubits; this is clear evidence that the
momentum of the ball, fired from the top of the tower, diminishes con-
tinually from the instant it leaves the barrel until it reaches the ground.
GALILEO — DIALOGUES H5
Therefore a fall from ever so great an altitude will not suffice to give to a
body that momentum which it has once lost through the resistance of
the air, no matter how it was originally acquired. In like manner, the
destructive effect produced upon a wall by a shot fired from a gun at a
distance of twenty cubits cannot be duplicated by the fall of the same shot
from any altitude however great. My opinion is, therefore, that under the
circumstances which occur in nature, the acceleration of any body falling
from rest reaches an end and that the resistance of the medium finally
reduces its speed to a constant value which is thereafter maintained.
SAGREDO. These experiments are in my opinion much to the purpose;
the only question is whether an opponent might not make bold to deny
the fact in the case of bodies which are very large and heavy or to assert
that a cannon ball, falling from the distance of the moon or from the
upper regions of the atmosphere, would deliver a heavier blow than if
just leaving the muzzle of the gun.
SALVIATI. No doubt many objections may be raised not all of which
can be refuted by experiment: however in this particular case the follow-
ing consideration must be taken into account, namely, that it is very
likely that a heavy body falling from a height will, on reaching the
ground, have acquired just as much momentum as was necessary to carry
it to that height; as may be clearly seen in the case of a rather heavy
pendulum which, when pulled aside fifty or sixty degrees from the verti-
cal, will acquire precisely that speed and force which are sufficient to
carry it to an equal elevation save only that small portion which it loses
through friction on the air. In order to place a cannon ball at such a height
as might suffice to give it just that momentum which the powder im-
parted to it on leaving the gun we need only fire it vertically upwards
from the same gun; and we can then observe whether on falling back it
delivers a blow equal to that of the gun fired at close range; in my opin-
ion it would be much weaker. The resistance of the air would, therefore,
I think, prevent the muzzle velocity from being equalled by a natural fall
from rest at any height whatsoever.
We come now to the other questions, relating to pendulums, a sub-
ject which may appear to many exceedingly arid, especially to those phi-
losophers who are continually occupied with the more profound ques-
tions of nature. Nevertheless, the problem is one which I do not scorn.
I am encouraged by the example of Aristotle whom I admire especially
because he did not fail to discuss every subject wliich he thought in any
degree worthy of consideration.
Impelled by your queries I may give you some of my ideas concern-
ing certain problems in music, a splendid subject, upoA which so many
eminent men have written: among these is Aristotle himself who has dis-
cussed numerous interesting acoustical questions. Accordingly, if on the
basis of some easy and tangible experiments, I shall explain some striking
phenomena in the domain of sound, I trust my explanations will meet
your approval.
SAGREDO. I shall receive them not only gratefully but eagerly. For,
H6 MASTERWORKS OF SCIENCE
although I take pleasure in every kind of musical instrument and have
paid considerable attention to harmony, I have never been able to fully
understand why some combinations of tones are more pleasing than others,
or why certain combinations not only fail to please but are even highly
offensive. Then there is the old problem of two stretched strings m uni-
son; when one of them is sounded, the other begins to vibrate and to
emit its note; nor do I understand the different ratios of harmony and
some other details.
SALVIATI. Let us see whether we cannot derive from the pendulum
a satisfactory solution of all these difficulties. And first, as to the question
whether one and the same pendulum really performs its vibrations, large,
medium, and small, all in exactly the same time, I shall rely upon what
I have already heard from our Academician. He has clearly shown that
the time of descent is the same along all chords, whatever the_arcs which
subtend them, as well along an arc of 180° (i. e., the whole diameter) as
along one of 100°, 60°, 10°, i°, y2°, or 4'. It is understood, of course, that
these arcs all terminate at the lowest point of the circle, where it touches
the horizontal plane.
If now we consider descent along arcs instead of their chords then,
provided these do not exceed 90°, experiment shows that they are all
traversed in equal times; but these times are greater for the chord than
for the arc, an effect which is all the more remarkable because at first
glance one would think just the opposite to be true. For since the termi-
nal points of the two motions are the same and since the straight line
included between these two points is the shortest distance between
them, it would seem reasonable that motion along this line should be
executed in the shortest time; but this is not the case, for the shortest
time — and therefore the most rapid motion — is that employed along the
arc of which this straight line is the chord.
As to the times of vibration of bodies suspended by threads of differ-
ent lengths, they bear to each other the same proportion as the square
roots of the lengths of the thread; or one might say the lengths are to each
other as the squares of the times; so that if one wishes to make the vibra-
tion time of one pendulum twice that of another, he must make its sus-
pension four times as long. In like manner, if one pendulum has a sus-
pension nine times as long as another, this second pendulum will execute
three vibrations during each one of the first; from which it follows that
the lengths of the suspending cords bear to each other the [inverse] ratio
of the squares of the number of vibrations performed in the same time.
SAGREDQ. Then, if I understand you correctly, I can easily measure
the length of a string whose upper end is attached at any height whatever
even if this end were invisible and I could see only the lower extremity.
For if I attach to the -lower end of this string a rather heavy weight and
give it a to-and-fro motion, and if I ask a friend to count a number of its
vibrations, while I, during the same time-interval, count the number of
vibrations of a pendulum which is exactly one cubit in length, then
knowing the number of vibrations which each pendulum makes in the
GALILEO — DIALOGUES 117
given interval of time one can determine the length of the string. Sup-
pose, for example, that my friend counts 20 vibrations of the long cord
during the same time in which I count 240 of my string which is one
cubit in length; taking the squares of the two numbers, 20 and 240,
namely 400 and 57600, then, I say, the long string contains 57600 units
of such length that my pendulum will contain 400 of them; and since the
length of my string is one cubit, I shall divide 57600 by 400 and thus
obtain 144. Accordingly I shall call the length of the string 144 cubits.
SALVIATI. Nor will you miss it by as much as a handsbreadth, espe-
cially if you observe a large number of vibrations.
SAGREDO. You give me frequent occasion to admire the wealth and
profusion of nature when, from such common and even trivial phenomena,
you derive facts which are not only striking and new but which are often
far removed from what we would have imagined. Thousands of times I
have observed vibrations especially in churches where lamps, suspended
by long cords, had been inadvertently set into motion; but the most which
I could infer from these observations was that the view of those who
think that such vibrations are maintained by the medium is highly im-
probable: for, in that case, the air must needs have considerable judgment
and little else to do but kill time by pushing to and fro a pendent weight
with perfect regularity. But I never dreamed of learning that one and the
same body, when suspended from a string a hundred cubits long and
pulled aside through an arc of 90° or even i° or %°, would employ the
same time in passing through the least as through the largest of these arcs;
and, indeed, it still strikes me as somewhat unlikely. Now I am waiting to
hear how these same simple phenomena can furnish solutions for those
acoustical problems — solutions which will be at least partly satisfactory.
SALVIATI. First of all one must observe that each pendulum has its
own time of vibration so definite and determinate that it is not possible to
make it move with any other period than that which nature has given it.
For let any one take in his hand the cord to which the weight is attached
and try, as much as he pleases, to increase or diminish the frequency of
its vibrations; it will be time wasted. On the other hand, one can confer
motion upon even a heavy pendulum which is at rest by simply blowing
against it; by repeating these blasts with a frequency which is the same as
that of the pendulum one can impart considerable motion. Suppose that
by the first puff we have displaced the pendulum from the vertical by, say,
half an inch; then if, after the pendulum has returned and is about to
begin the second vibration, we add a second puff, we shall impart addi-
tional motion; and so on with other blasts provided they are applied at
the right instant, and not when the pendulum is coming toward us since
in this case the blast would impede rather than aid the motion. Con-
tinuing thus with many impulses we impart to the pendulum such mo-
mentum that a greater impulse than that of a single blast will be needed
to stop it.
SAGREDO. Even as a boy, I observed that one man alone by giving these
impulses at the right instant was able to ring a bell so large that when
118 MASTERWORKS OF SCIENCE
four, or even six, men seized the rope and tried to stop it they were lifted
from the ground, all of them together being unable to counterbalance the
momentum which a single man, by properly timed pulls, had given it.
SALVIATI. Your illustration makes my meaning clear and is quite as
well fitted, as what I have just said, to explain the wonderful phenomenon
of the strings of the cittern or of the spinet, namely, the fact that a vibrat-
ing string will set another string in motion and cause it to sound not only
when the latter is in unison but even when it differs from the former by
an octave or a fifth. A string which has been struck begins to vibrate and
continues the motion as long as one hears the sound; these vibrations
cause the immediately surrounding air to vibrate and quiver; then these
ripples in the air expand far into space and strike not only all the strings
of the same instrument but even those of neighboring instruments. Since
that string which is tuned to unison with the one plucked is capable of
vibrating with the same frequency, it acquires, at the first impulse, a
slight oscillation; after receiving two, three, twenty, or more impulses,
delivered at proper intervals, it finally accumulates a vibratory motion
equal to that of the plucked string, as is clearly shown by equality of
amplitude in their vibrations. This undulation expands through the air
and sets into vibration not only strings, but also any other body which
happens to have the same period as that of the plucked string. Accord-
ingly if we attach to the side of an instrument small pieces of bristle or
other flexible bodies, we shall observe that, when a spinet is sounded, only
those pieces respond that have the same period, as the string which has
been struck; the remaining pieces do not vibrate in response to this string,
nor do the former pieces respond to any other tone.
If one bows the bass string on a viola rather smartly and brings near
it a goblet of fine, thin glass having the same tone as that of the string,
this goblet will vibrate and audibly resound. That the undulations of the
medium are widely dispersed about the sounding body is evinced by the
fact that a glass of water may be made to emit a tone merely by the fric-
tion of the finger tip upon the rim of the glass; for in this water is pro-
duced a series of regular waves. The same phenomenon is observed to
better advantage by fixing the base of the goblet upon the bottom of a
rather large vessel of water filled nearly to the edge of the goblet; for if,
as before, we sound the glass by friction of the finger, we shall see ripples
spreading with the utmost regularity and with high speed to large dis-
tances about the glass. I have often remarked, in thus sounding a rather
large glass nearly full of water, that at first the waves are spaced with
great uniformity, and when, as sometimes happens, the tone of the glass
jumps an octave higher I have noted that at this moment each of the
aforesaid waves divides into two; a phenomenon which shows clearly that
the ratio involved in the octave is two.
SAGREDO. More than once have I observed this same thing, much to
my delight and also to my profit. For a long time I have been perplexed
about these different harmonies since the explanations hitherto given by
those learned in music impress me as not sufficiently conclusive. They tell
GALILEO — DIALOGUES 119
us that the diapason, i. e., the octave, involves the ratio of two, that the
diapente which we call the fifth involves a ratio of 3:2, etc.; because if 'the
open string of a monochord be sounded and afterwards a bridge be placed
in the middle and the half length be sounded one hears the octave; and if
the bridge be placed at 1/3 the length of the string, then on plucking first
the open string and afterwards 2/3 of its length the fifth is given; for this,
reason they say that the octave depends upon the ratio of two to one and
the fifth upon the ratio of three to two. This explanation does not impress,
me as sufficient to establish 2 and 3/2 as the natural ratios of the octave
and the fifth; and my reason for thinking so is as follows. There are three-
different ways in which the tone of a string may be sharpened, namely, by-
shortening it, by stretching it, and by making it thinner. If the tension and
size of the string remain constant one obtains the octave by shortening it.
to one-half, i. e., by sounding first the open string and then one-half of it;
but if length and size remain constant and one attempts to produce the
octave by stretching he will find that it does not suffice to double the-
stretching weight; it must be quadrupled; so that, if the fundamental note
is produced by a weight of one pound, four will be required to bring out
the octave.
And finally if the length and tension remain constant, while one
changes the size of the string he will find that in order to produce the
octave the size must be reduced to 54 that which gave the fundamental-
And what I have said concerning the octave, namely, that its ratio as de-
rived from the tension and size of the string is the square of that derived
from the length, applies equally well to all other musical intervals.
Thus if one wishes to produce a fifth by changing the length he finds
that the ratio of the lengths must be sesquialteral, in other words he
sounds first the open string, then two-thirds of it; but if he wishes to
produce this same result by stretching or thinning the string then it be-
comes necessary to square the ratio 3/2 that is by taking 9/4; accordingly,,
if the fundamental requires a weight of 4 pounds, the higher note will be
produced not by 6, but by 9 pounds; the same is true in regard to size,,
the string which gives the fundamental is larger than that which yields
the fifth in the ratio of 9 to 4.
In view of these facts, I see no reason why those wise philosophers
should adopt 2 rather than 4 as the ratio of the octave, or why in the case
of the fifth they should employ the sesquialteral ratio, 3/2, rather than
that of 9/4. Since it is impossible to count the vibrations of a sounding
string on account of its high frequency, I should still have been in doubt
as to whether a string, emitting the upper octave, made twice as many
vibrations in the same time as one giving the fundamental, had it not
been for the following fact, namely, that at the instant when the tone
jumps to the octave, the waves which constantly accompany the vibrating
glass divide up into smaller ones which are precisely half as long as the
former.
SALVIATI. This is a beautiful experiment enabling us to distinguish
individually the waves which are produced by the vibrations of a sonorous
120 MASTERWORKS OF SCIENCE
body, which spread through the air, bringing to the tympanum of the ear
a stimulus which the mind translates into sound. But since these waves in
the water last only so long as the friction of the finger ^ continues and are,
even then, not constant but are always forming and disappearing, would
it not be a fine thing if one had the ability to produce waves which would
persist for a long while, even months and years, so as to easily measure
and count them?
SAGREDO. Such an invention would, I assure you, command my ad-
miration.
SALVIATI. The device is one which I hit upon by accident; my part
consists merely in the observation of it and in the appreciation of its
value as a confirmation of something to which I had given profound con-
sideration; and yet the device is, in itself, rather common. As I was
scraping a brass plate with a sharp iron chisel in order to remove some
spots from it and was running the chisel rather rapidly over it, I once or
twice, during many strokes, heard the plate emit a rather strong and clear
whistling sound; on looking at the plate more carefully, I noticed a long
row of fine streaks parallel and equidistant from one another. Scraping
with the chisel over and over again, I noticed that it was only when the
plate emitted this hissing noise that any marks were left upon it; when
the scraping was not accompanied by this sibilant note there was not the
least trace of such marks. Repeating the trick several times and making
the stroke, now with greater now with less speed, the whistling followed
with a pitch which was correspondingly higher and lower. I noted also
that the marks made when the tones were higher were closer together;
but when the tones were deeper, they were farther apart. I also observed
that when, during a single stroke, the speed increased toward the end the
sound became sharper and the streaks grew closer together, but always in
such a way as to remain sharply defined and equidistant. Besides when-
ever the stroke was accompanied by hissing I felt the chisel tremble In
my grasp and a sort of shiver run through my hand. In short we see and
hear in the case of the chisel precisely that which is seen and heard in the
case of a whisper followed by a loud voice; for, when the breath is emitted
without the production of a tone, one does not feel either in the throat or
mouth any motion to speak of in comparison with that which is felt in
the larynx and upper part of the throat when the voice is used, especially
when the tones employed are low and strong.
At times I have also observed among the strings of the spinet two
which were in unison with two of the tones produced by the aforesaid
scraping; and among those which differed most in pitch I found two
which were separated by an interval of a perfect fifth. Upon measuring
the distance between the markings produced by the two scrapings it was
found that the space which contained 45 of one contained 30 of the other,
which is precisely the ratio assigned to the fifth.
But now before proceeding any farther I want to call your attention
to the fact that, of the three methods for sharpening a tone, the one which
you refer to as the fineness of the string should be attributed to its weight
GALILEO — DIALOGUES 121
So long as the material of the string is unchanged, the size and weight
vary in the same ratio. Thus in the case of gut strings, we obtain the
octave by making one string 4 times as large as the other; so also in the
case of brass one wire must have 4 times the size of the other; but if now
we wish to obtain the octave of a gut string, by use of brass wire, we
must make it, not four times as large, but four times as heavy as the gut
string: as regards size therefore the metal string is not four times as big
but four times as heavy. The wire may therefore be even thinner than the
gut notwithstanding the fact that the latter gives the higher note. Hence
if two spinets are strung, one with gold wire the other with brass, and if
the corresponding strings each have the same length, diameter, and ten-
sion it follows that the instrument strung with gold will have a pitch
about one-fifth lower than the other because gold has a density almost
twice that of brass. And here it is to be noted that it is the weight rather
than the size of a moving body which offers resistance to change of mo-
tion contrary to what one might at first glance think. For it seems reason-
able to believe that a body which is large and light should suffer greater
retardation of motion in thrusting aside the medium than would one
which is thin and heavy; yet here exactly the opposite is true.
Returning now to the original subject of discussion, I assert that the
ratio of a musical interval is not immediately determined either by the
length, size, or tension of the strings but rather by the ratio of their fre-
quencies, that is, by the number of pulses of air waves which strike the
tympanum of the ear, causing it also to vibrate with the same frequency.
This fact established, we may possibly explain why certain pairs of notes,
differing in pitch, produce a pleasing sensation, others a less pleasant
effect, and still others a disagreeable sensation. Such an explanation would
be tantamount to an explanation of the more or less perfect consonances
and of dissonances. The unpleasant sensation produced by the latter
arises, I think, from the discordant vibrations of two different tones which
strike the ear out of time. Especially harsh is the dissonance between
notes whose frequencies are incommensurable; such a case occurs when
one has two strings in unison and sounds one of them open, together with
a part of the other which bears the same ratio to its whole length as the
side of a square bears to the diagonal; this yields a dissonance similar to
the augmented fourth or diminished fifth.
Agreeable consonances are pairs of tones which strike the ear with a
certain regularity; this regularity consists in the fact that the pulses de-
livered by the two tones, in the same interval of time, shall be commen-
surable in number, so as not to keep the eardrum in perpetual torment,
bending in two different directions in order to yield to the ever-discordant
impulses.
The first and most pleasing consonance is, therefore, the octave since,
for every pulse given to the tympanum by the lower string, the sharp
string delivers two; accordingly at every other vibration of the upper
string both pulses are delivered simultaneously so that one-half the entire
number of pulses are delivered in unison! But when two strings are in
122 MASTERWQRKS OF SCIENCE
unison their vibrations always coincide and the effect is that of a single
string; hence we do not refer to it as consonance. The fifth is also a pleas-
ing interval since for every two vibrations of the lower string the upper
one gives three, so that considering the entire number of pulses from the
upper string one-third of them will strike in unison, i. e., Between each
pair of concordant vibrations there intervene two single vibrations; and
when the interval is a fourth, three single vibrations intervene. In case the
interval is a second where the ratio is 9/8 it is only every ninth vibration
of the upper string which reaches the ear simultaneously with one of the
lower; all the others are discordant and produce a harsh effect upon the
recipient ear which interprets them as dissonances.
SIMPLICIO. Won't you be good enough to explain this argument a
little more clearly?
SALVIATI. Let AB denote the length of a wave emitted by the lower
string and CD that of a higher string which is emitting the octave of AB;
divide AB in the middle at E. If the two strings begin their motions at A
-A .g J3
O
and C, it is clear that when the sharp vibration has reached the end D,
the other vibration will have travelled only as far as E, which, not being a
terminal point, will emit no pulse; but there is a blow delivered at D.
Accordingly when the one wave comes back from D to C, the other passes
on from E to B; hence the two pulses from B and .C strike the drum of
the ear simultaneously. Seeing that these vibrations are repeated again
and again in the same manner, we conclude that each alternate pulse from
CD falls in unison with one from AB. But each of the pulsations at the
terminal points, A and B, is constantly accompanied by one which leaves
always from C or always from D. This is clear because if we suppose the
waves to reach A and C at the same instant, then, while one wave travels
from A to B, the other will proceed from C to D and back to C, so that
waves strike at C and B simultaneously; during the passage of the wave
from B back to A the disturbance at C goes to D and again returns to C,
so that once more the pulses at A and C are simultaneous.
Next let the vibrations AB and CD be separated by an interval of a
fifth, that is, by a ratio of 3/2; choose the points E and O such that they
will divide the wave length of the lower string into three equal parts and
imagine the vibrations to start at the same instant from each of the termi-
nals A and C. It is evident that when the pulse has been delivered at the
GALILEO — DIALOGUES 123
terminal D, the wave in AB has travelled only as far as O; the drum of the
ear receives, therefore, only the pulse from D. Then during the return of
the one vibration from D to C, the other will pass from O to B and then
back to O, producing an isolated pulse at B — a pulse which is out of time
but one which must be taken into consideration.
Now since we have assumed that the first pulsations started from the
terminals A and C at the same instant, it follows that the second pulsa-
tion, isolated at D, occurred after an interval of time equal to that re-
quired for passage from C to D or, what is the same thing, from A to O;
but the next pulsation, the one at B, is separated from the preceding by
only half this interval, namely, the time required for passage from O to B.
Next while the one vibration travels from O to A, the other travels from
C to D, the result of which is that two pulsations occur simultaneously at
A and D. Cycles of this kind follow one after another, i. e., one solitary
pulse of the lower string interposed between two solitary pulses of the
upper string. Let us now imagine time to be divided into very small equal
intervals; then if we assume that, during the first two of these intervals,
the disturbances which occurred simultaneously at A and C have travelled
as far as O and D and have produced a pulse at D; and if we assume that
during the third and fourth intervals one disturbance returns from D to C,
producing a pulse at C, while the other, passing on from O to B and back
to O, produces a pulse at B; and if finally, during the fifth and sixth inter-
vals, the disturbances travel from O and C to A and D, producing a pulse
at each of the latter two, then the sequence in which the pulses strike the
ear will be such that, if we begin to count time from any instant where
two pulses are simultaneous, the eardrum will, after the lapse of two of
the said intervals, receive a solitary pulse; at the end of the third interval,
another solitary pulse; so also at the end of the fourth interval; and two
intervals later, i. e., at the end of the sixth interval, will be heard two
pulses in unison. Here ends the cycle — the anomaly, so to speak — which
repeats itself over and over again.
SAGREDO. I can no longer remain silent; for I must express to you the
great pleasure I have in hearing such a complete explanation of phe-
nomena with regard to which I have so long been in darkness. Now I
understand why unison does not differ from a single tone; I understand
why the octave is the principal harmony, but so like unison as often to be
mistaken for it and also why it occurs with the other harmonies. It resem-
bles unison because the pulsations of strings in unison always occur simul-
taneously, and those of the lower string of the octave are always accompa-
nied by those of the upper string; and among the latter is interposed a
solitary pulse at equal intervals and in such a manner as to produce no
disturbance; the result is that such a harmony is rather too much softened
and lacks fire. But the fifth is characterized by its displaced beats and by
the interposition of two solitary beats of the upper string and one solitary
beat of the lower string between each pair of simultaneous pulses; these
three solitary pulses are separated by intervals of time equal to half the
interval which separates each pair of simultaneous beats from the solitary
124 MASTERWORKS OF SCIENCE
beats of the upper string. Thus the effect of the fifth is to produce a
tickling o£ the eardrum such that its softness is modified with sprightli-
ness, giving at the same moment the impression of a gentle kiss and of a
SALVIATI. Seeing that you have derived so much pleasure from these
novelties, I must show you a method by which the eye may enjoy the same
game as the ear. Suspend three balls of lead, or other heavy material, by
means of strings of different length such that while the longest makes two
vibrations the shortest will make four and the medium three; this will
take place when the longest string measures 16, either in handbreadths or
in any other unit, the medium 9 and the shortest 4, all measured in the
same unit.
Now pull all these pendulums aside from the perpendicular and release
them at the same instant; you will see a curious interplay of the threads
passing each other in various manners but such that at the completion of
every fourth vibration of the longest pendulum, all three will arrive simul-
taneously at the same terminus, whence they start over again to repeat the
same cycle. This combination of vibrations, when produced on strings, is
precisely that which yields the interval of the octave and the intermediate
fifth. If we employ the same disposition of apparatus but change the
lengths of the threads, always however in such a way that their vibrations
correspond to those of agreeable musical intervals, we shall see a different
crossing of these threads but always such that, after a definite interval of
time and after a definite number of vibrations, all the threads, whether
three or four, will reach the same terminus at the same instant, and then
begin a repetition of the cycle.
• If however the vibrations of two or more strings are incommensurable
so that they never complete a definite number of vibrations at the same
instant, or if commensurable they return only after a long interval of time
and after a large number of vibrations, then the eye is confused by the
disorderly succession of crossed threads. In like manner the ear is pained
by an irregular sequence of air waves which strike the tympanum without
any fixed order.
But, gentlemen, whither have we drifted during these many hours
lured on by various problems and unexpected digressions? The day is
already ended and we have scarcely touched the subject proposed for dis-
cussion. Indeed we have deviated so far that I remember only with diffi-
culty our early introduction and the little progress made in the way of
hypotheses and principles for use in later demonstrations.
SAGREDO. Let us then adjourn for today in order that our minds may
find refreshment in sleep and that we may return tomorrow, if so please
you, and resume the discussion of the main question.
SALVIATI. I shall not fail to be here tomorrow at the same hour, hoping
not only to render you service but also to enjoy your company.
END OF FIRST DAY
GALILEO — DIALOGUES 125
SECOND DAY
SAGREDO. While Simplicio and I were awaiting your arrival we were
trying to recall that last consideration which you advanced as a principle
and basis for the results you intended to obtain; this consideration dealt
with the resistance which all solids offer to fracture and depended upon a
certain cement which held the parts glued together so that they would
yield and separate only under considerable pull. Later we tried to find the
explanation of this coherence, seeking it mainly in the vacuum; this was
the occasion of our many digressions which occupied the entire day and
led us far afield from the original question which, as I have already
stated, was the consideration of the resistance that solids offer to fracture.
SALVTATI. I remember it all very well. Resuming the thread of our dis-
course, whatever the nature of this resistance which solids offer to large
tractive forces there can at least be no doubt of its existence; and thought
this resistance is very great in the case of a direct pull, it is found, as a
rule, to be less in the case of bending forces. Thus, for example, a rod of
steel or of glass will sustain a longitudinal pull of a thousand pounds
while a weight of fifty pounds would be quite sufficient to break it if the
rod were fastened at right angles into a vertical wall. It is this second type
of resistance which we must consider, seeking to discover in what propor-
tion it is found in prisms and cylinders of the same material, whether
alike or unlike in shape, length, and thickness. In this discussion I shall
take for granted the well-known mechanical principle which has been
shown to govern the behavior of a bar, which we call a lever, namely, that
the force bears to the resistance the inverse ratio of the distances which,
separate the fulcrum from the force and resistance respectively.
SIMPLICIO. This was demonstrated first of all by Aristotle, in his
Mechanics.
SALVTATI. Yes, I am willing to concede him priority in point of time;
but as regards rigor of demonstration the" first place must be given to
Archimedes. This principle established, I desire, before passing to any
other subject, to call your attention to the fact that these forces, resist-
ances, moments, figures, etc., may be considered either in the abstract,
dissociated from matter, or in the concrete, associated with matter. Hence
the properties which belong to figures that are merely geometrical and
non-material must be modified when we fill these figures with matter and
therefore give them weight. Take, for example, the lever BA which, rest-
ing upon the support E, is used to lift a heavy stone D. The principle just
demonstrated makes it clear that a force applied at the extremity B will
just suffice to equilibrate the resistance offered by the heavy body D pro-
vided this force bears to the force at D the same ratio as the distance AC
bears to the distance CB; and this is true so long as we consider only the
moments of the single force at B and of the resistance at D, treating the
lever as an immaterial body devoid of weight. But if we take into account
126 MASTERWQRKS OF SCIENCE
the weight of the lever itself — an instrument which may be made either of
wood or of iron — it is manifest that, when this weight has been added to
the force at B, the ratio will be changed and must therefore be expressed
in different terms. Hence before going further let us agree to distinguish
between these two points of view; when we consider an instrument in the
abstract, i. e:, apart from the weight of its own material, we shall speak of
"taking it in an absolute sense"; but if we fill one of these simple and
absolute figures with matter and thus give it weight, we shall refer to such
a material figure as a "moment" or "compound force."
Let us now return to our original subject; then, if what has hitherto
been said is clear, it will be easily understood that,
Proposition I
A prism or solid cylinder of glass, steel, wood or other breakable ma-
terial which is capable of sustaining a very heavy weight when applied
longitudinally is, as previously remarked, easily broken by the transverse
application of a weight which may be much smaller in proportion as the
length of the cylinder exceeds its thickness.
Let us imagine a solid prism ABCD fastened into a wall at the end
AB> and supporting a weight E at the other end; understand also that the
wall is vertical and that the prism or cylinder is fastened at right angles to
the wall. It is clear that, if the cylinder breaks, fracture will occur at the
point B where the edge of the mortise acts as a fulcrum for the lever BC,
to which the force is applied; the thickness of the solid BA is the other
arm of the lever along which is located the resistance. This resistance op-
poses the separation of the part BD, lying outside the wall, from that
portion lying inside. From the preceding, it follows that the magnitude
of the force applied at C bears to the magnitude of the resistance, found
in the thickness of the prism, i. e., in the attachment of the base BA to its
contiguous parts, the same ratio which the length CB bears to half the
length BA; if now we define absolute resistance to fracture as that offered
to a longitudinal pull (in which case the stretching force acts in the same
direction as that through which the body is moved), then it follows that
the absolute resistance of the prism BD is to the breaking load placed at
the end of the lever BC in the same ratio as the length BC is to the half
of AB in the case of a prism, or the semi-diameter in the case of a cylin-
der. This is our first proposition. Observe that in what has here been said
GALILEO — DIALOGUES
127
the weight of the solid BD itself has been left out of consideration, or
rather, the prism has been assumed to be devoid of weight. But if the
weight of the prism is to be taken account of in conjunction with the
weight E, we must add to the weight E one half that of the prism BD: so
that if, for example, the latter weighs two pounds and the weight E is ten
pounds we must treat the weight E as if it were eleven pounds,
SIMPLICIO. Why not twelve?
SALVIATI. The weight E, my dear Simplicio, hanging at the extreme
end C, acts upon the lever BC with its full moment of ten pounds: so also
would the solid BD if suspended at the same point exert its full mo-
ment of two pounds; but, as you know, this solid is uniformly distributed
throughout its entire length, BC, so that the parts which lie near the end
B are less effective than those more remote.
Accordingly if we strike a balance between the two, the weight of the
entire prism may be considered as concentrated at its center of gravity
which lies midway of the lever BC. But a weight hung at the extremity C
exerts a moment twice as great as it would if suspended from the middle:
therefore if we consider the moments of both as located at the end C we
must add to the weight E one-half that of the prism.
SIMPLICIO. I understand perfectly; and moreover, if I mistake not, the
force of the two weights BD and E, thus disposed, would exert the same
moment as would the entire weight BD together with twice the weight
E suspended at the middle of the lever BC.
SALVIATI. Precisely so, and a fact worth remembering. Now we can
readily understand
128
MASTERWORKS OF SCIENCE
Proposition II
How and in what proportion a rod, or rather a prism, whose width is
greater than its thickness offers more resistance to fracture when the
force is applied in the direction of its breadth than in the direction of its
thickness.
For the sake of clearness, take a ruler ad whose width is ac and whose
thickness, cb, is much less than its width. The question now is why will
the ruler, i£ stood on edge, as in the first figure, withstand a great weight
T, while, when laid flat, as in the second figure, it will not support the
weight X which is less than T. The answer is evident when we remember
that in the one case the fulcrum is at the line be, and in the other case at
caf while the distance at which the force is applied is the same in both
cases, namely, the length bd: but in the first case the distance of the re-
sistance from the fulcrum — half the line ca — is greater than in the other
case where it is only half of be. Therefore the weight T is greater than X
in the same ratio as half the width ca is greater than half the thickness be,
since the former acts as a lever arm for ca, and the latter for cbf against
the same resistance, namely, the strength of all the fibres in the cross-
section ab. We conclude, therefore, that any given ruler, or prism, whose
width exceeds its thickness, will offer greater resistance to fracture when
standing on edge than when lying flat, and this in the ratio of the width
to the thickness.
Proposition 111
Considering now the case of a prism or cylinder growing longer in a
horizontal direction, we must find out in what ratio the moment of its
•own weight increases in comparison with its resistance to fracture. This
moment I find increases in proportion to the square of the length. In
order to prove this let AD be a prism or cylinder lying horizontal with its
end A firmly fixed in a wall. Let the length of the prism be increased by
the addition of the portion BE. It is clear that merely changing the length
.of the lever from AB to AC will, if we disregard its weight, increase the
GALILEO — DIALOGUES
129
moment of the force [at the end] tending to produce fracture at A in the
ratio of CA to BA. But, besides this, the weight of the solid portion BE,
added to the weight of the solid AB, increases the moment of the total
weight in the ratio of the weight of the prism AE to that of the prism
AB, which is the same as the ratio of the length AC to AB.
It follows, therefore, that, when the length and weight are simultane-
ously increased in any given proportion, the moment, which is the prod-
uct of these two, is increased in a ratio which is the square of the pre-
ceding proportion. The conclusion is then that the bending moments due
to the weight of prisms and cylinder" which have the same thickness but
D E
^x-* " ' ^
J
1
different lengths bear to each other a ratio which is the square of the ratio
of their lengths, or, what is the same thing, the ratio of the squares of
their lengths.
SIMPLICIO. Before proceeding further I should like to have one of my
difficulties removed. Up to this point you have not taken into considera-
tion a certain other kind of resistance which, it appears to me, diminishes
as the solid grows longer, and this is quite as tr.ue in the case of bending;
as in pulling; it is precisely thus that in the case of a rope we observe that
a very long one is less able to support a large weight than a short one.
Whence, I believe, a short rod of wood or iron will support a greater
weight than if it were long, provided the force be always applied longi-
tudinally and not transversely, and provided also that we take into account
the weight of the rope itself which increases with its length.
SALVIATI. I fear, Sirnplicio, if I correctly catch your meaning, that in
this particular you are making the same mistake as many others; that is if
you mean to say that a long rope, one of perhaps 40 cubits, cannot hold
up so great a weight as a shorter length, say one or two cubits, of the
same rope.
130
MASTERWORKS OF SCIENCE
SIMPLICIO. That is what I meant, and as far as I see the proposition is
highly probable.
SALVIATI. On the contrary, I consider it not
merely improbable but false; and I think I can
easily convince you of your error. Let AB repre-
sent the rope, fastened at the upper end A: at the
lower end attach a weight C whose force is just
sufficient to break the rope. Now, Simplicio, point
out the exact place where you think the break
ought to occur.
SIMPLICIO. Let us say D.
SALVIATI. And why at D?
SIMPLICIO. Because at this point the rope is
not strong enough to support, say, 100 pounds,
made up of the portion of the rope DB and the
stone C.
SALVIATI. Accordingly whenever the rope is
stretched with the weight of 100 pounds at D it
will break there.
SIMPLICIO. I think so.
SALVIATI. But tell me, if instead of attaching
the weight at the end of the rope, B, one fastens
It at a point nearer D, say, at E: or if, instead of
fixing the upper end of the rope at A, one fastens
it at some point F, just above D, will not the rope,
at the point D, be subject to the same pull of 100 pounds?
SIMPLICIO. It would, provided you include with the stone C the por-
tion of rope EB.
SALVIATI. Let us therefore suppose that the rope is stretched at the
point D with a weight of 100 pounds, then according to your own admis-
sion it will break; but FE is only a small portion of AB; how can you
therefore maintain that the long rope is weaker than the short one? Give
up then this erroneous view which you share with many very intelligent
people, and let us proceed.
Proposition IV
Among heavy prisms and cylinders of similar figure, there is one and
only one which under the stress of its own weight lies just on the limit
between breaking and not breaking: so that every larger one is unable to
carry the load of its own weight and breaks; while every smaller one is
able to withstand some additional force tending to break it.
Let AB be a heavy prism, the longest possible that will just sustain its
own weight, so that if it be lengthened the least bit it will break. Then, I
say, this prism is unique among all similar prisms — infinite in number —
in occupying that boundary line between breaking and not breaking; so
that every larger one will break under its own weight, and every smaller
GALILEO — DIALOGUES 131
one will not break, but will be able to withstand some force in addition to
its own weight.
Let the prism CE be similar to, but larger than, AB: then, I say, it
will not remain intact but will break under its own weight. Lay off the
portion CD, equal in length to AB, And since the resistance [bending
strength] of CD is to that of AB as the cube of the thickness of CD is to
the cube of the thickness of AB, that is, as the prism CE is to the similar
prism AB, it follows that the weight of CE is the utmost load which a
prism of the length CD can sustain; but the length of CE is greater; there-
fore the prism CE will break. Now take another prism FG which is
smaller than AB. Let FH equal AB, then it can be shown in a similar
manner that the resistance [bending strength] of FG is to that of AB as
the prism FG is to the prism AB provided the distance AB that is FH is
equal to the distance FG; but AB is greater than FG, and therefore the
Z>
moment of the prism FG applied at G is not sufficient to break the
prism FG.
11 SAGREDO. The demonstration is short and clear; while the proposition
which, at first glance, appeared improbable is now seen to be both true
and inevitable. In order therefore to bring this prism into that limiting
condition which separates breaking from not breaking, it would be neces-
sary to change the ratio between thickness and length either by increasing
the thickness or by diminishing the length.
From what has already been demonstrated, you can plainly see the
impossibility of increasing the size of structures to vast dimensions either
in art or in nature; likewise the impossibility of building ships, palaces,
or temples of enormous size in such a way that their oars, yards, beams,
iron bolts, and, in short, all their other parts will hold together; nor can
nature produce trees of extraordinary size because the branches would
break down under their own weight; so also it would be impossible to
build up the bony structures of men, horses, or other animals so as to hold
together and perform their normal functions if these animals were to be
increased enormously in height; for this increase in height can be accom-
plished only by employing a material which is" harder and stronger than
usual, or by enlarging the size of the bones, thus changing their shape
until the form and appearance of the animals suggest a monstrosity. This
is perhaps what our wise Poet [Ariosto] had in mind, when he says, in
describing a huge giant:
Impossible it is to reckon his height
So beyond measure is his size.
132 MASTERWORKS OF SCIENCE
To illustrate briefly, I have sketched a bone whose natural length has
teen increased three times and whose thickness has been multiplied until,
for a correspondingly large animal, it would perform the same function
which the small bone performs for its small animal. From the figures here
shown you can see how out of proportion the enlarged bone appears.
Clearly then if one wishes to maintain in a great giant the same propor-
tion of limb as that found in an ordinary man he must either find a harder
and stronger material for making the bones, or he must admit a diminu-
tion of strength in comparison with men of medium stature; for if his
height be increased inordinately he will fall and be crushed under his
own weight. Whereas, if the size of a body be diminished, the strength
of that body is not diminished in the same proportion; indeed the smaller
the body the greater its relative strength. Thus a small dog could prob-
ably carry on his back two or three dogs of his own size; but I believe that
a horse could not carry even one of his own size.
SIMPLICIO. This may be so; but I am led to doubt it on account of the
enormous size reached by certain fish, such as the whale which, I under-
stand, is ten times as large as an elephant; yet they all support themselves.
SALVIATI. Your question, Simplicio, suggests another principle, one
which had hitherto escaped my attention and which enables giants and
other animals of vast size to support themselves and to move about as
well as smaller animals do. This result may be secured either by increas-
ing the strength of the bones and other parts intended to carry not only
their weight but also the superincumbent load; or, keeping the propor-
tions of the bony structure constant, the skeleton will hold together in the
same manner or even more easily, provided one diminishes, in the proper
proportion, the weight of the bony material, of the flesh, and of anything
else which the skeleton has to carry. It is this second principle which is
employed by nature in the structure of fish, making their bones and
muscles not merely light but entirely devoid of weight.
SIMPLICIO. The trend of your argument, Salviati, is evident. Since fish
live in water which on account of its density or, as others would say,
heaviness diminishes the weight of bodies immersed in it, you mean to
say that, for this reason, the bodies of fish will be devoid of weight and
GALILEO — DIALOGUES ' 133
will be supported without injury to their bones. But this is not all; for
although the remainder of the body of the fish may be without weight,
there can be no question but that their bones have weight. Take the case
of a whale's rib, having the dimensions of a beam; who can deny its great
weight or its tendency to go to the bottom when placed in water? One
would, therefore, hardly expect these great masses to sustain themselves..
SALVIATI. A very shrewd objection! And now, in reply, tell me:
whether you have ever seen fish stand motionless at will under watery
neither descending to the bottom nor rising to the top, without the exer-
tion of force by swimming?
SIMPLICIO. This is a well-known phenomenon.
SALVIATI. The fact then that fish are able to remain motionless under
water is a conclusive reason for thinking that the material of their bodies
has the same specific gravity as that of water; accordingly, if in their
make-up there are certain parts which are heavier than water there must
be others which are lighter, for otherwise they would not produce
equilibrium.
Hence, if the bones are heavier, it is necessary that the muscles or
other constituents of the body should be lighter in order that their buoy-
ancy may counterbalance the weight of the bones. In aquatic animals
therefore circumstances are just reversed from what they are with land
animals inasmuch as, in the latter, the bones sustain not only their own
weight but also that of the flesh, while in the former it is the flesh which
supports not only its own weight but also that of the bones. We must
therefore cease to wonder why these enormously large animals inhabit the
water rather than the land, that is to say, the air.
SIMPLICIO. I am convinced and I only wish to add that what we call
land animals ought really to be called air animals, seeing that they live in
the air, are surrounded by air, and breathe air.
SAGREDO. I have enjoyed Simplicio's discussion including both the
question raised and its answer. Moreover I can easily understand that one
of these giant fish, if pulled ashore, would not perhaps sustain itself for
any great length of time, but would be crushed under its own mass as
soon as the connections between the bones gave way.
SALVIATI. I am inclined to your opinion; and, indeed, I almost think
that the same thing would happen in the case of a very big ship which
floats on the sea without going to pieces under its load of merchandise
and armament, but which on dry land and in air would probably fall
apart. But let us proceed.
Hitherto we have considered the moments and resistances of prisms:
and solid cylinders fixed at one end with a weight applied at the other
end; three cases were discussed, namely, that in which the applied force
was the only one acting, that in which the weight of the prism itself is
also taken into consideration, and that in which the weight of the prism
alone is taken into consideration. Let us now consider these same prisms
and cylinders when supported at both ends or at a single point placed
somewhere between the ends. In the first place, I remark that a cylinder
134
MASTERWORKS OF SCIENCE
carrying only its own weight and having the maximum length, beyond
which it will break, will, when supported either in the middle or at both
ends, have twice the length of one which is mortised into a wall and sup-
ported only at one end. This is very evident because, if we denote the
cylinder by ABC and if we assume that one-half of it, AB3 is the greatest
possible length capable of supporting its own weight with one end fixed
at B, then, for the same reason, if the cylinder is carried on the point C,
the first half will be counterbalanced by the other half BC. So also in the
case of the cylinder DEF, if its length be such that it will support only
one-half this length when the end D is held fixed, or the other half when
the end F is fixed, then it is evident that when supports, such as H and I,
are placed under the ends D and F respectively the moment of any ad-
ditional force or weight placed at E will produce fracture at this point.
SAGREDO. What shall we say, Simplicio? Must we not confess that
geometry is the most powerful of all instruments for sharpening the wit
and training the mind to think correctly? Was not Plato perfectly right
when he wished that his pupils should be first of all well grounded in
mathematics? As for myself, I quite understood the property of the lever
and how, by increasing or diminishing its length, one can increase or
Biminish the moment of force and of resistance; and yet, in the solution
of the present problem I was not slightly, but greatly, deceived.
SIMPLICIO. Indeed I begin to understand that while logic is an excel-
lent guide in discourse, it does not, as regards stimulation to discovery,
compare with the power of sharp distinction which belongs to geometry.
SAGREDO. Logic, it appears to me, teaches us how to test the conclu-
siveness of any argument or demonstration already discovered and com-
pleted; but I do not believe that it teaches us to discover correct argu-
ments and demonstrations.
END OF SECOND DAY
GALILEO — DIALOGUES 135
THIRD DAY
CHANGE OF POSITION
MY PURPOSE is to set forth a very new science dealing with a very an-
cient subject. There is, in nature, perhaps nothing older than motion,
concerning which the books written by philosophers are neither few nor
small; nevertheless I have discovered by experiment some properties of it
which are worth knowing and which have not hitherto been either ob-
served or demonstrated. Some superficial observations have been made,
as, for instance, that the free motion of a heavy falling body is continu-
ously accelerated; but to just what extent this acceleration occurs has not
yet been announced; for so far as I know, no one has yet pointed out that
the distances traversed, during equal intervals of time, by a body falling
from rest, stand to one another in the same ratio as the odd numbers
beginning with unity.
It has been observed that missiles and projectiles describe a curved
path of some sort; however no one has pointed out the fact that this path
is a parabola. But this and other facts, not few in number or less worth
knowing, I have succeeded in proving; and what I consider more impor-
tant, there have been opened up to this vast and most excellent science, of
which my work is merely the beginning, ways and means by which other
minds more acute than mine will explore its remote corners.
NATURALLY ACCELERATED MOTION
The properties belonging to uniform motion have been discussed;
but accelerated motion remains to be considered.
And first of all it seems desirable to find and explain a definition best
fitting natural phenomena. For anyone may invent an arbitrary type of
motion and discuss its properties; thus, for instance, some have imagined
helices and conchoids as described by certain motions which are not met
with in nature, and have very commendably established the properties
which these curves possess in virtue of their definitions; but we have de-
cided to consider the phenomena of bodies falling with an acceleration
such as actually occurs in nature and to make this definition of accelerated
motion exhibit the essential features of observed accelerated motions. And
this, at last, after repeated efforts we trust we have succeeded in doing. In
this belief we are confirmed mainly by the consideration that experimen-
tal results are seen to agree with and exactly correspond with those prop-
erties which have been, one after another, demonstrated by us. Finally, in
the investigation of naturally accelerated motion we were led, by hand as
it were, in following the habit and custom of nature herself, in all her
various other processes, to employ only those means which are most
common, simple and easy.
136 MASTERWORKS OF SCIENCE
For I think no one believes that swimming or flying can be accom-
plished in a manner simpler or easier than that instinctively employed by
fishes and birds.
When, therefore, I observe a stone initially at rest falling from an
elevated position and continually acquiring new increments of speed, why
should I not believe that such increases take place in a manner which is
exceedingly simple and rather obvious to everybody? If now we examine
the matter carefully we find no addition or increment more simple than
that which repeats itself always in the same manner. This we readily
understand when we consider the intimate relationship between time and
motion; for just as uniformity of motion is defined by and conceived
through equal times and equal spaces (thus we call a motion uniform
when equal distances are traversed during equal time-intervals),, so also
we may, in a similar manner, through equal time-intervals, conceive ad-
ditions of speed as taking place without complication; thus we may pic-
ture to our mind a motion as uniformly and continuously accelerated
when, during any equal intervals of time whatever, equal increments of
speed are given to it. Thus if any equal intervals of time whatever have
elapsed, counting from the time at which the moving body left its posi-
tion of rest and began to descend, the amount of speed acquired during
the first two time-intervals will be double that acquired during the first
time-interval alone; so the amount added during three of these time-
intervals will be treble; and that in four, quadruple that of the first
time-interval. To put the matter more clearly, if a body were to continue
its motion with the same speed which it had acquired during the first
time-interval and were to retain this same uniform speed, then its motion
would be twice as slow as that which it would have if its velocity had
been acquired during two time-intervals.
And thus, it seems, we shall not be far wrong if we put the increment
of speed as proportional to the increment of time; hence the definition of
motion which we are about to discuss may be stated as follows; A motion
is said to be uniformly accelerated when, starting from rest, it acquires,
during equal time-intervals, equal increments of speed.
SAGREDO. Although I can offer no rational objection to this or indeed
to any other definition, devised by any author whomsoever, since all defi-
nitions are arbitrary, I may nevertheless without offense be allowed to
doubt whether such a definition as the above, established in an abstract
manner, corresponds to and describes that kind of accelerated motion
which we meet in nature in the case of freely falling bodies. And since
the Author apparently maintains that the motion described in his defini-
tion is that of freely falling bodies, I would like to clear my mind of
certain difficulties in order that I may later apply myself more earnestly to
the propositions and their demonstrations.
SALVIATL It is well that you and Simplicio raise these difficulties.
They are, I imagine, the same which occurred to me when I first saw this
treatise, and which were removed either by discussion with the Author
himself, or by turning the matter over in my own mind.
GALILEO — DIALOGUES 137
SAGREDO. When I think of a heavy body falling from rest, that is,
starting with zero speed and gaming speed in proportion to the time
from the beginning of the motion; such a motion as would, for instance,
in eight beats of the pulse acquire eight degrees of speed; having at the
end of the fourth beat acquired four degrees; at the end of the second,
two; at the end of the first, one: and since time is divisible without limit,
it follows from all these considerations that if the earlier speed of a body
is less than its present speed in a constant ratio, then there is no degree
of speed however small (or, one may say, no degree of slowness however
great) with which we may not find this body travelling after starting
from infinite slowness, i. e., from rest. So that if that speed which it had
at the end of the fourth beat was such that, if kept uniform, the body
would traverse two miles in an hour, and if keeping the speed which it
had at the end of the second beat, it would traverse one mile an hour, we
must infer that, as the instant of starting is more and more nearly ap-
proached, the body moves so slowly that, if it kept on moving at this rate,
it would not traverse a mile in an hour, or in a day, or in a year or in a
thousand years; indeed, it would not traverse a span in an even greater
time; a phenomenon which baffles the imagination, while our senses show
us that a heavy falling body suddenly acquires great speed.
SALVIATI. This is one of the difficulties which I also at the beginning
experienced, but which I shortly afterwards removed; and the removal
was effected by the very experiment which creates the difficulty for you.
You say the experiment appears to show that immediately after a heavy
body starts from rest it acquires a very considerable speed: and I say that
the same experiment makes clear the fact that the initial motions of a
falling body, no matter how heavy, are very slow and .gentle. Place a heavy
body upon a yielding material, and leave it there without any pressure
except that owing to its own weight; it is clear that if one lifts this body
a cubit or two and allows it to fall upon the same material, it will, with
this impulse, exert a new and greater pressure than that caused by its
mere weight; and this effect is brought about by the [weight of the] fall-
ing body together with the velocity acquired during the fall, an effect
which will be greater and greater according to the height of the fall, that
is, according as the velocity of the falling body becomes greater. From
the quality and intensity of the blow we are thus enabled to accurately
estimate the speed of a falling body. But tell me, gentlemen, is it not true
that if a block be allowed to fall upon a stake from a height of four cubits
and drives it into the earth, say, four finger breadths, that coming from a
height of two cubits it will drive the stake a much less distance, and from
the height of one cubit a still less distance; and finally if the block be
lifted only one fingerbreadth how much more will it accomplish than if
merely laid on top of the stake without percussion? Certainly very little.
If it be lifted only the thickness of a leaf, the effect will be altogether
imperceptible. And since the effect of the blow depends upon the velocity
of this striking body, can anyone doubt the motion is very slow and the
speed more than small whenever the effect [of the blow] is imperceptible?
138 MASTERWORKS OF SCIENCE
See now the power of truth; the same experiment which at first glance
seemed to show one thing, when more carefully examined, assures us of
the contrary.
But without depending upon the above experiment, which is doubt-
less very conclusive, it seems to me that it ought not to be difficult to
establish such a fact by reasoning alone. Imagine a heavy stone held in
the air at rest; the support is removed and the stone set free; then since
it is heavier than the air it begins to fall, and not with uniform motion
but slowly at the beginning and with a continuously accelerated motion.
Now since velocity can be increased and diminished without limit, what
reason is there to believe that such a moving body starting with infinite
slowness, that is, from rest, immediately acquires a speed of ten degrees
rather than one of four, or of two, or of one, or of a half, or of a hundredth;
or, indeed, of any of the infinite number of small values [of speed]?
Pray listen. I hardly think you will refuse to grant that the gain of speed
of the stone falling from rest follows the same sequence as the diminution
and loss of this same speed when, by some impelling force, the stone is
thrown to its former elevation: but even if you do not grant this, I do
not see how you can doubt that the ascending stone, diminishing in speed,
must before coming to rest pass through every possible degree of slowness.
SIMPLICIO. But if the number of degrees of greater and greater slow-
ness is limitless, they will never be all exhausted, therefore such an ascend-
ing heavy body will never reach rest, but will continue to move without
limit always at a slower rate; but this is not the observed fact.
SALVIATI. This would happen, Simplicio, if the moving body were to
maintain its speed for any length of time at each degree of velocity; but
it merely passes each point without delaying more than an instant: and
since each time-interval however small may be divided into an infinite
number of instants, these will always be sufficient [in number] to corre-
spond to the infinite degrees of diminished velocity.
That such a heavy rising body does not remain for any length of time
at any given degree of velocity is evident from the following: because if,
some time-interval having been assigned, the body moves with the same
speed in the last as in the first instant of that time-interval, it could from
this second degree of elevation be in like manner raised through an equal
height, just as it was transferred from the first elevation to the second,
and by the same reasoning would pass from the second to the third and
would finally continue in uniform motion forever.
SALVIATI. The present does not seem to be the proper time to investi-
gate the cause of the acceleration of natural motion concerning which
various opinions have been expressed by various philosophers, some ex-
plaining it by attraction to the center, others to repulsion between the
very small parts of the body, while still others attribute it to a certain
stress in the surrounding medium which closes in behind the falling body
and drives it from one of its positions to another. Now, all these fantasies,
and others too, ought to be examined; but it is not really worth while. At
present it is the purpose of our Author merely to investigate and to
GALILEO — DIALOGUES 139
demonstrate some of the properties of accelerated motion (whatever the
cause of this acceleration may be) — meaning thereby a motion, such that
the momentum of its velocity goes on increasing after departure from
rest, in simple proportionality to the time, which is the same as saying that
in equal time-intervals the body receives equal increments of velocity; and
if we find the properties [of accelerated motion] which will be demon-
strated later are realized in freely falling and accelerated bodies, we may
conclude that the assumed definition includes such a motion of falling
bodies and that their speed goes on increasing as the time and the du-
ration of the motion.
SAGREDO. So far as I see at present, the definition might have been put
a little more clearly perhaps without changing the fundamental idea,
namely, uniformly accelerated motion is such that its speed increases in
proportion to the space traversed; so that, for example, the speed acquired
by a body in falling four cubits would be double that acquired in falling
two cubits and this latter speed would be double that acquired in the first
cubit. Because there is no doubt but that a heavy body falling from the
height of six cubits has, and strikes with, a momentum double that it had
at the end of three cubits, triple that which it would have if it had fallen
from two, and sextuple that which it would have had at the end of one.
SALVIATI. It is very comforting to me to have had such a companion
in error; and moreover let me tell you that your proposition seems so
highly probable that our Author himself admitted, when I advanced this
opinion to him, that he had for some time shared the same fallacy. But
what most surprised me was to see two propositions so inherently prob-
able that they commanded the assent of everyone to whom they were
presented, proven in a few simple words to be not only false, but impos-
sible.
SIMPLICIO. I am one of those who accept the proposition, and believe
that a falling body acquires force in its descent, its velocity increasing in
proportion to the space, and that the momentum of the falling body is
doubled when it falls from a doubled height; these propositions, it appears
to me, ought to be conceded without hesitation or controversy.
SALVIATI. And yet they are as false and impossible as that motion
should be completed instantaneously; and here is a very clear demonstra-
tion of it. If the velocities are in proportion to the spaces traversed, or to
be traversed, then these spaces are traversed in equal intervals of time; if,
therefore, the velocity with which the falling body traverses a space of
eight feet were double that with which it covered the first four feet (just
as the one distance is double the other) then the time-intervals required
for these passages would be equal. But for one and the same body to fall
eight feet and four feet in the same time is possible only in the case of
instantaneous [discontinuous] motion; but observation shows us that the
motion of a falling body occupies time, and less of it in covering a dis-
tance of four feet than of eight feet; therefore it is not true that its velocity
increases in proportion to the space.
The falsity of the other proposition may be shown with equal clear-
140 MASTERWORKS OF SCIENCE
ness. For if we consider a single striking body the difference of momen-
tum in its blows can depend only upon difference of velocity; for if the
striking body falling from a double height were to deliver a blow of
double momentum, it would be necessary for this body to strike with a
doubled velocity; but with this doubled speed it would traverse a doubled
space in the same time-interval; observation however shows that the time
required for fall from the greater height is longer.
SAGREDO. You present these recondite matters with too much evidence
and ease; this great facility makes them less appreciated than they would
be had they been presented in a more abstruse manner. For, in my opinion,
people esteem more lightly that knowledge which they acquire with so
little labor than that acquired through long and obscure discussion.
SALVIATI. If those who demonstrate with brevity and clearness the
fallacy of many popular beliefs were treated with contempt instead of
gratitude the injury would be quite bearable; but on the other hand it is
very unpleasant and annoying to see men, who claim to be peers of any-
one in a certain field of study, take for granted certain conclusions which
later are quickly and easily shown by another to be false. I do not describe
such a feeling as one of envy, which usually degenerates into hatred and
anger against those who discover such fallacies; I would call it a strong
desire to maintain old errors, rather than accept newly discovered truths.
This desire at times induces them to unite against these truths, although
at heart believing in them, merely for the purpose of lowering the esteem
in which certain others are held by the unthinking crowd. Indeed, I have
heard from our Academician many such fallacies held as true but easily
refutable; some of these I have in mind.
^AGREDO. You must not withhold them from us, but, at the proper
time, tell us about them even though an extra session be necessary. But
now, continuing the thread of our talk, it would seem that up to the
present we have established the definition of uniformly accelerated motion
which is expressed as follows:
A motion is said to be equally or uniformly accelerated when, start-
ing from rest, its momentum receives equal increments in equal
times.
SALVIATI. This definition established, the Author makes a single as-
sumption, namely,
The speeds acquired by one and the same body moving down
planes of different inclinations are equal when the heights of these
planes are equal.
By the height of an inclined plane we mean the perpendicular let
fall from the upper end of the plane upon the horizontal line drawn
through the lower end of the same plane. Thus, to illustrate, let the line
AB be horizontal, and let the planes CA and CD be inclined to it; then
the Author calls the perpendicular CB the "height" of the planes CA and
CD; he supposes that the speeds acquired by one and the same body,
descending along the planes CA and CD to the terminal points A and D,
are equal since the heights of these planes are the same, CB; and also it
GALILEO — DIALOGUES 141
must be understood that this speed is that which would be acquired by
the same body falling from C to B.
SAGREDO. Your assumption appears to me so reasonable that it ought
to be conceded without question, provided of course there are no chance
or outside resistances, and that the planes are hard and smooth, and that
the figure of the moving body is perfectly round, so that neither plane
nor moving body is rough. All resistance and opposition having been
removed, my reason tells me at once that a heavy and perfectly round ball
descending along the lines CA, CD, CB would reach the terminal points
A, D, B, with equal momenta.
C
SALVIATI. Your words are very plausible; but I hope by experiment to
Increase the probability to an extent which shall be little short of a rigid
demonstration.
Imagine this page to represent a vertical wall, with a nail driven into
it; and from the nail let there be suspended a lead bullet of one or two
ounces by means of a fine vertical thread, AB, say from four to six feet
long. On this wall draw a horizontal line DC, at right angles to the vertical
thread AB, which hangs about two fingerbreadths in front of the wall.
Now bring the thread AB with the attached ball into the position AC
and set it free; first it will be observed to descend along the arc CBD,
to pass the point B, and to travel along the arc BD, till it almost reaches
the horizontal CD, a slight shortage being caused by the resistance of the
air and the string; from this we may rightly infer that the ball in its
descent through the arc CB acquired a momentum on reaching B, which
was jus^ sufficient to carry it through a similar arc BD to the same height.
Having repeated this experiment many times, let us now drive a nail into
the wall close to the perpendicular AB, say at E or F, so that it projects
out some five or six fingerbreadths in order that the thread, again carrying
the bullet through the arc CB, may strike upon the nail E when the bullet
reaches B, and thus compel it to traverse the arc BG, described about E
as center. From this we can see what can be done by the same momentum
which previously starting at the same point B carried the same body
through the arc BD to the horizontal CD. Now, gentlemen, you will
observe with pleasure that the ball swings to the point G in the horizontal,
and you would see the same thing happen if the obstacle were placed at
some lower point, say at F, about which the ball would describe the arc
BI, the rise of the ball always terminating exactly on the line CD. But
when the nail is placed so low that the remainder of the thread below it
142
MASTERWORKS OF SCIENCE
will not reach to the height CD (which would happen if the nail were
placed nearer B than to the intersection of AB with the horizontal CD)
then the thread leaps over the nail and twists itself about it.
This experiment leaves no room for doubt as to the truth of our
supposition; for since the two arcs CB and DB are equal and similarly
placed, the momentum acquired by the fall through the arc CB is the
same as that gained by fall through the arc DB; but the momentum
acquired at B, owing to fall through CB3 is able to lift the same body
through the arc BD; therefore, the momentum acquired in the fall BD is
equal to that which lifts the same body through the same arc from B to
D; so, in general, every momentum acquired by fall through an arc is
equal to that which can lift the same body through the same arc. But all
these momenta which cause a rise through the arcs BD? BG, and BI are
equal, since they are produced by the same momentum, gained by fall
through CB, as experiment shows. Therefore all the momenta gained by
fall through the arcs DB, GB, IB are equal.
SAGREDO. The argument seems to me so conclusive and the experiment
so well adapted to establish the hypothesis that we may, indeed, consider
it as demonstrated.
SALVIATI. I do not wish3 Sagredo, that we trouble ourselves too much
about this matter, since we are g'oing to apply this principle mainly in
motions which occur on plane surfaces, and not upon curved, along which
acceleration varies in a manner greatly different from that which we have
assumed for planes.
So that, although the above experiment shows us that the descent
of the moving body through the arc CB confers upon it momentum just
sufficient to carry it to the same height through any of the arcs BD, BG,
BI, we are not able, by similar means, to show that the event would be
identical in the case of a perfectly round ball descending along planes
whose inclinations are respectively the same as the chords of these arcs.
It seems likely, on the other hand, that, since these planes form angles at
GALILEO — DIALOGUES
143
the point B, they will present an obstacle to the ball which has descended
along the chord CB and starts to rise along the chord BD, BG, BI.
In striking these planes some of its momentum will be lost and it
will not be able to rise to the height of the line CD; but this obstacle,
which interferes with the experiment, once removed, it is clear that the
momentum (which gains in strength with descent) will be able to carry
the body to the same height. Let us then, for the present, take this as a
postulate, the absolute truth of which will be established when we find
that the inferences from it correspond to and agree perfectly with experi-
ment. The Author having assumed this single principle passes next to the
propositions which he clearly demonstrates; the first of these is as follows:
Theorem I, Proposition I
The time in which any space is traversed by a body starting from
rest and uniformly accelerated is equal to the time in which that
same space would be traversed by the same body moving at a uni-
form speed whose value is the mean of the highest speed and the
speed just before acceleration began.
Let us represent by the line AB the time in which the space CD is
traversed by a body which starts from rest at C and is uniformly acceler-
ated; let the final and highest value of the speed ^
gained during the interval AB be represented by
the line EB drawn at right angles to AB; draw the
line AE, then all lines drawn from equidistant
points on AB and parallel to BE will represent the
increasing values of the speed, beginning with
the instant A. Let the point F bisect the line EB;
draw FG parallel to BA, and GA parallel to FB,
thus forming a parallelogram AGFB which will be
equal in area to the triangle AEB, since the side
GF bisects the side AE at the point I; for if the
parallel lines in the triangle AEB are extended to
GI, then the sum of all the parallels contained in
the quadrilateral is equal to the sum of those con-
tained in the triangle AEB; for those in the tri-
angle IEF are equal to those contained in the
triangle GIA, while those included in the trape-
zium AIFB are common. Since each and every in-
stant of time in the time-interval AB has its cor-
responding point on the line AB, from which
points parallels drawn in and limited by the triangle AEB represent the
increasing values of the growing velocity, and since parallels" contained
within the rectangle represent the values of a speed which is not increas-
ing, but constant, it appears, in like manner, that the momenta assumed
by the moving body may also be represented, in the case of the accelerated
144
MASTERWORKS OF SCIENCE
motion, by the increasing parallels of the triangle AEB, and, in the case
of the uniform motion, by the parallels of the rectangle GB. For, what
the momenta may lack in the first part of the accelerated motion (the
deficiency of the momenta being represented by the parallels of the
triangle AGI) is made up by the momenta represented by the parallels
of the triangle IEF.
Hence it is clear that equal spaces will be traversed in equal times
by two bodies, one of which, starting from rest, moves with a uniform
acceleration, while the momentum of the other, moving with uniform
speed, is one-half its maximum momentum under accelerated motion.
Q.E.D.
Theorem II, Proposition II
The spaces described by a body failing from rest with a uniformly
accelerated motion are to each other as the squares of the time-
intervals employed in traversing these distances.
Let the time beginning with any Instant A be represented by the
straight line AB in which are taken any two time-intervals AD and AE.
Let HI represent the distance through which the body, starting from rest
at H, falls with uniform acceleration. If HL repre-
sents the space traversed during the time-interval
AD, and HM that covered during the interval AE,
then the space MH stands to the space LH in a
ratio which is the square of the ratio of the time AE
to the time AD; or we may say simply that the dis-
tances HM and HL are related as the squares of AE
and AD.
Draw the line AC making any angle whatever
with the line AB; and from the points D and E,
draw the parallel lines DO and EP; of these two
lines, DO represents the greatest velocity attained^
during the interval AD, while EP represents the
maximum velocity acquired during the interval AE.
But it has just been proved that so far as distances
traversed are concerned it is precisely the same
whether a body falls from rest with a uniform ac-
celeration or whether it falls during an, equal time-
interval with a constant speed which is one-half the
maximum speed attained during the accelerated mo-
tion. It follows therefore that the distances HM and
HL are the same as would be traversed, during the
time-intervals AE and AD, by uniform velocities
equal to one-half those represented by DO and EP
respectively. If, therefore, one can show that the dis-
tances HM and HL are in the same ratio as the
GALILEO — DIALOGUES 145
squares of the time-intervals AE and AD, our proposition will be proven.
It has been shown that the spaces traversed by two particles in uni-
form motion bear to one another a ratio which is equal to the product
of the ratio of the velocities by the ratio of the times. But in this case the
ratio of the velocities is the same as the ratio of the time-intervals (for
the ratio of AE to AD is the same as that of %EP to %DO or of EP to
DO). Hence the ratio of the spaces traversed is the same as the squared
ratio of the time-intervals. Q.E.D.
Evidently then the ratio of the distances is the square of the ratio of
the final velocities, that is, of the lines EP and DO, since these are to
each other as AE to AD.
Corollary
Hence it is clear that if we take any equal intervals of time whatever,
counting from the beginning of the motion, such as AD, DE, EF, FG, in
which the spaces HL, LM, MN, NI are traversed, these spaces will bear
to one another the same ratio as the series of odd numbers, i, 3, 5, 7; for
this is the ratio of the differences of the squares of the lines [which repre-
sent time], differences which exceed one another by equal amounts, this
excess being equal to the smallest line [viz. the one representing a single
time-interval]: or we may say [that this is the ratio] of the differences of
the squares of the natural numbers beginning with unity.
While, therefore, during equal intervals of time the velocities increase
as the natural numbers, the increments in the distances traversed during
these equal time-intervals are to one another as the odd numbers begin-
ning with unity.
SIMPLICIO. I am convinced that matters 'are as described, once having
accepted the definition of uniformly accelerated motion. But as to whether
this acceleration is that which one meets in nature in the case of falling
bodies, I am still doubtful; and it seems to me, not only for my own sake
but also for all those who think as I do, that this would be the proper
moment to introduce one of those experiments — and there are many of
them, I understand — which illustrate in several ways the conclusions
reached.
SALVIATI. The request which you, as a man of science, make, is a very
reasonable one; for this is the custom — and properly so — in those sciences
where mathematical demonstrations are applied to natural phenomena,
as is seen in the case of perspective, astronomy, mechanics, music, and
others where the principles, once established by well-chosen experiments,
become the foundations of the entire superstructure. I hope therefore it
will not appear to be a waste of time if we discuss at considerable length
this first and most fundamental question upon which hinge numerous
consequences of which we have in this book only a small number, placed
there by the Author, who has done so much to open a pathway hitherto
closed to minds of speculative turn. So far as experiments go they have
146 MASTERWORKS OF SCIENCE
not been neglected by the Author; and often, in his company, I have
attempted in the following manner to assure myself that the acceleration
actually experienced by falling bodies is that above described.
A piece of wpoden moulding or scantling, about 12 cubits long, half
a cubit wide, and three fmgerbreadths thick, was taken; on its edge was
cut a channel a little more than one finger in breadth; having made this
groove very straight, smooth, and polished, and having lined it with parch-
ment, also as smooth and polished as possible, we rolled along it a hard,,
smooth, and very round bronze ball. Having placed this board in a sloping
position, by lifting one end some one or two cubits above the other, we
rolled the ball, as I was just saying, along the channel, noting, in a man-
ner presently to be described, the time required to make the descent. We
repeated this experiment more than once in order to measure the time
with an accuracy such that the deviation between two observations never
exceeded one-tenth of a pulse beat. Having performed this operation and
having assured ourselves of its reliability, we now rolled the ball only one-
quarter the length of the channel; and having measured the time of its
descent, we found it precisely one-half of the former. Next we tried other
distances, comparing the time for the whole length with that for the half,
or with that for two-thirds, or three-fourths, or indeed for any fraction; in
such experiments, repeated a full hundred times, we always found that the
spaces traversed were to each other as the squares of the times, and this
was true for all inclinations of the plane, i. e., of the channel, along which
we rolled the ball. We also observed that the times of descent, for various
inclinations of the plane, bore to one another precisely that ratio which,
as we shall see later, the Author had predicted and demonstrated for
them.
For the measurement of time, we employed a large vessel of water
placed in an elevated position; to the bottom of this vessel was soldered
a pipe of small diameter giving a thin jet of water, which we collected in a
small glass during the time of each descent, whether for the whole length
of the channel or for a part of its length; the water thus collected was
weighed, after each descent, on a very accurate balance; the differences
and ratios of these weights gave us the differences and ratios of the times,
and this with such accuracy that although the operation was repeated
many, many times, there was no appreciable discrepancy in the results.
SIMPLICIO. I would like to have been present at these experiments;
but feeling confidence in the care with which you performed them, and
in the fidelity with which you relate them, I am satisfied and accept them
as true and valid.
SALVIATI. Then we can proceed without discussion.
Theorem HI, Proposition III
If one and the same body, starting from rest, falls along an inclined
plane and also along a vertical, each having the same height, the
GALILEO — DIALOGUES
147
times of descent will be to each other as the lengths of the inclined
plane and the vertical.
Let AC be the inclined plane and AB the perpendicular, each having
the same vertical height above the horizontal, namely, BA; then I say,
the time of descent of one and the same body along the plane AC bears
a ratio to the time of fall along the perpendicular AB, which is the same
as the ratio of the length AC to the length AB. Let DG, El and LF be any
lines parallel to the horizontal CB; then it follows from what has preceded
that a body starting from A will acquire the same speed at the point G
as at D, since in each case the vertical fall is the same; in like manner the
speeds at I and E will be the same; so also those at L and F. And in
general the speeds at the two extremities of any parallel drawn from any
point on AB to the corresponding point on AC will be equal.
Thus the two distances AC and AB are traversed at the same speed.
But it has already been proved that if two distances are traversed by a
body moving with equal speeds, then the ratio of the times of descent
will be the ratio of the distances themselves; therefore, the time of descent
along AC is to that along AB as the length of the plane AC is to the
vertical distance AB. Q.E.D.
SAGREDO. It seems to me that the above could have been proved clearly
and briefly on the basis of a proposition already demonstrated, namely,
that the distance traversed in the case of accelerated motion along AC or
AB is the same as that covered by a uniform speed whose value is one-
half the maximum speed, CB; the two distances AC and AB having been
traversed at the same uniform speed it is evident, from Proposition I,
that the times of descent will be to each other as the distances.
Theorem IV, Proposition IV
If from the highest or lowest point in a vertical circle there be
drawn any inclined planes meeting the circumference the times of
descent along these chords are each equal to the other.
On the horizontal line GH construct a vertical circle. From its lowest
point — the point of tangency with the horizontal — draw the diameter FA
148
MASTERWORKS OF SCIENCE
and from the highest point, A, draw inclined planes to B and C, any
points whatever on the circumference; then the times of descent along
these are equal. Draw BD and CE perpendicular to the diameter; make
AI a mean proportional between the heights of the planes, AE and AD;
and since the rectangles FA.AE and FA.AD are respectively equal to the
squares of AC and AB, while the rectangle FA.AE is to the rectangle
FA.AD as AE is to AD, it follows that the square of AC is to the square
of AB as the length AE is to the length AD. But since the length AE is
to AD as the square of AI is to the square of AD, it follows that the
squares on the lines AC and AB are to each other as the squares on the
lines AI and AD, and hence also the length AC is to the length AB as AI
is to AD. But it has previously been demonstrated that the ratio of the
time of descent along AC to that along AB is equal to the product of the
two ratios AC to AB and AD to AI; but this last ratio is the same as that
of AB to AC. Therefore the ratio of the time of descent along AC to that
along AB is the product of the two ratios, AC to AB and AB to AC. The
ratio of these times is therefore unity. Hence follows our proposition.
By use of the principles of mechanics one may obtain the same result.
Scholium
We may remark that any velocity once imparted to a moving body will
be rigidly maintained as long as the external causes of acceleration or retar-
dation are removed, a condition which is found only on horizontal planes;
for in the case of planes which slope downwards there is already present
a cause of acceleration, while on planes sloping upward there is retar-
dation; from this it follows that motion along a horizontal plane is per-
petual; for, if the velocity be uniform, it cannot be diminished or slackened,
much less destroyed. Further, although any velocity which a body may
have acquired through natural fall is permanently maintained so far as
GALILEO — DIALOGUES 149
its own nature is concerned, yet it must be remembered that if, after
descent along a plane inclined downwards, the body is deflected to a plane
inclined upwards, there is already existing in this latter plane a cause of
retardation; for in any such plane this same body is subject to a natural
acceleration downwards. Accordingly we have here the superposition of
two different states, namely, the velocity acquired during the preceding
fail which if acting alone would carry the body at a uniform rate to
infinity, and the velocity which results from a natural acceleration down-
wards common to all bodies. It seems altogether reasonable, therefore, if
we wish to trace the future history of a body which has descended along
some inclined plane and has been deflected along some plane inclined
upwards, for us to assume that the maximum speed acquired during
descent is permanently maintained during the ascent. In the ascent, how-
ever, there supervenes a natural inclination downwards, namely, a motion
which, starting from rest, is accelerated at the usual rate. If perhaps this
discussion is a little obscure, the following figure will help to make it
clearer.
C F A.
Let us suppose that the descent has been made along the downward
sloping plane AB, from which the body is deflected so as to continue its
motion along the upward sloping plane BC; and first let these planes be
of equal length and placed so as to make equal angles with the horizontal
line GH. Now it is well known that a body, starting from rest at A, and
descending along AB, acquires a speed which is proportional to the time,
which is a maximum at B, and which is maintained by the body so long
as all causes of fresh acceleration or retardation are removed; the acceler-
ation to which I refer is that to which the body would be subject if its
motion were continued along the plane AB extended, while the retarda-
tion is that which the body would encounter if its motion were deflected
along the plane BC inclined upwards; but, upon the horizontal plane GH,
the body would maintain a uniform velocity equal to that which it had
acquired at B after fall from A; moreover this velocity is such that, during
an interval of time equal to the time of descent through AB, the body will
traverse a horizontal distance equal to twice AB. Now let us imagine this
same body to move with the same uniform speed along the plane BC so
that here also during a time-irfterval equal to that of descent along AB, it
will traverse along BC extended a distance twice AB; but let us suppose
that, at the very instant the body begins its ascent it is subjected, by its
very nature, to the same influences which surrounded it during its descent
from A along AB, namely, it descends from rest under the same acceler-
MASTERWORKS OF SCIENCE
atlon as that which was effective in AB, and it traverses, during an equal
interval of time, the same distance along this second plane as it did along
AB; it is clear that, by thus superposing upon the body a uniform motion
of ascent and an accelerated motion of descent, it will be carried along
the plane BC as far as the point C where these two velocities become
equal.
If now we assume any two points D and E, equally distant from the
vertex B, we may then infer that the descent along BD takes place in the
same time as the ascent along BE. Draw DF parallel to BC; we know
that, after descent along AD, the body will ascend along DF; or, if, on
reaching D, the body is carried along the horizontal DE, it will reach E
with the same momentum with which it left D; hence from E the body
will ascend as far as C, proving that the velocity at E is the same as
that at D.
- From this we may logically infer that a body which descends along
any inclined plane and continues its motion along a plane inclined up-
wards will, on account of the momentum acquired, ascend to an equal
height above the horizontal; so that if the descent is along AB the body will
be carried up the plane BC as far as the horizontal line ACD: and this is
true whether the inclinations of the planes are the same or different, as in
the case of the planes AB and BD. But by a previous postulate the speeds
acquired by fall along variously inclined planes having the same vertical
height are the same. If therefore the planes EB and BD have the same
slope, the descent along EB will be able to drive the body along BD as far
as D; and since this propulsion comes from the speed acquired on reach-
ing the point B, it follows that this speed at B is the same whether the
body has made its descent along AB or EB. Evidently then the body will
be carried up BD whether the descent has been made along AB or along
EB. The time of ascent along BD is however greater than that along BC?
just as the descent along EB occupies more time than that along AB;
moreover it has been demonstrated that the ratio between the lengths of
these times is the same as that between the lengths of the planes.
Conclusion
SAGREDO. Indeed, I think we may concede to our Academician, with-
out flattery, his claim that in the principle laid down in this treatise he
has established a new science dealing with a very old subject. Observing
GALILEO — DIALOGUES 151
with what ease and clearness he deduces from a single principle the proofs
of so many theorems, I wonder not a little how such a question escaped
the attention of Archimedes, Apollonius, Euclid and so many other mathe-
maticians and illustrious philosophers, especially since so many ponderous
tomes have been devoted to the subject of motion.
SALVIATI. There is a fragment of Euclid which treats of motion, but
in it there is no indication that he ever began to investigate the property
of acceleration and the manner in which it varies with slope. So that we
may say the door is now opened, for the first time, to a new method
fraught with numerous and wonderful results which in future years will
command the attention of other minds.
SAGREDO. I really believe that just as, for instance, the few properties
of the circle proven by Euclid in the Third Book of his Elements lead to
many others more recondite, so the principles which are set forth in this
little treatise will, when taken up by speculative minds, lead to many
another more remarkable result; and it is to be believed that it will be so
on account of the nobility of the subject, which is superior to any other
in nature.
During this long and laborious day, I have enjoyed these simple
theorems more than their proofs, many of which, for their complete
comprehension, would require more than an hour each; this study, if you
will be good enough to leave the book in my hands, is one which I mean
to take up at my leisure after we have read the remaining portion which
deals with the motion of projectiles; and this if agreeable to you we shall
take up tomorrow.
SALVIATI, I shall not fail to be with you.
END OF THIRD DAY
FOURTH DAY
SALVIATI. Once more, Simplicio is here on time; so let us without
delay take up the question of motion. The text of our Author is as follows:
THE"MOTION OF PROJECTILES
In the preceding pages we have discussed the properties of motion
naturally accelerated. I now propose to set forth those properties which
belong to a body whose motion is compounded of two other motions,
namely, one uniform and one naturally accelerated; these properties, well
worth knowing, I propose to demonstrate in a rigid manner. This is the
kind of motion seen in a moving projectile; its origin I conceive to be
as follows:
Imagine any particle projected along a horizontal plane without fric-
152 MASTERWORKS OF SCIENCE
tion; then we know, from what has been more fully explained in the
preceding pages, that this particle will move along this same plane with
a motion which is uniform and perpetual, provided the plane has no
limits. But if the plane is limited and elevated, then the moving particle,
which we imagine to be a heavy one, will on passing over the edge of
the plane acquire, in addition to its previous uniform and perpetual
motion, a downward propensity due to its own weight; so that the result-
ing motion which I call projection is compounded of one which is uni-
form and horizontal and of another which is vertical and naturally ac-
celerated. We now proceed to demonstrate some of its properties, the first
-of which is as follows:
Theorem I, Proposition I
A projectile which is carried by a uniform horizontal motion com-
pounded with a naturally accelerated vertical motion describes a
path which is a semi-parabola.
SAGREDO. Here, Salviati, it will be necessary to stop a little while for
my sake and, I believe, also for the benefit of Simplicio; for it so happens
that I have not gone very far in my study of Apollonius and am merely
aware of the fact that he treats of the parabola and other conic sections,
without an understanding of which I hardly think one will be able to
follow the proof of other propositions depending upon them. Since even
in this first beautiful theorem the Author finds it necessary to prove that
the path of a projectile is a parabola, and since, as I imagine, we shall
have to deal with only this kind of curves, it will be absolutely necessary
to have a thorough acquaintance, if not with all the properties which
Apollonius has demonstrated for these figures, at least with those which
are needed for the present treatment.
SIMPLICIO. Now even though Sagredo is, as I believe, well equipped
for all his needs, I do not understand even the elementary terms; for
.although our philosophers have treated the motion of projectiles, I do
not recall their having described the path of a projectile except to state
in a general way that it is always a curved line, unless the projection be
vertically upwards. But if the little Euclid which I have learned since our
previous discussion does not enable me to understand the demonstrations
which are to follow, then I shall be obliged to "accept the theorems on
.faith without fully comprehending them.
SALVIATI. On the contrary, I desire that you should understand them
from the Author himself, who, when he allowed me to see this work
•of his, was good enough to prove for me two of the principal properties
of the parabola because I did not happen to have at hand the books of
Apollonius. These properties, which are the only ones we shall need in the
present discussion, he proved in such a way that no prerequisite knowl-
edge was required. These theorems are, indeed, given by Apollonius, but
after many preceding ones, to follow which would take a long while. I
GALILEO — DIALOGUES 153
wish to shorten our task by deriving the first property purely and simply
from the mode of generation of the parabola.
Beginning now with the first, imagine a right cone, erected upon the
circular base ib\c with apex at /. The section of this cone made by a
plane drawn parallel to the side l\ is the curve which is called a parabola*
The base of this parabola be cuts at right angles the diameter i\ of the
circle lb\c, and the axis ad is parallel to the side l\; now having taken,
any point / in the curve bja draw the straight line fe parallel to bd; then,,
I say, the square of bd is to the square of fe in the same ratio as the axis
ad is to the portion ae.
I
We can now resume the text and see how the Author demonstrates
his first proposition in which he shows that a body falling with a motion
compounded of a uniform horizontal and a naturally accelerated one
describes a semi-parabola.
Let us imagine an elevated horizontal line or plane ab along which
a body moves with uniform speed from a to b. Suppose this plane to
end abruptly at b; then at this point the body will, on account of its
weight, acquire also a natural motion downwards along the perpendicu-
lar bn. Draw the line be along the plane ba to represent the flow, or
measure, of time; divide this line into a number of segments, be, cd, det
representing equal intervals of time; from the points b, c, d, e, let fall
lines which are parallel to the perpendicular bn. On the first of these lay
off any distance cit on the second a distance four times as long, dj; on
the third, one nine times as long, eh; and so on, in proportion to the
•squares of cb, db, eb, or, we may say, in the squared ratio of these same
lines. Accordingly we see that while the body moves from b to c with
uniform speed, it also falls perpendicularly through the distance el, and
at the end of the time-interval be finds itself at the point /. In like manner
at the end of the time-interval bd, which is the double of be, the vertical
fall will be four times the first distance ci; for it has been shown in a
previous discussion that the distance traversed by a freely falling body
varies as the square of the time; in like manner the space eh traversed
154
MASTERWORKS OF SCIENCE
during the time be will be nine times ci; thus it is evident that the dis-
tances eh, df, ci will be to one another as the squares of the lines be, bdf
be. Now from the points i, f, h draw the straight lines io, fg, hi parallel
to be; these lines hi, fg, Jo are equal to eb, db and cb, respectively; so also
are the lines bo, bg, bl respectively equal to ci, dj, and eh. The square of
hi is to that of fg as the line Ib is to bg; and the square of fg is to that
of io as gb is to bo; therefore the points /, /, h, lie on one and the same
parabola. In like manner it may be shown that, if we take equal time-
intervals of any size whatever, and if we imagine the particle to be carried
by a similar compound motion, the positions of this particle, at the ends
of these time-intervals, will lie on one and the same parabola. Q.E.D.
This conclusion follows the converse of the first of the two propo-
sitions given above. For, having drawn a parabola through the points
b and h, any other two points, / and /, not falling on the parabola
must lie either within or without; consequently the line fg is either
longer or shorter than the line which terminates on the parabola. There-
fore the square of hi will not bear to the square of fg the same ratio as
the line Ib to bg, but a greater or smaller; the fact is, however, that the
square of hi does bear this same ratio to the square of fg. Hence the point
/ does lie on the parabola, and so do all the others.
SAGREDO. One cannot deny that the argument is new, subtle and con-
clusive, resting as it does upon this hypothesis, namely, that the hori-
zontal motion remains uniform, that the vertical motion continues to be
accelerated downwards in proportion to the square of the time, and that
such motions and velocities as these combine without altering, disturb-
ing, or hindering each other, so that as the motion proceeds the path
of the projectile does not change into a different curve: but this, in my
opinion, is impossible. For the axis of the parabola along which we
imagine the natural motion of a falling body to take place stands perpen-
dicular to a horizontal surface and ends at the center of the earth; and
since the parabola deviates more and more from its axis no projectile
can ever reach the center of the earth or, if it does, as seems necessary,
then the path of the projectile must transform itself into some other curve
very different from the parabola.
GALILEO — DIALOGUES 155
SIMPLICIO. To these difficulties, I may add others. One of these is
that we suppose the horizontal plane, which slopes neither up nor down,
to be represented by a straight line as if each point on this line were
equally distant from the center, which is not the case; for as one starts
from the middle [of the line] and goes toward either end, he departs
farther and farther from the center [of the earth] and is therefore con-
stantly going uphill. Whence it follows that the motion cannot remain
uniform through any distance whatever, but must continually dimmish.
Besides, I do not see how it is possible to avoid the resistance of the
medium which must destroy the uniformity of the horizontal motion and
change the law of acceleration of falling bodies. These various difficulties
render it highly improbable that a result derived from such unreliable
hypotheses should hold true in practice.
SALVIATI. All these difficulties and objections which you urge are so
well founded that it is impossible to remove them; and, as for me, I am
ready to admit them all, which indeed I think our Author would also do.
I grant that these conclusions proved in the abstract will be different
when applied in the concrete and will be fallacious to this extent, that
neither will the horizontal motion be uniform nor the natural accelera-
tion be in the ratio assumed, nor the path of the projectile a parabola,
etc. But, on the other hand, I ask you not to begrudge our Author that
which other eminent men have assumed even if not strictly true. The
authority of Archimedes alone will satisfy everybody. In his Mechanics
and in his first quadrature of the parabola he takes for granted that the
beam of a balance or steelyard is a straight line, every point of which is
equidistant from the common center of all heavy bodies, and that the
cords by which heavy bodies are suspended are parallel to each other.
Some consider this assumption permissible because, in practice, our in-
struments and the distances involved are so small in comparison with the
enormous distance from the center of the earth that we may consider a
minute of arc on a great circle as a straight line, and may regard the per-
pendiculars let fall from its two extremities as parallel. For if in actual prac-
tice one had to consider such small quantities, it would be necessary firs^t of
all to criticise the architects who presume, by use of a plumb line, to erect
high towers with parallel sides. I may add that, in all their discussions,
Archimedes and the others considered themselves as located at an infinite
distance from the center of the earth, in which case their assumptions were
not false, and therefore their conclusions were absolutely correct. When we
wish to apply our proven conclusions to distances which, though finite,
are very large, it is necessary for us to infer, on the basis of demonstrated
trjith, what correction is to be made for the fact that our distance from
the center of the earth is not really infinite, but merely very great in com-
parison with the small dimensions of our apparatus. The largest of the^se
will be the range of our projectiles — and even here we need consider only
the artillery — which, however great, will never exceed four of those miles
of which as many thousand separate us from the center of the earth; and
since these paths terminate upon the surface of the earth only very slight
156 MASTERWQRKS OF SCIENCE
changes can take place in their parabolic figure which, it is conceded,
would be greatly altered if they terminated at the center of the earth.
As to the perturbation arising from the resistance of the medium this
is more considerable and does not, on account of its manifold forms, sub-
mit to fixed laws and exact description. Thus if we consider only the
resistance which the air offers to the motions studied by us, we shall see
that it disturbs them all and disturbs them in an infinite variety of ways
•corresponding to the infinite variety in the form, weight, and velocity
of the projectiles. For as to velocity, the greater this is, the greater will
be the resistance offered by the air; a resistance which will be greater as
the moving bodies become less dense. So that although the falling body
ought to be displaced in proportion to the square of the duration of its
motion, yet no matter how heavy the body, if it falls from a very consid-
erable height, the resistance of the air will be such as to prevent any
increase in speed and will render the motion uniform; and in proportion
as the moving body is less dense this uniformity will be so much the
more quickly attained and after a shorter fall. Even horizontal motion
which, if no impediment were offered, would be uniform and constant is
altered by the resistance of the air and finally ceases; and here again the
less dense the body the quicker the process. Of these properties of weight,
of velocity, and also of form, infinite in number, it is not possible to give
.any exact description; hence, in order to handle this matter in a scientific
way, it is necessary to cut loose from these difficulties; and having discov-
ered and demonstrated the theorems, in the case o£ no resistance, to
use them and apply them with such limitations as experience will teach.
And the advantage of this method will not be small; for the material and
.shape of the projectile may be chosen, as dense and round as possible, so
that it will encounter the least resistance in the medium. Nor will the
spaces and velocities in general be so great but that we shall be easily able
to correct them with precision.
In the case of those projectiles which we use, made of dense material
and round in shape, or of lighter material and cylindrical in shape, such
as arrows, thrown from a sling or crossbow, the deviation from an exact
parabolic path is quite insensible. Indeed, if you will allow me a little
greater liberty, I can show you, by two experiments, that the dimensions
of our apparatus are so small that these external and incidental resistances,
among which that of the medium is the most considerable, are scarcely
observable.
I now proceed to the consideration of motions through the air, since
it is with these that we are now especially concerned; the resistance of
the air exhibits itself in two ways: first by offering greater impedance to
less dense than to very dense bodies, and secondly by offering greater
resistance to a body in rapid motion than to the same body in slow
motion.
Regarding the first of these, consider the case of two balls having
the same dimensions, but one weighing ten or twelve times as much as
GALILEO — DIALOGUES 157
the other; one, say, of lead, the other of oak, both allowed to fall from
an elevation of 150 or 200 cubits.
Experiment shows that they will reach the earth with slight differ-
ence in speed, showing us that in both cases the retardation caused by
the air is small; for if both balls start at the same moment and at the same
elevation, and if the leaden one be slightly retarded and the wooden one
greatly retarded, then the former ought to reach the earth a considerable
distance in advance of the latter, since it is ten times as heavy. But this
does not happen; indeed, the gain in distance of one over the other does
not amount to the hundredth part of the entire fall. And in the case of a
ball of stone weighing only a third or half as much as one of lead, the
difference in their times of reaching the earth will be scarcely noticeable-
Now since the speed acquired by a leaden ball in falling from a height
of 200 cubits is so great that if the motion remained uniform the ball
would, in an interval of time equal to that of the fall, traverse 400 cubits,
and since this speed is so considerable in comparison with those which,
by use of bows or other machines except firearms, we are able to give to
our projectiles, it follows that we may, without sensible error, regard as
absolutely true those propositions which we are about to prove without
considering the resistance of the medium.
Passing now to the second case, where we have to show that the
resistance of the air for a rapidly moving body is not very much greater
than for one moving slowly, ample proof is given by the following experi-
ment. Attach to two threads of equal length — say four or five yards — two
equal leaden balls and suspend them from the ceiling; now pull them
aside from the perpendicular, the one through 80 or more degrees, the
other through not more than four or five degrees; so that, when set free,
the one falls, passes through the perpendicular, and describes large but
slowly decreasing arcs of 160, 150, 140 degrees, etc.; the other swinging
through small and also slowly diminishing arcs of 10, 8, 6 degrees, etc.
In the first place it must be remarked that one pendulum passes
through its arcs of 180°, 160°, etc., in the same time that the other swings
through its 10°, 8°, etc., from which it follows that the speed of the first
ball is 1 6 and 18 times greater than that of the second. Accordingly, if
the air offers more resistance to the high speed than to the low, the fre-
quency of vibration in the large arcs of 180° or 160°, etc., ought to be less
than in the small arcs of 10°, 8°, 4°, etc., and even less than in arcs
of 2°, or i°; but this prediction is not verified by experiment; because
if two persons start to count the vibrations, the one the large, the other
the small, they will discover that after counting tens and even hundreds
they will not differ by a single vibration, not even by a fraction of one.
This observation justifies the two following propositions, namely,
that vibrations of very large and very small amplitude all occupy the
same time and that the resistance of the air does not affect motions of
high speed more than those of low speed, contrary to the opinion hitherto
generally entertained.
SAGREDO. On the contrary, since we cannot deny that the air hinders
158 MASTERWORKS OF SCIENCE
both of these motions, both becoming slower and finally vanishing, we
have to admit that the retardation occurs in the same proportion in each
case. But how? How, indeed, could the resistance offered to the one body
be greater than that offered to the other except by the impartation of
more momentum and speed to the fast body than to the slow? And if
this is so the speed with which a body moves is at once the cause and
measure of the resistance which it meets. Therefore, all motions, fast or
slow, are hindered and diminished in the same proportion; a result, it
seems to me, of no small importance.
SALVIATI. We are able, therefore, in this second case to say that the
errors, neglecting those which are accidental, in the results which we are
about to demonstrate are small in the case of our machines where the
velocities employed are mostly very great and the distances negligible in
comparison with the semi-diameter of the earth or one of its great circles.
SIMPLICIO. I would like to hear your reason for putting the projectiles
of firearms, i. e., those using powder, in a different class from the projec-
tiles employed in bows, slings, and crossbows, on the ground of their not
being equally subject to change and resistance from the air. *
SALVIATI. I am led to this view by the excessive and, so to speak,
supernatural violence with which such projectiles are launched; for, in-
deed, it appears to me that without exaggeration one might say that the
speed of a ball fired either from a musket or from a piece of ordnance
is supernatural. For if such a ball be allowed to fall from some great ele-
vation its speed will, owing to the resistance of the air, not go on increas-
ing indefinitely; that which happens to bodies of small density in falling
through short distancesr— I mean the reduction of their motion to uni-
formity— will also happen to a ball of iron or lead after it has fallen a few
thousand cubits; this terminal or final speed is the maximum which such
a heavy body can naturally acquire in falling through the air. This speed
I estimate to be much smaller than that impressed upon the ball by the
burning powder.
An appropriate experiment will serve to demonstrate this fact. From
a height of one hundred or more cubits fire a gun loaded with a lead bul-
let vertically downwards upon a stone pavement; with the same gun
shoot* against a similar stone from a distance of one or two cubits, and
observe which of the two balls is the more flattened. Now if the ball
which has come from the greater elevation is found to be the less flattened
of the two, this will show that the air has hindered and diminished the
speed initially imparted to the bullet by the powder, and that the air will
not permit a bullet to acquire so great a speed, no matter from what
height it falls; for if the speed impressed upon the ball by the fire does
not exceed that acquired by it in falling freely then its downward blow
ought to be greater rather than less.
This experiment I have not performed, but I am of the opinion that
a musket ball or cannon shot, falling from a height as great as you please,
will not deliver so strong a blow as it would if fired into a wall only a
few cubits distant, i. e., at such a short range that the splitting or rending
GALILEO — DIALOGUES 159
of the air will not be sufficient to rob the shot of that excess of super-
natural violence given it by the powder.
The enormous momentum of these violent shots may cause some
deformation of the trajectory, making the beginning of the parabola flat-
ter and less curved than the end; but, so far as our Author is concerned,
this is a matter of small consequence in practical operations, the main
one of which is the preparation of a table of ranges for shots of high
elevation, giving the distance attained by the ball as a function of the
angle of elevation; and since shots of this kind are fired from mortars
using small charges and imparting no supernatural momentum they fol-
low their prescribed paths very exactly.
But now let us proceed with the discussion in which the Author
invites us to the study and investigation of the motion of a body when
that motion is compounded of two others; and first the case in which the
two are uniform, the one horizontal, the other vertical.
Theorem II, Proposition 11
When the motion of a body is the resultant of two uniform mo-
tions, one horizontal, the other perpendicular, the square of the
resultant momentum is equal to the sum of the squares of the two
component momenta.
a
SIMPLICIO. At this point there is just one slight difficulty which
needs to be cleared up; for it seems to me that the conclusion just reached
contradicts a previous proposition in which it is claimed that the speed
of a body coming from a to b is equal to that in coming from a to c;
while now you conclude that the speed at c is greater than that at b.
SALVIATI. Both propositions, Simplicio, are true, yet there is a great
difference between them. Here we are speaking of a body urged by a
single motion which is the resultant of two uniform motions, while there
we were speaking of two bodies each urged with naturally accelerated
motions, one along the vertical ab the other along the inclined plane ac.
Besides the time-intervals were there not supposed to be equal, that along
the incline ac being greater than that along the vertical ab; but the
motions of which we now speak, those along ab, be, ac, are uniform and
simultaneous.
SIMPLICIO. Pardon me; I am satisfied; pray go on.
SALVIATI. Our Author next undertakes to explain what happens- when
a body is urged 'by a motion compounded of one which is horizontal and
uniform and of another which is vertical but naturally accelerated; from
these two components results the path of a projectile, which is a parab-
160 MASTERWQRKS OF SCIENCE _
ola, The problem is to determine the speed of the projectile at each point.
With this purpose in view our Author sets forth as follows the manner,
or rather the method, of measuring such speed along the path which is
taken by a heavy body starting from rest and falling with a naturally
accelerated motion.
Theorem III, Proposition HI
Let the motion take place along the line ab, starting from rest at a,
and in this line choose any point c. Let ac represent the time, or the
measure of the time, required for the body to fall through the space ac;
let ac also represent the velocity at c acquired by a fall through the dis-
tance ac. In the line ab select any other point b. The problem now is to
determine the velocity at b acquired by a body in falling through the
distance ab and to express this in terms of the velocity at c, the measure
of which is the length ac. Take as a mean proportional between ac and
ab. We shall prove that the velocity at b is to that at c as the length as
is to the length ac. Draw the horizontal line cd, having twice the length
of ac, and be, having twice the length of ba. It then follows, from the pre-
ceding theorems, that a body falling through the distance ac, and turned
so as to move along the horizontal cd with a uniform speed equal to that
acquired on reaching c, will traverse the distance cd in the same interval
of time as that required to fall with accelerated motion from a to c. Like-
wise be will be traversed in the same time as ba. But the time of descent
through ab is as; hence the horizontal distance be is also traversed in the
time as. Take a point / such that the time as is to the time ac as be is to
bl; since the motion along be is uniform, the distance bl, if traversed with
the speed acquired at b, will occupy the time ac; but in this same time-
interval, ac, the distance cd is traversed with the speed acquired in c.
Now two speeds are to each other as the distances traversed in equal in-
tervals of time. Hence the speed at c is to the speed at b as cd is to bl. But
since dc is to be as their halves, namely, as ca is to ba, and since be is to
bl as ba is to sa; it follows that dc is to bl as ca is to sa. In other words,
the speed at c is to that at b as ca is to sa, that is, as the time to fall
through ab.
\ The method of measuring the speed of a body along the direction
of its fall is thus clear; the speed is assumed to increase directly as the
time.
GALILEO — DIALOGUES 161
Problem. Proposition IV
SALVIATI. Concerning motions and their velocities or momenta
whether uniform or naturally accelerated, one cannot speak definitely
until he has established a measure for such velocities and also for time.
As foretime we have the already widely adopted hours, first minutes and
second minutes. So for velocities, just as for intervals of time, there is
need of a common standard which shall be understood and accepted by
everyone, and which shall be the same for all. As has already been stated,
the Author considers the velocity of a freely falling body adapted to this
purpose, since this velocity increases according to the same law in all
parts of the world; thus for instance the speed acquired by a leaden ball
of a pound weight starting from rest and falling vertically through the
height of, say, a spear's length is the same in all places; it is therefore
excellently adapted for representing the momentum acquired in the case
of natural fall.
It still remains for us to discover a method of measuring momentum
in the case of uniform motion in such a way that all who discuss the
subject will form the same conception of its size and velocity. This will
prevent one person from imagining it larger, another smaller, than It
really is; so that in the composition of a given uniform motion with one
which is accelerated different men may not obtain different values for
the resultant. In order to determine and represent such a momentum
and particular speed our Author has found no better method than to use
the momentum acquired by a body in naturally accelerated motion. The
speed of a body which has in this manner acquired any momentum what-
ever will, when converted into uniform motion, retain precisely such a
speed as, during a time-interval equal to that of the fall, will carry the
body through a distance equal to twice that of the fall. But since this
matter is one which is fundamental in our discussion it is well that we
make it perfectly clear by means of some particular example.
Let us consider the speed and momentum acquired by a body falling
through the height, say, of a spear as a standard which we may use in the
measurement of other speeds and momenta as occasion demands; assume
for instance that the time of such a fall is four seconds; now in order
to measure the speed acquired from a fall through any other height,
whether greater or less, one must not conclude that these speeds bear to
one another the same ratio as the heights of fall; for instance, it is not
true that a fall through four times a given height confers a speed four
times as great as that acquired by descent through the given height;
because the speed of a naturally accelerated motion does not vary in pro-
portion to the time. As has been shown above, the ratio of the spaces
is equal to the square of the ratio of the times.
If, then, as is often done for the sake of brevity, we take the same
limited straight line as the measure of the speed, and of the time, and
162 MASTERWORKS OF SCIENCE
also of the space traversed during that time, it follows that the duration
of fall and the speed acquired by the same body in passing over any other
distance, is not represented by this second distance, but by a mean propor-
tional between the two distances. This I can better illustrate by an exam-
ple. In the vertical line ac, lay off the portion ab to represent the distance
traversed by a body falling freely with accelerated motion: the time of
fall may be represented by any limited straight line, but for the sake of
brevity, we shall represent it by the same length ab; this length may also
be employed as a measure of the momentum and speed acquired during
the motion; in short, let ab be a measure of the various physical quanti-
ties which enter this discussion.
Having agreed arbitrarily upon ab as a measure of these
three different quantities, namely, space, time, and momentum,
our next task is to find the time required for fall through a
given vertical distance ac, also the momentum acquired at
the terminal point c9 both of which are to be expressed in
terms of the time and momentum represented by ab. These
two required quantities are obtained by laying off ud, a mean
proportional between ab and ac; in other words, the time of
fall from a to c is represented by ad on the same scale on
which we agreed that the time of fall from a to b should be
represented by ab. In like manner we may say that the mo-
mentum acquired at c is related to that acquired at b, in the
same manner that the line ad is related to ab, since the velocity
varies directly as the time, a conclusion which, although employed as a
postulate in Proposition III, is here amplified by the Author.
This point being clear and well-established we pass to the considera-
tion of the momentum in the case of two compound motions, one of
which is compounded of a uniform horizontal and a uniform vertical
motion, while the other is compounded of a uniform horizontal and a
naturally accelerated vertical motion. If both components are uniform,
and one at right angles to the other, we have already said that the square
of the resultant is obtained by adding the squares of the components as
will be clear from the following illustration.
Let us imagine a body to move along the vertical ab with a uniform
momentum of 3, and on reaching b to move toward c with a momentum
of 4, so that during the same time-interval it will traverse 3 cubits along
the vertical and 4 along the horizontal. But a particle which moves with
the resultant velocity will, in the same time, traverse the diagonal ac,
whose length is not 7 cubits— the sum of ab (3) and be (4)— but 5, which
GALILEO — DIALOGUES 163
is in potenza equal to the sum of 3 and 4; that is, the squares of 3 and
4 when added make 25, which is the square of act and is equal to the
sum of the squares of ab and be. Hence ac is represented by the side — or
we may say the root — of a square whose area is 25, namely 5.
As a fixed and certain rule for obtaining the momentum which re-
sults from two uniform momenta, one vertical, the other horizontal, we
have therefore the following: take the square of each, add these together,
and extract the square root of the sum, which will be the momentum
resulting from the two. Thus, in the above example, the body which in
virtue of its vertical motion would strike the horizontal plane with a
momentum of 3, would owing to its horizontal motion alone strike at c
with a momentum of 4; but if the body strikes with a momentum which
is the resultant of these two, its blow will be that of a body moving with
a momentum of 5; and such a blow will be the same at all points of
the diagonal ac, since its components are always the same and never
increase or dimmish.
Let us now pass to the consideration of a uniform horizontal motion
compounded with the vertical motion of a freely falling body starting
from rest. It is at once clear that the diagonal which represents the
motion compounded of these two is not a straight line, but, as has been
demonstrated, a semi-parabola, in which the momentum is always increas-
ing because the speed of the vertical component is always increasing.
Wherefore, to determine the momentum at any given point in the para-
bolic diagonal, it is necessary first to fix upon the uniform horizontal mo-
mentum and then, treating the body as one falling freely, to find the
vertical momentum at the given point; this latter can be determined only
by taking into account the duration of fall, a consideration which does
not enter into the composition of two uniform motions where the
velocities and momenta are always the same; but here where one of the
component motions has an initial value of zero and increases its speed
in direct proportion to the time, it follows that the time must determine
the speed at the assigned point. It only remains to obtain the momentum
resulting from these two components (as in the case of uniform motions)
by placing the square of the resultant equal to the sum of the squares
of the two components.
To what has hitherto been said concerning the momenta, blows or
shocks of projectiles, we must add another very important consideration;
to determine the force and energy of the shock it is not sufficient to con-
sider only the speed of the projectiles, but we must also take into account
the nature and condition of the target which, in no small degree, deter-
mines the efficiency of the blow. First of all it is well known that the
target suffers violence from the speed of the projectile in proportion as it
partly or entirely stops the motion; because if the blow falls upon an
object which yields to the impulse without resistance such a blow will be
of no effect; likewise when one attacks his enemy with a spear and over-
takes him at an instant when he is fleeing with equal speed there will be
no blow but merely a harmless touch. But if the shock falls upon an
164 MASTERWORKS OF SCIENCE
object which yields only in part then the blow will not have its full effect,
but the damage will be in proportion to the excess of the speed of the
projectile over that of the receding body; thus, for example, if the shot
reaches the target with a speed of 10 while the latter recedes with a speed
of 4, the momentum and shock will be represented by 6. Finally the blow
will be a maximum, in so far as the projectile is concerned, when the
target does not recede at all but if possible completely resists and stops
the motion of the projectile. I have said in so far as the projectile is con-
cerned because if the target should approach the projectile the shock of
collision would be greater in proportion as the sum of the two speeds 'is
greater than that oF the projectile alone.
Moreover it is "to be observed that the amount of yielding in the
target depends not only upon the quality of the material, as regards hard-
ness, whether it be of iron, lead, wool, etc., but also upon its position.
If the position is such that the shot strikes it at right angles, the momen-
tum imparted -by the blow will be a maximum; but if the motion be
oblique, that is to say slanting, the blow will be weaker; and more and
more so in proportion to the obliquity; for, no matter how hard the
material of the target thus situated, the entire momentum of the shot
will not be spent and stopped; the projectile will slide by and will, to
some extent, continue its motion along the surface of the opposing body.
All that has been said above concerning the amount of momentum
in the projectile at the extremity of the parabola must be understood
to refer to a blow received on a line at right angles to this parabola or
along the tangent to the parabola at the given point; for, even though the
motion has two components, one horizontal, the other vertical, neither
will the momentum along the horizontal nor that upon a plane perpen-
dicular to the horizontal be a maximum, since each of these will be re-
ceived obliquely.
SAGREDO. Your having mentioned these blows and shocks recalls to
my mind a problem, or rather a question, in mechanics of which no
author has given a solution or said anything which diminishes my aston-
ishment or even partly relieves my mind.
My difficulty and surprise consist in not being able to see whence
and upon what principle is derived the energy and immense force which
makes its appearance in a blow; for instance we see the simple blow
of a hammer, weighing not more than 8 or 10 Ibs., overcoming resistances
which, without a blow, would not yield to the weight of a body produc-
ing impetus by pressure alone, even though that body weighed many
hundreds of pounds. I would like to discover a method of measuring the
force of such a percussion. I can hardly think it infinite, but incline
rather to the view that it has its limit and can be counterbalanced and
measured by other forces, such as weights, or by levers or screws or other
mechanical instruments which are used to multiply forces in a manner
which I satisfactorily understand.
SALVIATI. You are not alone in 'your surprise at this effect or in
obscurity as to the cause of this remarkable property. I studied this mat-
GALILEO — DIALOGUES
165
ter myself for a while in vain; but my confusion merely increased until
finally meeting our Academician I received from him great consolation.
First he told me that he also had for a long time been groping in the
dark; but later he said that, after having spent some thousands of hours
in speculating and contemplating thereon, he had arrived at some notions
which are far removed from our earlier ideas and which are remarkable
for their novelty. And since now I know that you would gladly hear what
these novel ideas are I shall not wait for you to ask but promise that, as
soon as our discussion of projectiles is completed, I will explain all these
fantasies, or if you please, vagaries, as far as I can recall them from the
words of our Academician. In the meantime we proceed with the propo-
sitions of the Author.
Theorem. Proposition V.
If projectiles describe semi-parabolas of the same amplitude, the
momentum required to describe that one whose amplitude is
double its altitude is less than that required for any other.
Let bd be a semi-parabola whose amplitude cd is double its altitude
cb; on its axis extended upwards lay off ba equal to its altitude be. Draw
the line ad which will be a tangent to the parabola at d and will cut the
horizontal line be at the point ef making be equal to be and also to ba.
It is evident that this parabola will be described by a projectile whose
uniform horizontal momentum is that which it would acquire at b in
falling from rest at a and whose naturally accelerated vertical momentum
166 MASTERWORKS OF SCIENCE
is that of the body falling to c, from rest at b. From this it follows that
the momentum at the terminal point d, compounded of these two, is
represented by the diagonal ae, whose square is equal to the sum of the
squares of the two components. Now let gd be any other parabola what-
ever having the same amplitude cd, but whose altitude eg is either greater
or less than the altitude be. Let hd be the tangent cutting the horizontal
through g at ^. Select a point / such that hg:g\=^gJ^:gl. Then from a
preceding proposition, it follows that gl will be the height from which
a body must fall in order to describe the parabola gd.
Let gm be a mean proportional between ab and gl; then gm will
represent the time and momentum acquired at g by a fall from /; for ab
has been assumed as a measure of both time and momentum. Again let
gn be a mean proportional between be and eg; it will then represent the
time and momentum which the body acquires at e in falling from g. If
now we join m and n, this line mn will represent the momentum at d
of the projectile traversing the parabola dg; which momentum is, I say,
greater than that of the projectile travelling along the parabola bd whose
measure was given by ae. For since gn has been taken as a mean propor-
tional between be and gc; and since be is equal to be and also to J^g (each
of them being the half of dc) it follows that cg:gn—gn:g\, and as eg or
{hg) is to g\ so is ng2 to gl^: but by construction hg:g^=g\:gl. Hence
ng*:gl^=g\:gL But g^:gl==g^:gm2, since gm is a mean proportional
between ^g and gl. Therefore the three squares ng, \g, rng form a con-
tinued proportion, gn2:g^==g^:gm2. And the sum of the two extremes
which is equal to the square of mn is greater than twice the square of g{;
but the square of ae is double the square of g\. Hence the square of mn
is greater than the square of ae and the length mn is greater than the
length ae. Q.E.D.
Corollary
Conversely it is evident that less momentum will be required to send
£ projectile from the terminal point d along the parabola bd than along
any other parabola having an elevation greater or less than that of the
parabola bd, for which the tangent at d makes an angle of 45° with the
horizontal. From which it follows that if projectiles are fired from the
terminal point d, all having the same speed, but each having a different
elevation, the maximum range, i. e., amplitude of the semi-parabola or of
the entire parabola, will be obtained when the elevation is 45°: the other
shots, fired at angles greater or less, will have a shorter range.
SAGREDO. The force of rigid demonstrations such as occur only in
mathematics fills me with wonder and delight. From accounts given by
gunners, I was already aware of the fact that in. the use of cannon* and
mortars, the maximum range, that is, the one in which the shot goes
farthest, is obtained when the elevation is 45° or, as they say, at the sixth
point of the quadrant; but to understand why this happens far outweighs
GALILEO — DIALOGUES 167
the mere information obtained by the testimony of others or even by
repeated experiment.
SALVIATI. What you say is very true. The knowledge of a single fact
acquired through a discovery of its causes prepares the mind to under-
stand and ascertain other facts without need of recourse to experiment,
precisely as in the present case, where by argumentation alone the Author
proves with certainty that the maximum range occurs when the elevation
is 45°. He thus demonstrates what has pefhaps never been observed in
experience, namely, that of other shots those which exceed or fall short of
45° by equal amounts have equal ranges; so that if the balls have been
fared one at an elevation of 7 points, the other at 5, they will strike the
level at the same distance: the same is true if the shots are fired at 8 and
at 4 points, at 9 and at 3, etc.
SIMPLICIO. I am fully satisfied. So now Salviati can present the specu-
lations of our Academician on the subject of impulsive forces.
SALVIATI. Let the preceding discussions suffice for today; the hour is
already late and the time remaining will not permit us to clear up the
subjects proposed; we may therefore postpone our meeting until another
and more opportune occasion.
SAGREDO. I concur in your opinion, because after various conversations
with intimate friends of our Academician I have concluded that this ques-
tion of impulsive forces is very obscure, and I think that, up to the pres-
ent, none of those who have treated this subject have been able to clear up
its dark corners which lie almost beyond the reach of human imagination;
among the various views which I have heard expressed one, strangely fan-
tastic, remains in my memory, namely, that impulsive forces are indeter-
minate, if not infinite. Let us, therefore, await the convenience of Salviati,
SND OF FOURTH DAY
PRINCIPIA
The Mathematical Principles of
Natural Philosophy
by
ISAAC NEWTON
CONTENTS
Principia
The Mathematical Principles of Natural Philosophy
Definitions
Axioms, or Laws of Motion
Book One: Of the Motion of Bodies
Section One: Of the method of first and last ratios of quantities, by
the help whereof we demonstrate the propositions that follow
Section Two: Of the invention of centripetal forces
Section Twelve: Of the attractive forces of sphserical bodies
Book Two: Of the Motion of Bodies
Section Six: Of the motion and resistance of funependulous bodies
Book Three: Natural Philosophy
Rules of Reasoning in Philosophy
Phenomena, or Appearances
Propositions
General Scholium
ISAAC NEWTON'
16^2-1727
THE most familiar story about Isaac Newton concerns his
curiosity about a falling apple and his consequent discovery
of the law of gravity. This story, first recorded by Voltaire,
who had it from Newton's favorite niece, may be true. It is at
least not improbable; for Newton from an early age habitually
observed natural phenomena closely, constantly asked "Why?"
and constantly tried to set his explanations in mathematical
forms.
Born on Christmas Day in 1642, the posthumous son of
a freehold farmer at Woolsthorpe in Lincolnshire, Newton
had his early education in small schools in his neighbor-
hood. In 1654 he entered the grammar school at Grantham, six
miles away. When he graduated from this school at the top
of his class, he had, like his schoolmates, built kites and
water clocks and dials; he had also contrived a four-wheeled
carriage to be propelled by the occupant, and had made
marked progress in mathematics. Yet when he came home to
his mother — now the widow of Barnabas Smith, a clergyman
— at Woolsthorpe, no one thought of any career for him but
that of a small farmer. He engaged in ordinary farm routine,
performed chores, went to market with his mother's agent.
The agent reported that on market days the boy spent his
time at bookstalls. He was frequently observed poring over
mathematical treatises. Eventually his mother's brother, the
rector of a parish near by, and himself a graduate of Trinity
College, Cambridge, persuaded the widow Smith that her son
should also go to Trinity. He was entered as a subsizar in
1661.
At Cambridge, Newton showed that he had already mas-
tered Sanderson's Logic, and that, scorning Euclid as too easy
to be worth studying, he had gone deep into Descartes's
Geometry. His low opinion of Euclid he later revised; but not
until after he had mastered Wallis's Arithmetic of Infinites.
172 MASTERWORKS OF SCIENCE
As an undergraduate, he did make series of observations on
natural phenomena such as the moon's halo, but his genius
was for mathematics. In 1665 he discovered what is now
known as the binomial theorem, and a little later, the ele-
ments of the differential calculus, which he called "fluxions."
When, in 1668, he took his master's degree at Trinity, of
which he was now a fellow, he wrote a paper which attracted
the attention of the chief mathematicians of England. The
following year his friend and teacher, Barrow, resigned as
Lucasian professor of mathematics at Cambridge, and New-
ton was appointed to succeed him.
As Lucasian professor, Newton was required to lecture
once a week on some portion of geometry, arithmetic, astron-
omy, geography, optics, statics, or other mathematical subject,
and to receive students two hours a week. Choosing optics as
his first topic, and later other subjects in mathematics, he lec-
tured regularly until 1701, when he resigned his professorship.
His lectures on algebra were published in 1707 by his succes-
sor in the Lucasian chair, Whiston, under the title Arithme-
tica Unwersalis. Other unpublished lectures may be of equal
merit. Yet these years were surely productive less of great
lectures than of great papers for the Royal Society.
To the Society, Newton had early sent a paper comment-
ing on a reflecting telescope of his own invention. So well was
it received that he sent other papers, several of them the de-
veloped forms of ideas and discoveries really dating from his
student days. In 1672, after the Royal Society had elected him
to membership, there was read to it Newton's "New Theory
about Light and Color," the paper in which he reported his
discovery of the composition of white light. An immense con-
troversy ensued, for Hooke, among the eminent English scien-
tists, and Lucas and Linus, among the continental scientists,
were only three of many men who violently denied the plau-
sibility of Newton's announcement. He quietly stood his
ground — content that experiment rather than argument
should prove him right.
Many of Newton's papers, for the Society — reports on
polarization, on double refraction, on binocular vision, and so
on — are now obsolete. One of them, however, developed his
emission, or corpuscular, theory of light which contemporary
physicists have been seriously reconsidering. And another, "De
Motu," contained the germ of the Principia.
Celestial mechanics had been fascinating to Newton for a
long time. As early as 1666, when the plague closed Cam-
bridge and sent the undergraduate Newton home to Wools-
thorpe, he was considering the possibility that gravity might
extend as far as the orb of the moon. Later, to explain why
NEWTON— PR IN GIF I A 173
the planets keep to elliptical orbits round the attracting sun,
he calculated the inverse-square law. Then he applied the law
to explain the path o£ the moon round the earth, and was dis-
satisfied with his computations. He convinced himself that in
order to apply the law, he would first have to demonstrate
mathematically that spherical bodies such as the sun and the
moon act as point centers of force. By 1684, when Halley,
Wren, and Hooke had all agreed on the inverse-square law —
although they could not prove it — Newton had completed his
calculations. He was sure now that the law applied, and he
explained his solution of the great problem in "De Motu."
During the next two years Newton composed the Prin-
cipia Mathematica Philosophiae Naturalls. In 1685 he an-
nounced his law of universal gravitation and simultaneously
gave the Royal Society the first book of the Principia. The
whole of the great work was finally published in 1687. In
1729, Andrew Motte published the first English translation;
from the 1803 edition of this translation the following pas-
sages are taken.
A nervous illness — described by Pepys as "an attack of
phrenitis," that is, madness — afflicted Newton in 1692. Within
eighteen months he had recovered. But from the time of this
illness until his death thirty-five years later, he made no great
contribution to scientific knowledge. The Options, published
in 1704, and Newton's only large work in English, really con-
tains the results of studies made much earlier; and his Law of
Cooling, announced to the Royal Society in 1701, he had also
computed and used much earlier.
During his later years honors in abundance came to New-
ton. He became the president of the Royal Society in ^703,
and by annual re-election held the office until his death. In
1695 he was appointed Warden of the Mint, and, in 1699,
Master of the Mint. These appointments returned him many
times the income he earned as Lucasian professor at Cam-
bridge, and made possible the rather elaborate style of living
he came to enjoy. Twice, in 1689 and again in 1701, he repre-
sented Cambridge as the university's member in Parliament.
The French Academy made him a foreign member in 1699. In
1705, Queen Anne's consort, Prince George of Denmark, who
as a member of the Royal Society greatly admired Newton
and his work, persuaded the queen to knight Newton.
Unmarried, Newton seemed to enjoy equally the pleas-
ures of London, of the Cambridge cloisters, and of his estate
at Woolsthorpe. Gradually he gave more and more attention
to matters not wholly scientific. He compiled a Chronology of
Ancient Kingdoms (1728), wrote theological treatises such as
Observations on the Prophecies of Daniel, and a Church His-
174 MASTERWORKS OF SCIENCE
tory. Though his health declined as he aged, and though he
suffered much from stone and gout, his mind retained such
acuteness that all mathematicians deferred to him and Eng-
land acknowledged him as her greatest living scientist.
The Principles has been for two centuries recognized as one
of the world's great books. In it Newton not only sums up his
own researches, but, to support them, magnificently taps the
experimental and theoretical work of all the physical scholars
of his and preceding times. He states definitively the first two
laws of motion and adds a third, the result of his own labors;
he presents and proves his Law of Universal Gravitation (see
Book I, Section XII, and Book III, Proposition VIII); he
shows that mass and weight are proportional to each other at
any given spot on the earth (Book II, Proposition XXIV); he
deduces the velocity of sound, explains the tides, traces the
paths of comets, demonstrates that the sun is the center of our
system, and so on.
To make the calculations upon which his generalizations
rest, Newton frequently used "fluxions" — what we call calcu-
lus. But though he suggests his method in Book I, Lemmae I>
II, and XI, he did not fully explain his new method until he
presented it formally in 1693, in the third volume of Dr.
Wallis's works. Rather, in the Principia, he presents every-
thing in the Euclidean manner. From a small number of
axioms he proceeds to a series of mathematical — generally
geometrical — propositions and demonstrations. Thus, like
Euclid and Archimedes, he moves steadily, logically, relent-
lessly, from the known and acknowledged to the new and sur-
prising. As a result, until Planck announced the Quantum
Theory in 1900, Newton's conclusions controlled all physical
thinking; and the validity of the Principia remains unchal-
lenged today within the area of gross mechanics. It is Newton's
monument.
(Since terminology has changed in two centuries, the con-
temporary reader needs to be aware that Newton's terms
must be understood as follows: subducted, subtracted; con-
junctly, cross multiplied; congress, impact; invention, discov-
ery; used to be, are usually; observed the duplicate ratio, vary
as the square; in the duplicate ratio, as the square; in the tripli-
cate ratio, as the cube; in the sesquiplicate ratio, as the 3/21
power; in the subduplicate ratio, as the square root; in the sub-
triplicate ratio, as the cube root. Thus, in modern terminol-
ogy, Book One, Section Two, Proposition IV, Corollary 2 will
read: "And since the periodic times are as the radii divided
by the velocities; the centripetal forces are as the radii divided
by the square of the periodic times.")
PRINCIPIA
The Mathematical Principles of Natural
Philosophy
DEFINITIONS
DEFINITION I
The quantity of matter is the measure of the same, arising from its density
and bul^ conjunctly.
THUS air of a double density, in a double space, is quadruple in quantity;
in a triple space, sextuple in quantity. The same thing is to be understood
of snow, and fine dust or powders, that are condensed by compression or
liquefaction; and of all bodies that are by any causes whatever differently
condensed. I have no regard in this place to a medium, if any such there
is, that freely pervades the interstices between the parts of bodies. It is
this quantity that I mean hereafter everywhere under the name of body or
mass. And the same is known by the weight of each body; for it is pro-
portional to the weight, as I have found by experiments on pendulums,
very accurately made, which shall be shewn hereafter.
DEFINITION II
The quantity of motion is the measure of the same, arising from the
velocity and quantity of matter conjunctly.
The motion of the whole is the sum of the motions of all the parts;
and therefore in a body double in quantity, with equal velocity, the
motion is double; with twice the velocity, it is quadruple.
DEFINITION III
The vis insita, or innate force of matter, is a power of resisting, by which
every body, as much as in it lies, endeavours to persevere in its pres-
NEWTON — PRINCIPIA 177
to, and detains them in their orbits, which I therefore call centripetal,
would fly off in right lines, with an uniform motion. A projectile, if it was
not for the force of gravity, would not deviate towards the earth, but
would go off from it in a right line, and that with an uniform motion, if
the resistance of the air was taken away. It is by its gravity that it is drawn
aside perpetually from its rectilinear course, and made to deviate towards
the earth, more or less, according to the force of its gravity, and the veloc-
ity of its motion. The less its gravity is, for the quantity of its matter, or
the greater the velocity with which it is projected, the less will it deviate
from a rectilinear course, and the farther it will go. If a leaden ball, pro-
jected from the top of a mountain by the force of gunpowder with a given
velocity, and in a direction parallel to the horizon, is carried in a curve
line to the distance of two miles before it falls to the ground; the same,
if the resistance of the air were taken away, with a double or decuple
velocity, would fly twice or ten times as far. And by increasing the veloc-
ity, we may at pleasure increase the distance to which it might be pro-
jected, and diminish the curvature of the line, which it might describe, till
at last it should fall at the distance of 10, 30, or 90 degrees, or even might
go quite round the whole earth before it falls; or lastly, so that it might
never fall to the earth, but go forward into the celestial spaces, and pro-
ceed in its motion in infinitum. And after the same manner that a pro-
jectile, by the force of gravity, may be made to revolve in an orbit, and go
round the whole earth, the moon also, either by the force of gravity, if it
is endued with gravity, or by any other force, that impels it towards the
earth, may be perpetually drawn aside towards the earth, out of the recti-
linear way, which by its innate force it would pursue; and would be made
to revolve in the orbit which it now describes; nor could the moon, with-
out some such force, be retained in its orbit. If this force was too small,
it would not sufficiently turn the moon out of a rectilinear course: if it
was too great, it would turn it too much, and draw down the moon from
its orbit towards the earth. It is necessary, that the force be of a just
quantity, and it belongs to the mathematicians to find the force, that may
serve exactly to retain a body in a given orbit, with a given velocity; and
vice versa, to determine the curvilinear way, into which a body projected
from a given place, with a given velocity, may be made to deviate from
its natural rectilinear way, by means of a given force.
The quantity of any centripetal force may be considered as of three
kinds; absolute, accelerative, and motive.
DEFINITION VI
The absolute quantity of a centripetal force is the measure of the same
proportional to the efficacy of the cause that propagates it from the
centre, through the spaces round about.
Thus the magnetic force is greater in one loadstone and less in an-
other according to their sizes and strength of intensity.
178 MASTERWORKS OF SCIENCE
DEFINITION VII
The accelerative quantity of a centripetal force is the measure of the same,
proportional to the velocity which it generates in a given time.
Thus the force of the same loadstone is greater at a less distance, and
less at a greater: also the force of gravity is greater in valleys, less on tops
of exceeding high mountains; and yet less (as shall hereafter be shown)
at greater distances from the body of the earth; but at equal distances, it
is the same everywhere; because (taking away, or allowing for, the re-
sistance of the air), it equally accelerates all falling bodies, whether heavy
or light, great or small.
DEFINITION VIII
The motive quantity of a centripetal force is the measure of the same,
proportional to the motion which it generates in a given time.
Thus the weight is greater in a greater body, less in a less body; and,
in the same body, it is greater near to the earth, and less at remoter dis-
tances. This sort of quantity is the centripetency, or propension of the
whole body towards the centre, or, as I may say, its weight; and it is
always known by the quantity of an equal and contrary force just sufficient
to hinder the descent of the body.
These quantities of forces, we may, for brevity's sake, call by the
names of motive, accelerative, and absolute forces; and, for distinction's
sake, consider them, with respect to the bodies that tend to the centre; to
the places of those bodies; and to the centre of force towards which they
tend; that is to say, I refer the motive force to the body as an endeavour
and propensity of the whole towards a centre, arising from the propensi-
ties of the several parts taken together; the accelerative force to the place
of the body, as a certain power or energy diffused from the centre to all
places around to move the bodies that are in them; and the absolute force
to the centre, as endued with some cause, without which those motive
forces would not be propagated through the spaces round about; whether
that cause be some central body (such as is the loadstone, in the centre of
the magnetic force, or the earth in the centre of the gravitating force), or
anything else that does not yet appear. For I here design only to give a
mathematical notion of those forces, without considering their physical
causes and seats.
Wherefore the accelerative force will stand in the same relation to the
motive, as celerity does to motion. For the quantity of motion arises from
the celerity drawn into the quantity of matter; and the motive force arises
from the accelerative force drawn into the same quantity of matter. For
the sum of the actions of the accelerative force, upon the several particles
of the body, is the motive force of the whole. Hence it is, that near the
NEWTON—- PRINCIPIA 179
surface of the earth, where the accelerative gravity, or force productive of
gravity, in all bodies is the same, the rriotive gravity or the weight is as
the body: but if we should ascend to higher regions, where the accelera-
tive gravity is less, the weight would be equally diminished, and would
always be as the product of the body, by the accelerative gravity. So in
those regions, where the accelerative gravity is diminished into one half,
the weight of a body two or three times less will be four or six times less.
I likewise call attractions and impulses, in the same sense, accelera-
tive, and motive; and use the words attraction, impulse or propensity of
any sort towards a centre, promiscuously, and indifferently, one for an-
other; considering those forces not physically, but mathematically: where-
fore, the reader is not to imagine, that by those words, I anywhere take
upon me to define the kind, or the manner of any action, the causes or the
physical reason thereof, or that I attribute forces, in a true and physical
sense, to certain centres (which are only mathematical points); when at
any time I happen to speak of centres as attracting, or as endued with
attractive powers.
SCHOLIUM
Hitherto I have laid down the definitions of such words as are less
known, and explained the sense in which I would have them to be under-
stood in the following discourse. I do not define time, space, place and
motion, as being well known to all. Only I must observe, that the vulgar
conceive those quantities under no other notions but from the relation
they bear to sensible objects. And thence arise certain prejudices, for the
removing of which, it will be convenient to distinguish them into absolute
and relative, true and apparent, mathematical and common.
I. Absolute, true, and mathematical time, of itself, and from its own
nature, flows equably without regard to anything external, and by another
name is called duration: relative, apparent, and common time is some sen-
sible and external (whether accurate or unequable) measure of duration
by the means of motion, which is commonly used instead of true time;
such as an hour, a day, a month, a year.
II. Absolute space, in its own nature, without regard to anything ex-
ternal, remains always similar and immovable. Relative space is some
movable dimension or measure of the absolute spaces; which our senses
determine by its position to bodies; and which is vulgarly taken for im-
movable space; such is the dimension of a subterraneous, an aereal, or
celestial space, determined by its position in respect of the earth. Absolute
and relative space are the same in figure and magnitude; but they do not
remain always numerically the same. For if the earth, for instance, moves,
a space of our air, which relatively and in respect of the earth remains
always the same, will at one time be one part of the absolute space into
which the air passes; at another time it will be another part of the same,
and so, absolutely understood, it will be perpetually mutable.
180 MASTERWORKS OF SCIENCE
III. Place is a part of space which a body takes up, and is, according
to the space, either absolute or relative. I say, a part of space; not the situ-
ation, nor the external surface of the body. For the places of equal solids
are always equal; but their superficies, by reason of their dissimilar figures,
are often unequal. Positions properly have no quantity, nor are they so
much the places themselves, as the properties of places. The motion of the
whole is the same thing with the sum of the motions of the parts; that is,
.the translation of the whole, out of its place, is the same thing with the
sum of the translations of the parts out of their places; and therefore the
place of the whole is the same thing with the sum of the places of the
parts, and for that reason, it is internal, and in the whole body.
IV. Absolute motion is the translation of a body from one absolute
place into another; and relative motion, the translation from one relative
place into another. Thus in a ship under sail, the relative place of a body
is that part of the ship which the body possesses; or that part of its cavity
which the body fills, and which therefore moves together with the ship:
and relative rest is the continuance of the body in the same part of the
ship, or of its cavity. But real, absolute rest is the continuance of the
body in the same part of that immovable space, in which the ship itself,
its cavity, and all that it contains, is moved. Wherefore, if the earth is
really at rest, the body, which relatively rests in the ship, will really and
absolutely move with the same velocity which the ship has on the earth.
But if the earth also moves, the true and absolute motion of the body wall
arise, partly from the true motion of the earth, in immovable space; partly
from the relative motion of the ship on the earth; and if the body moves
also relatively in the ship its true motion will arise, partly from the true
motion of the earth, in immovable space, and partly from the relative mo-
tions as well of the ship on the earth, as of the body in the ship; and from
these relative motions will arise the relative motion of the body on the
earth. As if that part of the earth, where the ship is,, was truly moved
toward the east, with a velocity of 10010 parts; while the ship itself, with
a fresh gale, and full sails, is carried towards the west, with a velocity ex-
pressed by 10 of those parts; but a sailor walks in the ship towards the
east, with i part of the said velocity; then the sailor will be moved truly
in immovable space towards the east, with a velocity of 10001 parts, and
relatively on the earth towards the west, with a velocity of 9 of those
parts.
Absolute time, in astronomy, is distinguished from relative, by the
equation or correction of the vulgar time. For the natural days are truly
unequal, though they are commonly considered as equal, and used for a
measure of time; astronomers correct this inequality for their more accu-
rate deducing of the celestial motions. It may be that there is no such
thing as an equable motion, whereby time may be accurately measured.
All motions may be accelerated and retarded, but the true, or equable,
progress of absolute time is liable to no change. The duration or perse-
verance of the existence of things remains the same, whether the motions
are swift or slow, or none at all: and therefore it ought to be distinguished
NEWTON — PR INC IP I A 181
from what are only sensible measures thereof; and out of which we collect
it, by means of the astronomical equation. The necessity of which equa-
tion, for determining the times of a phenomenon, is evinced as well from
the experiments of the pendulum clock, as by eclipses of the satellites of
Jupiter.
As the order of the parts of time is immutable, so also is the order of
the parts of space. Suppose those parts to be moved out of their places,
and they will be moved (if the expression may be allowed) out of them-
selves. For times and spaces are, as it were, the places as well of them-
selves as of all other things. All things are placed in time as to order of
succession; and in space as to order of situation. It is from their essence
or nature that they are places; and that the primary places of things
should be movable is absurd. These are therefore the absolute places; and
translations out of those places are the only absolute motions.
But because the parts of space cannot be seen, or distinguished from
one another by our senses, therefore in their stead we use sensible meas-
ures of them. For from the positions and distances of things from any
body considered as immovable, we define all places; and then with respect
to such places, we estimate all motions, considering bodies as transferred
from some of those places into others. And so, instead of absolute places
and motions, we use relative ones; and that without any inconvenience in
common affairs; but in philosophical disquisitions, we ought to abstract
from our senses, and consider things themselves, distinct from what are
only sensible measures of them. For it may be that there is no body really
at rest, to which the places and motions of others may be referred.
But we may distinguish rest and motion, absolute and relative, one
from the other by their properties, causes and effects. It is a property of
rest, that bodies really at rest do rest in respect to one another. And there-
fore as it is possible, that in the remote regions of the fixed stars, or per-
haps far beyond them, there may be some body absolutely at rest; but
impossible to know, from the position of bodies to one another in our
regions, whether any of these do keep the same position to that remote
body; it follows that absolute rest cannot be determined from the position
of bodies in our regions.
It is a property of motion, that the parts, which retain given positions
to their wholes, do partake of the motions of those wholes. For all the
parts of revolving bodies endeavour to recede from the axis of motion;
and the impetus of bodies moving forward arises from the joint impetus
of all the parts. Therefore, if surrounding bodies are moved, those that
are relatively at rest within them will partake of their motion. Upon
which account, the true and absolute motion of a body cannot be deter-
mined by the translation of it from those which only seem to rest; for the
external bodies ought not only to appear at rest, but to be really at rest.
For otherwise, all included bodies, beside their translation from near the
surrounding ones, partake likewise of their true motions; and though that
translation were not made they would not be really at rest, but only seem
to be so. For the surrounding bodies stand in the like relation to the
182 MASTERWORKS OF SCIENCE
surrounded as the exterior part of a whole does to the interior, or as the
shell does to the kernel; but, if the shell moves, the kernel will also move,
as being part of the whole, without any removal from near the shell.
A property, near akin to the preceding, is this, that if a place is
moved, whatever is placed therein moves along with it; and therefore a
body, which is moved from a place in motion, partakes also of the motion
of its place. Upon which account, all motions, from places in motion, are
no other than parts of entire and absolute motions; and every entire mo-
tion is composed of the motion of the body out of its first place, and the
motion of this place out of its place; and so on, until we come to some
immovable place, as in the before-mentioned example of the sailor. Where-
fore, entire and absolute motions can be no otherwise determined than by
immovable places; and for that reason I did before refer those absolute
motions to immovable places, but relative ones to movable places. Now
no other places are immovable but those that, from infinity, to infinity, do
all retain the same given position one to another; and upon this account
must ever remain unmoved; and do thereby constitute immovable space.
The causes by which true and relative motions are distinguished, one
from the other, are the forces impressed upon bodies to generate motion.
True motion is neither generated nor altered, but by some force impressed
upon the body moved; but relative motion may be generated or altered
without any force impressed upon the body. For it is sufficient only to
impress some force on other bodies with which the former is compared,
that by their giving way, that relation may be changed, in which the rela-
tive rest or motion of this other body did consist. Again, true motion
suffers always some change from any force impressed upon the moving
body; but relative motion does not necessarily undergo any change by
such forces. For if the same forces are likewise impressed on those other
bodies, with which the comparison is made, that the relative position may
be preserved, then that condition will be preserved in which the relative
motion consists. And therefore any relative motion may be changed when
the true motion remains unaltered, and the relative may be preserved
when the true suffers some change. Upon which accounts, true motion
does by no means consist in such relations.
The effects which distinguish absolute from relative motion are the
forces of receding from the axis of circular motion. For there are no such
forces in a circular motion purely relative, but in a true and absolute cir-
cular motion they are greater or less, according to the quantity of the
motion. If a vessel, hung by a long cord, is so often turned about that the
cord is strongly twisted, then filled with water, and held at rest together
with the water; after, by the sudden action of another force, it is whirled
about the contrary way, and while the cord is untwisting itself, the vessel
continues for some time in this motion; the surface of the water will at
first be plain, as before the vessel began to move; but the vessel, by grad-
ually communicating its motion to the water, will make it begin sensibly
to revolve, and recede by little and little from the middle, and ascend to
the sides of the vessel, forming itself into a concave figure (as I have ex-
NEWTON — PR IN GIF I A
perienced), and the swifter the motion becomes, the higher will the water
rise, till at last, performing its revolutions in the same times with the
vessel, it becomes relatively at rest in it. This ascent of the water shows
its endeavour to recede from the axis of its motion; and the true and abso-
lute circular motion of the water, which is here directly contrary to the
relative, discovers itself, and may be measured by this endeavour. At first,
when the relative motion of the water in the vessel was greatest, it pro-
duced no endeavour to recede from the axis; the water showed no tend-
ency to the circumference, nor any ascent towards the sides of the vessel,
but remained of a plain surface, and therefore its true circular motion had
not yet begun. But afterwards, when the relative motion of the water had
decreased, the ascent thereof towards the sides of the vessel proved its
endeavour to recede from the axis; and this endeavour showed the real
circular motion of the water perpetually increasing, till it had acquired its
greatest quantity, when the water rested relatively in the vessel. And
therefore this endeavour does not depend upon any translation of the
water in respect of the ambient bodies, nor can true circular motion be
defined by such translation. There is only one real circular motion of any
one revolving body, corresponding to only one power of endeavouring to
recede from its axis of motion, as its proper and adequate effect; but rela-
tive motions, in one and the same body, are innumerable, according to the
various relations it bears to external bodies, and, like other relations, are
altogether destitute of any real effect, any otherwise than they may per-
haps partake of that one only true motion. And therefore in their system
who suppose that our heavens, revolving below the sphere of the fixed
stars, carry the planets along with them; the several parts of those heavens,
and the planets, which are indeed relatively at rest in their heavens, do
yet really move. For they change their position one to another (which
never happens to bodies truly at rest), and being carried together with
their heavens, partake of their motions, and as parts of revolving wholes,
endeavour to recede from the axis of their motions.
Wherefore relative quantities are not the quantities themselves,
whose names they bear, but those sensible measures of them (either accu-
rate or inaccurate), which are commonly used instead of the measured
quantities themselves. And if the meaning of words is to be determined
by their use, then by the names time, space, place and motion, their
measures are properly to be understood; and the expression will be un-
usual, and purely mathematical, if the measured quantities themselves are
meant. Upon which account, they do strain the sacred writings, who there
interpret those words for the measured quantities. Nor do those less defile
the purity of mathematical and philosophical truths, who confound real
quantities themselves with their relations and vulgar measures.
It is indeed a matter of great difficulty to discover, and effectually to
distinguish, the true motions of particular bodies from the apparent; be-
cause the parts of that immovable space, in which those motions are per-
formed, do by no means come under the observation of our senses. Yet
the thing is not altogether desperate; for we have some arguments to
184 MASTERWORKS OF SCIENCE
guide us, partly from the apparent motions, which are the differences of
the true motions; partly from the forces, which are the causes and effects
of the true motions. For instance, if two globes, kept at a given distance
one from the other by means of a cord that connects them, were revolved
about their common centre of gravity, we might, from the tension of the
cord, discover the endeavour of the globes to recede from the axis of their
motion, and from thence we might compute the quantity of their circular
motions. And then if any equal forces should be impressed at once on the
alternate faces of the globes to augment or diminish their circular mo-
tions, from the increase or decrease of the tension of the cord, we might
infer the increment or decrement of their motions; and thence would be
found on what faces those forces ought to be impressed, that the motions
of the globes might be most augmented; that is, we might discover their
hindermost faces, or those which, in the circular motion, do follow. But
the faces which follow being known, and consequently the opposite ones
that precede, we should likewise know the determination of their mo-
tions. And thus we might find both the quantity and the determination
of this circular motion, even in an immense vacuum, where there was
nothing external or sensible with which the globes could be compared.
But now, if in that space some remote bodies were placed that kept
always a given position one to another, as the fixed stars do in our regions,
we could not indeed determine, from the relative translation of the globes
among those bodies, whether the motion did belong to the globes or to
the bodies. But if we observed the cord, and found that its tension was
that very tension which the motions of the globes required, we might
conclude the motion to be in the globes, and the bodies to be at rest; and
then, lastly, from the translation of the globes among the bodies, we
should find the determination of their motions. But how we are to collect
the true motions from their causes, effects, and apparent differences; and,
vice versa, how from the motions, either true or apparent, we may come
to the knowledge of their causes and effects, shall be explained more at
large in the following tract. For to this end it was that I composed it.
AXIOMS, OR LAWS OF MOTION
LAW 1
Every ' body perseveres in its state of rest, or of uniform motion in a right
' linet unless it is compelled to change that state by forces impressed
thereon.
Projectiles persevere in their motions, so far as they are not retarded
by the resistance of the air, or impelled downwards by the force of gravity.
A top, whose parts by their cohesion are perpetually drawn aside from
rectilinear motions, does not cease its rotation, otherwise than as it is re-
tarded by the air. The greater bodies of the planets and comets, meeting
NEWTON — PRINCIPI A 185
with less resistance in more free spaces, preserve their motions both pro-
gressive and circular for a much longer time.
LAW 11
The alteration of motion is ever proportional to the motive -force im-
pressed; and is made in the direction of the right line in which that
force is impressed.
If any force generates a motion, a double force will generate double
the motion, a triple force triple the motion, whether that force be im-
pressed altogether and at once, or gradually and successively. And this
motion (being always directed the same way with the generating force),
if the body moved before, is added to or subducted from the former mo-
tion, according as they directly conspire with or are directly contrary to
each other; or obliquely joined, when they are oblique, so as to produce a
new motion compounded from the determination of both.
LAW III
To every action there is always opposed an equal reaction: or the mutual
actions of two bodies upon each other are always equal, and directed
to contrary parts.
Whatever draws or presses another is as much drawn or pressed by
that other. If you press a stone with your finger, the finger is also pressed
by the stone. If a horse draws a stone tied to a rope, the horse (if I may so
say) will be equally drawn back towards the stone: for the distended rope,
by the same endeavour to relax or unbend itself, will draw the horse as
much towards the stone, as it does the stone towards the horse, and will
obstruct the progress of the one as much as it advances that of the other.
If a body impinge upon another, and by its force change the motion of the
other, that body also (because of the equality of the mutual pressure) will
undergo an equal change, in its own motion, towards the contrary part.
The changes made by these actions are equal, not in the velocities but in
the motions of bodies; that is to say, if the bodies are not hindered by any
other impediments. For, because the motions are equally changed, the
changes of the velocities made towards contrary parts are reciprocally pro-
portional to the bodies. This law takes place also in attractions.
COROLLARY 1
A body by two forces conjoined will describe the diagonal of a parallelo-
gram', in the same time that it would describe the sides, by those
•forces apart.
186 MASTERWORKS OF SCIENCE
If a body in a given time, by the force M impressed apart in the
place A, should with an uniform motion be carried from A to B; and by
the force N impressed apart in the same place, should be carried from A
to C; complete the parallelogram ABCD, and, by both forces acting to-
gether, it will in the same time be carried in the diagonal from A to D.
For since the force N acts in the direction of the line AC, parallel to BD,
this force (by the second law) will not at all alter the velocity generated
by the other force M, by which the body is carried towards the line BD.
The body therefore will arrive at the line BD in the same time, whether
the force N be impressed or not; and therefore at the end of that time it
will be found somewhere in the line BD. By the same argument, at the
end of the same time it will be found somewhere in the line CD. There-
fore it will be found in the point D, where both lines meet. But it will
move in a right line from A to D, by Law I.
COROLLARY II
And hence is explained the composition of any one direct force AD, out
of any two oblique forces AC and CD; and, on the contrary, the reso-
lution of any one direct force AD into two oblique forces AC and
CD: which composition and resolution are abundantly confirmed
from mechanics.
COROLLARY 111
The quantity of motion, which is collected by taking the sum of the mo-
tions directed towards the same parts, and the difference of those
that are directed to contrary parts, suffers no change from the action
of bodies among themselves.
For action and its opposite re-action are equal, by Law III, and there-
fore, by Law II, they produce in the motions equal changes towards oppo-
site parts. Therefore if the motions are directed towards the same parts,
whatever is added to the motion of the preceding body will be subducted
from the motion of that which follows; so that the sum will be the same
as before. If the bodies meet, with contrary motions, there will be an
equal deduction from the motions of both; and therefore the difference of
the motions directed towards opposite parts will remain the same.
Thus if a spherical body A with two parts of velocity is triple of a
spherical body B which follows in the same right line with ten parts of
NEWTON — PRINCIPIA 187
velocity, the motion of A will be to that of B as 6 to 10. Suppose, then,,
their motions to be of 6 parts and of 10 parts, and the -sum will be 16
parts. Therefore, upon the meeting of the bodies, if A acquire 3, 4, or 5
parts of motion, B will lose as many; and therefore after reflexion A will
proceed with 9, 10, or n parts, and B with 7, 6, or 5 parts; the sum re-
maining always of 16 parts as before. If the body A acquire 9, 10, n, or
12 parts of motion, and therefore after meeting proceed with 15, 16, 17,
or 18 parts, the body B, losing so many parts as A has got, will either pro-
ceed with i part, having lost 9, or stop and remain at rest, as having lost
its whole progressive motion of 10 parts; or it will go back with I part,
having not only lost its whole motion, but (if I may so say) one part
more; or it will go back with 2 parts, because a progressive motion of 12
parts is taken off. And so the sums of the conspiring motions i5-j-i, or
i6-f-o, and the differences of the contrary motions 17 — i and 18 — 2, will
always be equal to 16 parts, as they were before the meeting and reflexion
of the bodies. But, the motions being known with which the bodies pro-
ceed after reflexion, the velocity of either will be also known, by taking
the velocity after to the velocity before reflexion, as the motion after is to
the motion before. As in the last case, where the motion of the body A
was of 6 parts before reflexion and of 18 parts after, and the velocity was
of 2 parts before reflexion, the velocity thereof after reflexion will be
found to be of 6 parts; by saying, as the 6 parts of motion before to 18
parts after, so are 2 parts of velocity before reflexion to 6 parts after.
But if the bodies are either not spherical, or, moving in different
right lines, impinge obliquely one upon the other, and their motions after
reflexion are required, in those cases we are first to determine the position
of the plane that touches the concurring bodies in the point of concourse,,
then the motion of each body (by Corol. II) is to be resolved into two,
one perpendicular to that plane, and the other parallel to it. This done,
because the bodies act upon each other in the direction of a line perpen-
dicular to this plane, the parallel motions are to be retained the same after
reflexion as before; and to the perpendicular motions we are to assign
equal changes towards the contrary parts; in such manner that the sum
of the conspiring and the difference of the contrary motions may remain
the same as before. From such kind of reflexions also sometimes arise
the circular motions of bodies about their own centres. But these are
cases which I do not consider in what follows; and it would be too tedi-
ous to demonstrate every particular that relates to this subject.
COROLLARY IV
The common centre of gravity of two or more bodies does not alter its
state of motion or rest by the actions of the bodies among themselves;
and therefore the common centre of gravity of all bodies acting upon
each other (excluding outward actions and impediments) is either at
rest or moves uniformly in a right line.
188 MASTERWORKS OF SCIENCE
COROLLARY V .
The motions of bodies included in a given space are the same among
themselves, whether that space is at rest or moves uniformly forwards
in a right line without any circular motion.
For the differences of the motions tending towards the same parts,
and the sums of those that tend towards contrary parts, are, at first (by
supposition), in both cases the same; and it is from those sums and dif-
ferences that the collisions and impulses do arise with which the bodies
mutually impinge one upon another. Wherefore (by Law II), the effects
of those collisions will be equal in both cases; and therefore the mutual
motions of the bodies among themselves in the one case will remain equal
to the mutual motions of the bodies among themselves in the other. A
clear proof of which we have from the experiment of a ship; where all
motions happen after the same manner, whether the ship is at rest or is
carried uniformly forwards in a right line.
COROLLARY VI
If bodies, any how moved among themselves, are urged in the direction
of parallel lines by equal accelerative forces, they will all continue to
move among themselves, after the same manner as if they had been
urged by no such forces.
For these forces acting equally (with respect to the quantities of the
bodies to be moved), and in the direction of parallel lines, will (by Law
II) move all the bodies equally (as to velocity), and therefore will never
produce any change in the positions or motions of the bodies among
themselves.
SCHOLIUM
Hitherto I have laid down such principles as have been received by
mathematicians, and are confirmed by abundance of experiments. By the
first two Laws and the first two Corollaries, Galileo discovered that the
descent of bodies observed the duplicate ratio of the time, and that the
motion of projectiles was in the curve of a parabola; experience agreeing
with both, unless so far as these motions are a little retarded by the re-
sistance of the air. When a body is falling, the uniform force of its
gravity, acting equally, impresses, in equal particles of time, equal forces
upon that body, and therefore generates equal velocities; and in the whole
time impresses a whole force, and generates a whole velocity proportional
to the time. And the spaces described in proportional times are as the
velocities and the times conjunctly; that is, in a duplicate ratio of the
NEWTON — PRINCIPIA 189
times. And when a body is thrown upwards, its uniform gravity im-
presses forces and takes off velocities proportional to the times; and the
times of ascending to the greatest heights are as the velocities to be taken
off, and those heights are as the velocities and the times conjunctly, or in
the duplicate ratio of the velocities. And if a body be projected in any
direction, the motion arising from its projection is compounded with the
motion arising from its gravity. As if the body A by its motion of pro-
jection alone could describe in a given time the right line AB, and with
its motion of falling alone could describe in the same time the altitude
AC; complete the parallelogram ABDC, and the body by that com-
pounded motion will at the end of the time be found in the place D; and
the curve line AED, which that body describes, will be a parabola, to-
which the right line AB will be a tangent in A; and whose ordinate BD
will be as the square of the line AB. On the same Laws and Corollaries
depend those things which have been demonstrated concerning the times
of the vibration of pendulums, and are confirmed by the daily experi-
ments of pendulum clocks. By the same, together with the third Law, Sir
Christ. Wren, Dr. Wallis, and Mr. Huygens, the greatest geometers of our
times, did severally determine the rules of the congress and reflexion of
hard bodies, and much about the same time communicated their discover-
ies to the Royal Society, exactly agreeing among themselves as to those
rules. Dr. Wallis, indeed, was something more early in the publication;
then followed Sir Christopher Wren, and, lastly, Mr. Huygens. But Sir
Christopher Wren confirmed the truth of the thing before the Royal
Society by the experiment of pendulums, which Mr. Mariotte soon after
thought fit to explain in a treatise entirely upon that subject.
190
MASTERWORKS OF SCIENCE
Book One: Of the Motion of Bodies
SECTION ONE
Of the method of first and last ratios of quantities, by the help whereof
we demonstrate the propositions that follow.
LEMMA I
Quantities, and the ratios of quantities, which in any finite time converge
continually to equality, and before the end of that time approach
nearer the one to the other than by any given difference, become ulti-
mately equal.
If you deny it, suppose them to be ultimately unequal, and let D
be their ultimate difference. Therefore they cannot approach nearer to
equality than by that given difference D; which is against the supposition.
LEMMA II
If in any figure AacE, terminated by the right lines Aa, AE, and the curve
acE, there be inscribed any number of parallelograms Ab, Be, Cd,
&c., comprehended under equal bases AB, BC, CD, &c,, and the sides]
XT
g
n'
b
£
X
71
c
2f
\
d
\
Bb, Cc, Dd, &c., parallel to one side Aa of the figure; and the parallelo-
grams aKbl, bLcm, cMdn, &c., are completed. Then if the breadth of
those parallelograms be supposed to be diminished, and their number
to be augmented in infinitum; 1 say, that the ultimate ratios which
the inscribed figure AKbLcMdD, the circumscribed figure Aalbmcn-
doE, and curvilinear figure AabcdE will have to one another are ratios
of equality.
NEWTON — PRINCIPI A
191
For the difference of the inscribed and circumscribed figures is the
sum of the parallelograms K/, L,mf Mn, Do, that is (from the equality of
all their bases), the rectangle under one of their bases K& and the sum of
their altitudes Aa, that is, the rectangle AEla. But this rectangle, because
its breadth AB is supposed diminished in infinitum, becomes less than
any given space. And therefore (by Lem. I) the figures inscribed and
circumscribed become ultimately equal one to the other; and much more
will the intermediate curvilinear figure be ultimately equal to either.
Q.E.D.
LEMMA III
The same ultimate ratios are also ratios of equality, when the breadths,
AB, BC, DC, &c., of the parallelograms are unequal, and are all di-
minished in infinitum.
For suppose AF equal to the greatest breadth, and complete the
parallelogram FAfl/. This parallelogram will be greater than the difference
of the inscribed and circumscribed figures; but, because its breadth AF is
a I .
b
N
72.
C
Ti/r
\
H.
d
\
J3F C
diminished in infinitum, it will become less than any given rectangle.
Q.E.D.
COR. i. Hence the ultimate sum of those evanescent parallelograms
will in all parts coincide with the curvilinear figure.
COR. 2. Much more will the rectilinear figure comprehended under
the chords of the evanescent arcs ab, be, cd, &c., ultimately coincide with
the curvilinear figure.
COR. 3. And also the circumscribed rectilinear figure comprehended
under the tangents of the same arcs.
COR. 4. And therefore these ultimate figures (as to their perimeters
acE) are not rectilinear, but curvilinear limits of rectilinear figures.
LEMMA IV
If in two figures AacE, PprT, you inscribe (as before) two ran%s of paral-
lelograms, an equal number in each ran\, and, when their breadths
are diminished in infinitum, the ultimate ratios of the parallelograms:
192
MASTERWORKS OF SCIENCE
in one figure to those in the other, each to each respectively, are the
same; I say, that those two figures AacE, PprT, are to one another
in that same ratio.
For as the parallelograms in the one are severally to the parallelograms
in the other, so (by composition) is the sum of all in the one to the sum
of all in the other; and so is the one figure to the other; because (by Lem.
Ill) the former figure to the former sum, and the latter figure to the latter
sum, are both in the ratio of equality. Q.EJD.
COR. Hence if two quantities of any kind are any how divided into
an equal number of parts, and those parts, when their number is aug-
mented, and their magnitude diminished in infinitum, have a given ratio
one to the other, the first to the first, the second to the second, and so on
£
x
in order, the whole quantities will be one to the other in that same given
jratio. For if, in the figures of this Lemma, the parallelograms are taken
one to the other in the ratio of the parts, the sum of the parts will always
be as the sum of the parallelograms; and therefore supposing the number
of the parallelograms and parts to be augmented, and their magnitudes
diminished in infinitum, those sums will be in the ultimate ratio of the
parallelogram in the one figure to the correspondent parallelogram in the
other; that is (by the supposition), in the ultimate ratio of any part of
the one quantity to the correspondent part of the other.
LEMMA V
In similar figures, all sorts of homologous sides, whether curvilinear or
rectilinear, are proportional' and the areas are in the duplicate ratio
of the homologous sides.
LEMMA VI
If any arc ACB, given in position, is subtended by its chord AB, and in
any point A, in the middle of the continued curvature, is touched by
a right line AD, produced both ways; then if the points A and B
approach one another and meet, I say, the angle BAD, contained
NEWTON — PRINCIPIA 193
between the chord and the tangent, will be diminished in infmitum,
and ultimately will vanish.
For if that angle does not vanish, the arc ACB will contain with the
tangent AD an angle equal to a rectilinear angle; and therefore the cur-
vature at the point A will not be continued, which is against the sup-
position.
LEMMA VII
The same things being supposed, I say that the ultimate ratio of the arc,
chord, and tangent, any one to any other, is the ratio of equality.
For while the point B approaches towards the point A, consider
always AB and AD as produced to the remote points b and d, and parallel
to the secant BD draw bd: and let the arc Kcb be always similar to the arc
ACB. Then, supposing the points A and B to coincide, the angle dhb
will vanish, by the preceding Lemma; and therefore the right lines Kby
Ad (which are always finite), and the intermediate arc Kcb, will coincide,
and become equal among themselves. Wherefore, the right lines AB, AD,
and the intermediate arc ACB (which are always proportional to the
former), will vanish, and ultimately acquire the ratio of equality. Q.E.D.
COR. i. Whence if through B we draw BF parallel to the tangent,
always cutting any right line AF passing through A in F, this line BF
will be ultimately in die ratio of equality with the evanescent arc ACB;
because, completing the parallelogram AFBD, it is always in a ratio o£
equality with AD.
COR. 2. And if through B and A more right lines are drawn, as BE,
BD, AF, AG, cutting the tangent AD and its parallel BF; the ultimate
ratio of all the abscissas AD, AE, BF, BG, and of the chord and arc AB,
any one to any other, will be the ratio of equality.
COR. 3. And therefore in all our reasoning about ultimate ratios, we
may freely use any one of those lines for any other.
194 MASTERWORKS OF SCIENCE
LEMMA VIII
If the right lines AR, BR, with the arc ACB, the chord AB, and the tan-
gent AD, constitute three triangles RAB, RACE, RAD, and the points
A and B approach and meet: I say, that the ultimate form of these
evanescent triangles is that of similitude f and their ultimate ratio that
of equality.
COR. And hence in all reasonings about ultimate ratios, we may indif-
ferently use any one of those triangles for any other.
LEMMA IX
If a right line AE, and a curve line ABC, both given by position, cut each
other in a given angle, A; and to that right line, in another given
angle, BD, CE are ordinately applied, meeting the curve in B, C; and
the points B and C together approach towards and meet in the point
A: / say, that the areas of the triangles ABD, ACE, will ultimately be
one to the other in the duplicate ratio of the sides.
LEMMA X
The spaces which a body describes by any finite force urging it, whether
that force is determined and immutable, or is continually augmented
or continually diminished, are in the very beginning of the motion
one to the other in the duplicate ratio of the times.
COR. i. And hence one may easily infer, that the errors of bodies
describing similar parts of similar figures in proportional times are nearly
as the squares of the times in which they are generated; if so be these
errors are generated by any equal forces similarly applied to the bodies,
and measured by the distances of the bodies from those places of the
similar figures, at which, without the action of those forces, the bodies
would have arrived in those proportional times.
COR. 2. But the errors that are generated by proportional forces, simi-
larly applied to the bodies at similar parts of the similar figures, are as
the forces and the squares of the times conjunctly.
NEWTON — PR INC IP I A
195
COR. 3. The same thing is to be understood of any spaces whatsoever
described by bodies urged with different forces; all which, in the very
beginning of the motion, are as the forces and the squares of the times
conjunctly.
COR. 4. And therefore the forces are as the spaces described in the very
beginning of the motion directly, and the squares of the times inversely.
COR. 5. And the squares of the times are as the spaces described
directly, and the forces inversely.
LEMMA XI
The evanescent subtense of the angle of contact, in all curves which at
the point of contact have a finite curvature, is ultimately in the dupli-
cate ratio of the subtense of the conterminate arc,
CASE r. Let AB be that arc, AD its tangent, BD the subtense of the
angle of contact perpendicular on the tangent, AB the subtense of the arc.
Draw BG perpendicular to the subtense AB, and AG to the tangent AD,
meeting in G; then let the points D, B, and G
approach to the points d, b, and gf and suppose
J to be the ultimate intersection of the lines BG,
AG, when the points D, B, have come to A. It is
evident that the distance GJ may be less than any
assignable. But (from the nature of the circles
passing through the points A, B, G, A, b, g,)
AB2=AG X BD, and AP=A^ X bd; and there-
fore the ratio of AB2 to A&2 is compounded of
the ratios of AG to A£, and of Bd to b d. But be-
cause GJ may be assumed of less length than any
assignable, the ratio of AG to Ag may be such
as to differ from the ratio of equality by less than
any assignable difference; and therefore the ratio
of AB2 to A£2 may be such as to differ from the ratio of BD to bd by
less than any assignable difference, Therefore, by Lem. I, the ultimate
ratio of AB2 to A£2 is the same with the ultimate ratio of BD to bd.
Q.E.D.
CASE 2. Now let BD be inclined to AD in any given angle, and the
ultimate ratio of BD to bd will always be the same as before, and there-
fore the same with the ratio of AB2 to A&2. Q.E.D.
CASE 3. And if we suppose the angle D not to be given, but that the
right line BD converges to a given point, or is determined by any other
condition whatever; nevertheless the angles D, d, being determined by the
same law, will always draw nearer to equality, and approach nearer to
each other than by any assigned difference, and therefore, by Lem, I5 will
at last be equal; and therefore the lines BD, bd are in the same ratio to
each other as before. Q.E.D.
COR. i. Therefore sinc^ the tangents AD, Adf the arcs AB, Ab, and
196
MASTERWORKS OF SCIENCE
their sines, BC, be, become ultimately equal to the chords AB, Ab, their
squares will ultimately become as the subtenses BD, bd.
COR. 2. Their squares are also ultimately as the versed sines of the
arcs, bisecting the chords, and converging to a given point. For those
versed sines are as the subtenses BD, bd.
COR. 3. And therefore the versed sine is in the duplicate ratio of the
time in which a body will describe the arc with a given velocity.
COR. 4. The rectilinear triangles ADB, Adb
are ultimately in the triplicate ratio of the sides
AD, Ad, and in a sesquiplicate ratio of the sides
DB, db; as being in the ratio compounded of the
sides AD to DB, and of Ad to db. So also the
triangles ABC, Abe are ultimately in the triplicate
ratio of the sides BC, be. What I call the sesquipli-
cate ratio is the subduplicate of the triplicate, as
being compounded of the simple and subduplicate
ratio.
COR. 5. And because DB, db are ultimately
parallel and in the duplicate ratio of the lines AD,
Ad, the ultimate curvilinear areas ADB, Adb will
be (by the nature of the parabola) two thirds of
the rectilinear triangles ADB, Adb and the segments AB, Ab will be one
third of the same triangles. And thence those areas and those segments
will be in the triplicate ratio as well of the tangents AD, Ad, as of the
chords and arcs AB, Ab.
SCHOLIUM
But we have all along supposed the angle of contact to be neither
infinitely greater nor infinitely less than the angles of contact made by
circles and their tangents; that is, that the curvature at the point A is
neither infinitely small nor infinitely great, or that the interval AJ is of a
finite magnitude. For DB may be taken as AD3: in which case no circle
can be drawn through the point A, between the tangent AD and the curve
AB, and therefore the angle of contact will be infinitely less than those of
circles. And by a like reasoning, if DB be made successively as AD4, AD5,
AD6, AD7, &c., we shall have a series of angles of contact, proceeding in
infinitum, wherein every succeeding term is infinitely less than the pre-
ceding. And if DB be made successively as AD2, AD%, AD%, AD%,
AD%, AD%, &c., we shall have another infinite series of angles of con-
tact, the first of which is of the same sort with those of circles, the second
infinitely greater, and every succeeding one infinitely greater than the pre-
ceding. But between any two of these angles another series of inter-
mediate angles of contact may be interposed, proceeding both ways in
infinitum, wherein every succeeding angle shall be infinitely greater or
infinitely less than the preceding. As if between the terms AD2 and AD3
there were interposed the series AD1%, AD*%, AD%, AD%, AD%,
NEWTON — PRINCIPIA 197
AD%, ADll/4> AD1^;, AD1%, &c. And again, between any two angles
of this series, a new series of intermediate angles may be interposed, dif-
fering from one another by infinite intervals. Nor is nature confined to
any bounds.
Those things which have been demonstrated of curve lines, and the
superficies which they comprehend, may be easily applied to the curve
superficies and contents of solids. These Lemmas are premised to avoid
the tediousness of deducing perplexed demonstrations ad absurdum, ac-
cording to the method of the ancient geometers. For demonstrations are
more contracted by the method of indivisibles: but because the hypothesis
of indivisibles seems somewhat harsh, and therefore that method is
reckoned less geometrical, I chose rather to reduce the demonstrations of
the following propositions to the first and last sums and ratios of nascent
and evanescent quantities, that is, to the limits of those sums and ratios;
and so to premise, as short as I could, the demonstrations of those limits,
For hereby the same thing is performed as by the method of indivisibles;
and now those principles being demonstrated, we may use them with
more safety. Therefore if hereafter I should happen to consider quantities
as made up of particles, or should use little curve lines for right ones,
I would not be understood to mean indivisibles, but evanescent divisible
quantities; not the sums and ratios of determinate parts, but always the
limits of sums and ratios; and that the force of such demonstrations
always depends on the method laid down in the foregoing Lemmas.
Perhaps it may be objected that there is no ultimate proportion o£
evanescent quantities; because the proportion, before the quantities have
vanished, is not the ultimate, and when they are vanished, is none. But
by the same argument, it may be alleged that a body arriving at a certain
place, and there stopping, has no ultimate velocity: because the velocity,
before the body comes to the place, is not its ultimate velocity; when it
has arrived, is none. But the answer is easy; for by the ultimate velocity
is meant that with which the body is moved, neither before it arrives at
its last place and the motion ceases, nor after, but at the very instant it
arrives; that is, that velocity with which the body arrives at its last place,
and with which the motion ceases. And in like manner, by the ultimate
ratio of evanescent quantities is to be understood the ratio of the quanti-
ties not before they vanish, nor afterwards, but with which they vanish.
In like manner the first ratio of nascent quantities is that "with which they
begin to be. And the first or last sum is that with which they begin and
cease to be (or to be augmented or diminished). There is a limit which
the velocity at the end of the motion may attain, but not exceed. This is
the ultimate velocity. And there is the' like limit in all quantities and pro-
portions that begin and cease to be. And since such limits are certain and
definite, to determine the same is a problem strictly geometrical. But
whatever is geometrical we may be allowed to use in determining and
demonstrating any other thing that is likewise geometrical.
It may also be objected, that if the ultimate ratios of evanescent
quantities are given, their ultimate magnitudes will be also given: and so
198 MASTERWORKS OF SCIENCE
all quantities will consist o£ indivisibles, which is contrary to what Euclid
has demonstrated concerning incommensurables, in the loth Book of his
Elements. But this objection is founded on a false supposition. For those
ultimate ratios with which quantities vanish are not truly the ratios of
ultimate quantities, but limits towards which the ratios of quantities de-
creasing without limit do always converge; and to which they approach
nearer than by any given difference, but never go beyond, nor in effect
attain to, till the quantities are diminished in infinitum. This thing will
appear more evident in quantities infinitely great. If two quantities, whose
difference is given, be augmented in infinitum, the ultimate ratio of these
quantities will be given, to wit, the ratio of equality; but it does not from
thence follow that the ultimate or greatest quantities themselves, whose
ratio that is, will be given. Therefore if in what follows, for the sake of
being more easily understood, I should happen to mention quantities as
least, or evanescent, or ultimate, you are not to suppose that quantities of
any determinate magnitude are meant, but such as are conceived to be
always diminished without end.
SECTION TWO
Of the invention of centripetal forces. -
PROPOSITION I. THEOREM I.
The areas which revolving bodies describe by radii drawn to an immov-
able centre of force do lie in the same immovable planes, and are pro-
portional to the times in which they are described.
For suppose the time to be divided into equal parts, and in the first
part of that time let the body by its innate force describe the right line
AB, In the second part of that time, the same would (by Law I), if not
hindered, proceed directly to c, along the line Be equal to AB; so that by
the radii AS, BS, <rS, drawn to the centre, the equal areas ASB, BSer, would
be described. But when the body is arrived at B, suppose that a centrip-
etal force acts at once with a great impulse, and, turning aside the body
from the right line Be, compels it afterwards to continue its motion along
the right line BC. Draw cC parallel to BS meeting BC in C; and at the
end of the second part of the time, the body (by Cor. I of the Laws) will
be found in C, in the same plane with the triangle ASB. Join SC, and,
because SB and Cc are parallel, the triangle SBC will be equal to the
triangle SB<r, and therefore also to the triangle SAB. By the like argument,
if the centripetal force acts successively in C, D, E, &c., and makes the
body, in each single particle of time, to describe the right lines CD, DE,
EF, &c., they will all lie in the same plane; and the triangle SCD will be
equal to the triangle SBC, and SDE to SCD, and SEF to SDE. And there-
fore, in equal times, equal areas are described in one immovable plane:
and, by composition, any sums SADS, SAFS, of those areas, are one to the
^^__ NEWTON-— PRINCIPIA 199
other as the times in which they are described. Now let the number of
those triangles be augmented, and their breadth diminished in infinitum;
and (by Cor. IV, Lem. III) their ultimate perimeter ADF will be a curve
line: and therefore the centripetal force, by which the body is perpetually
drawn back from the tangent of this curve will act continually; and any
described areas SADS, SAFS, which are always proportional to the times
of description, will, in this case also, be proportional to those times. Q.E.D.
COR. i. The velocity of a body attracted towards an immovable centre,
in spaces void of resistance, is reciprocally as the perpendicular let ^ fall
from that centre on the right line that touches the orbit. For the velocities
in those places A, B, C, D, E, are as the bases AB, BC, CD, DE, EF, of
equal triangles; and these bases are reciprocally as the perpendiculars let
fall upon them.
COR. 2. If the chords AB, BC of two arcs, successively described in
equal times by the same body, in spaces void of resistance, are completed
into a parallelogram ABCV, and the diagonal BV of this parallelogram,
in the position which it ultimately acquires when those arcs are di-
minished in infinitum, is produced both ways, it will pass through the
centre of force.
PROPOSITION II. THEOREM II.
moves in any curve line described in <
/*«**<*.», t*,»wn to a point either immovable, or mov,.^ ,
an uniform rectilinear motion, describes about that point areas pro-
portional to the times, is urged by a centripetal force directed to that
Every body that moves in any curve line described in a plane, and by a
radius, drawn to a point either immovable, or moving forward with
point.
200 MASTERWORKS OF SCIENCE
For every body that moves in a curve line is (by Law I) turned aside
from its rectilinear course by the action of some force that impels it. And
that force by which the body is turned off from its rectilinear course, and
is made to describe, in equal times, the equal least triangles SAB, SBC,
SCD, &c., about the immovable point S (by Prop. XL. Book One, Elem.
and Law II), acts in the place B, according to the direction of a line par-
allel to cC, that is, in the direction of the line BS, and in the place C,
according to the direction of a line parallel to dD, that is, in the direc-
tion of the line CS, &c.; and therefore acts always in the direction of lines
tending to the immovable point S. QJE.D.
SCHOLIUM
A body may be urged by a centripetal force compounded of several
forces; in which case the meaning of the Proposition is that the force
which results out of all tends to the point S. But if any force acts perpetu-
ally in the direction of lines perpendicular to the described surface, this
force wiU make the body to deviate from the plane of its motion: but will
neither augment nor diminish the quantity of the described surface and
is therefore to be neglected in the composition of forces.
PROPOSITION III. THEOREM III.
Every body that by a radius drawn to the centre of another body, howso-
ever moved, describes areas about that centre frofortional to the
times is urged by a force compounded out of the centripetal forge
NEWTON — PRINCIPIA 201
tending to that other body, and of all the accelerative force by which
that other body is impelled.
Let L represent the one, and T the other body; and (by Cor. VI of
the Laws) if both bodies are urged in the direction of parallel lines, by a
new force equal and contrary to that by which the second body T is
urged, the first body L will go on to describe about the other body T the
same areas as before: but the force by which that other body T was urged
will be now destroyed by an equal and contrary force; and therefore (by
Law I) that other body T, now left to itself, will either rest or move uni-
formly forward in a right line: and the first body L, impelled by the dif-
ference of the forces, that is, by the force remaining, will go on^ to de-
scribe about the other body T areas proportional to the times. And there-
fore (by Theor. II) the difference of the forces is directed to the other
body T as its centre. Q.EJD.
SCHOLIUM
Because the equable description of areas indicates that a centre is
respected by that force with which the body is most affected, and by
which it is drawn back from its rectilinear motion, and retained in its
orbit; why may we not be allowed, in the following discourse, to use the
equable description of areas as an indication of a centre, about which all
circular motion is performed in free spaces?
PROPOSITION IV. THEOREM IV.
The centripetal forces of bodies, which by equable motions describe dif-
ferent circles, tend to the centres of the same circles; and are one to
the other as the squares of the arcs described in equal times applied
to the radii of the circles.
These forces tend to the centres of the circles (by Prop. II and Cor.
II, Prop. I), and are one to another as the versed sines of the least arcs
described in equal times; that is, as the squares of the same arcs applied
to the diameters of the circles (by Lem. VII); and therefore since those
arcs are as arcs described in any equal times, and the diameters are as the
radii, the forces will be as the squares of any arcs described in the same
time applied to the radii of the circles. Q.E.D.
COR. i. Therefore, since those arcs are as the velocities of the bodies,
the centripetal forces are in a ratio compounded of the duplicate ratio of
the velocities directly, and of the simple ratio of the radii inversely.
COR. 2. And since the periodic times are in a ratio compounded of
the ratio of the radii directly and the ratio of the velocities inversely, the'
centripetal forces are in a ratio compounded of the ratio of the radii
directly and the duplicate ratio of the periodic times inversely.
202 MASTERWORKS OF SCIENCE
COR. 3. Whence if the periodic times are equal, and the velocities
therefore as the radii, the centripetal forces will be also as the radii; and
the contrary.
COR. 4. If the periodic times and the velocities are both in the sub-
duplicate ratio of the radii, the centripetal forces will be equal among
themselves; and the contrary.
COR. 5. If the periodic times are as the radii, and therefore the veloci-
ties equal, the centripetal forces will be reciprocally as the radii; and the
contrary.
COR. 6. If the periodic times are in the sesquiplicate ratio of the radii,
and therefore the velocities reciprocally in the subduplicate ratio of the
radii, the centripetal forces will be in the duplicate ratio of the radii in-
versely; and the contrary.
COR. 7. And universally, if the periodic time is as any power Rn of the
radius R, and therefore the velocity reciprocally as the power Rn — l of
the radius, the centripetal force will be reciprocally as the power R2n — x
of the radius; and the contrary.
COR. 8. The same things all hold concerning the times, the velocities,
and forces by which bodies describe the similar parts of any similar fig-
ures that have their centres in a similar position with those figures; as
appears by applying the demonstration of the preceding cases to those.
And the application is easy, by only substituting the equable description
of areas in the place of equable motion, and using the distances of the
bodies from the centres instead of the radii. .
COR. 9. From the same demonstration it likewise follows that the arc
which a body, uniformly revolving in a circle by means .of a given centrip-
etal force, describes in any time is a mean proportional between the
diameter of the circle and the space which the same body falling by the
same given force would descend through in the same given time.
SCHOLIUM
The case of the 6th Corollary obtains in the celestial bodies (as Sir
Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed);
and therefore in what follows, I intend to treat more at large of those
things which relate to centripetal force decreasing in a duplicate ratio
of the distances from the centres.
Moreover, by means of the preceding Proposition and its Corollaries,
we may discover the proportion of a centripetal force to any other known
force, such as that of gravity. For if a body by means of its gravity re-
volves in a circle concentric to the earth, this gravity is the centripetal
force of that body. But from the descent of heavy bodies, the time of one
entire revolution, as well as the arc described in any given time, is given
(by Cor. 9 of this Prop.). And by such propositions, Mr. Huygens, in his
excellent book De Horologio Oscillatorio, has compared the force of
gravity with the centrifugal forces of revolving bodies.
NEWTON — PRINCIPIA 203
The preceding Proposition may be likewise demonstrated after this
manner. In any circle suppose a polygon to be inscribed of any number
of sides. And if a body, moved with a given velocity along the sides of the
polygon, is reflected from the circle at the several angular points, the force,
with which at every reflection it strikes the circle, will be as its velocity:
and therefore the sum of the forces, in a given time, will be as that ve-
locity and the number of reflections conjunctly; that is (if the species of
the polygon be given), as the length described in that given time, and in-
creased or diminished in the ratio of the same length to the radius of the
circle; that is, as the square of that length applied to the radius; and
therefore the polygon, by having its sides diminished in infinitum, coin-
cides with the circle, as the square of the arc described in a given time
applied to the radius. This is the centrifugal force, with which the body
impels the circle; and to which the contrary force, wherewith the circle
continually repels the body towards the centre, is equal.
PROPOSITION V. PROBLEM I.
There Being given, in any places, the velocity with which a body de-
scribes a given figure, by means of forces directed to some common
centre: to find that centre.
Let the three right lines PT, TQV, VR touch the figure described
in as many points, P5 Q, R, and meet in T and V. On the tangents erect
the perpendiculars- PA, QB, RC, reciprocally proportional to the veloci-
ties of the body in the points P, Q, R, from which the perpendiculars
were raised; that is, so that PA may be to' QB as the velocity in Q to the
velocity in P, and QB to RC as the velocity in R to the velocity in Q.
Through the ends A, B, C, of the perpendiculars draw AD, DBE, EC,
at right angles, meeting in D and E: and the right lines TD, VE pro-
duced, will meet in S, the centre required.
For the perpendiculars let fall from the centre S on the tangents PT,
QT, are reciprocally as the velocities of the bodies in the points P and Q
(by Cor. i, Prop. I), and therefore, by construction, as the perpendiculars
AP, BQ directly; that is, as the perpendiculars let fall from the point D
on the tangents. Whence it is easy to infer that the points S, D, T are in
one right line. And by the like argument the points S, E, V are also in one
204 MASTERWQRKS OF SCIENCE
right line; and therefore the centre S is in the point where the right lines
TD, VE meet. Q.E.D.
SECTION TWELVE
Of the attractive -forces of sphcerical bodies.
SCHOLIUM
These Propositions naturally lead us to the analogy there is between
centripetal forces, and the central bodies to which those forces used to be
directed; for it is reasonable to suppose that forces which are directed to
bodies should depend upon the nature and quantity of those bodies, as
we see they do in magnetical experiments. And when such cases occur, we
are to compute the attractions of the bodies by assigning to each of their
particles its proper force, and then collecting the sum of them all. I here
use the word attraction in general for any endeavour, of what kind soever,
made by bodies to approach to each other; whether that endeavour arise
from the action of the bodies themselves, as tending mutually to or agitat-
ing each other by spirits emitted; or whether it arises from the action
of the aether or of the air, or of any medium whatsoever, whether corporeal
or ^ incorporeal, any how impelling bodies placed therein towards each
other. In the same general sense I use the word impulse, not defining in
this treatise the species or physical qualities of forces, but investigating
the quantities and mathematical proportions of them; as I observed before
in the Definitions. In mathematics we are to investigate the quantities of
forces with their proportions consequent upon any conditions supposed;
then, when we enter upon physics, we compare those proportions with
the phenomena of Nature, that we may know what conditions of those
forces answer to the several kinds of attractive bodies. And this prepara-
tion being made, we argue more safely concerning the physical species,
causes, and proportions of the forces. Let us see, then, with what forces
sphaerical bodies consisting of particles endued with attractive powers in
the manner above spoken of must act mutually upon one another; and
what kind of motions will follow from thence.
PROPOSITION LXX. THEOREM XXX.
If to every point of a sphcerical surface there tend equal centripetal forces
decreasing in the duplicate ratio of the distances from those points;
I say, that a corpuscle placed within that superficies will not be at-
tracted by those forces any way.
NEWTON — PRINCIPIA 205
Let HIKL be that sphaerical superficies, and P a corpuscle placed
within. Through P let there be drawn to this superficies two lines HK, IL,
intercepting very small arcs HI, KL; and because (by Cor. 3, Lem. VII)
the triangles HPI, LPK are alike, those arcs will be proportional to the
distances HP, LP; and any particles at HI and KL of the spherical super-
ficies, terminated by right lines passing through P, will be in the duplicate
ratio of those distances. Therefore the forces of these particles exerted
upon the body P are equal between themselves. For the forces are as the
particles directly, and the squares of the distances inversely. And these
two ratios compose the ratio of equality. The attractions therefore, being
made equally towards contrary parts, destroy each other. And by a like
reasoning all the attractions through the whole spherical superficies are
destroyed by contrary attractions. Therefore the body P will not be any
way impelled by those attractions. Q.E.D.
PROPOSITION LXXL THEOREM XXXI.
The same things supposed as above, 1 say, that a corpuscle placed without
the sphterical superficies is attracted towards the centre of the sphere
with a force reciprocally proportional to the square of its distance
-from that centre.
PROPOSITION LXXIL THEOREM XXXII.
If to the several points of a sphere there tend equal centripetal forces de-
creasing in a duplicate ratio of the distances from those points; and
there be given both the density of the sphere and the ratio of the
diameter of the sphere to the distance of the corpuscle from its centre;
I say, that the force with which the corpuscle is attracted is propor-
tional to the semi-diameter of the sphere.
For conceive two corpuscles to be severally attracted by two spheres,
one by one, the other by the other, and their distances from the centres
of the spheres to be proportional to the diameters of the spheres respec-
tively, and the spheres to be resolved into like particles, disposed in a like
206 MASTERWQRKS OF SCIENCE
situation to the corpuscles. Then the attractions of one corpuscle towards
the several particles of one sphere will be to the attractions of the other
towards as many analogous particles of the other sphere in a ratio com-
pounded of the ratio of the particles directly, and the duplicate ratio of
the distances inversely. But the particles are as the spheres, that is, in a
triplicate ratio of the diameters, and the distances are as the diameters;
and the first ratio directly with the last ratio taken twice inversely be-
comes the ratio of diameter to diameter. Q.E.D.
COR. i. Hence if corpuscles revolve in circles about spheres composed
of matter equally attracting, and the distances from the centres of the
spheres be proportional to their diameters, the periodic times will be
equal.
COR. 2. And, vice versa, if the periodic times are equal, the distances
will be proportional to the diameters. These two Corollaries appear from
Cor. 3, Prop. IV.
COR. 3. If to the several points of any two solids whatever, of like
figure and equal density, there tend equal centripetal forces decreasing in
a duplicate ratio of the distances from those points, the forces, with which
corpuscles placed in a like situation to those two solids will be attracted
by them, will be to each other as the diameters of the solids.
PROPOSITION LXXIIL THEOREM XXXIII.
If to the several points of a given sphere there tend equal centripetal
•forces decreasing in a duplicate ratio of the distances from the point;
I say, that a corpuscle placed within the sphere is attracted by a force
proportional to its distance from the centre.
In the sphere ABCD, described about the centre S, let there be placed
the corpuscle P; and about the same centre S, with the interval SP, con-
ceive described an interior sphere PEQF. It is plain (by Prop. LXX) that
the concentric sphaerical superficies, of which the difference AEBF of the
spheres is composed, have no effect at all upon the body P, their attrac-
tions being destroyed by contrary attractions. There remains, therefore,
only the attraction of the interior sphere PEQF. And (by Prop. LXXII)
this is as the distance PS. Q.E.D.
NEWTON — PRINCIPIA 207
SCHOLIUM
By the superficies of which I here imagine the solids composed, I do
not mean superficies purely mathematical, but orbs so extremely thin that
their thickness is as nothing; that is, the evanescent orbs of which the
sphere will at last consist, when the number of the orbs is increased, and
their thickness diminished without end. In like manner, by the points of
which lines, surfaces, and solids are said to be composed, are to be under-
stood equal particles, whose magnitude is perfectly inconsiderable.
PROPOSITION LXXIV. THEOREM XXXIV.
The same things supposed, I say, that a corpuscle situate without the
sphere is attracted with a force reciprocally proportional to the square
of its distance from the centre.
For suppose the sphere to be divided into innumerable concentric
sphaerical superficies, and the attractions of the corpuscle arising from the
several superficies will be reciprocally proportional to the square of the
distance of the corpuscle from the centre of the sphere (by Prtfp. LXXI).
And, by composition, the sum of those attractions, that is, the attraction
of the corpuscle towards the entire sphere, will be in the same ratio.
Q.E.D.
COR. i. Hence the attractions of homogeneous spheres at equal dis-
tances from the centres will be as the spheres themselves. For (by Prop.
LXXII) if the distances be proportional to the diameters of the spheres,
the forces will be as the diameters. Let the greater distance be diminished
in that ratio; and the distances now being equal, the attraction will be
increased in the duplicate of that ratio; and therefore will be to the other
attraction in the triplicate of that ratio; that is, in the ratio of the spheres.
COR. 2. At any distances whatever the attractions are as the spheres
applied to the squares of the distances.
COR. 3. If a corpuscle placed without an homogeneous sphere is at-
tracted by a -force reciprocally proportional to the square of its distance
from the centre, and the sphere consists of attractive particles, the force
of every particle will decrease in a duplicate ratio of the distance from
each particle.
PROPOSITION LXXV. THEOREM XXXV.
If to the several points of a given sphere there tend equal centripetal
forces decreasing in a duplicate ratio of the distances from the point;
I say, that another similar sphere will be attracted by it with a force
reciprocally proportional to the square of the distance of the centres.
208 MASTERWORKS OF SCIENCE
For the attraction of every particle is reciprocally as the square of its
distance from the centre of the attracting sphere (by Prop. LXXIV), and
is therefore the same as if that whole attracting force issued from one
single corpuscle placed in the centre of this sphere. But this attraction is
as great as on the other hand the attraction of the same corpuscle would
be if that were itself attracted by the several particles of the attracted
sphere with the same force with which they are attracted by it. But that
attraction of the corpuscle would be (by Prop. LXXIV) reciprocally pro-
portional to the square of its distance from the centre of the sphere;
therefore the attraction of the sphere, equal thereto, is also in the same
ratio. Q.E.D.
COR. i. The attractions of spheres towards other homogeneous spheres
are as the attracting spheres applied to the squares of the distances of
their centres from the centres of those which they attract.
COR. 2. The case is the same when the attracted sphere does also at-
tract. For the several points of the one attract the ^several points of the
other with the same force with which they themselves are attracted by the
others again; and therefore since in all attractions (by Law III) the at-
tracted and attracting point are both equally acted on, the force will be
doubled by their mutual attractions, the proportions remaining.
COR. 3. Those several truths demonstrated above concerning the mo-
tion of bodies about the focus of the conic sections will take place when
an attracting sphere is placed in the focus, and the bodies move without
the sphere.
COR. 4. Those things which were demonstrated before of the motion
of bodies about the centre of the conic sections take place when the
motions are performed within the sphere.
PROPOSITION LXXVI. THEOREM XXXVI.
If spheres be however dissimilar (as to density of matter and attractive
force) in the same ratio onward from the centre to the circumfer-
ence; but every where similar, at every given distance from the centre,
on all sides round about; and the attractive force of every point de-
' creases in the duplicate ratio of the distance of the body attracted;
I say, that the whole force with which one of these spheres attracts
the other will be reciprocally proportional to the square of the dis-
tance of the centres.
Imagine several concentric similar spheres, AB, CD, EF, &c., the
innermost of which added to the outermost may compose a matter more
dense towards the centre, or subducted from them may leave the same
more lax and rare. Then, by Prop. LXXV, these spheres will attract other
similar concentric spheres GH, IK, LM, &c., each the other, with forces
reciprocally proportional to the square of the distance SP. And, by com-
position or division, the sum of all those forces, or the excess of any of
NEWTON — PRINCIPIA
209
them above the others; that is, the entire force with which the whole
sphere AB (composed of any concentric spheres or of their differences)
will attract the whole sphere GH (composed of any concentric spheres or
their differences) in the same ratio. Let the number of the concentric
spheres be increased in infinitum, so that the density of the matter to-
gether with the attractive force may, in the progress from the circum-
H
ference to the centre, increase or decrease according to any given law; and
by the addition of matter not attractive, let the deficient density be sup-
plied, that so the spheres may acquire any form desired; and the force
with 'which one of these attracts the other will be still, by the former rea-
soning, in the same ratio of the square of the distance inversely. Q.E.D.
COR. i. Hence if many spheres of this kind, similar in all respects,
attract each other mutually, the accelerative attractions of each to each, at
any equal distances of the centres, will be as the attracting spheres.
COR. 2. And at any unequal distances, as the attracting spheres ap-
plied to the squares of the distances between the centres.
COR. 3. The motive attractions, or the weights of the spheres towards
one another, will be at equal distances of the centres as the attracting and
attracted spheres conjunctly; that is, as the products arising from multi-
plying the spheres into each other.
COR. 4. And at unequal distances, as those products directly, and the
squares of the distances between the centres inversely.
COR. 5. These proportions take place also when the attraction arises
from the attractive virtue of both spheres mutually exerted upon each
other. For the attraction is only doubled by the conjunction of the forces,
the proportions remaining as before.
COR. 6. If spheres of this kind revolve about others at rest, each about
each; and the distances between the centres of the quiescent and revolv-
ing bodies are proportional to the diameters of the quiescent bodies; the
periodic times will be equal.
COR 7. And, again, if the periodic times are equal, the distances will
be proportional to the diameters.
COR. 8. All those truths above demonstrated, relating to the motions
of bodies about the foci of conic sections, will take place when an attract-
ing sphere, of any form and condition like that above described, is placed
in the focus.
210 MASTERWORKS OF SCIENCE
COR. 9. And also when the revolving bodies are also attracting spheres
of any condition like that above described.
PROPOSITION LXXVIL THEOREM XXXVII.
If to the several points of spheres there tend centripetal forces propor-
tional to the distances of the points from the attracted bodies; I say,
that the compounded force with which two spheres attract each other
mutually is as the distance between the centres of the spheres.
PROPOSITION LXXVIIL THEOREM XXXVIII.
If spheres in the progress from the centre to the circumference be how-
ever dissimilar and unequable, but similar on every side round about
at all given distances from the centre; and the attractive force of
every point be as the distance of the attracted body; I say, that the
entire force with which two spheres of this "kjnd attract each other
mutually is proportional to the distance between the centres of the
spheres.
SCHOLIUM
I have now explained the two principal cases of attractions; to wit,
when the centripetal forces decrease in a duplicate ratio of the distances,
or increase in a simple ratio of the distances, causing the bodies in both
cases to revolve in conic sections, and composing sphaerical bodies whose
centripetal forces observe the same law of increase or decrease in the
recess from the centre as the forces or the particles themselves do; which
is very remarkable. It would be tedious to run over the other cases, whose
conclusions are less elegant and important, so particularly as I have done
these.
NEWTON — PRINCIPIA 211
Book Two: Of the Motion of Bodies
SECTION SIX
Of the motion and resistance of funependulous bodies
PROPOSITION XXIV. THEOREM XIX.
The quantities of matter in funependulous bodies, whose centres of oscil-
lation are equally distant from the centre of suspension, are in a ratio
compounded of the ratio of the weights and the duplicate ratio of
the times of the oscillations in vacuo.
For the velocity which a given force can generate in a given matter in
a given time is as the force and the time directly, and the matter inversely.
The greater the force or the time is, or the less the matter, the greater
velocity will be generated. This is manifest from the second Law of Mo-
tion. Now if pendulums are of the same length, the motive forces in places
equally distant from the perpendicular are as the weights: and therefore
if two bodies by oscillating describe equal arcs, and those arcs are divided
into equal parts; since the times in which the bodies describe each of the
correspondent parts of the arcs are as the times of the whole oscillations,
the velocities in the correspondent parts of the oscillations will be to each
other as the motive forces and the whole times of the oscillations directly,
and the quantities of matter reciprocally: and therefore the quantities of
matter are as the forces and the times of the oscillations directly and the
velocities reciprocally. But the velocities reciprocally are as the times,
and therefore the times directly and the velocities reciprocally are as the
squares of the times; and therefore the quantities of matter are as the
motive forces and the squares of the times, that is, as the weights and the
squares of the times. Q.E.D.
COR. i. Therefore if the times are equal, the quantities of matter in
each of the bodies are as the weights.
COR. 2. If the weights are equal, the quantities of matter will be as
the squares of the times.
COR. 3. If the quantities of matter are equal, the weights will be recip-
rocally as the squares of the times.
COR. 4. Whence since the squares of the times, cceteris paribus, are as
the lengths of the pendulums, therefore if both the times and quantities
of matter are equal, the weights will be as the lengths of the pendulums.
COR. 5. And universally, the quantity of matter in the pendulous
body is as the square of the time directly, and the length of the pendulum
inversely.
212 MASTERWORKS OF SCIENCE
COR. 6. But in a non-resisting medium, the quantity of matter in the
pendulous body is as the comparative weight and the square o£ the time
directly, and the length of the pendulum inversely. For the comparative
weight is the motive force of the body in any heavy medium, as was
shown above; and therefore does the same thing in such a non-resisting
medium as the absolute weight does in a vacuum.
COR. 7. And hence appears a method both of comparing bodies one
among another, as to the quantity of matter in each; and of comparing
the weights of the same body in different places, to know the variation
of its gravity. And by experiments made with the greatest accuracy, I
have always found the quantity of matter in bodies to be proportional
to their weight.
Book Three: Natural Philosophy
IN THE preceding Books I have laid down the principles of philosophy,
principles not philosophical, but mathematical: such, to wit, as we may
build our reasonings upon in philosophical inquiries. These principles are
the laws and conditions of certain motions, and powers or forces, which
chiefly have respect to philosophy; but, lest they should have appeared
of themselves dry and barren, I have illustrated them here and there with
some philosophical scholiums, giving an account of such things as are of
more general nature, and which philosophy seems chiefly to be founded
on; such as the density and the resistance of bodies, spaces void of all
bodies, and the motion of light and sounds. It remains that, from the same
principles, I now demonstrate the frame of the System of the World. Upon
this subject I had, indeed, composed the third Book in a popular method,
that it might be read by many; but afterward, considering that such as
had not sufficiently entered into the principles could not easily discern the
strength of the consequences, nor lay aside the prejudices to which they
had been many years accustomed, therefore, to prevent the disputes which
might be raised upon such accounts, I chose to reduce the substance of
this Book into the form of Propositions (in the mathematical way), which
should be read by those only who had first made themselves masters of
the principles established in the preceding Books.
RULES OF REASONING IN PHILOSOPHY
RULE I
We are to admit no more causes of natural things than such as are both
true and sufficient to explain their appearances.
To this purpose the philosophers say that Nature does nothing in
vain, and more is in vain when less will serve; for Nature is pleased with
simplicity, and affects not the pomp of superfluous causes.
NEWTON— -PR INC IP I A 213
RULE II
Therefore to the same natural effects we must, as jar as possible, assign
the same causes.
As to respiration in a man and in a beast; the descent of stones in
Europe and in America; the light of our culinary fire "and of the sun; the
reflection of light in the earth, and in the planets.
RULE 111
The qualities of bodies, which admit neither intension nor remission of
degrees, and which are found to belong to all bodies within the reach
of our experiments, are to be esteemed the universal qualities of all
bodies whatsoever.
For since the qualities -of bodies are only known to us by experiments,
we are to hold for universal all such as universally agree with experiments;
and such as are not liable to diminution can never be quite taken away.
We are certainly not to relinquish the evidence of experiments for the sake
of dreams and vain fictions of our own devising; nor are we to recede
from the analogy of Nature, which uses to be simple, and always conso-
nant to itself. We no other way know the extension of bodies than by our
senses, nor do these reach it in all bodies; but because we perceive exten-
sion in all that are sensible, therefore we ascribe it universally to all others
also. That abundance of bodies are hard, we learn by experience; and be-
cause the hardness of the whole arises from the hardness of the parts, we
therefore justly infer the hardness of the undivided particles not only of
the bodies we feel but of all others. That all bodies are impenetrable, we
gather not from reason, but from sensation. The bodies which we handle
we find impenetrable, and thence conclude impenetrability to be an uni-
versal property of all bodies whatsoever. That all bodies are movable,
and endowed with certain powers (which we call the vires inertits) of
persevering in their motion, or in their rest, we only infer from the like
properties observed in the bodies which we have seen. The extension,
hardness, impenetrability, mobility, and vis inertice of the whole, result
from the extension, hardness, impenetrability, mobility, and vires inertias
of the parts; and thence we conclude the least particles of all bodies to be
also all extended, and hard and impenetrable, and movable, and endowed
with their proper vires inertice. And this is the foundation of all philoso-
phy. Moreover, that the divided but contiguous particles of bodies may be
separated from one another is matter of observation; and, in the particles
that remain undivided, our minds are able to distinguish yet lesser parts,
as is mathematically demonstrated. But whether the parts so distin-
guished, and not yet divided, may, by the powers of Nature, be actually
214 MASTERWQRKS OF SCIENCE
divided and separated from one another, we cannot certainly determine.
Yet, had we the proof of but one experiment that any undivided particle,
in breaking a hard and solid body, suffered a division, we might by virtue
of this rule conclude that the undivided as well as the divided particles
may be divided and actually separated to infinity.
Lastly, if it universally appears, by experiments and astronomical ob-
servations, that all bodies about the earth gravitate towards the earth, and
that in proportion to the quantity of matter which they severally contain;
that the moon likewise, according to the quantity of its matter, gravitates
towards the earth; that, on the other hand, our sea gravitates towards the
moon; and all the planets mutually one towards another; and the comets
in like manner towards the sun; we must, in consequence of this, rule, uni-
versally allow that all bodies whatsoever are endowed with a principle of
mutual gravitation. For the argument from the appearances concludes with
more force for the universal gravitation of all bodies than for their impen-
etrability; of which, among those in the celestial regions, we have no ex-
periments, nor any manner of observation. Not that I affirm gravity to be
essential to bodies: by their vis insita I mean nothing but their vis inertice.
This is immutable. Their gravity is diminished as they recede from the
earth.
In experimental philosophy we are to loo\ upon proposition's collected "by
general induction from phenomena as accurately or very nearly true,
notwithstanding any contrary hypotheses that may be imagined, till
such time as other phenomena occur, by which they may either be
made more accurate or liable to exceptions.
This rule we must follow, that the argument of induction may not
be evaded by hypotheses.
PHENOMENA, OR APPEARANCES
PHENOMENON I
That the circumjovial planets, by radii drawn to Jupiter's centre, describe
areas proportional to the times of description; and that their periodic
times, the fixed stars being at rest, are in the sesquiplicate proportion
of their distances from its centre.
This we know from astronomical observations. For the orbits of these
planets differ but insensibly from circles concentric to Jupiter; and their
motions in those circles are found to be uniform. And all astronomers
agree that their periodic times are in the sesquiplicate proportion of the
semi-diameters of their orbits; and so it manifestly appears from the fol-
lowing table.
NEWTON — PRINCIPIA
215
The periodic times of the satellites of Jupiter.
d. i8h. 27' 34". 3d. 13*. 13' 42". /. 3\ 42' 36". i6d. i6\ 32' 9".
distances of the satellites from Jupiter's centre.
From the observations of
i
2
3
4
Borelli . .
S24
82^
14
24%
Townly by the Microm.
Cassini by the Telescope .
Cassini by the eclip. of the satel.
J /O
5>52
5%
8,78
8
9
13,47
J3
i42%o
""r /o
24,72
233/
25%o
semi-diameter
of Jupiter
From the periodic times
5,667
9,017
14,384
25,299
PHENOMENON II
That the circumsaturnal planets, by radii drawn to Saturn's centre, de-
scribe areas proportional to the times of description; and that their
periodic times, the fixed stars being at rest, are in the sesquiplicate
proportion of their distances from its centre.
PHENOMENON III
That the five primary planets, Mercury, Venus, Mars, Jupiter, and Saturn,
with their several orbits, encompass the sun.
That Mercury and Venus revolve about the sun is evident from their
moon-like appearances. When they shine out with a full face, they are, in
respect of us, beyond or above the sun; when they appear half full, they
are about the same height on one side or other of the sun; when horned,
they are below or between us and the sun; and they are sometimds, when
directly under, seen like spots traversing the sun's disk. That Mars sur-
rounds the sun is as plain from its full face when near its conjunction
with the sun, and from the gibbous figure which it shews in its quadra-
tures. And the same thing is demonstrable of Jupiter and Saturn, from
their appearing full in all situations; for the shadows of their satellites
that appear sometimes upon their disks make it plain that the light they
shine with is not their own, but borrowed from the sun.
PHENOMENON IV
That the fixed stars being at rest, the periodic times of the five primary
planets, and (whether of the sun about the earth, or) of the earth
about the sun, are in the sesquiplicate proportion of their mean dis-
tances from the sun.
This proportion, first observed by Kepler, is now received by all as-
tronomers; for the periodic times are the same, and the dimensions of the
216 MASTERWORKS OF SCIENCE
orbits are the same, whether the sun revolves about the earth, or the earth
about the sun. And as to the measures of the periodic times, all astrono-
mers are agreed about them.
PHENOMENON V
Then the primary planets, by radii drawn to the earth, describe areas no
wise proportional to the times; but that the areas which they describe
by radii drawn to the sun are proportional to the times of descrip-
tion.
For to the earth they appear sometimes direct, sometimes stationary,
nay, and sometimes retrograde. But from the sun they are always seen
direct, and to proceed with a motion nearly uniform, that is to say, a little
swifter in the perihelion and a little slower in the aphelion distances, so as
to maintain an equality in the description of the areas. This a noted
proposition among astronomers, and particularly demonstrable in Jupiter,
from the eclipses of his satellites; by the help of which eclipses, as we
have said, the heliocentric longitudes of that planet, and its distances
from the sun, are determined.
PHENOMENON VI
That the moon, by a radius drawn to the earth's centre, describes an area
proportional to the time of description.
This we gather from the apparent motion of the moon, compared
with its apparent diameter. It is true that the motion of the moon is a
little disturbed by the action of the sun: but in laying down these Phae-
nomena, I neglect those small and inconsiderable errors.
PROPOSITIONS
PROPOSITION L THEOREM I.
That the forces by which the circumjovial planets are continually drawn
off from rectilinear motions, and retained in their proper orbits, tend
to Jupiter s centre; and are reciprocally as the squares of the distances
of the places of those planets from that centre.
The former part of this Proposition appears from Phaen. I and Prop.
II or III, Book One; the latter from Phaen. I and Cor. 6, Prop. IV, of the
same Book.
The same thing we are to understand of the planets which encompass
Saturn, by Priam. II.
NEWTON — PR INC I PI A 217
PROPOSITION II. THEOREM IL
That the forces by which the primary planets are continually drawn off
from rectilinear motions, and retained in their proper orbits, tend to
the sun; and are reciprocally as the squares of the distances of the
places of those planets from the sun's centre.
The former part of the Proposition is manifest from Phaen. V and
Prop. II, Book One; the latter from Phaen. IV and Cor. 6, Prop. IV, of the
same Book. But this part of the Proposition is, with great accuracy, de-
monstrable from the quiescence of the aphelion points; for a very small
aberration from the reciprocal duplicate proportion would produce a
motion of the apsides sensible enough in every single revolution, and in
many of them enormously great.
PROPOSITION III. THEOREM III.
That the force by which the moon is retained in its orbit tends to the
earth; and is reciprocally as the square of the distance of its place
from the earth's centre.
The former part of the Proposition is evident from Phaen. VI and
Prop. II or III, Book One; the latter from the very slow motion of the
moon's apogee; which in every single revolution amounting but to 3° 3'
in consequentiaf may be neglected.
PROPOSITION IV. THEOREM IV.
That the moon gravitates towards the earth, and by the force of gravity
is continually drawn off from a rectilinear motion, and retained in its
orbit.
The mean distance of the moon from the earth in the syzygies in
semi-diameters of the earth is, according to Ptolemy and most astrono-
mers, 59; according to Vendelin and Huygens, 60; to Copernicus, 60%; to
Street, 60%; and to Tychot 56%. But Tychof and all that follow his
tables of refraction, making the refractions of the sun and moon (alto-
gether against the nature of light) to exceed the refractions of the fixed
stars, and that by four or five minutes near the horizon, did thereby in-
crease the moon's horizontal, parallax by a like number of minutes, that is,
by a twelfth or fifteenth part of the whole parallax. Correct this error, and
the distance will become about 60% semi-diameters of the earth, near to
what others have assigned. Let us assume the mean distance of 60 diame-
ters in the syzygies; and suppose one revolution of the moon, in respect
of the fixed stars, to be completed in 27*. 7*. 43', as astronomers have de-
218 MASTERWQRKS OF SCIENCE
termined; and the circumference of the earth- to amount to 123249600
Paris feet, as the French have found by mensuration. And now if we
imagine, the moon, deprived of all motion, to be let go, so as to descend
towards the earth with the impulse of all that force by which (by Prop.
Ill) it is retained in its orb, it will in the space of one minute of time,
describe in its fall 15% 2 Paris feet- This we gather by a calculus, founded
upon Cor. 9, Prop. IV, of the same Book. For the versed sine of that arc,
which the moon, in the space of one minute of time, would by its mean
motion describe at the distance of 60 semi-diameters of the earth, is nearly
I5%2 Paris feet> °r more accurately 15 feet, i inch, and i line %. Where-
fore, since that force, in approaching to the earth, increases in the recipro-
cal duplicate proportion of the distance, and, upon that account, at the
surface of the earth, is 60X60 times greater than at the moon, a body
in our regions, falling with that force, ought, in the space of one minute of
time, to describe 6oX^oXi5%2 Paris feet; and, in the space of one sec-
ond of time, to describe 15^2 °£ those feet; or, more accurately, 15 feet, i
inch, and i line %, And with this very force we actually find that bodies
here upon earth do really descend; for a pendulum oscillating seconds in
the latitude of Paris will be 3 Paris feet, and 8 lines % in length, as Mr.
Huygens has observed. -And the space which a heavy body describes by
falling in one second of time is to half the length of this pendulum in the
duplicate ratio of the circumference of a circle to its diameter (as Mr.
Huygens has also shewn), and is therefore 15 Paris feet, i inch, i line %.
And therefore the force by which the moon is retained in its orbit be-
comes, at the very surface of the earth, equal to the force of gravity which
we observe in heavy bodies there. And therefore (by Rule I and II) the
force by which the moon is retained in its orbit is that very same force
which we commonly call gravity; for, were gravity another force different
from that, then bodies descending to the earth with the joint impulse of
both forces would fall with a double velocity, and in the space of one
second of time would describe 30% Paris feet; altogether against ex-
perience.
This calculus is founded on the hypothesis of the earth's standing
still; for if both earth and moon move about the sun, and at the same time
about their common centre of gravity, the distance of the centres of the
moon and earth from one another will be 60% semi-diameters of the
earth.
SCHOLIUM
The demonstration of this Proposition may be more diffusely ex-
plained after the following manner. Suppose several moons to revolve
about the earth, as in the system of Jupiter or Saturn; the periodic times
of these moons (by the argument of induction) would observe the same
law which Kepler found to obtain among the planets; and therefore their
centripetal forces would be reciprocally as the squares of the distances
from the centre of the earth, by Prop. I of this Book. Now if the lowest of
NEWTON — PR INC IP I A 219
these were very small, and were so near the earth as almost to touch the
tops of the highest mountains, the centripetal force thereof, retaining it in
its orb, would be very nearly equal to the weights of any terrestrial bodies
that should be found upon the tops of those mountains, as may be known
by the foregoing computation. Therefore If the same little moon should
be deserted by its centrifugal force that carries it through its orb, and so
be disabled from going onward therein, it would descend to the earth;
and that with the same velocity as heavy bodies do actually fall with upon
the tops of those very mountains; because of the equality of the forces
that oblige them both to descend. And if the force by which that lowest
moon would descend were different from gravity, and if that moon were
to gravitate towards the earth, as we find terrestrial bodies do upon the
tops of mountains, it would then descend with twice the velocity, as being
impelled by both these forces conspiring together. Therefore since both
these forces, that is, the gravity of heavy bodies, and the centripetal forces
of the moons, respect the centre of the earth, and are similar and equal
between themselves, they will (by Rule I and II) have one and the same
cause. And therefore the force which retains the moon in its orbit is that
very force which we commonly call gravity; because otherwise this little
moon at the top of a mountain must either be without gravity or fall
twice as swiftlv as heavy bodies are wont to do.
PROPOSITION V. THEOREM V.
That the circumjovial planets gravitate towards Jupiter; the circumsa-
turnal towards Saturn; the circumsolar towards the sun; and by the
forces of their gravity are drawn off from rectilinear motions, and
retained in curvilinear orbits.
COR. i. There is, therefore, a power of gravity tending to all the
planets; for, doubdess, Venus, Mercury, and the rest, are bodies of the
same sort with Jupiter and Saturn. And since all attraction (by Law III) is
mutual, Jupiter will therefore gravitate towards all his own satellites,,
Saturn towards his, the earth towards the moon, and the sun towards all
the primary planets.
COR. 2. The force of gravity which tends to any one planet is re-
ciprocally as the square of the distance of places from that planet's centre.
COR. 3. All the planets do mutually gravitate towards one another, by
Cor. i and 2. And hence it is that Jupiter and Saturn, when near their
conjunction, by their mutual attractions sensibly disturb each other's mo-
tions. So the sun disturbs the motions of the moon; and both sun and
moon disturb our sea, as we shall hereafter explain.
SCHOLIUM
The force which retains the celestial bodies in their orbits has been
hitherto called centripetal force; but it being now made plain that it can
220 MASTERWQRKS OF SCIENCE
be no other than a gravitating force, we shall hereafter call it gravity.
For the cause of that centripetal force which retains the moon in its orbit
will extend itself to all the planets, by Rules I, II, and IV.
PROPOSITION VI. THEOREM VI.
That all bodies gravitate towards every planet; and that the weights of
bodies towards any the same planet, at equal distances from the
centre of the planet, are proportional to the quantities of matter
which they severally contain.
It has been, now of a long time, observed by others that all sorts of
heavy bodies (allowance being made for the inequality of retardation
which they suffer from a small power of resistance in the air) descend to
the earth from equal heights in equal times; and that equality of times we
may distinguish to a great accuracy, by the help of pendulums. I tried the
thing in gold, silver, lead, glass, sand, common salt, wood, water, and
wheat, I provided two wooden boxes, round and equal: I filled the one
with wood, and suspended an equal weight of gold (as exactly as I could)
in the centre of oscillation of the other. The boxes hanging by equal
threads of n feet made a couple of pendulums perfectly equal in weight
and figure, and equally receiving the resistance . of the air. And, placing
the one by the other, I observed them to play together forward and back-
ward, for a long time, with equal vibrations. And therefore the quantity
of matter in the gold (by Cor. i and 6, Prop. XXIV, Book Two) was to
the quantity of matter in the wood as the action of the motive force (or
v is motrix) upon all the gold to the action of the same upon all the wood;
that is, as the weight of the one to the weight of the other: and the like
happened in the other bodies. By these experiments, in bodies of the same
weight, I could manifestly have discovered a difference of matter less than
the thousandth part of the whole, had any such been. But, without all
doubt, the nature of gravity towards the planets is the same as towards
the earth. For, should we imagine our terrestrial bodies removed to the
orb of the moon, and there, together with the moon, deprived of all mo-
tion, to be let go, so as to fall together towards the earth, it is certain,
from what we have demonstrated before, that, in equal times, they would
describe equal spaces with the moon, and of consequence are to the moon,
in quantity of matter, as their weights to its weight. Moreover, since the
satellites of Jupiter perform their revolutions in times which observe the
sesquiplicate proportion of their distances from Jupiter's centre, their ac-
celerative gravities towards Jupiter will be reciprocally as the squares of
their distances from Jupiter's centre; that is, equal, at equal distances.
And, therefore, these satellites, if supposed to fall towards Jupiter from
equal heights, would describe equal spaces in equal times, in like manner
as heavy bodies do on our earth. And, by the same argument, if the cir-
cumsolar planets were supposed to be let fall at equal distances from the
sun, they would, in their descent towards the sun, describe equal spaces
NEWTON — PR INC IP I A ; 221
in equal times. But forces which equally accelerate unequal bodies must
be as those bodies: that is to say, the weights of the planets towards the
sun must be as their quantities of matter. Further, that the weights of
Jupiter and of his satellites towards the sun are proportional to the several
quantities of their matter appears from the exceedingly regular motions
of the satellites. For if some of those bodies were more strongly attracted
to the sun in proportion to their quantity of matter than others, the mo-
tions of the satellites would be disturbed by that inequality of attraction.
If, at equal distances from the sun, any satellite, in proportion to the
quantity of its matter, did gravitate towards the sun with a force greater
than Jupiter in proportion to his, according to any given proportion, sup-
pose of d to c; then the distance between the centres of the sun and of the
satellite's orbit would be always greater than the distance between the
centres of the sun and of Jupiter nearly in the subduplicate of that propor-
tion: as by some computations I have found. And if the satellite did gravi-
tate towards the sun with a force, lesser in the proportion of <? to 3f the
distance of the centre of the satellite's orb from the sun would be less than
the distance of the centre of Jupiter from the sun in the subduplicate of
the same proportion. Therefore if, at equal distances from the sun, the
accelerative gravity of any satellite towards the sun were greater or less
than the, accelerative gravity of Jupiter towards the sun but by one %ooo
part of the whole gravity, the distance of the centre of the satellite's orbit
from the sun would be greater or less than the distance of Jupiter from
the sun by one %ooo Part °£ ^e whole distance; that is, by a fifth part of
the distance of the utmost satellite from the centre of Jupiter; an eccen-
tricity of the orbit which would be very sensible. But the orbits of the
satellites are concentric to Jupiter, and therefore the accelerative gravities
of Jupiter, and of all its satellites towards the sun, are equal among them-
selves. And by the same argument, the weights of Saturn and of his satel-
lites towards the sun, at equal distances from the sun, are as their several
quantities of matter; and the weights of the moon and of the earth
towards the sun are either none, or accurately proportional to the masses
of matter which they contain. But some they are, by Cor. i and 3, Prop. V.
But further; the weights of all the parts of every planet towards any
other planet are one to another as the matter in the several parts; for if
some parts did gravitate more, others less, than for the quantity of their
matter, then the' whole planet, according to the sort of parts with which it
most abounds, would gravitate more or less than in proportion to the
quantity of matter in the whole. Nor is it of any moment whether these
parts are external or internal; for if, for example, we should imagine the
terrestrial- bodies with us to be raised up to the orb of the moon, to be
there compared with its body: if the weights of such bodies were to the
weights of the external parts of the moon as the quantities of matter in
the one and in the other respectively; but to the weights of the internal
parts in a greater or less proportion, then likewise the weights of those
bodies would be to the weight of the whole moon in a greater or less pro-
portion; against what we have shewed above.
222 MASTERWORKS OF SCIENCE
COR. i. Hence the weights of bodies do not depend upon their forms
and textures; for if the weights could be altered with the forms, they
would be greater or less, according to the variety of forms, in equal mat-
ter; altogether against experience.
COR. 2. Universally, all bodies about the earth gravitate towards the
earth; and the weights of all, at equal distances from the earth's centre,
are as the quantities of matter which they severally contain. This is the
quality of all bodies within the reach of our experiments; and therefore
(by Rule III) to be affirmed of all bodies whatsoever.
COR. 3. All spaces are not equally full; for if all spaces were equally
full, then the specific gravity of the fluid which fills the region of the air,
on account of the extreme density of the matter, would fall nothing short
of the specific gravity of quicksilver, or gold, or any other the most dense
body; and, therefore, neither gold, nor any other body, could descend in
air; for bodies do not descend in fluids, unless they are specifically heavier
than the fluids. And if the quantity of matter in a given space can, by
any rarefaction, be diminished, what should hinder a diminution to
infinity ?
COR. 4. If all the solid particles of all bodies are of the same density,
nor can be rarefied without pores, a void, space, or vacuum must be
granted. By bodies of the same density, I mean those whose vires inertics
are in the proportion of their bulks.
COR. 5. The power of gravity is of a different nature from the power
of magnetism; for the magnetic attraction is not as the matter attracted.
Some bodies are attracted more by the magnet; others less; most bodies
not at all. The power of magnetism in one and the same body may be
increased and diminished; and is sometimes far stronger, for the quantity
of matter, than the power of gravity; and in receding from the magnet
decreases not in the duplicate but almost in the triplicate proportion of
the distance, as nearly as I could judge from some rude observations.
PROPOSITION VII. THEOREM VII.
That there is a power of gravity tending to all bodies, proportional to the
several quantities of matter which they contain.
That all the planets mutually gravitate one towards another, we have
proved before; as well as that the force of gravity towards every one of
them, considered apart, is reciprocally as the square of the distance of
places from the centre of the planet. And thence it follows that the gravity
tending towards all the planets is proportional to the matter which they
contain.
Moreover, since all the parts of any planet A gravitate towards any
other planet B; and the gravity of every part is to the gravity of the
whole as the matter of the part to the matter of the whole; and (by Law
III) to every action corresponds an equal re-action; therefore the planet B
will, on the other hand, gravitate towards all the parts of the planet A;
NEWTON — PRINCIPIA 223
and its gravity towards any one part will be to the gravity towards the
whole as the matter of the part to the matter of the whole. Q.E.D.
COR. i. Therefore the force of gravity towards any whole planet arises
from, and is compounded of, the forces of gravity towards all its parts*
Magnetic and electric attractions afford us examples of this; for all attrac-
tion towards the whole arises from the attractions towards the several
parts. The thing may be easily understood in gravity, if we consider a
greater planet, as formed of a number of lesser planets, meeting together
in one globe; for hence it would appear that the force of the whole must
arise from the forces of the component parts. If it is objected, that, ac-
cording to this law, all bodies with us must mutually gravitate one
towards another, whereas no such gravitation any where appears, I an-
swer, that since the gravitation towards these bodies is to the gravitation
towards the whole earth as these bodies are to the whole earth, the gravi-
tation towards them must be far less than to fall under the observation of
our senses.
COR. 2. The force of gravity towards the several equal particles of any
body is reciprocally as the square of the distance of places from the par-
ticles; as appears from Cor. 3, Prop. LXXIV, Book One.
PROPOSITION VIII. THEOREM VIII.
In two spheres mutually gravitating each towards the other, if the matter-
in places on all sides round about and equidistant from the centres is-
similar, the weight of either sphere towards the other will be recipro*
colly as the square of the distance between their centres.
After I had found that the force of gravity towards a whole planet did
arise from and was compounded of the forces of gravity towards all its
parts, and towards every one part was in the reciprocal proportion of the
squares of the distances from the part, I was yet in doubt whether that
reciprocal duplicate proportion did accurately hold, or but nearly so, In
the total force compounded of so many partial ones; for it might be that
the proportion which accurately enough took place in greater distances
should be wide of the truth near the surface of the planet, where the dis-
tances of the particles are unequal, and their situation dissimilar. But by
the help of Prop. LXXV and LXXVI, Book One, and their Corollaries, I
was at last satisfied of the truth of the Proposition, as it now lies before us.
COR. i. Hence we may find and compare together the weights of
bodies towards different planets; for the weights of bodies revolving ia
circles about planets are (by Cor. 2, Prop. IV, Book One) as the diameters
of the circles directly, and the squares of their periodic times reciprocally;
and their weights at the surfaces of the planets, or at any other distances
from their centres, are (by. this Prop.) greater or less in the reciprocal du-
plicate proportion of the distances. Thus from the periodic times of
Venus, revolving about the sun, in 224*. i6%\ of the utmost circumjovial
satellite revolving about Jupiter, in i6d. i6%5\; of the Huygenian satel-
224 MASTERWORKS OF SCIENCE
lite about Saturn in 15*. 22 %h.; and of the moon about the earth in 27*.
7*. 43'; compared with the mean distance of Venus from the sun, and with
the greatest heliocentric elongations of the outmost circumjovial satellite
from Jupiter's centre, 8' 16"; of the Huygenian satellite from the centre
of Saturn, 3' 4"; and of the moon from the earth, 10' 33": by computation
I found that the weight of equal bodies, at equal distances from the
centres of the sun, of Jupiter, of Saturn, and of the earth, towards the sun,
Jupiter, Saturn, and the earth, were one to another, as i, %067> %o2i>
and % 6 92 82 respectively. Then because as the distances are increased or
diminished, the weights are diminished or increased in a duplicate ratio,
the weights of equal bodies towards the sun, Jupiter, Saturn, and the
earth, at the distances 10000, 997, 791, and 109 from their centres, that is,
at their very superficies, will be as 10000, 943, 529, and 435 respectively.
How much the weights of bodies are at the superficies of the moon will
be shewn hereafter.
COR. 2. Hence likewise we discover the quantity of matter in the
several planets; for their quantities of matter .are as the forces of gravity
at equal distances from their centres; that is, in the sun, Jupiter, Saturn,
and the earth, as i, %067? %02l> and %69282 respectively. If the paral-
lax of the sun be taken greater or less than 10" 30% the quantity of mat-
ter in the earth must be augmented or diminished in the triplicate of that-
proportion.
COR. 3. Hence also we find the densities of the planets; for (by Prop.
LXXII, Book One) the weights of equal and similar bodies towards simi-
lar spheres are, at the surfaces of those spheres, as the diameters of the
spheres; and therefore the densities of dissimilar spheres are as those
weights applied to the diameters of the spheres. But the true diameters of
the sun, Jupiter, Saturn, and the earth were one to another as 10000, 997,
791, and 109; and the weights towards the same as 10000, 943, 529, and
435 respectively; and therefore their densities are as 100, 94%, 67, and
400. The density of the earth, which comes out by this computation, does
not depend upon the parallax of the sun, but is determined by the paral-
lax of the moon, and therefore is here truly defined. The sun, therefore, is
a little denser than Jupiter, and Jupiter than Saturn, and the earth four
times denser than the sun; for the sun, by its great heat, is kept in a sort
of a rarefied state. The moon is denser than the earth, as shall appear
afterward.
COR. 4. The smaller the planets are, they are, cceteris paribus, of so
much the greater density; for so the powers of gravity on their several
surfaces come nearer to equality. They are likewise, cceteris faribus, of
the greater density, as they are nearer to the sun. So Jupiter is more dense
than Saturn, and the earth than Jupiter; for the planets were to be placed
at different distances from the sun, that, according to their degrees of
density, they might enjoy a greater or less proportion to the sun's heat.
Our water, if it were removed as far as the orb of Saturn, would be con-
verted into ice, and in the orb of Mercury would quickly fly away in va-
pour; for the light of the sun, to which its heat is proportional, is seven
NEWTON — PRINCIPIA 225
times denser in the orb of Mercury than with us: and by the thermometer
I have found that a sevenfold heat of our summer sun will make water
boil. Nor are we to doubt that the matter of Mercury is adapted to its
heat, and is therefore more dense than the matter of our earth; since, in a
denser matter, the operations of Nature require a stronger heat.
PROPOSITION IX. THEOREM IX.
That the force of gravity, considered downward from the surface of the
planets, decreases nearly in the proportion of the distances from their
centres.
PROPOSITION X. THEOREM X.
That the motions of the planets in the heavens may subsist an exceedingly
long time.
I have shewed that a globe of water frozen into ice, and moving freely
in-our air, in the time that it would describe the length of its semi-diame-
ter, would lose by the resistance of the air ^sse Part °f 'lts motion; and
the same proportion holds nearly in all globes, how great soever, and
moved with whatever velocity. But that our globe of earth is of greater
density than it would be if the whole consisted of water only, I thus make
out. If the whole consisted of water only, whatever was of less density
than water, because of its less specific gravity, would emerge and float
above. And upon this account, if a globe of terrestrial matter, covered on
all sides with water, was less dense than water, it would emerge some-
where; and, the subsiding water falling back, would be gathered to the
opposite side. And such is the condition of our earth, which in a great
measure is covered with seas. The earth, if it was not for its greater den-
sity, would emerge from the seas, and, according to -its degree of levity,
would be raised more or less above their surface, the water of the seas
flowing backward to the opposite side. By the same argument, the spots of
the sun, which float upon the lucid matter thereof, are lighter than that
matter; and, however the planets have been formed while they were yet
in fluid masses, all the heavier matter subsided to the centre. Since, there-
fore, the common matter of our earth on the surface thereof is about twice
as heavy as water, and a little lower, in mines, is found about three, or
four, or even five times more heavy, it is probable that the quantity of the
whole matter of the earth may be five or six times greater than if it con-
sisted all of water; especially since I have before shewed that the earth is
about four times more dense than Jupiter. If, therefore, Jupiter is a little
more dense than water, in the space of thirty days, in which that planet
describes the length of 459 of its semi-diameters, it would, in a medium
of the same density with our air, lose almost a tenth part of its motion.
But since the resistance of mediums decreases in proportion to their
weight or density, so that water, which, is 13% times lighter than quick-
226 MASTERWORKS OF SCIENCE
silver, resists less in that proportion; and air, which is 860 times lighter
than water, resists less in the same proportion; therefore in the heavens,
where the weight of the medium in which the planets move is immensely
diminished, the resistance will almost vanish.
It is shewn that at the height of 200 miles above the earth the air is
more rare than it is at the superficies of the earth in the ratio of 30 to
0,0000000000003998, or as 75000000000000 to i nearly. And hence the
planet Jupiter, revolving in a medium of the same density with that supe-
rior air, would not lose by the resistance of the medium the looooooth
part of its motion in 1000000 years. In the spaces near the earth the resist-
ance is produced only by the air, exhalations, and vapours. When these
are carefully exhausted by the air pump from under the receiver, heavy
bodies fall within the receiver with perfect freedom, and without the least
sensible resistance: gold itself, and the lightest down, let fall together, will
descend with equal velocity; and though they fall through a space of four,
six, and eight feet, they will come to the bottom at the same time; as
appears from experiments. And therefore the celestial regions being per-
fectly void of air and exhalations, the planets and comets meeting no sen-
sible resistance in those spaces will continue their motions through them
for an immense tract of time.
HYPOTHESIS I
That the centre of the system of the world is immovable.
This is acknowledged by all, while some contend that the earth,
others that the sun, is fixed in that center. Let us see what may from
hence follow.
PROPOSITION XL THEOREM XL
That the common centre of gravity of the earth, the sun, and all the
planets is immovable.
For (by Cor. 4 of the Laws) that centre either is at rest or moves uni-
formly forward in a right line; but if that centre moved, the centre of th<*
world would move also, against the Hypothesis,
PROPOSITION XIL THEOREM XII.
That the sun is agitated by a perpetual motion, but never recedes far from
the common centre of gravity of all the planets.
For since (by Cor. 2, Prop. VIII) the quantity of matter in the sun is
to the quantity of matter in Jupiter as 1067 to i; and the distance of Jupi-
ter from the sun is to the semi-diameter of the sun in a proportion but a
small matter greater, the common centre of gravity of Jupiter and the sun
NE.WTON — PRINCIPIA 227
will fall upon a point a little without the surface of the sun. By the same
argument, since the quantity of matter in the sun is to the quantity of
matter in Saturn as 3021 to i, and the distance of Saturn from the sun is
to the semi-diameter of the sun in a proportion but a small matter less>
the common centre of gravity of Saturn and the sun will fall upon a point
a little within the surface of the sun. And, pursuing the principles of this
computation, we should find that though the earth and all the planets
were placed on one side of the sun, the distance of the common centre of
gravity of all from the centre of the sun would scarcely amount to one
diameter of the sun. In other cases, the distances of those centres are
always less; and therefore, since that centre of gravity is in perpetual rest,
the sun, according to the various positions of the planets, must perpetu-
ally be moved every way, but will never recede far from that centre.
COR. Hence the common centre of gravity of the earth, the sun, and
all the planets Is to be esteemed the centre of the world; for since the
earth, the sun, and all the planets mutually gravitate one towards another,,
and are therefore, according to their powers of gravity, in perpetual agita-
tion, as the Laws of Motion require, it is plain that their movable cen-
tres cannot be taken for the immovable centre of the world. If that body
were to be placed in the centre, towards which other bodies gravitate
most (according to common opinion), that privilege ought to be allowed
to the sun; but since the sun itself is moved, a fixed point is to be chosen
from which the centre of the sun recedes least, and from which it would
recede yet less if the body of the sun were denser and greater > and there-'
fore less apt to be moved.
PROPOSITION XIII. THEOREM XIII.
The planets move in ellipses which have their common focus in the centre
of the sun; and, by radii drawn to that centre, they describe areas
proportional to the times of description.
We have discoursed above of these motions from the Phenomena.
Now that we know the principles on which they depend, from those
principles we deduce the motions of the heavens a priori. Because the
weights of the planets towards the sun are reciprocally as the squares of
their distances from the sun's centre, if the sun was at rest, and the other
planets did not mutually act one upon another, their orbits would be
ellipses, having the sun in their common focus; and they would describe
areas proportional to the times of description, by Prop. I, Book One. But
the mutual actions of the planets one upon another are so very small, that
they may be neglected.
It is true that the action of Jupiter upon Saturn is not to be neglected:
for the force of gravity towards Jupiter is to the force^of gravity towards
the sun as r to 1067; and therefore in the conjunction of Jupiter and
Saturn, because the distance of Saturn from Jupiter is to the distance of
Saturn from the sun almost as 4 to 9, the gravity of Saturn towards Jupi-
228 _ MASTERWORKS OF SCIENCE _
ter will be to the gravity of Saturn towards the sun as 81 to 16X1067; or,
as i to about 211. And hence arises a perturbation of the orb of Saturn in
every conjunction of this planet with Jupiter, so sensible that astronomers
are puzzled with it. As the planet is differently situated in these conjunc-
tions, its eccentricity is sometimes augmented, sometimes diminished; its
aphelion is sometimes carried forward, sometimes backward, and its mean
motion is by turns accelerated and retarded; yet the whole error in its
motion about the sun, though arising from so great a force, may be almost
avoided (except in the mean motion) by placing the lower focus of its
orbit in the common centre of gravity of Jupiter and the sun, and there-
fore that error, when it is greatest, scarcely exceeds two minutes; and the
greatest error in the mean motion scarcely exceeds two minutes yearly.
But in the conjunction of Jupiter and Saturn, the accelerative forces of
gravity of the sun towards Saturn, of Jupiter towards Saturn, and of Jupi-
11 i /- o i
ter towards the sun, are almost as 16, 81, and — — — *-** - , or 156609;
and therefore the difference of the forces of gravity of the sun towards
Saturn, and of Jupiter towards Saturn, is to the force of gravity of Jupiter
towards the sun as 65 to 156609, or as i to 2409. But the greatest power of
Saturn to disturb the motion of Jupiter is proportional to this difference;
and therefore the perturbation of the orbit of Jupiter is much less than
that of Saturn's. The perturbations of the other orbits are yet far less,
except that the orbit of the earth is sensibly disturbed by the moon. The
common centre of gravity of the earth and moon moves in an ellipsis
about the sun in the focus thereof, and, by a radius drawn to the sun, de-
scribes areas proportional to the times of description. But the earth in
the meantime by a menstrual motion is revolved about this common
centre.
PROPOSITION XIV. THEOREM XIV.
The aphelions and nodes of the orbits of the planets are fixed.
It is true that some inequalities may arise from the mutual actions of
the planets and comets in their revolutions; but these will be so small that
they may be here passed by.
COR. i. The fixed stars are immovable, seeing they keep the same po-
sition to the aphelions and nodes of the planets.
COR. 2. And since these stars are liable to no sensible parallax from
the annual motion of the earth, they can have no force, because of their
immense distance, to produce any sensible effect in our system. Not to
mention that the fixed stars, every where promiscuously dispersed in the
heavens, by their contrary attractions destroy their mutual actions, by
Prop. LXX, Book One.
NEWTON — PRINCIPIA 229
SCHOLIUM
Since the planets near the sun (viz. Mercury, Venus, the Earth, and
Mars) are so small that they can act with but little force upon each other,
therefore their aphelions and nodes must be fixed, excepting in so far as
they are disturbed by the actions of Jupiter and Saturn, and other higher
bodies. And hence we may find, by the theory of gravity, that their aphe-
lions move a little in consequentia, in respect of the fixed stars, and that
in the sesquiplicate proportion of their several distances from the sun. So
that if the aphelion of Mars, in the space of a hundred years, is carried
33' 20" in consequentia, in respect of the fixed stars, the aphelions of the
Earth, of Venus, and of Mercury, will in a hundred years be carried for-
wards if 40", 10' 53", and 4' 16", respectively. But these motions are so
inconsiderable that we have neglected them in this Proposition.
PROPOSITION XV. PROBLEM I.
To find the principal diameters of the orbits of the planets.
They are to be taken in the sub-sesquiplicate proportion of the
periodic times.
PROPOSITION XVI. PROBLEM II.
To find the eccentricities and aphelions of the planets.
PROPOSITION XVII. THEOREM XV.
That the diurnal motions of the planets are uniform, and that the
libration of the moon arises from its diurnal motion.
PROPOSITION XVIIL THEOREM XVI.
That the axes of the planets are less than the diameters drawn perpen-
dicular to the axes.
The equal gravitation of the parts on all sides would give a spherical
figure to the planets, if it was not for their diurnal revolution in a circle.
By that circular motion it comes to pass that the parts receding from the
axis endeavour to ascend about the equator; and therefore if the matter is
in a fluid state, by its ascent towards the equator it will enlarge the di-
ameters there, and by its descent towards the poles it will shorten the axis.
So the diameter of Jupiter (by the concurring observations of astrono-
230 MASTERWORKS OF SCIENCE
mers) is found shorter betwixt pole and pole than from east to west. And,
by the same argument, if our earth was not higher about the equator than
at the poles, the seas would subside about the poles, and, rising towards
the equator, would lay all things there under water.
PROPOSITION XIX. PROBLEM III.
To find the proportion of the axis of a planet to the diameters perpen-
dicular thereto.
Our countryman, Mr. Norwood, measuring a distance of 995751 feet
of London measure between London and Yor%, in 1635, and observing the
difference of latitudes to be 2° 28', determined the measure of one degree
to be 367196 feet of London measure, that is, 57300 Paris toises. M.
Picart, measuring an arc of one degree, and 22' 55" of the meridian be-
tween Amiens and Malvoisine, found an arc of one degree to be 57060
Paris toises. M. Cassini, the father, measured the distance upon the me-
ridian from the town of Collioure in Roussillon to the Observatory of
Paris; and his son added the distance from the Observatory to the Cita-
del of Dunkirk The whole distance was 486156% toises and the differ-
ence of the latitudes of Collioure and Dun^irJ^ was 8 degrees, and 31'
n%". Hence an arc of one degree appears to be 57061 Paris toises. And
from these measures we conclude that the circumference of the earth is
123249600, and its semi-diameter 19615800 Paris feet, upon the suppo-
sition that the earth is of a spherical figure.
In the latitude of Paris a heavy body falling in a second of time de-
scribes 15 Paris feet, i inch, i% line, as above, that is, 2173 lines %. The
weight of the body is diminished by the weight of the ambient air. Let
us suppose the weight lost thereby to be M.IOOO part of the whole weight;
then that heavy body falling in vacua will describe a height of 2174 lines
in one second of time.
A body in every sidereal day of 23*. 56' 4" uniformly revolving in a
circle at the distance of 19615800 feet from the centre, in one second of
time describes an arc of 1433,46 feet; the versed sine of which is 0,05236561
feet, or 7,54064 lines. And therefore the force with which bodies descend
in the latitude of Paris is to the centrifugal force of bodies in the equator
arising from the diurnal motion of the earth as 2174 to 7,54064.
The centrifugal force of bodies in the equator is to the centrifugal
force with which bodies recede directly from the earth in the latitude of
Paris 48° 50' 10" in the duplicate proportion of the radius to the cosine of
the latitude, that is, as 7,54064 to 3,267. Add this force to the force with
which bodies descend by their weight in the latitude of Paris, and a body,
in the latitude of Paris, falling by its whole undiminished force of gravity,
in the time of one second, will describe 2177,267 lines, or 15 Paris feet,
r inch, and 5,267 lines. And the total force of gravity in that latitude will
be to the centrifugal force of bodies in the equator of the earth as 2177,267
to 7,54064, or as 289 to i.
NEWTON — PRINCIPIA 231
Wherefore if APBQ represent the figure of the earth, now no longer
spherical, but generated by the rotation of an ellipsis about its lesser axis
PQ; and ACQ qca a canal full of water, reaching from the pole Qq to the
centre Cc, and thence rising to the equator Aa; the weight of the water in
the leg of the canal ACca will be to the weight of water in the other leg
QCcq as 289 to 288, because the centrifugal force arising from the circu-
lar motion sustains and takes off one of the 289 parts of the weight (in the
one leg), and the weight of 288 in the other sustains the rest. But by
computation I find that if the matter of the earth was all uniform, and
without any motion, and its axis PQ were to the diameter AB as 100 to
1 01, the force of gravity in the place Q towards the earth would be to the
force of gravity in the same place Q towards a sphere described about the
A.CL
centre C with the radius PC, or QC, as 126 to 125, And, by the same argu-
ment, the force of gravity in the place A towards the spheroid generated
by the rotation of the ellipsis APBQ about the axis AB is to the force of
gravity in the same place A, towards the sphere described about the centre
C with the radius AC, as 125 to 126. But the force of gravity in the place
A towards the earth is a mean proportional betwixt the forces of gravity
towards the spheroid and this sphere; because the sphere, by having its
diameter PQ diminished in the proportion of 101 to 100, is transformed
into the figure of the earth; and this figure, by having a third diameter
perpendicular to the two diameters AB and PQ diminished in the same
proportion, is converted into the said spheroid; and the force of gravity in
A, in either case, is diminished nearly in the same proportion. Therefore
the force of gravity in A towards the sphere described about the centre C
with the radius AC is to the force of gravity in A towards the earth as 126
to 125%. And the force of gravity in the place Q towards the sphere de-
scribed about the centre C with the radius QC, is to the force of gravity
in the place A towards the sphere described about the centre C, with the
radius AC, in the proportion of the diameters (by Prop. LXXII, Book
One), that is, as 100 to 101. If, therefore, we compound those three pro-
portions 126 to 125, 126 to 125%, and 100 to 101, into one, the force of
gravity in the place Q towards the earth will be to the force of gravity in
die place A towards the earth as 126X126X100 to 12.^12.^^101; or as
501 to 500.
Now since the force of gravity in either leg of the canal ACca, or
QCcq, is as the distance of the places from the centre of the earth, if those
232 MASTERWORKS OF SCIENCE
legs are conceived to be divided by transverse, parallel, and equidistant
surfaces, into parts proportional to the wholes, the weights of any num-
ber of parts in the one leg ACca will be to the weights of the same num-
ber of parts in the other leg as their magnitudes and the accelerative
forces of their gravity conjunctly, that is, as 101 to 100, and 500 to 501, or
as 505 to 501. And therefore if the centrifugal force of every part in the
leg ACca, arising from the diurnal motion, was to the weight of the same
part as 4 to 505, so that from the weight of every part, conceived to be
divided into 505 parts, the centrifugal force might take of! four of those
parts, the weights would remain equal in each leg, and therefore the fluid
would rest in an equilibrium. But the centrifugal force of every part is to
the weight of the same part as i to 289; that is, the centrifugal force,
which should be %QS parts of the weight, is only %§9 Part thereof. And,
therefore, I say, by the rule of proportion, that if the centrifugal force
%05 make the height of the water in the leg ACca to exceed the height
of the water in the leg QCcq by one %oo Part °^ *ts whole height, the
centrifugal force %§9 w^& make the excess of the height in the leg ACca
only Y289 Part °£ tke height of the water in the other leg QCcq; and
therefore the diameter of the earth at the equator, is to its diameter from
pole to pole as 230 to 229. And since the mean semi-diameter of the earth,
according to Picart's mensuration, is 19615800 Paris feet, or 3923,16 miles
(reckoning 5000 feet to a mile)," the earth will be higher at the equator
than at the poles by 85472 feet, or iy%o miles. And its height at the
equator will be about 19658600 feet, and at the poles 19573000 feet.
If, the density and periodic time of the diurnal revolution remaining
the same, the planet was greater or less than the earth, the proportion of
the centrifugal force to that of gravity, and therefore also of the diameter
betwixt the poles to the diameter at the equator, would likewise remain
the same. But if the diurnal motion was accelerated or retarded in any
proportion, the centrifugal force would be augmented or diminished
nearly in the same duplicate proportion; and therefore the difference of
the diameters will be increased or diminished in the same duplicate ratio
very nearly. And if the density of the planet was augmented or diminished
in any proportion, the force of gravity tending towards it would also be
augmented or diminished in the same proportion: and the difference of
the diameters contrariwise would be diminished in proportion as the
force of gravity is augmented, and augmented in proportion as the force
of gravity is diminished. Wherefore, since the earth, in respect of the
fixed stars, revolves in 23*. 56', but Jupiter in 9h. 56', and the squares of
their periodic times are as 29 to 5, and their densities as 400 to 94%, the
difference of the diameters of Jupiter will be to its lesser diameter as
_^^ji_^ to j^ or as j to ^1^ nearly. Therefore the diameter of
5 94 /2 229
Jupiter from east to west is to its diameter from pole to pole nearly as
10% to 9%. Therefore since its greatest diameter is 37", its lesser diame-
ter lying between the poles will be 33" 25"'. Add thereto about 3" for the
NEWTON — PRI NCI PI A
233
irregular refraction of light, and the apparent diameters of this planet will
become 40" and 36" 25"'; which are to each other as 11% to 10%, very
nearly. These things are so upon the supposition that the body of Jupiter
is uniformly dense. But now _if its body be denser towards the plane of
the equator than towards the poles, its diameters may be to each other
as 12 to ii, or 13 to 12, or perhaps as 14 to 13.
And Cassini observed in the year 1691 that the diameter of Jupiter
reaching from east to west is greater by about a fifteenth part than the
other diameter. Mr. Pound with his 123-feet telescope, and an excellent
micrometer, measured the diameters of Jupiter in the year 1719 and found
them as follow.
The Times.
Greatest
diam.
Lesser
diam.
The diam. to
each other
Day. Hours.
January 28 6
March 6 7
March 9 7
April 9 9
Parts
1340
13,12
13,12
12,32
Parts
12,28
12,20
12,08
11,48
As 12 to ii
13% to i2#
12% tO 11%
14 Ji tO I3 Ji
So that the theory agrees with the phenomena; for the planets are
more heated by the sun's rays towards their equators, and therefore are a
little more condensed by that heat than towards their poles.
Moreover, that there is a diminution of gravity occasioned by the
diurnal rotation of the earth, and therefore the earth rises higher there
than it does at the poles (supposing that its matter is uniformly dense),
will appear by the experiments of pendulums related under the following
Proposition.
PROPOSITION XX. PROBLEM IV.
To find and compare together the weights of bodies in the different
regions of our earth.
Because the weights of the unequal legs of the canal of water ACQ-
qca are equal; and the weights of the parts proportional to the whole legs,
and alike situated in them, are one to another as the weights of the wholes,
and therefore equal betwixt themselves; the weights of equal parts, and
alike situated in the legs, will be reciprocally as the legs, that is, recipro-
cally as 230 to 229. And the case is the same in all homogeneous equal
bodies alike situated in the legs of the canal. Their weights are recipro-
cally as the legs, that is, reciprocally as the distances of the bodies from
the centre of die earth. Therefore if the bodies are situated in the tipper-
most parts of the canals, or on the surface of the earth, their weights will
be one to another reciprocally as their distances from the centre. And, by
the same argument, the weights in all other places round the whole
surface of the earth are reciprocally as the distances of the places from
234
MASTERWORKS OF SCIENCE
the centre; and, therefore, in the hypothesis of the earth's being a spheroid
are given in proportion.
Whence arises this Theorem, that the increase of weight in passing
from the equator to the poles is nearly as the versed sine of double the
latitude; or, which comes to the same thing, as the square of the right
sine of the latitude; and the arcs of the degrees of latitude in the meridian
ACL
increase nearly in the same proportion. And, therefore, since the latitude
of Paris is 48° 50', that of places under the equator 00° oo', and that of
places under the poles 90°; and the versed sines of double those arcs are
11334,00000 and 20000, the radius being 10000; and the force of gravity
at the pole is to the force of gravity at the equator as 230 tQ 229; and the
excess of the force of gravity at the pole to the force of gravity at the
equator as i to 229; the excess of the force of gravity in the latitude of
Paris will be to the force of gravity at the equator as i X 11S3%0000 to
229, or as 5667 to 2290000. And therefore the whole forces of gravity in
those places will be one to the other as 2295667 to 2290000. Wherefore
since the lengths of pendulums vibrating in equal times are as the forces
of gravity, and in the latitude of Paris, the length of a pendulum vibrating
seconds is 3 Paris feet, and 8% lines, or rather because of the weight of
the air, 8% lines, the length of a. pendulum vibrating in the same time
under the equator will be shorter by 1,087 lines. And by a like calculus
the table on the following page is made.
By this table, therefore, it appears that the inequality of degrees is so
small that the figure of the earth, in geographical matters, may be con-
sidered as spherical; especially if the earth be a little denser towards the
plane of the equator than towards the poles.
Now several astronomers, sent into remote countries to make astro-
nomical observations, have found that pendulum clocks do accordingly
move slower near the equator than in our climates. And, first of all, in the
year 1672 M. Richer took notice of it in the island of Cayenne; for when,
in the month of August, he was observing the transits of the fixed stars
over the meridian, he found his clock to go slower than it ought in respect
of the mean motion of the sun at the rate of 2' 28" a day. Therefore, fitting
up a simple pendulum to vibrate in seconds, which were measured by an
excellent clock, he observed the length of that simple pendulum; and this
he did over and over every week for ten months together. And upon his
return to France, comparing the length of that pendulum with the length
NEWTON — PR I NCI PI A
235
Latitude of
the place
Length of the
pendulum
Measure of one degree
in the meridian
Deg.
Feet Lines.
Toises.
0
3 - 7,468
56637
5
3 • 7*482
56642
10
3 - 7>5^6
56659
15
3 • 7,596
56687
20
3 - 7,692
56724
25
3 • 7,812
56769
30
3 - 7,948
56823
35
3 • 8,099
56882
40
3 . 8,261
56945
i
3 • 8,294
56958
2
3 • 8,327
56971
3
3 - 8,361
56984
4
3 • 8,394
56997
45
3 - 8,428
57010
6
3 - 8,461
57022
7
3 - 8,494
57°35
8
3 - 8,528
57048
9
3 • 8,561
57061
50
3 - 8,594
57074
55
3- 8,756
57137
60
3 • 8,907
57196
65
3 - 9,°44
57250
70
3 • 9,162
57295
75
3 - 9,258
57332
80
3 - 9,329
57360
%
3 - 9,372
57377
90
3 • 9,387
57382
of the pendulum at Paris (which was 3 Paris feet and 8% lines), he found
it shorter by 1% line.
Afterwards, our friend Dr. H 'alley , about the year 1677, arriving at
the island of St. Helena, found his pendulum clock to go slower there
than at London without marking the difference. But he shortened the rod
of his clock by more than the % of an inch, or i% line; and to effect
this, because the length of the screw at the lower end of the rod was not
sufficient, he interposed a wooden ring betwixt the nut and the ball.
Then, in the year 1682, M. Varin and M. des Hayes found the length,
of a simple pendulum vibrating in seconds at the Royal Observatory of
Paris to be 3 feet and 8% lines. And by the same method in the island of
Goree, they found the length of an isochronal pendulum to be 3 feet and
6% lines, differing from the former by two lines. And in the same year,
going to the islands of Guadaloupe and Martinico, they found that the
length of an isochronal pendulum in those islands was 3 feet and 6% lines.
After this, M. Couplet, the son, in the month of July 1697, at the Royal
Observatory of Paris, so fitted his pendulum clock to the mean motion of
236 MASTERWQRKS OF SCIENCE
the sun that for a considerable time together the clock agreed with" the
motion of the sun. In November following, upon his arrival at Lisbon, he
found his clock to go slower than before at the rate of 2' 13" in 24 hours.
And next March coming to Paraiba, he found his clock to go slower than
at Paris, and at the rate 4' 12" in 24 hours; and he affirms, that the pen-
dulum vibrating in seconds was shorter at Lisbon by 2% lines, and at
Paraiba by 3% lines, than at Paris. He had done better to have reckoned
those differences 1% and 2%: for these differences correspond to the
differences of the times 2' 13" and 4' 12". But this gentleman's obser-
vations are so gross, that we cannot confide in them.
In the following years, 1699 and 1700, M. des Hayes, making another
voyage to America, determined that in the island of Cayenne and Granada
the length of the pendulum vibrating in seconds was a small matter less
than 3 feet and 6% lines; that in the island of St. Christophers it was
3 feet and 6% lines; and in the island of St. Domingo 3 feet and 7 lines.
And in the year 1704, P. Feuille, at Puerto Bello in America, found
that the length of the pendulum vibrating in seconds was 3 Paris feet, and
only 5% 2 lines, that is, almost 3 lines shorter than at Paris; but the obser-
vation was faulty. For afterward, going to the island of Martinicof he
found the length of the isochronal pendulum there 3 Paris feet and 5X%2
lines.
Now the latitude of Paraiba is 6° 38' south; that of Puerto Bello 9°
33' north; and the latitudes of the islands Cayenne, Goree, Guadaloupe,
Martinico, Granada, St. Christophers, and St. Domingo are respectively
4° 55', 14° 40", 15° oo', 14° 44', 12° 06', 17° 19', and 19° 48' north. And
the excesses of the length of the pendulum at Paris above the lengths of
the isochronal pendulums observed in those latitudes are a little greater
than by the table of the lengths of the pendulum before computed. And
therefore the earth is a little higher under the equator than by the preced-
ing calculus, and a little denser at the centre than in mines near the
surface, unless, perhaps, the heats of the torrid zone have a little extended
the length of the pendulums.
For M. Picart has observed that a rod of iron, which in frosty weather
in the winter season was one foot long, when heated by fire was lengthened
into one foot and % line. Afterward M. de la Hire found that a rod of
iron, which in the like winter season was 6 feet long, when exposed to the
heat of the summer sun, was extended into 6 feet and % line. In the
former case the heat was greater than in the latter; but in the latter it was
greater than the heat of the external parts of a human body; for metals
exposed to the summer sun acquire a very considerable degree of heat.
But the rod of a pendulum clock is never exposed to the heat of the
summer sun, nor ever acquires a heat equal to that of the external parts
of a human body; and, therefore, though the 3 feet rod of a pendulum
clock will indeed be a little longer in the summer than in the winter
season, yet the difference will scarcely amount to % line. Therefore the
total difference of the lengths of isochronal pendulums in different cli-
mates cannot be ascribed to the difference of heat; nor indeed to the
NEWTON — PR INC IP I A 237
mistakes of the French astronomers. For although there is not a perfect
agreement betwixt their observations, yet the errors are so small that they
may be neglected; and in this they all agree, that isochronal pendulums
are shorter under the equator than at the Royal Observatory of Paris, by
a difference not less than i% line nor greater than 2% lines. By the obser-
vations of M. Richer, in the island of Cayenne, the difference was i% line.
That difference, being corrected by those of M. des Hayes, becomes i%
line or i% line. By the less accurate observations of others, the same was
made about two lines. And this disagreement might arise partly from the
errors of the observations, partly from the dissimilitude of the internal
parts of the earth, and the height of mountains; partly from the different
heats of the air.
I take an iron rod of 3 feet long to be shorter by a sixth part of one
line in winter time with us here in England than in the summer. Because
of the great heats under the equator, subduct this quantity from the dif-
ference of one line and a quarter observed by M. Richer, and there will
remain one line %2> which agrees very well with is%ooo lme collected,
by the theory a little before. M, Richer repeated his observations, made in
the island of Cayenne, every week for ten months together, and compared
the lengths of the pendulum which he had there noted in the iron rods
with the lengths thereof which he observed in France. This diligence and
care seems to have been wanting to the other observers. If this gentleman's
observations are to be depended on, the earth is higher under the equator
than at the poles, and that by an excess of about 17 miles; as appeared
above by the theory.
PROPOSITION XXIV. THEOREM XIX.
That the flux and reflux of the sea arise from the actions of the sun
and moon.
By Cor. 19 and 20, Prop. LXVI, Book One, it appears that the waters
of the sea ought twice to rise and twice to fall every day, as well lunar as
solar; and that the greatest height of the waters in the open and deep
seas ought to follow the appulse of the luminaries t-o the meridian of the
place by a less interval than 6 hours; as happens in all that eastern tract
of the Atlantic and Mthioflc seas between France and the Cafe of Good
Hope; and on the coasts of Chili and Peru in the South Sea; in all which
shores the flood falls out about the second, third, or fourth hour, unless
where the motion propagated from the deep ocean is by the shallowness
of the channels, through which it passes to some particular places, retarded
to the fifth, sixth, or seventh hour, and even later. The hours I reckon
from the appulse of each luminary to the meridian of the place, as well
under as above the horizon; and oy the hours of the lunar day I under-
stand the 24th parts of that time which the moon, by its apparent diurnal
motion, employs to come about again to the meridian of the place which
it left the day before. The force of the sun or moon in raising the sea is
238 MASTERWQRKS OF SCIENCE
greatest in the appulse of the luminary to the meridian of the place; but
the force impressed upon the sea at that time continues a little while after
the impression, and is afterwards increased by a new though less force
still acting upon it. This makes the sea rise higher and higher, till this
new force becoming too weak to raise It any more, the sea rises to its
greatest height. And this will come to pass, perhaps, in one or two hours,
but more frequently near the shores in about three hours, or even more,
where the sea is shallow.
The two luminaries excite two motions, which will not appear dis-
tinctly, but between them will arise one mixed motion compounded out
of both. In the conjunction or opposition of the luminaries their forces
will be conjoined, and bring on the greatest flood and ebb. In the quadra-
tures the sun will raise the waters which the moon depresses, and depress
the waters which the moon raises, and from the difference of their forces
the smallest of all tides will follow. And because (as experience tells us)
the force of the moon is greater than that of the sun, the greatest height
of the waters will" happen about the third lunar hour. Out of the syzygies
and quadratures, the greatest tide, which by the single force of the moon
ought to fall out at the third lunar hour, and by the single force of the
sun at the third solar hour, by the compounded forces of both must fall
out in an intermediate time that approaches nearer to the third hour of
the moon than to that of the sun. And, therefore, while the moon is
passing from the syzygies to the quadratures, during which time the 3d
hour of the sun precedes the 3d hour of the moon, the greatest height of
the waters will also precede the 3d hour of the moon, and that, by the
greatest interval, a little after the octants of the moon; and, by like inter-
vals, the greatest tide will follow the 3d lunar hour, while the moon is
passing from the quadratures to the syzygies. Thus it happens in the
open sea; for in the mouths of rivers the greater tides come later to their
height.
But the effects of the luminaries depend upon their distances from
the earth; for when they are less distant, their effects are greater, and
when more distant, their effects are less, and that in the triplicate pro-
portion of their apparent diameter. Therefore it is that the sun, in the
winter time, being then in its perigee, has a greater effect, and makes the
tides in the syzygies something greater, and those in the quadratures
something less than in the summer season; and every month the moon,
while in the perigee, raises greater tides than at the distance of 15 days
before or after, when it is in its apogee. Whence it comes to pass that two
highest tides do not follow one the other in two immediately succeeding
syzygies.
The effect of either luminary doth likewise depend upon its decli-
nation or distance from the equator; for if the luminary was placed at
the pole, it would constantly attract all the parts of the waters without any
intension or remission of its action, and could cause no reciprocation of
motion. And, therefore, as the luminaries decline from the equator towards
either pole, they will, by degrees, lose their force, and on this account will
NEWTON — P RING IPI A 239
excite lesser tides in the solstitial than in the equinoctial syzygies. But in
the solstitial quadratures they will raise greater tides than in the quadra-
tures about the equinoxes; because the force of the moon, then situated in
the equator, most exceeds the force of the sun. Therefore the greatest
tides fall out in those syzygies, and the least in those quadratures, which
happen about the time of both equinoxes: and the greatest tide in the
syzygies is always succeeded by the least tide in the quadratures, as we
find by experience. But, because the sun is less distant from the earth in
winter than in summer, it comes to pass that the greatest and least tides
more frequently appear before than after the vernal equinox, and more
frequently after than before the autumnal.
Moreover, the effects of the luminaries depend upon the latitudes of
places. Let ApEP represent the earth covered with deep waters; C its
centre; P, p its poles; AE the equator; F any place without the equator;
F/ the parallel of the place; Dd the correspondent parallel on the other
side of the equator; L the place of the moon three hours before; H the
place of the earth directly under it; h the opposite place; K, \ the places at
90 degrees distance; CH, Ch, the greatest heights of the sea from the centre
of the earth; and CK, C%, its least heights: and if with the axes Hh, K^, an
ellipsis is described, and by the revolution of that ellipsis about its longer
axis Hh a spheroid HPKA/^ is formed, this spheroid will nearly represent
the figure of the sea; and CF, C/, CD, Cd, will represent the heights of
the sea in the places F/, Dd. But farther; in the said revolution of the
ellipsis any point N describes the circle NM cutting the parallels F/, Ddf
in any places RT, and the equator AE in S; CN will represent the height
of the sea in all those places R, S, T, situated in this circle. Wherefore,
in the diurnal revolution of any place F, the greatest flood will be in F,
at the third hour after the appulse of the moon to the meridian above the
horizon; and afterwards the greatest ebb in Q, at the third hour after
the setting of the moon; and then the greatest flood in /, at the third hour
after the appulse of the moon to the meridian under the horizon; and,
lastly, the greatest ebb in Q, at the third hour after the rising of the moon;
and the latter flood in / will be less than the preceding flood in F. For
the whole sea is divided into two hemispherical floods, one in the hemi-
sphere KH^ on the north side, the other in the opposite hemisphere
^f which we may therefore call the northern and the southern floods.
240 MASTERWQRKS OF SCIENCE
These floods, being always opposite the one to the other, come by turns
to the meridians of all places, after an interval of 12 lunar hours. And
seeing the northern countries partake more of the northern flood, and
the southern countries more of the southern flood, thence arise tides,
alternately greater and less in all places without the equator, in which
the luminaries rise and set. But the greatest tide will happen when the
moon declines towards the vertex of the place, about the third hour
after the appulse of the moon to the meridian above the horizon; and
when the moon changes its decimation to the other side of the equator,
that which was the greater tide will be changed into a lesser. And the
greatest difference of the floods will fall out about the times of the
solstices; especially if the ascending node of the moon is about the first
of Aries. So it is found by experience that the morning tides in winter
exceed those of the evening, and the evening tides in summer exceed those
of the morning; at Plymouth by the height of one foot, but at Bristol by
the height of 15 inches, according to the observations of Colepress and
Sturmy.
But the motions which we have been describing suffer some alteration
from that force of reciprocation, which the waters, being once moved,
retain a little while by their vis insita. Whence it comes to pass that the
tides may continue for some time, though the actions of the luminaries
should cease. This power of retaining the impressed motion lessens the
difference of the alternate tides, and makes those tides which immediately
succeed after the syzygies greater, and those which follow next after the
quadratures less. And hence it is that the alternate tides at Plymouth and
Bristol do not differ much more one from the other than by the height of
a foot or 15 inches, and that the greatest tides of all at those ports are not
the first but the third after the syzygies. And, besides, all the motions are
retarded in their passage through shallow channels, so that the greatest
tides of all, in some straits and mouths of rivers, are the fourth or even the
fifth after the syzygies.
Farther, it may happen that the tide may be propagated from the
ocean through different channels towards the same port, and may pass
quicker through some channels than through others; in which case the
same tide, divided into two or more succeeding one another, may com-
pound new motions of different kinds. Let us suppose two equal tides
flowing towards the same port from different places, the one preceding
the other by 6 hours; and suppose the first tide to happen at the third
hour of the appulse of the moon to the meridian of the port. If the moon
at the time of the appulse to the meridian was in the equator, every 6
hours alternately there would arise equal floods, which, meeting with as
many equal ebbs, would so balance one the other that for that day the
water would stagnate and remain quiet. If the moon then declined from
the equator, the tides in the ocean would be alternately greater and less,
as was said; and from thence two greater and two lesser tides would be
alternately propagated towards that port. But the two greater floods would
make the greatest height of the waters to fall out in the middle
NEWTON — PRINCIPIA 241
betwixt both; and the greater and lesser floods would make the waters
to rise to a mean height in the middle time between them, and in the
middle time between the two lesser floods the waters would rise to their
least height. Thus in the space of 24 hours the waters would come, not
twice, as commonly, but once only to their greatest, and once only to
their least height; and their greatest height, if the moon declined towards
the elevated pole, would happen at the 6th or 30th hour after the appulse
of the moon to the meridian; and when the moon changed its declination,
this flood would be changed into an ebb. An example of all which Dr.
Halley has given us, from the observations of seamen in the port of Bat-
sham, in the kingdom of Tunquin, in the latitude of 20° 50' north. In
that port, on the day which follows after the passage of the moon over
the equator, the waters stagnate: when the moon declines to the north,
they begin to flow and ebb, not twice, as in other ports, but once only
every day: and the flood happens at the setting, and the greatest ebb at
the rising of the moon. This tide increases with the decimation of the
moon till the yth or 8th day; then for the 7 or 8 days following it decreases
at the same rate as it had increased before, and ceases when the moon
changes its declination, crossing over the equator to the south'. After
which the flood is immediately changed into an ebb;^ and thenceforth
the ebb happens at the setting and the flood at the rising of the moon;
till the moon, again passing the equator, changes its declination. There
are two inlets to this port and the neighboring channels, one from the seas
of China, between the continent and the island of Leuconia; the other
from the Indian sea, between the continent and the island of Borneo. But
whether there be really two tides propagated through the said channels,
one from the Indian sea in the space of 12 hours, and one from the sea of
China in the space of 6 hours, which therefore happening at the 3^ and
9th lunar hours, by being compounded together, produce those motions;
or whether there be any other circumstances in the state of those seas, I
leave to be determined by observations on the neighbouring shores.
Thus I have explained the causes of the motions of the moon and of
the sea.
GENERAL SCHOLIUM
Bodies projected in our air suffer no resistance but from^the air. With-
draw the air, as is done in Mr, Boyle's vacuum, and the resistance? ceases;
for in this void a bit of fine down and a piece of solid gold descend with
equal velocity. And the parity of reason must take place in the celestial
spaces above the earth's atmosphere; in which spaces, where there is no
air to resist their motions, all bodies will move with the greatest freedom;
and the planets and comets will constantly pursue their revolutions in
orbits given in kind and position, according to the laws above explained;
but though these bodies may, indeed, persevere in their orbits by the mere
laws of gravity, yet they could by no means have at first derived the
regular position of the orbits themselves from those laws.
242 MASTERWORKS OF SCIENCE
The six primary planets are revolved about the sun in circles concen-
tric with the sun, and with motions directed towards the same parts, and
almost in the same plane. Ten moons are revolved about the earth, Jupiter
and Saturn, in circles concentric with them, with the same direction of
motion, and nearly in the planes of the orbits of those planets; but it is
not to be conceived that mere mechanical causes could give birth to so
many regular motions, since the comets range over all parts of the heavens
in very eccentric orbits; for by that kind of motion they pass easily
through the orbs of the planets, and with great rapidity; and in their
aphelions, where they move the slowest, and are detained the longest,
they recede to the greatest distances from each other, and thence suffer
the least disturbance from their mutual attractions. This most beautiful
system of the sun, planets, and comets could only proceed from the counsel
and dominion of an intelligent and powerful Being. And if the fixed stars
are the centres of other like systems, these, being formed by the like wise
counsel, must be all subject to the dominion of One; especially since the
light of the fixed stars is of the same nature with the light of the sun,
and from every system light passes into all the other systems: and lest the
systems of the fixed stars should, by their gravity, fall on each other mutu-
ally, he hath placed those systems at immense distances one from another.
Hitherto we have explained the phenomena of the heavens and of our
sea by the power of gravity, but have not yet assigned the cause of this
power. This is certain, that it must proceed from a cause that penetrates
to the very centres of the sun and planets, without suffering the least
diminution of its force; that operates not according to the quantity of
the surfaces of the particles upon which it acts (as mechanical causes use
to do), but according to the quantity of the solid matter which they con-
tain, and propagates its virtue on all sides to immense distances, de-
creasing always in the duplicate proportion of the distances. Gravitation
towards the sun is made up out of the gravitations towards the several
particles of which the body of the sun is composed; and in receding from
the sun decreases accurately in the duplicate proportion of the distances
as far as the orb of Saturn, as evidently appears from the quiescence of
the aphelions of the planets; nay, and even to the remotest aphelions of the
comets, if those aphelions are also quiescent. But hitherto I have not been
able to discover the cause of those properties of gravity from phenomena,
and I frame no hypotheses; for whatever is not deduced from the phe-
nomena* is to be called an hypothesis; and hypotheses, whether metaphysi-
cal or physical, whether of occult qualities or mechanical, have no place
in experimental philosophy. In this philosophy particular propositions
are inferred from the phenomena, and afterwards rendered general by
induction. Thus it was that the impenetrability, the mobility, and the
impulsive force of bodies, and the laws of motion and of gravitation, were
discovered. And to us it is enough that gravity does really exist, and act
according to the laws which we have explained, and abundantly serves to
account for all the motions of the celestial bodies, and of our sea.
And now we might add something concerning a certain most subtle
^ NEWT ON — PR IN GIF I A 243
Spirit which pervades and lies hid in all gross bodies; by the force and
action of which Spirit the particles of bodies mutually attract one another
at near distances, and cohere, if contiguous; and electric bodies operate
to greater distances, as well repelling as attracting the neighbouring cor-
puscles; and light is emitted, reflected, refracted, inflected, and heats
bodies; and all sensation is excited, and the members of animal bodies
move at the command of the will, namely, by the vibrations of this Spirit,
mutually propagated along the solid filaments of the nerves, from the out-
ward organs of sense to the brain, and from the brain into the muscles.
But these are things that cannot be explained in few words, nor are we
furnished with that sufficiency of experiments which is required to an
accurate determination and demonstration of the laws by which this elec-
tric and elastic Spirit operates.
END OF THE MATHEMATICAL PRINCIPLES
THE ATOMIC THEORY
by
JOHN DALTON
CONTENTS
The Atomic Theory
I. On the Constitution of Bodies
Section i. On the Constitution of Pure Elastic Fluids
Section 2. On the Constitution of Mixed Elastic Fluids
Section 3. On the Constitution of Liquids, and the Mechanical
Relations betwixt Liquids and Elastic Fluids
Section 4. On the Constitution of Solids
II. On Chemical Synthesis
Explanation of Plate
JOHN D ALTON
1^66-1844
AT THE HEIGHT OF HIS FAME, John Dalton wrote the following
note in the autograph album belonging to a friend of his:
The writer of this was born at the village of Eaglesfield, about two
miles west of Cockermouth, Cumberland. Attended the village
schools, there and in the neighborhood, till eleven years of age, at
which period he had gone through a course of mensuration, sur-
veying, navigation, etc.; began about twelve to teach the village
school and continued it about two years; afterwards was occasion-
ally employed in husbandry for a year or more; removed to Kenda!
at fifteen years of age as assistant in a boarding school; remained in
that capacity for three or four years; then undertook the same
school as principal and continued it for eight years; whilst at
Kendal employed his leisure in studying Latin, Greek, French and
the mathematics, with natural philosophy; removed thence to Man-
chester in 1793 as tutor in mathematics and natural philosophy in
the New College; was six years in that engagement and after was
employed as private and public teacher of mathematics and chem-
istry in Manchester, but occasionally by invitation in London, Edin-
burgh, Glasgow, Birmingham and Leeds.
Oct. 22, 1832. JOHN DALTON
These bare bones of biography can fortunately be clothed
with flesh. Dal ton was born in 1766, one of the six children
of Joseph and Deborah Dalton, humble Quakers. Joseph Dai-
ton was a hand-loom weaver and the farmer of a small patch
of land which he owned. Nothing in the family life conduced
to special refinement save the simple Quaker faith. The elder
Daltons had benefited by neither formal education nor wealth;
they differed little from their neighbors, most of them also
plain, honest, rugged small farmers and tradespeople. The
town schools provided only such provender as John D^lton
-was able to exhaust in a half dozen years, and required of a
248 MASTERWORKS OF SCIENCE
teacher no further qualifications than Dalton was able to offer
when he was twelve. One may question his success as a
teacher at that age; it was evidently sufficient to persuade
him to elect teaching as his profession.
When he journeyed to Kendal to assist in a boarding
school, Dalton went on the invitation of a cousin who was
head of the school. He had, as he reports, leisure there to
study languages, mathematics, and natural philosophy. He
had also leisure to contribute vapid answers to vapid ques-
tions in two periodicals, the Ladles' Diary and the Gentle-
man s Diary. For example, to the question, Can one who has
loved sincerely love a second time? he replied with a curi-
ously silly essay.
Much more important, during these Kendal years Dalton
met John Gough. Gough was twice Dalton's age, and as a
result of smallpox had been blind from his infancy. Yet he
was a good classical scholar, and it was he who provoked
Dalton to study Greek and Latin. Well-informed about the
science of the day, he thought scientifically; and he taught his
younger friend to think similarly. He persuaded him to make
and record his first scientific observations, a series of local
weather data collected with the aid of homemade barometers,
thermometers, and hygro scopes. During these same years,
while Dalton was intermittently considering law and medi-
cine as possible professions, he also collected and dried botani-
cal specimens, collected insects, experimented with his own
body to determine what proportion of food and drink in-
gested passed off as "insensible perspiration."
In 1793, through Cough's influence, Dalton was appointed
tutor in mathematics and natural philosophy at New College
in Manchester. Almost at once he published his Meteorologi-
cal Observations and Essays (Manchester, 1793). This opens
with an account of an aurora borealis he had observed in 1787
and a discussion of the causes and effects of auroras. One
essay considers the rise and fall of the barometer and the
causes therefor. The most important essay, historically, is the
one on evaporation, for in it he first states the idea now known
as Dalton's law, the law of partial pressures.
In 1794 the Manchester Literary and Philosophical So-
ciety elected Dalton to membership. The first paper he pre-
sented to the Society he titled "On Vision of Colour," and
In it he used data from his own and his brother's experiences.
They were both color-blind, as they had discovered when
they brought their mother, as a good Quaker present, a pair
of silk stockings of brilliant crimson. Later he presented to
the Society papers on rain and dew, on heat conduction, on
"Heat and Cold Produced by Mechanical Condensation and
DALTON — THE ATOMIC THEORY 249
Rarefaction of Air." In all of these papers Dalton relied for
data on his own loose experiments and his own inaccurate
instruments. His numerical results have not been confirmed
by later students. Yet the essays are valuable, for the experi-
ments are most sagaciously interpreted, and Dalton exercised
in them his wonderful faculty for happy generalization. Thus,
in 1803, in a paper "On the Tendency of Elastic Fluids to
Diffuse Through Each Other," from quite insufficient data
he evolved the final form of the law of partial pressures. Simi-
larly, in a paper on the expansion of gases by heat, he antici-
pated by six months Gay-Lussac's conclusions.
During these years in Manchester, Dalton was teaching
mechanics, algebra, geometry, bookkeeping, chemistry, and
natural philosophy to private students as well as in New
College. He traveled very little — only occasionally to Bristol
and to London, which he thought the "most disagreeable
place for one of a contemplative turn to exist in" — and his
contact with the intellectual and scientific .world was wholly
through the books available to him in the free library of
Manchester. Yet his papers were attracting such attention that
in 1803 he was invited to give a course of lectures at the
Royal Institution in London, and his teaching was drawing
to him so many private pupils that he withdrew from New
College.
Between 1803 and 1820, after which Daltonrs powers
faded and his production diminished, he prepared studies on
fog, on alloys, on sulphuric ether, on respiration, and on ani-
mal heat. Most important, he developed his atomic theory. He
first presented his ideas on atoms in a series of lectures given
in Glasgow in 1807; and in a second course of lectures at the
Royal Institution in London, in 1809-10, he explained how he
had come to his conclusions. The real publication came, how-
ever, in the first volume of his New System of Chemical
Philosophy, 1808. From this volume pertinent passages are
here reprinted.
In person, Dalton was of middle height, robust, muscu-
lar, and awkward. His mouth was firm, his voice gruff, his
chin massive. He was said to resemble Newton. His mode of
living was always quiet, adjusted to the contemplative life
he preferred. For thirty years he occupied the same lodgings
in Manchester (he never married) going thence daily to his
rooms at the Literary and Philosophical Society to receive his
pupils and do his own experimenting. On Sundays he faith-
fully attended the Quaker services, and on Thursdays he
played a weekly game of bowls.
Dalton's theory o£ the atomic composition of all matter
won quick recognition and acceptance. It earned him such
250 MASTERWORKS OF SCIENCE
high regard from the scientific and academic world that in
his last years honors showered upon him. In 1816 he was
elected a corresponding member of the French Academy o£
Science; in 1822 he was elected Fellow of the Royal Society;
in 1826 he was the first recipient of the annual royal medal
and prize recently established by George IV; in 1832 Oxford
made him a Doctor of Common Law; in 1833 the government
awarded him a pension for life, and in the announcement
of the grant he was named "one of the greatest legislators of
chemical science." He held also a degree as Doctor o£ Law
from Edinburgh, and memberships in learned societies in
Munich, Moscow, and Berlin. When he visited Paris in 1822,
Biot, Ampere, Arago, Fresnel, Laplace, Cuvier, and other
French scientists combined their efforts to honor him.
Many of Dalton's ideas in chemistry have been super-
seded. His theories of heat are as out-of-date as his use of
elastic fluid for "gas/' azotic gas for "nitrogen," oxygenous
gas for "oxygen," et cetera. His fame is nevertheless secure.
It rests upon his discovery of a simple principle, universally
applicable to the facts of chemistry — that elements combine
always in fixed proportions. Sir Humphry^ Davy rightly said
that in laying the foundation for future labors, Dalton's labors
in chemistry resembled those of Kepler in astronomy.
THE ATOMIC THEORY
/. 02V THE CONSTITUTION OF BODIES
THERE ARE three distinctions in the kinds of bodies, or three states, which
have more especially claimed the attention of philosophical chemists;
namely, those which are marked by the terms elastic fluids, liquids, and
solids. A very familiar instance is exhibited to us in water, of a body,
which, in certain circumstances, is capable of assuming all the three
states. In steam we recognise a perfectly elastic fluid, in water, a perfect
liquid, and in ice, a complete solid. These observations have tacitly led
to the conclusion which seems universally adopted, that all bodies of sen-
sible magnitude, whether liquid or solid, are constituted of a vast num-
ber of extremely small particles, or atoms of matter bound together by a
force of attraction, which is more or less powerful according to circum-
stances, and which, as it endeavours to prevent their separation, is very
properly called, in that view, attraction of cohesion; but as it collects
them from a dispersed state (as from steam into water) it is called,
attraction of aggregation, or, more simply, affinity. Whatever names it
may go by, they still signify one and the same power. It is not my design
to call in question this conclusion, which appears completely satisfactory;
but to shew that we have hitherto made no use of it, and that the conse-
quence of the neglect has been a very obscure view of chemical agency,
which is daily growing more so in proportion to the new lights attempted
to be thrown upon it.
Whether the ultimate particles of a body, such as water, are all alike,
that is, of the same figure, weight, &c., is a question of some importance.
From what is known, we have no reason to apprehend a diversity in these
particulars: If it does exist in water, it must equally exist in the elements
constituting water, namely, hydrogen and oxygen. Now it is scarcely pos-
sible to conceive how the aggregates of dissimilar particles should be so
uniformly the same. If some of the particles of water were heavier than
others, if a parcel of the liquid on any occasion were constituted princi-
pally of these heavier particles, it must be supposed to affect the specific
gravity of the mass, a circumstance not known. Similar observations may
be made on other substances. Therefore we may conclude that the ulti-
mate particles of all homogeneous bodies are perfectly ali\e In weight,
figure, &c. In other words, every particle of water is like every other
particle of water; every particle of hydrogen is like every other particle
of hydrogen, &c.
Besides the force of attraction, which, in one character or another,
252 MASTERWORKS OF SCIENCE
belongs universally to ponderable bodies, we find another force that is
likewise universal, or acts upon all matter which comes under our cogni-
sance, namely, a force of repulsion. This is now generally, and I think
properly, ascribed to the agency of heat. An atmosphere of this subtile
fluid constantly surrounds the atoms of all bodies, and prevents them
from being drawn into actual contact. This appears to be satisfactorily
proved by the observation that the bulk of a body may be diminished
by abstracting some of its heat; but it should seem that enlargement and
diminution of bulk depend perhaps more on the arrangement than on the
size of the ultimate particles.
We are now to consider how these two great antagonist powers of
attraction and repulsion are adjusted, so as to allow of the three different
states of elastic fluids, liquids, and solids. We shall divide the subject into
four Sections; namely, first, on the constitution of pure elastic fluids; sec-
ond, on the constitution of mixed elastic fluids; third, on the constitution
of liquids, and fourth, on the constitution of solids.
Section I. On the Constitution of Pure Elastic Fluids
A pure elastic fluid is one, the constituent particles of which are all
alike, or in no way distinguishable. Steam, or aqueous vapour, hydrog-
enous gas, oxygenous gas, azotic gas, and several others are of this kind.
These fluids are constituted of particles possessing very diffuse atmos-
pheres of heat, the capacity or bulk of the atmosphere being often one
or two thousand times that of the particle in a liquid or solid form. What-
ever therefore may be the shape or figure of the solid atom abstractedly,
when surrounded by such an atmosphere it must be globular; but as all
the globules in any small given volume are subject to the same pressure,
they must be equal in bulk, and will therefore be arranged in horizontal
strata, like a pile of shot. A volume of elastic fluid is found to expand
whenever the pressure is taken off. This proves that the repulsion exceeds
the attraction in such case. Thefabsolute attraction! and repulsion of the
particles of an elastic fluid, we have no means of estimating, though we
can have little doubt but that the cotemporary energy of both is great;
but the excess of the repulsive energy above the attractive can be esti-
mated,, and the law of increase and diminution be ascertained in many
cases. Thus, in steam, the density may be taken at %?28 tnat °f water;
consequently each particle of steam has 12 times the diameter that one
of water has, and must press upon 144 particles of a watery surface; but
the pressure upon each is equivalent to that of a column of water of 34
feet; therefore the excess of the elastic force in a particle of steam is equal
to the weight of a column of particles of water, whose height is 34 X
144=4896 feet. And further, this elastic force decreases as the distance
of the particles increases. With respect to steam and other elastic fluids
then, the force of cohesion is entirely counteracted by that of repulsion,
and the only force which is efficacious to move the particles is the excess
of the repulsion above the attraction. Thus, if the attraction be as 10 and
DALTON — THE ATOMIC THEORY 253
the repulsion as 12, the effective repulsive force is as 2. It appears, then
that an elastic fluid, so far from requiring any force to separate its parti-
cles, always requires a force to retain them in their situation, or to pre-
vent their separation.
Some elastic fluids, as hydrogen, oxygen, &c., resist any pressure that
has yet been applied to them. In such then it is evident the repulsive force
of heat is more than a match for the affinity of the particles and the ex-
ternal pressure united, T^o what extent this would continue we cannot
say; but from analogy we might apprehend that a still greater pressure
would succeed in giving the attractive force the superiority, when the
elastic fluid would become a liquid or solid. In other elastic fluids, as
steam, upon the application of compression to a certain degree, the elas-
ticity apparently ceases altogether, and the particles collect in small drops
of liquid, and fall down. This phenomenon requires explanation.
The constitution of a liquid, as water, must then be conceived to be
that of an aggregate of particles, exercising in a most powerful manner
the forces of attraction and repulsion, but nearly in an equal degree. — Of
this more in the sequel.
Section 2. On the Constitution of Mixed Elastic Fluids
When two or more elastic fluids, whose particles do not unite chemi-
cally upon mixture, are brought together, one measure of each, they oc-
cupy the space of two measures, but become uniformly diffused through
each other, and remain so, whatever may be their specific gravities. The
fact admits of no doubt; but explanations have been given in various
ways, and none of them completely satisfactory. As the subject is one of
primary importance in forming a system *of chemical principles, we must
enter somewhat more fully into the discussion.
Dr. Priestley was one of the earliest to notice the fact: it naturally
struck him with surprise that two elastic fluids, having apparently no
affinity for each other, should not arrange themselves according to their
specific gravities, as liquids do in like circumstances. Though he found
this was not the case after the elastic fluids had once been thoroughly
mixed, yet he suggests it as probable that if two of such fluids could be
exposed to each other without agitation, the one specifically heavier would
retain its lower situation. He does not so much as hint at such gases being
retained in a mixed state by affinity. With regard to his suggestion of two
gases being carefully exposed to each other without agitation, I made a
series of experiments expressly to determine the question. From these it
seems to be decided that gases always intermingle and gradually diffuse
themselves amongst each other, if exposed ever so carefully; but it requires
a considerable time to produce a complete intermixture, when the surface
of communication is small. This time may vary from a minute to a day
or more, according to the quantity of the gases and the freedom 0f com-
munication.
When or by whom the notion of mixed gases being held together
254 MASTERWORKS OF SCIENCE
by chemical affinity was first propagated, I do not know; but it seems
probable that the notion of water being dissolved in air led to that of air
being dissolved in air.— Philosophers found that water gradually disap-
peared or evaporated in air, and increased its elasticity; but steam at a
low temperature was known to be unable to overcome the resistance of
the air, therefore the agency of affinity was necessary to account for the
effectljn the permanently elastic fluids indeed, this agency did not seem
to be so much wanted, as they are all able to support themselves; but the
diffusion through each other was a circumstance which did not admit of
an easy solution any other way. In regard to the solution of water in air,
it was natural to suppose, nay, one might almost have been satisfied with-
out the aid of experiment, that the different gases would have had differ-
ent affinities for water, and that the quantities of water, dissolved in like
circumstances, would have varied according to the nature of the gas.
Saussure found however that there was no difference in this respect in the
solvent powers of carbonic acid, hydrogen gas, and common ain— It
might be expected that at least the density of the gas would have some
influence upon its solvent powers, that air of half density would take half
the water, or the quantity of water would diminish in some proportion
to the density; but even here again we are disappointed; whatever be the
rarefaction, if water be present, the vapour produces the same elasticity,
and the hygrometer finally settles at extreme moisture, as in air of com-
mon density in like circumstances. These facts are sufficient to create
extreme difficulty in the conception how any principle of affinity or
cohesion between air and water can be the agent. It is truly astonishing
that the same quantity of vapour should cohere to one particle of air in a
given space as to one thousand in the same space. But the wonder does
not cease here; a Torricellian vacuum dissolves water; and in this in-
stance we have vapour existing independently of air at all temperatures;
what makes it still more remarkable is, the vapour in such vacuum is
precisely the same in quantity and force as in the like volume of any kind
of air of extreme moisture.
J^ These and other considerations which occurred to me some years ago
were sufficient to make me altogether abandon the hypothesis of air dis-
solving water, and to explain the phenomena some other way, or to ac-
knowledge they were inexplicable. In the autumn of 1801, I hit upon an
idea which seemed to be exactly calculated to explain the phenomena
of vapour; it gave rise to a great variety of experiments.
The distinguishing feature of the new theory was that the particles
of one gas are not elastic or repulsive in regard to the particles of another
gas, but only to the particles of their own kind. Consequently when a
vessel contains a mixture of two such elastic fluids, each acts independ-
ently upon the vessel, with its proper elasticity, just as if the other were
absent, whilst no mutual action between the fluids themselves is ob-
served. This position most effectually provided for the existence of vapour
of any temperature in the atmosphere, because it could have nothing but
its own weight to support; and it was perfectly obvious why neither more
DALTON — THE ATOMIC THEORY 255
nor less vapour could exist in air of extreme moisture than in a vacuum
of the same temperature. So far then the great object of the theory was
attained. The law of the condensation of vapour in the atmosphere by
cold was evidently the same on this scheme as that of the condensation
of pure steam, and experience was found to confirm the conclusion at all
temperatures. The only thing now wanting to completely establish the
independent existence of aqueous vapour in the atmosphere was the con-
formity of other liquids to water, in regard to the diffusion and conden-
sation of their vapour. This was found to take place in several liquids,
and particularly in sulphuric ether, one which was most likely to shew
any anomaly to advantage if it existed, on account of the great change
of expansibility in its vapour at ordinary temperatures. The existence of
vapour in the atmosphere and its occasional condensation were thus ac-
counted for; but another question remained, how does it rise from a sur-
face of water subject to the pressure of the atmosphere?
From the novelty, both in the theory and the experiments, and their
importance, provided they were correct, the new facts and experiments
were highly valued, some of the latter were repeated, and found correct,
and none of the results, as far as I know, have been controverted; but the
theory was almost universally misunderstood, and consequently repro-
bated. This must have arisen partly at least from my being too concise,
and not sufficiently clear in its exposition.
Dr. Thomson was the first, as far as I know, who publicly animad-
verted upon the theory; this gentleman, so well known for his excellent
System of Chemistry, observed in the first edition of that work that the
theory would not account for the equal distribution of gases; but that,
granting the supposition of one gas neither attracting nor repelling an-
other, the two must still arrange themselves according to their specific
gravity. But the most general objection to it was quite of a different kind;
it was admitted that the theory was adapted so as to obtain the mpst
uniform and permanent diffusion of gases; but it was urged that as one
gas was as a vacuum to another, a measure of any gas being put to a
measure of another, the two measures ought to occupy the space of one
measure only. Finding that my views on the subject were thus misappre-
hended, I wrote an illustration of the theory, which was published in the
3d Vol. of Nicholson's Journal, for November, 1802. In that paper I en-
deavoured to point out the conditions of mixed gases more at large,
according to my hypothesis; and particularly touched upon the discrimi-
nating feature of it, that of two particles of any gas A, repelling each other
by the known stated law, whilst one or more particles of another gas B ,
were interposed in a direct line, without at all affecting the reciprocal
action of the said two particles of A. Or, if any particle of B were casually
to come in contact with one of A, and press against it, this pressure did
not preclude the cotemporary action of all the surrounding particles of
A upon the one in contact with B. In this respect the mutual action o£
particles of the same gas was represented as resembling magnetic action,
which is not disturbed by the intervention o£ a body not magnetic.
256 MASTERWORKS OF SCIENCE
Berthollet in his Chemical Statics (1804) has given a chapter on the
constitution of the atmosphere, in which he has entered largely into a
discussion of the new theory. This celebrated chemist, upon comparing
the results of experiments made by De Luc, Saussure, Volta, Lavoisier,
Watt, &c., together with those of Gay-Lussac, and his own, gives his full
assent to the fact that vapours of every kind increase the elasticity of each
species of gas alike, and just as much as the force of the said vapours in
vacuo; and not only so, but that the specific gravity of vapour in air and
vapour in vacuo is in all cases the same (Vol. i. Sect. 4). Consequently
he adopts the theorem for finding the quantity of vapour which a given
volume of air can dissolve, which 1 have laid down; namely,
- P
where p represents the pressure upon a given volume (i) of dry air,
expressed in inches of mercury, / = the force of the vapour in vacuo
at the temperature, in inches of mercury, and s = the space which the
mixture of air and vapour occupies under the given pressure, p, after
saturation. So far therefore we perfectly agree: but he objects to the
theory by which I attempt to explain these phenomena, and substitutes
another of his own.
The first objection I shall notice is one that clearly shews Berthollet
either does not understand or does not rightly apply the theory he op-
poses; he says, "If one gas occupied the interstices of another, as though
they were vacancies, there would not be any augmentation of volume
when aqueous or ethereal vapour was combined with the air; neverthe-
less there is one proportional to the quantity of vapour added: humidity
should increase the specific gravity of the air, whereas it renders it spe-
cifically lighter, as has been already noticed by Newton." This is the
objection which has been so frequently urged. Let a tall cylindrical glass
vessel cpntaining dry air be inverted over mercury, and a portion of the
air drawn out by a syphon, till an equilibrium of pressure is established
within and without; let a small portion of water, ether, &c., be then
thrown up into the vessel; the vapour rises and occupies the interstices
of the air as a void; but what is the obvious consequence? Why, the sur-
face of the mercury being now pressed both by the dry air and by the new
raised vapour is more pressed within than without, and an enlargement
of the volume of air is unavoidable, in order to restore the equilibrium.
Again, in the open air: suppose there were no aqueous atmosphere
around the earth, only an azotic one = 23 inches of mercury, and an oxyg-
enous one = 6 inches. The air being thus perfectly dry, evaporation
would commence with great speed. The vapour first formed, being con-
stantly urged to ascend by that below, and as constantly resisted by the
.air, must, in the first instance, dilate the other two atmospheres (for the
.ascending steam adds its force to the upward elasticity of the two gases,
and in part alleviates their pressure, the necessary consequence of which
DALTON — THE ATOMIC THEORY 257
Is dilatation). At last, when all the vapour has ascended that the tempera-
ture will admit of, the aqueous atmosphere attains an equilibrium; it no
longer presses upon the other two, but upon the earth; the others return
to their original density and pressure throughout. In this case, it is true,
there would not be any augmentation of volume when aqueous vapour
was combined with the air; humidity would increase the weight of the
congregated atmospheres, but diminish their specific gravity under a
given pressure. One would have thought that this solution of the phe-
nomenon upon my hypothesis was too obvious to escape the notice of
anyone in any degree conversant with pneumatic chemistry.
Another objection is derived from the very considerable time requi-
site for a body of hydrogen to descend into one of carbonic acid; if one
gas were as a vacuum for another, why is the equilibrium not instantly
established? This objection is certainly plausible; we shall consider it
more at large hereafter.
In speaking of the pressure of the atmosphere retaining water in a
liquid state, which I deny, Berthollet adopts the idea of Lavoisier, "that
without it the molecuke would be infinitely dispersed, and that nothing
would limit their separation, unless their own weight should collect them
to form an atmosphere." This, I may remark, is not the language dic-
tated by a correct notion on the subject. Suppose our atmosphere were
annihilated, and the waters on the surface of the globe were instantly
expanded into steam; surely the action of gravity would collect the molec-
ulae into an atmosphere of similar constitution to the one we now pos-
sess; but suppose the whole mass of water evaporated amounted in weight
to 30 inches of mercury, how could it support Its own weight at the com-
mon temperature? It would in a short time be condensed into water
merely by its weight, leaving a small portion, such as the temperature
could support, amounting perhaps to half an inch of mercury in weight,
as a permanent atmosphere, which would effectually prevent any more
vapour from rising, unless there were an increase of temperature. Does
not everyone know that water and other liquids can exist In a Torricellian
vacuum at low temperatures solely by the pressure of vapour arklng from
them? What need then of the pressure of the atmosphere In order to
prevent an excess of vapourisation?
The experiments of Fontana on the distillation of water and ether
in close vessels containing air are adduced to prove that vapours do not
penetrate air without resistance. This is true no doubt; vapour cannot
make its way in such circumstances through a long and circuitous route
without time, and if the external atmosphere keep the vessel cool, the
vapour may be condensed by its sides, and fall down in a liquid form
as fast as it is generated, without ever penetrating in any sensible quan-
tity to its remote extremity.
Dr. Thomson, in the 3d Edition of his System of Chemistry, has
entered into a discussion on the subject of mixed gases; he seems to
comprehend the excellence and defects of my notions on these subjects,
with great acuteness. He does not conclude with Berthollet that, on my
258 MASTERWORKS OF SCIENCE
hypothesis, "there would not be any augmentation o£ volume when
aqueous and ethereal vapour was combined with the air," which has
been so common an objection. There is however one objection which this
gentleman urges that shews he does not completely understand the
mechanism of my hypothesis. At page 448, Vol. 3, he observes that from
the principles of hydrostatics, "each particle of a fluid sustains the whole
pressure. Nor can I perceive any reason why this principle should not
hold, even on the supposition that Dalton's hypothesis is well founded,"
Upon this I would observe that when once an equilibrium is established
in any mixture of gases, each particle of gas is pressed as if by the sur-
rounding particles of its own \ind only. It is in the renunciation of that
hydrostatical principle that the leading feature of the theory consists. The
lowest particle of oxygen in the atmosphere sustains the weight of all the
particles of oxygen above it, and the weight of no other. It was therefore
a maxim with me that every particle of gas is equally pressed in every
direction, but the pressure arises from the particles of its own kind only.
Indeed when a measure of oxygen is put to a measure of azote, at the
moment the two surfaces come in contact, the particles of each gas press
against those of the other with their full force; but the two gases get
gradually intermingled, and the force which each particle has to sustain
proportionally diminishes, till at last it becomes the same as that of the
original gas dilated to twice its volume. The ratio of the forces is as the
cube root of the spaces inversely; that is, 3 \/2 : I> °r as I-2^ : i nearly.
In such a mixture as has just been mentioned, then, the common hypothe-
sis supposes the pressure of each particle of gas to be 1.26; whereas mine
supposes it only to be i; but the sum of the pressure of both gases on the
containing vessel, or any other surface, is exactly the same on both
hypotheses.
With regard to the objection that one gas makes a more durable
resistance to the entrance of another than it ought to do on my hypothe-
sis: This occurred to me in a very early period of my speculations; I
devisecl the train of reasoning which appeared to obviate the objection;
but it bekig necessarily of a mathematical nature, I did not wish to ob-
trude it upon the notice of chemical philosophers, but rather to wait till
it was called for. — The resistance which any medium makes to the motion
of a body depends upon the surface of that body, and is greater as the
surface is greater, all other circumstances being the same. A ball of lead
i inch in diameter meets with a certain resistance in falling through the
air; but the same ball, being made into a thousand smaller ones of %Q of
an inch diameter, and falling with the same velocity, meets with 10 times
the resistance it did before: because the force of gravity increases as the
cube of the diameter of any particle, and the resistance only as the square
of the diameter. Hence it appears that in order to increase the resistance
of particles moving in any medium, it is only necessary to divide them,
and that the resistance will be a maximum when the division is a maxi-
mum. We have only then to consider particles of lead falling through
air by their own gravity, and we may have an idea of the resistance of
DALTON — THE ATOMIC THEORY 259
one gas entering another, only the particles of lead must be conceived
to be infinitely small, if I may be allowed the expression. Here we shall
find great resistance, and yet no one, I should suppose, will say that the
air and the lead are mutually elastic.
Mr. Murray has lately edited a system o£ chemistry, in which he has
given a very clear description of the phenomena of the atmosphere, and
of other similar mixtures of elastic fluids, He has ably discussed the dif-
ferent theories that have been proposed on the subject, and given a per-
spicuous view of mine, which he thinks is ingenious, and calculated to
explain several of the phenomena well, but, upon the whole, not equally
satisfactory with that which he adopts. He does not object to the
mechanism of my hypothesis in regard to the independent elasticity of the
several gases entering into any mixture, but argues that the phenomena
do not require so extraordinary a postulatum; and more particularly dis-
approves of the application of my theory to account for the evaporation.
The principal feature in Mr. Murray's theory, and which he thinks
distinguishes it from mine, is "that between mixed gases, which are
capable, under any circumstances of combining, an attraction must always
be exerted."
Before we animadvert on these principles, it may be convenient to
extend the first a little farther, and to adopt as a maxim, "that between
the particles of pure gases, which are capable under any circumstances
of combining, an attraction must always be exerted." This, Mr. Murray
cannot certainly object to, in the case of steam, a pure elastic fluid, the
particles of which are known in certain circumstances to combine. Nor
will it be said that steam and a permanent gas are different; for he justly
observes, "this distinction (between gases and vapours) is merely relative,
and arises from the difference of temperature at which they are formed;
the state with regard to each, while they exist in it, is precisely the same."
Is steam then constituted of particles in which the attraction is so far
exerted as to prevent their separation? No: they exhibit no traces of
attraction, more than the like number of particles of oxygen do, when in
the gaseous form. What then is the conclusion? It is this: notwithstand-
ing it must be allowed that all bodies, at all times, and in every situation,
attract one another; yet in certain circumstances f they are likewise actu-
ated by a repulsive power; the only efficient motive "force is then the
difference of these two powers,
From the circumstance of gases mixing together without experienc-
ing any sensible diminution of volume, the advocates for the agency of
chemical affinity characterise it as a "slight action," and "a weak reciprocal
action." So far I think they are consistent; but when we hear of this
affinity being so far exerted as to prevent the separation of elastic parti-
cles, I do not conceive with what propriety it can be called weak. Sup-
pose this affinity should be exercised in the case of steam of 212°; then
the attraction becoming equal to the repulsion, the force which any one
particle would exercise must be equal to the weight of a column of water
of 4896 feet high.
260 MASTERWORKS OF SCIENCE
It is somewhat remarkable that those gases which are known to com-
bine occasionally, as azote and oxygen, and those which are never known
to combine, as hydrogen and carbonic acid, should dissolve one another
with equal facility; nay, these last exercise this solvent power with more
effect than the former; for hydrogen can draw up carbonic acid from the
bottom to the top of any vessel, notwithstanding the latter is 20 times the
specific gravity of the former. One would have thought that a force of ad-
hesion was more to be expected in the particles of steam than in a mixture
of hydrogen and carbonic acid. But it is the business of those who adopt
the theory of the mutual solution of gases to explain these difficulties.
In a mixture where are 8 particles of oxygen for i of hydrogen, it is
demonstrable that the central distances of the particles of hydrogen are
at a medium twice as great as those of oxygen. Now supposing the central
distance of two adjacent particles of hydrogen to be denoted by 12, query,
what is supposed to be the central distance of any one particle of hydro-
gen from that one particle, or those particles -of oxygen with which it is
connected by this weak chemical union? It would be well if those who
understand and maintain the doctrine of chemical solution would rep-
resent how they conceive this to be; it would enable those who are
desirous to learn, to obtain a clear idea of the system, and those who are
dissatisfied with it, to point out its defects with more precision.
In discussing the doctrines of elastic fluids mixed with vapour, Mr.
Murray seems disposed to question the accuracy of the fact that the
quantity of vapour is the same in vacuo as in air, though he has not
attempted to ascertain in which case it more abounds. This is certainly
the touchstone of the mechanical and chemical theories; and I had thought
that whoever admitted the truth of the fact must unavoidably adopt the
mechanical theory. Berthollet however, convinced from his own experi-
ence that the fact was incontrovertible, attempts to reconcile it, inimical
as it is, to the chemical theory; with what success it is left to others to
judge. Mr. Murray joins with Berthollet in condemning as extravagant the
position which I maintain, that if the atmosphere were annihilated, we
should have little more aqueous vapour than at present exists in it. Upon
. which I shall only remark that if either of those gentlemen will calculate,
or give a rough estimate upon their hypothesis, of the quantity of aqueous
vapour that would be collected around the earth, on the said supposition,
I will engage to discuss the subject with them more at large.
In 1802, Dr. Henry announced a very curious and important discov-
ery, which was afterwards published in the Philosophical Transactions;
namely, that the quantity of any gas absorbed by water is increased in
direct proportion to the pressure of the gas on the surface of the water.
Previously to this, I was engaged in an investigation of the quantity of
carbonic acid in the atmosphere; it was matter of surprise to me that lime
water should so readily manifest the presence of carbonic acid in the air,
whilst pure water, by exposure for any length of time, gave not the least
traces of that acid. I thought that length of time ought to compensate for
weakness of affinity. In pursuing the subject I found that the quantity of.
DALTQN — THE ATOMIC THEORY 261
this acid taken up by water was greater or less in proportion to its greater
or less density in the gaseous mixture, incumbent upon the surface, ancf
therefore ceased to be surprised at water absorbing so insensible a portion
from the atmosphere. I had not however entertained any suspicion that
this law was generally applicable to the gases till Dr. Henry's discovery
was announced. Immediately upon this, it struck me as essentially neces-
sary, in ascertaining the quantity of any gas which a given volume o£
water will absorb, that we must be careful the gas is perfectly pure or un-
mixed with any other gas whatever; otherwise the maximum effect for
any given pressure cannot be produced. This thought was suggested to
Dr. Henry, and found to be correct; in consequence of which it became
expedient to repeat some of his experiments relating to the quantity of
gas absorbed under a given pressure. Upon due consideration of all these
phenomena, Dr. Henry became convinced that there was no system of
elastic fluids which gave so simple, easy and intelligible a solution of them
as the one I adopt, namely, that each gas in any mixture exercises a dis-
tinct pressure, which continues the same if the other gases are withdrawn.
I shall now proceed to give my present views on the subject of mixed
gases, which are somewhat different from what they were when the
theory was announced, in consequence of the fresh lights which succeed-
ing experience has diffused. In prosecuting my enquiries into the nature
of elastic fluids, I soon perceived it was necessary, if possible, to ascertain
whether the atoms or ultimate particles of the different gases are of the
same size or volume in like circumstances of temperature and pressure,
By the size or volume of an ultimate particle, I mean, in this place, the
space it occupies in the state of a pure elastic fluid; in this sense the bulk
of the particle signifies the bulk of the supposed impenetrable nucleus,
together with that of its surrounding repulsive atmosphere of heat. At the
time I formed the theory of mixed gases, I had a confused idea, as many
have, I suppose, at this time, that the particles of elastic fluids are all of
the same size; that a given volume of oxygenous gas contains just as many
particles as the same volume of hydrogenous; or, if not, that we had no-
data from which the question could be solved. But from a train of reason-
ing I became convinced that different gases have not their particles o£
the same size; and that the following may be adopted as a maxim, till
some reason appears to the contrary: namely, —
That every species of pure elastic fluid has its particles globular and
all of a size; but that no two species agree in the size of their particles,
the pressure and temperature being the same.
When we contemplate upon the disposition of the globular particles
in a volume of pure elastic fluid, we perceive it must be analogous to that
of a square pile of shot; the particles must be disposed into horizontal
strata, each four particles forming a square: in a superior stratum, each
particle rests upon four particles below, the points of its contact with all
four being 45° above the horizontal plane, or that plane which passes
through the centres of the four particles. On this account the pressure is
steady and uniform throughout. But when a measure of one gas is pre-
262 MASTERWORKS OF SCIENCE
sented to a measure of another in any vessel, we have then a surface of
elastic globular particles of one size in contact with an equal surface of
particles of another: in such case the points of contact of the heterogene-
ous particles must vary all the way from 40° to 90°; an intestine motion
must arise from this inequality, and the particles of one kind be propelled
amongst those of the other. The same cause which prevented the two
elastic surfaces from maintaining an equilibrium will always subsist, the
particles of one kind being from their size unable to apply properly to the
other, so that no equilibrium can ever take place amongst the heteroge-
neous particles. The intestine motion must therefore continue till the par-
ticles arrive at the opposite surface of the vessel against any point of
which they can rest with stability, and the equilibrium at length is ac-
quired when each ga-s is uniformly diffused through the other. In the
open atmosphere no equilibrium can take place in such case till the parti-
cles have ascended so far as to be restrained by their own weight; that is,
till they constitute a distinct atmosphere.
It is remarkable that when two equal measures of different gases are
thus diffused, and sustain an invaried pressure, as that of the atmosphere,
the pressure upon each particle after the mixture is less than before. This
points out the active principle of diffusion; for particles of fluids are
always disposed to move to that situation where the pressure is least.
Thus, in a mixture of equal measures of oxygen and hydrogen, the com-
mon pressure on each particle before mixture being denoted by i, that
after the mixture, when the gas becomes of half its density, will be de-
noted by 3V%=-794-
This view of the constitution of mixed gases agrees with that which
I have given before, in the two following particulars, which I consider as
essential to every theory on the subject to give it plausibility.
ist. The diffusion of gases through each other is effected by means
of the repulsion belonging to the homogenous particles; or to that prin-
ciple which is always energetic to produce the dilatation of the gas.
2d. When any two or more mixed gases acquire an equilibrium, the
elastic energy of each against the surface of the vessel or of any liquid is
precisely the same as if it were the only gas present occupying the whole
space, and all the rest were withdrawn.
In other respects I think the last view accords better with the
phenomena.
Section 3. On the Constitution of Liquids, and the Mechanical
Relations betwixt Liquids and Elastic Fluids
A liquid or inelastic fluid may be defined to be a body, the parts of
which yield to a very small impression, and are easily moved one upon
another. This definition may suffice for the consideration of liquids in an
hydrostatical sense, but not in a chemical sense. Strictly speaking, there is
no substance inelastic; but we commonly apply the word elastic to such
fluids only as have the property of condensation in a very conspicuous de-
DALTON — THE ATOMIC THEORY 263
gree. Water is a liquid or inelastic fluid; but if it is compressed by a great
force, it yields a little, and again recovers its original bulk when the pres-
sure is removed. We are indebted to Mr. Canton for a set of experiments
by which the compressibility of several liquids is demonstrated. Water, he
found, lost about %i74otn Part °^ *ts kulk by the pressure of the at-
mosphere.
When we consider the origin of water from steam, we have no reason
to wonder at its compressibility, and that in a very small degree; it would
be wonderful if water had not this quality. The force of steam at 212° is
equal to the pressure of the atmosphere; what a prodigious force must it
have when condensed 15 or 18 hundred times? The truth is, water, and,
by analogy, other liquids, must be considered as bodies, under the control
of two most powerful and energetic agents, attraction and repulsion, be-
tween which there is an equilibrium. If any compressing force is applied,
it yields, indeed, but in such a manner as a strong spring would yield
when wound up almost to the highest pitch. When we attempt to sepa-
rate one portion of liquid from another, the case is different: here the
attraction is the antagonist force, and that being balanced by the repulsion
of the heat, a moderate force is capable of producing the separation. But
even here we perceive the attractive force to prevail, there being a mani-
fest cohesion of the particles. Whence does this arise? It should seem that
when two particles of steam coalesce to form water, they take their station
so as to effect a perfect equilibrium between the two opposite powers; but
if any foreign force intervene, so as to separate the two molecules an
evanescent space, the repulsion decreases faster than the attraction, and
consequently this last acquires a superiority or excess, which the foreign
force has to overcome. If this were not the case, why do they at first, or
upon the formation of water, pass from the greater to the less distance?
With regard to the collocation and arrangement of particles in an
aggregate of water or any other liquid, I have already observed that this
is not, in all probability, the same as in air. It seems highly improbable
from the phenomena of the expansion of liquids by heat. The law of ex-
pansion is unaccountable for, if we confine liquids to one and the same
arrangement of their ultimate particles in all temperatures; for we cannot
avoid concluding, if that were the case, the expansion would go on in a
progressive way with the heat, like as in air; and there would be no such
thing observed as a point of temperature at which the expansion was
stationary.
•RECIPROCAL PRESSURE OF LIQUIDS AND ELASTIC FLUIDS
When an elastic fluid is confined by a vessel of certain materials, such
as wood, earthenware, &c., it is found slowly to communicate with the ex-
ternal air, to give and receive successively, till a complete intermixture .
takes place. There is no doubt but this is occasioned by those vessels
being porous, so as to transmit the fluids. Other vessels, as those of metal,
glass, &c., confine air most completely. These therefore cannot be porous;
264 MASTERWQRKS OF SCIENCE
or rather, their pores are too small to admit of the passage of air. I believe
no sort of vessel has yet been found to transmit one gas and confine an-
other; such a one is a desideratum in practical chemistry. All the gases
appear to be completely porous, as might be expected, and therefore oper-
ate very temporarily in confining each other. How are liquids in this re-
spect? Do they resemble glass, or earthenware, or gases, in regard to their
power of confining elastic fluids? Do they treat all gases alike, or do they
confine some and transmit others? These are important questions: they
are not to be answered in a moment. We must patiently examine the facts.
Before we can proceed, it will be necessary to lay down a rule, if pos-
sible, by which to distinguish the chemical from the mechanical action of
a liquid upon an elastic fluid. I think the following cannot well be ob-
jected to: When an elastic fluid is fept in contact with a liquid, ij any
change is perceived, either in the elasticity or any other property of the
elastic fluid, so far the mutual action must be pronounced CHEMICAL: but
if NO change is perceived, either in the elasticity or any other property of
the elastic fluid, then the mutual action of the two must be pronounced
wholly MECHANICAL.
If a quantity of lime be kept in water and agitated, upon standing a
sufficient time, the lime falls down, and leaves the water transparent: but
the water takes a small portion of the lime which it permanently retains^
contrary to the Laws of specific gravity. Why? Because that portion of
lime is dissolved by the water. If a quantity of air be put to water and
agitated, upon standing a sufficient time, the air rises up to the surface of
the water and leaves it transparent; but the water permanently retains a
portion of air, contrary to the Laws of specific gravity. Why? Because that
small portion of air is dissolved by the water. So far the two explanations
are equally satisfactory. But if we place the two portions of water under
the receiver of an air pump, and exhaust the incumbent air, the whole
portion of air absorbed by the water ascends, and is drawn out of the
receiver; whereas the lime remains still in solution as before. If now the
question be repeated, why is the air retained in the water? The answer
must be, because there is an elastic force on the surface of the water
which holds it in. The water appears passive in the business. But, perhaps,
the pressure on the surface of the water may have some effect upon its
affinity for air, and none on that for lime? Let the air be drawn off from
the surfaces of the two portions of water, and another species induced
without alleviating the pressure. Tbfe lime water remains unchanged; the
air escapes from the other much the same as in vacuo. The question of the
relation of water to air appears by this fact to be still more difficult; at
first the air seemed to be retained by the attraction of the water; in the
second case, the water seemed indifferent; in the third, it appears as if
repulsive to the air; yet in all three, it is the same air that has to act on
the same water. From these facts, there seems reason then for maintaining
three opinions on the subject of the mutual action of air and water;
namely, that water attracts air, that water does not attract it, and that
water repels air. One of these must be true; but we must not decide
DALTQN— ~ THE ATOMIC THEORY 265
hastily. Dr. Priestley once imagined that the clay of a porous earthen
retort, when red hot, "destroys for a time the aerial form of whatever air
is exposed to the outside of it; which aerial form it recovers, after it has
been transmitted in combination from one part of the clay to another, till
it has reached the inside of the retort." But he soon discarded so ex-
travagant an opinion.
From the recent experiments of Dr. Henry, with those of my own,
there appears reason to conclude that a given volume of water absorbs the
following parts of its bulk of the several gases.
Bulk of gas absorbed.
i = i Carbonic acid
i = i Sulphuretted hydrogen
i = i Nitrous oxide
% = .125 Olefiant gas
%r = .037 Oxygenous gas
%7 = .037 Nitrous gas
%r =: .037 Carburetted hydrogen
%7 zz .037 Carbonic oxide?
%4 = .0156 Azotic gas
%4 = .0156 Hydrogenous gas
%i = .0156 Carbonic oxide?
These fractions are the cubes of Vi, %5 %, % &c. This shews the distances
of the gaseous particles in the water to be always same multiple of the distances
without.
In a mixture of two or more gases, the rule holds the same as when
the gases are alone; that is, the quantity of each absorbed is the same as if
it was the only gas present.
As the quantity of any gas in a given volume is subject to variation
from pressure and temperature, it is natural to enquire whether any
change is induced in the absorption of these circumstances; the experi-
ments of Dr. Henry have decided this point, by ascertaining that if the
exterior gas is condensed or rarefied in any degree, the gas absorbed is
condensed or rarefied in the same degree; so that the proportions ab-
sorbed given above are absolute.
One remarkable fact, which has been hinted at, is that no one gas is
capable of retaining another in water; it escapes, not indeed instantly, like
as in a vacuum, but gradually, like as carbonic acid escapes into the at-
mosphere from the bottom of a cavity communicating with it.
It remains now to decide whether the relation between water and the
above-mentioned gases is of a chemical or mechanical nature^ From the
facts just stated, it appears evident that the elasticity of carbonic acid and
the other two gases of the first class is not at all affected by the water. It
remains exactly of the same energy whether the water is present or absent.
All the other properties of those gases continue just the same, as far as I
know, whether they are alone or blended with water: we must therefore,
MASTERWORKS OF SCIENCE
.ceive, if we abide by the Law just laid down, pronounce the mutual
n between these gases and water to be mechanical.
[n the other gases it is very remarkable their density within the water
id be such as to require the distance of the particles to be just 2, 3 or
les what it is without. In defiant gas, the distance of the particles
in is^just twice that without, as is inferred from the density being
n oxygenous gas, &c., the distance is 3 times as great, and in hydrog-
s, &c., 4 times. This is certainly curious, and deserves further investi-
n; but at present we have only to decide whether the general phe-
;na denote the relation to be of a chemical or mechanical nature. In
ise whatever does it appear that the elasticity of any of these gases is
:ed; if water takes %T of its bulk of any gas, the gas so absorbed
s %7 of the elasticity that the exterior gas does, and of course it
>es from the water when the pressure is withdrawn from its surface,
tien a foreign one is induced, against which it is not a proper match.
ir as is known too, all the other properties of the gases continue the
; thus, if water containing oxygenous gas be admitted to nitrous gas,
inion of the two gases is certain; after which the water takes up %7
i bulk of nitrous gas, as it would have done, if this circumstance had
»ccurred. It seems clear then that the relation is a mechanical one.
Carbonic acid gas then presses upon water in the first instance with
iiole force; in a short time it partly enters the water, and then the
ion of the part entered contributes to support the incumbent atmos-
*. Finally, the gas gets completely diffused through the water, so as
of the same density within as without; the gas within the water then
es on the containing vessel only, and reacts upon the incumbent gas.
water then sustains no pressure either from the gas within or with-
in olefiant gas the surface of the water supports % of the pressure,
ygenous, &c., 2%7, and in hydrogenous, &c., 6%4-
When any gas is confined in a vessel over water in the pneumatic
rh, so as to communicate with the atmosphere through the medium
ater, that gas must constantly be filtring through the water into the
sphere, whilst the atmospheric air is filtring through the water the
•ary way, to supply its place in the*vessel; so that in due time the air
e vessel becomes atmospheric, as various chemists have experienced.
:r in this respect is like an earthenware retort: it admits the gases to
oth ways at the same time.
[t is not easy to assign a reason why water should be so permeable to
mic acid, &c., and not to the other gases; and why there should be
; differences observable in the others. The densities %, %? and %4
most evidently a reference to a mechanical origin, but none whatever
chemical one. No mechanical equilibrium could take place if the den-
> of the gases within were not regulated by this law; but why the gases
Id not all agree in some one of these forms, I do not see any reason.
Upon the whole it appears that water, like earthenware, is incapable
rming a perfect barrier to any kind of air; but it differs from earthen-
in one respect; the last is alike permeable to all the gases, but water
DALTQN — THE ATOMIC THEORY 267
Is much more permeable to some gases than to others. Other liquids have
not been sufficiently examined in this respect.
Section q. On the Constitution of Solids
A solid body is one, the particles of which are in a state of equilib-
rium betwixt two great powers, attraction and repulsion, but in such a
manner that no change can be made in their distances without con-
siderable force.
Notwithstanding the hardness of solid bodies, or the difficulty of
moving the particles one amongst another, there are several that admit of
such motion without fracture, by the application of proper force, espe-
cially if assisted by heat. The ductility and malleability of the metals need
only to be mentioned. It should seem the particles glide along each other's
surface, somewhat like a piece o£ polished iron at the end of a magnet,
without being at all weakened in their cohesion. The absolute force of
cohesion, which constitutes the strength of bodies, is an enquiry of great
practical importance. It has been found by experiment that wires of the
several metals beneath, being each %Q of an inch in diameter, were just
broken by the annexed weights.
, Lead 29%
Tin 49%
Copper 299%
Brass 360 Pounds,
Silver 370
Iron 450
Gold 500
A piece of good oak, an inch square and a yard ±ong, will just bear
in the middle 330 Ibs. But such a piece of wood should not in practice
be trusted, for any length of time, with above % or % of that weight.
Iron is about 10 times as strong as oak, of the same dimensions.
One would be apt to suppose that strength and hardness ought to be
found proportionate to each other; but this is not the case. Glass is harder
than iron, yet the latter is much the stronger of the two.
Crystallization exhibits to us the effects of the natural arrangement of
the ultimate particles of various compound bodies; but we are scarcely yet
sufficiently acquainted with chemical synthesis and analysis to understand
the rationale of this process. The rhomboidal form may arise from the
proper position of 4, 6, 8, or 9 globular particles, the cubic form from 8
particles, the triangular form from 3, 6 or 10 particles, the hexahedral
prism from 7 particles, &c. Perhaps, in due time, we may be enabled to
ascertain the number and order of elementary particles, constituting any
given compound element, and from that determine the figure which it
will prefer on crystallization, and vice versa; but it seems premature to
form any theory on this subject till we have discovered from other prin-
ciples the number and order of the primary elements which combine to
268 MASTERWORKS OF SCIENCE
form some of the compound elements of most frequent occurrence; the
method for which we shall endeavour to point out in the ensuing chapter.
//. ON CHEMICAL SYNTHESIS
WHEN any body exists in the elastic state, its ultimate particles are sepa-
rated from each other to a much greater distance than in any other state;
each particle occupies the centre of a comparatively large sphere, and sup-
ports its dignity by keeping all the rest, which by their gravity, or other-
wise, are disposed to encroach up it, at a respectful distance. When we
attempt to conceive the number of particles in an atmosphere, it is some-
what like attempting- to conceive the number of stars in the universe; we
are confounded with the thought. But if we limit the subject, by taking a
given volume of any gas, we seem persuaded that, let the divisions be ever
so minute, the number of particles must be finite; just as in a given space
of the universe, the number of stars and planets cannot be infinite.
Chemical analysis and synthesis go no farther than to the separation
of particles one from another, and to their reunion. No new creation or
destruction of matter is within the reach of chemical agency. We might
as well attempt to introduce a new planet into the solar system, or to an-
nihilate one already in existence, as to create or destroy a particle of hy-
drogen. All the changes we can produce consist in separating particles
that are in a state of cohesion or combination, and joining those that were
previously at a distance.
In all chemical investigations, it has justly been considered an impor-
tant object to ascertain the relative weights of the simples which consti-
tute a compound. But unfortunately the enquiry has terminated here;
whereas from the relative weights in the mass, the relative weights of the
ultimate particles or atoms of the bodies might have been inferred, from
which their number and weight in various other compounds would ap-
pear, in order to assist and to guide future investigations, and to correct
their results. Now it is one great object of this work to shew the impor-
tance and advantage of ascertaining the relative weights of the ultimate
particles, both of simple and compound bodies, the number of simple
elementary particles which constitute one compound particle, and the
number of less compound particles which enter into the formation of one
more compound particle.
If there are two bodies, A and B, which are disposed to combine, the
following is the order in which the combinations may take place, be-
ginning with the most simple: namely,
i atom of A -f- i atom of B = i atom of C, binary.
1 atom of A + 2 atoms of B = I atom of D, ternary.
2 atoms of A + i atom of B = i atom of E, ternary.
i atom of A + 3 atoms of B r= i atom of F, quaternary.
3 atoms of A + i atom of B = i atom of G, quaternary.
&c. &c.
DALTQN — THE ATOMIC THEORY 269
The following general rules may be adopted as guides in all our in-
vestigations respecting chemical synthesis.
i st. When only one combination of two bodies can be obtained, it
must be presumed to be a binary one, unless some cause appear to the
contrary.
2d. When two combinations are observed, they must be presumed to
be a binary and a ternary.
3d. When three combinations are obtained, we may expect one to be
a binary, and the other two ternary.
4th. When four combinations are observed, we should expect one
binary, two ternary, and one quaternary, &c.
5th. A binary compound should always be specifically heavier than
the mere mixture of its two ingredients.
6th. A ternary compound should be specifically heavier than the mix-
ture of a binary and a simple, which would, if combined, constitute it; &c.
7th. The above rules and observations equally apply when two
bodies, such as C and D, D and E, &c., are combined.
From the application of these rules to the chemical facts already well
ascertained, we deduce the following conclusions: ist. That water is a
binary compound of hydrogen and oxygen, and the relative weights of the
two elementary atoms are as 1:7, nearly; 2d. That ammonia is a binary
compound of hydrogen and azote, and the relative weights of the two
atoms are as 1:5, nearly; 3d. That nitrous gas is a binary compound of
azote and oxygen, the atoms of which weigh 5 and 7 respectively; that
nitric acid is a binary or ternary compound according as it is derived, and
consists of one atom of azote and two of oxygen, together weighing 19;
that nitrous oxide is a compound similar to nitric acid, and consists of
one atom of oxygen and two of azote, weighing 17; that nitrous acid is a
binary compound of nitric acid and nitrous gas, weighing 31; that oxy-
nitric acid is a binary compound of nitric acid and oxygen, weighing 26;
4th. That carbonic oxide is a binary compound, consisting of one atom of
charcoal and one of oxygen, together weighing nearly 12; that carbonic
acid is a ternary compound (but sometimes binary), consisting of one
atom of charcoal and two of oxygen, weighing 19; &c., &c. In all these
cases the weights are expressed in atoms of hydrogen, each of which is
denoted by unity.
From the novelty as well as importance of the ideas suggested in this
chapter, it is deemed expedient to give a plate exhibiting the mode of
combination in some of the more simple cases. The elements or atoms of
such bodies as are conceived at present to be simple are denoted by a
small circle, with some distinctive mark; and the combinations consist in
the juxtaposition of two or more of these; when three or more particles of
elastic fluids are combined together in one, it is to be supposed that the
partiples of the same kind repel each other, and therefore take their
stations accordingly.
270
MASTERWORKS OF SCIENCE
i 2, 3 4 6 €> 7 8
© (D • O ©
ii
o
© © ©
9 10 ii i2 i3
IS
17 IB 19 20
Binary
23 24
©O OXD (DO ©• O®
Ikrnary
27 28
29
(DO® OCDO O«O 0®O
Qtutternary
3O
33
36
DALTON — THE ATOMIC THEORY 271
EXPLANATION OF PLATE
This plate contains the arbitrary marks or signs chosen to represent
the several chemical elements or ultimate particles.
1. Hydrog. its rel. weight ... i n. Strontites 46
2. Azote 5 12. Barytes 68
3. Carbone or charcoal 5 13. Iron 38
4. Oxygen 7 14- Zinc 56
5. Phosphorus 9 15- Copper 56
6. Sulphur 13 16. Lead 95
7. Magnesia 20 17. Silver 100
8. Lime 23 18. Platina 100
9. Soda 28 19. Gold 140
10. Potash 42 20. Mercury 167
21. An atom of water or steam, composed of i of oxygen and i of
hydrogen, retained in physical contact by a strong affinity, and
supposed to be surrounded by a common atmosphere of heat;
its relative weight = 8
22. An atom of ammonia, composed of i of azote and i of hydrogen 6
23. An atom of nitrous gas, composed of i of azote and i of oxygen 12
24. An atom of olefiant gas, composed of i of carbone and i of
hydrogen 6
25.. An atom of carbonic oxide composed of I of carbone and i of
oxygen I2
26. An atom of nitrous oxide, 2 azote-|-i oxygen 17
27. An atom of nitric acid, i azote-(-2 oxygen 19
28. An atom of carbonic acid, i carbone-f-2 oxygen 19
29. An atom of carburetted hydrogen, i carbone~j-2 hydrogen 7
30. An atom of oxynitric acid, i azote-f~3 oxygen 26
31. An atom of sulphuric acid, i sulphur-f3 oxygen 34
32. An atom of sulphuretted hydrogen, i sulphur+3 hydrogen 16
33. An atom of alcohol, 3 carbone-j-i hydrogen 16
34. An atom of nitrous acid, i nitric acid+i nitrous gas 31
35. An atom of acetous acid, 2 carbone+2 water .^ . . . . 26
36. An atom of nitrate of ammonia, i nitric acid+i ammonia+i
water 33
37. An atom of sugar, i alcohol-j-i carbonic acid 35
Enough has been given to shew the method; it will be quite unneces-
sary to devise characters and combinations of them to exhibit to view in this
way all the subjects that come under investigation; nor is it necessary to in- *
sist upon the accuracy of all these compounds, both in number and weight;
the principle will be entered into more particularly hereafter, as far as
respects the individual results. It is not to be understood that all those
particles marked as simple substances are necessarily such by the theory;
272 MASTERWORKS OF SCIENCE
they are only necessarily of such weights. Soda and potash, such as they
are found in combination with acids, are 28 and 42 respectively in weight;
but according to Mr. Davy's very important discoveries, they are metallic
oxides; the former then must be considered as composed of an atom of
metal, 21, and one of oxygen, 7; and the latter, of an atom of metal, 35,
and one of oxygen, 7. Or, soda contains 75 per cent metal and 25 oxygen;
potash, 83.3 metal and 16.7 oxygen. It is particularly remarkable that ac-
cording to the above-mentioned gentleman's essay on the Decomposition
and Composition of the fixed alkalies in the Philosophical Transactions (a
copy of which essay he has just favoured me with), it appears that "the
largest quantity of oxygen indicated by these experiments was, for potash
17, and for soda, 26 parts in 100, and the smallest 13 and 19."
PRINCIPLES OF GEOLOGY
by
CHARLES LYELL
CONTENTS
Principles of Geology
I. Geology Defined
II. Prejudices which Have Retarded the Progress of Geology
III. Doctrine of the Discordance of the Ancient and Modern Causes of
Change Controverted
IV. Farther Examination of the Question as to the Assumed Discord-
ance of the Ancient and Modern Causes of Change
V, On Former Changes in Physical Geography and Climate
VI. Supposed Intensity of Aqueous Forces at Remote Periods
VII. On the Supposed Former Intensity of the Igneous Forces
VEIL Uniformity in the Series of Past Changes in the Animate and In-
animate World
CHARLES LYELL
1797-1875
CHARLES LYELL, a devoted student of Dante and a good bota-
nist, had married the daughter of Thomas Smith of Yorkshire
and had settled in Forfarshire in Scotland. His eldest child —
the first of ten — was horn there in 1797 and named Charles. A
year later the family moved to Bartley Lodge in the New
Forest, in the extreme south of England. The boy had his
early training in private schools and at nineteen entered
Exeter College, Oxford. He took a very good degree in 1819
(second class in Classical Honors) and an M.A. in 1821.
Though he had early shown the traits of the amateur natural-
ist, he did not follow his father into botany, but assiduously
studied entomology. Before he had finished his undergraduate
work at Oxford, he had been attracted to geology by the lec-
tures of Dr. William Buckland. During a holiday he had noted
the evidence of recent changes in the coast line near Norwich;
he had used another holiday for a tour of the central Gram-
pians (in Scotland), and others for tours of the western isle
of Mull, and of Europe across the Juras and Alps to Florence.
His family afforded Lyell such expeditions. His choice took
him where he could foster his growing interest in geology.
When he settled in London in 1819 to read law — to
which he was faithful for ten years — at Lincoln's Inn, he natu-
rally joined the Linnaean Society and the Geological Society.
Four years later he became secretary of the Geological Society,
and in the next year read to its members a paper, "On a Re-
cent Formation of Freshwater Limestone in Forfarshire." In
this paper he emphasized the resemblance between deposits
in ancient and modern lakes. He was already moving toward
the generalization which his subsequent work in geology is
based upon: that the processes o£ the past must be judged by
those now in progress.
Another paper resulting from his tour of the Grampians,
276 MASTERWORKS OF SCIENCE
"On a Dike of Serpentine in the County o£ Forfar," appeared
in the Edinburgh Journal of Science in 1825, Ly ell's first pub-
lished paper. The following year he was elected a Fellow o£
the Royal Society. Now he collaborated with Dr. Mandell in
some studies of the cretaceous beds of southeast England, and
he began to meet the first of those great scientists who
were to be his lifelong friends: Cuvier, Laplace, Arago, Hum-
boldt.
An article by Lyell in the Quarterly Review in 1827 criti-
cizes those who measure facts not by observation but by ap-
peal to the literal text of the Holy Scriptures. Lyell did not
intend an attack upon revealed religion, for he was all his life
a religious man. Convinced of the validity of the methods of
the natural scientist, he saw that scientists' results could not
have their appropriate influence so long as misguided, even
ignorant, criticism misinterpreted them. Once convinced, he
spoke his mind. About the same time he reached another con-
clusion which entered into his later theorizing: that negative
evidence can never be conclusive. Already, in distinction from
his predecessors in whose times paleontology was an infant
science, he was ardently following the discoveries and conclu-
sions of the paleontologists. At the moment he was concerned
with the claims that birds and mammals were created late in
the history of the world, inasmuch as no evidence of them
had been discovered in the earlier geologic strata. He insisted
that the evidence, being negative, proved nothing; subsequent
discoveries proved him at least partly right.
In 18283 Lyell journeyed in Auvergne, went on to Padua,
and then, despite some physical hazards involved, proceeded
to Sicily. There he saw evidence of recent mountain building
and of land elevation. He was now confirmed in his earlier
idea that existing causes have always been the efficient causes
of geological change. On the same trip, in concurrence with
the French conchologist Deshayes, he observed that the rela-
tive ages of the deposits in the more recent rocks could be
determined by the proportion among their molluscan fossils
o£ extinct to still extant species. He therefore classified the
strata o£ the tertiary rocks in the order of their age as Eocene
(dawn o£ recent), Miocene (less recent), and Pliocene (more
recent). This classification he presented to the public in the
third volume of the Principles of Geology in 1833.
The first volume of the Principles had appeared in 1830;
the completed work did not appear until 1834. It was revolu-
tionary. In 1830 the prevailing method among geologists o£
explaining the physical characteristics of the earth's crust was
to adumbrate numerous cataclysms in the course of its his-
tory. Some geologists believed that a series of fiery, volcanic
LYELL — PRINCIPLES OF GEOLOGY 277
crises had occurred at various times. Others, like Buckland,
talked of recurrent deluges. Still others held that there had
been catastrophes of both kinds. To the catastrophic school of
thought the Principles gave a mortal wound. Appealing to
paleontological evidence and logically marshaling his tremen-
dous data, Lyell proved — what James Hutton had earlier sug-
gested— that the phenomena could all be explained on the
basis of still acting . causes as the constant efficient causes.
Simultaneously he enormously extended the concept of geo-
logic time. Whereas his predecessors and even his early con-
temporaries confined the history of the world to a few thou-
sand years, he showed that in this history time must be reck-
oned in eons, in millions of years.
In 1831, Lyell had been named professor of geology in
King's College, London7 But he never cared for his profes-
sorial duties; he actually gave only two courses of lectures
(1832, 1833) at the college. In 1832 he delivered seven lectures
at the Royal Institution. In 1834 the Royal Society voted him
one of its two gold medals for the Principles.
Meantime, in 1832, Lyell had married Mary Horner,
daughter of a man influential in the early history of the
Geological Society. She became the constant companion of his
many expeditions, and because of his increasing myopia she
served him as amanuensis. They both enjoyed social life, and
their house in Harley Street was a regular meeting place for a
group of friends who in their letters have made it famous —
Hallam, Dean Milman, Rogers, Darwin. They both enjoyed
traveling, and they journeyed to the United States in 1841, in
1845, in 1852, and again in 1853; to the Canary Islands in
1854; frequently to various parts of Europe. When he was
more than sixty Lyell went once more to Sicily to climb Etna
and to study the formation of its lava beds.
Two of the trips to the United States were undertaken
partly that Lyell might deliver the Lowell Institute lectures in
Boston; another, that he might serve as British Commissioner
to the New York International Exhibition of 1853. Every
journey resulted in a paper — such as the study of changes in
the level of the Baltic in recent times (1835) — or a book —
such as Travels in North America with Geological Observa-
tions, 1845. Besides, Lyell wrote other papers indefatigably —
seventy-six of them for the Royal Society — and so constantly
revised his Principles, bringing it up to date, that no two of
the eleven editions which appeared in his lifetime are identi-
cal. In 1838 he published an elaborated portion of the original
Principles as a separate work, Elements of Geology, a descrip-
tive textbook. In 1863 he completed his Antiquity of Man,
278 MASTERWQRKS OF SCIENCE
and in 1871 published The Students' Elements of Geology,
long the one standard text for beginners in geology.
Lyell served the Geological Society as president in 1835
and 1836, and again in 1849 and 1850, Queen Victoria
knighted him in 1848 and raised him to a baronetcy in 1864.
Oxford granted him the degree of D.C.L. in 1854. In 1862 the
Institute of France elected him a foreign correspondent, and
in 1864 the British Association made him its president. He
was everywhere recognized in his latest years as one of Eng-
land's foremost scientists. When he died in 1875, he was
buried in Westminster Abbey among his peers.
LyelPs friends greatly mourned his death; so did the
learned world which knew his great and honest abilities. He
had early refused to accept Darwin's new theories, friends
though the two men were. Yet it was he who procured the
publication of Darwin's and Wallace's first studies; and when
the accumulated evidence persuaded him of the evolutionary
doctrine, no one more wholeheartedly gave it support. The
change in view was characteristic of the man. Greatly learned,
he never became pedantic; tenacious in his beliefs, he was
always open to reason.
PRINCIPLES OF GEOLOGY
I. Geology Defined
GEOLOGY is the science which investigates the successive changes that have
taken place in the organic and inorganic kingdoms of nature; it inquires
into the causes of these changes, and the influence which they have
exerted in modifying the surface and external structure of our planet.
Geology is intimately related to almost all the physical sciences, as
history is to the moral. An historian should, if possible, be at once pro-
foundly acquainted with ethics, politics, jurisprudence, the military art,
theology; in a word, with all branches of knowledge by which any insight
into human affairs, or into the moral and intellectual nature of man, can
be obtained. It would be no less desirable that a geologist should be well
versed in chemistry, natural philosophy, mineralogy, zoology, comparative
anatomy, botany; in short, in every science relating to organic and inor--
ganic nature. With these accomplishments, the historian and geologist
would rarely fail to draw correct and philosophical conclusions from the
various monuments transmitted to them of former occurrences. They
would know to what combination o£ causes analogous effects were refer-
able, and they would often be enabled to supply, by inference, information
concerning many events unrecorded in the defective archives of former
ages. But as such extensive acquisitions are scarcely within the reach of
any individual, it is necessary that men who have devoted their lives to
different departments should unite their efforts; and as the historian re-
ceives assistance from the antiquary, and from those who have cultivated
different branches of moral and political science, so the geologist should
avail himself of the aid of many naturalists, and particularly of those wha
have studied the fossil remains of lost species of animals and plants.
The analogy, however, of the monuments consulted in geology, and
those available in history, extends no farther than to one class of historical
monuments — those which may be said to be undesignedly commemora-
tive of former events. The canoes, for example, and stone hatchets found
in our peat bogs, afford an insight into the rude arts and manners of the
earliest inhabitants of our island; the buried coin fixes the date of the
reign of some Roman emperor; the ancient encampment indicates the dis«
trkts once occupied by invading armies, and the former method of con-
structing military defences: the Egyptian mummies throw light on the art
of embalming, the rites of sepulture, or the average stature of the human.
280 MASTERWORKS OF SCIENCE
race In ancient Egypt. This class of memorials yields to no other in au-
thenticity, but it constitutes a small part only of the resources on which
the historian relies, whereas in geology it forms the only kind of evidence
which Is at our command. For this reason we must not expect to obtain a
full and connected account of any series of events beyond the reach of
history. But the testimony of geological monuments, if frequently imper-
fect, possesses at least the advantage of being free from all intentional
misrepresentation. We may be deceived in the inferences which we draw,
in the same manner as we often mistake the nature and import of phe-
nomena observed in the daily course of nature; but our liability to err is
confined to the interpretation, and, if this be correct, our information is
certain.
II Prejudices Which Have Retarded the Progress of
Geology
IF WE REFLECT on the history of the progress of geology, we perceive that
there have been great fluctuations of opinion respecting the nature of the
causes to which all former changes of the earth's surface are referable. The
first observers conceived the monuments which the geologist endeavours
to decipher to relate to an original state of the earth, or to a period when
there were causes in activity, distinct, in kind and degree, from those now
constituting the economy of nature. These views were gradually modified,
and some of them entirely abandoned in proportion as observations were
multiplied, and the signs of former mutations more skilfully interpreted.
Many appearances, which had for a long time been regarded as indicating
mysterious and extraordinary agency, were finally recognized as the neces-
sary result of the laws now governing the material world; and the discov-
ery of this unlooked-for conformity has at length induced some philoso-
phers to infer that, during the ages contemplated in geology, there has
never been any interruption to the agency of the same uniform laws of
change. The same assemblage of general causes, they conceive, may have
been sufficient to produce, by their various combinations, the endless di-
versity of effects, of which the shell of the earth has preserved the memo-
rials; and, consistently with these principles, the recurrence of analogous
changes is expected by them in time to come.
Prepossessions in regard to the duration of past time. — Now the
reader may easily satisfy himself that, however undeviating the course of
nature may have been from the earliest epochs, it was impossible for the
first cultivators of geology to come to such a conclusion, so long as they
were under a delusion as to the age of the world, and the date of the first
creation of animate beings. However fantastical some theories of the six-
teenth century may now appear to us — however unworthy of men of great
LYELL — PRINCIPLES OF GEOLOGY 281
talent and sound judgment — we may rest assured that, if the same mis-
conception now prevailed in regard to the memorials of human transac-
tions, it would give rise to a similar train of absurdities. Let us imagine,
for example, that Champollion, and the French and Tuscan literati lately
engaged in exploring the antiquities of Egypt, had visited that country
with a firm belief that the banks of the Nile were never peopled by the
human race before the beginning of the nineteenth century, and that their
faith in this dogma was as difficult to shake as the opinion of our ances-
tors, that the earth was never the abode of living beings until the creation
of the present continents, and of the species now existing — it is easy to
perceive what extravagant systems they would frame, while under the in-
, fluence of this delusion, to account for the monuments discovered in
Egypt. The sight of the pyramids, obelisks, colossal statues, and ruined
temples, would fill them with such astonishment, that for a time they
would be as men spellbound — wholly incapable of reasoning with sobri-
ety. They might incline at first to refer the construction of such stupen-
dous works to some superhuman powers of a primeval world. A system
might be invented resembling that so gravely advanced by Manetho, who
relates that a dynasty of gods originally ruled in Egypt, of whom Vulcan,
the first monarch, reigned nine thousand years; after whom came Her-
cules and other demigods, who were at last succeeded by human kings.
These speculations, if advocated by eloquent writers, would not fail
to attract many zealous votaries, for they would relieve men from the
painful necessity of renouncing preconceived opinions. But when one gen-
eration had passed away, and another, not compromised to the support of
antiquated dogmas, had succeeded, they would review the evidence af-
forded by mummies more impartially, and would no longer controvert the
preliminary question, that human beings had lived in Egypt before the
nineteenth century: so that when a hundred years perhaps had been lost^
the industry and talents of the philosopher would be at last directed to
the elucidation of points of real historical importance.
But the above arguments are aimed against one only of many preju-
dices with which the earlier geologists had to contend. Even when they
conceded that the earth had been peopled with animate beings at an
earlier period than was at first supposed, they had no conception that the
quantity of time bore so great a proportion to the historical era as is now
generally conceded. How fatal every error as to the quantity of time must
prove to the introduction of rational views concerning the state of things
in former ages may be conceived by supposing the annals of the civil and
military transactions of a great nation to be perused under the impression
that they occurred in a period of one hundred instead of two thousand
years. Such a portion of history would immediately assume the air o£ a
romance; the events, would seem devoid of credibility, and inconsistent
with the present course of human affairs. A crowd of Incidents would fol-
low each other in thick succession. Armies and fleets would appear to be
assembled only to be destroyed, and cities built merely to fall in ruins.
There would be the most violent transitions from foreign or intestine war
282 MASTERWORKS OF SCIENCE
to periods of profound peace, and the works effected during the years of
disorder or tranquillity would appear alike superhuman in magnitude.
We should be warranted in ascribing the erection of the great pyra-
mid to superhuman power, if we were convinced that it was raised in one
day; and if we imagine, in the same manner, a continent or mountain
chain to have been elevated, during an equally small fraction of the time
which was really occupied in upheaving it, we might then be justified in
inferring that the subterranean movements were once far more energetic
than in our own times. We know that during one earthquake the coast of
Chili may be raised for a hundred miles to the average height of about
three feet. A repetition of two thousand shocks, of equal violence, might
produce a mountain chain one hundred miles long and six thousand feet
high. Now, should one or two only of these convulsions happen in a cen-
tury, it would be consistent with the order of events experienced by the
Chilians from the earliest times: but if the whole of them were to occur in
the next hundred years, the entire district must be depopulated, scarcely
any animals or plants could survive, and the surface would be one con*
fused heap of ruin and desolation.
Prejudices arising from our peculiar position as inhabitants of the
land. — The sources of prejudice hitherto considered may be deemed pe-
culiar for the most part to the infancy of the science, but others are com-
mon to the first cultivators of geology and to ourselves, and are all singu-
larly calculated to produce the same deception and to strengthen our
belief that the course of nature in the earlier ages differed widely from
that now established.
The first and greatest difficulty consists in an habitual unconscious-
ness that our position as observers is essentially unfavourable, when we
endeavour to estimate the nature and magnitude of the changes now in
progress. In consequence of our inattention to this subject, we are liable
to serious mistakes in contrasting the present with former states of the
globe. As dwellers on the land, we inhabit about a fourth part of the sur-
face; and that portion is almost exclusively a theatre of decay, and not of
reproduction. We know, indeed, that new deposits are annually formed in
seas and lakes, and that every year some new igneous rocks are produced
in the bowels of the earth, but we cannot watch the progress of their for-
mation; and as they are only present to our minds by the aid of reflection,
it requires an effort both of the reason and the imagination to appreciate
duly their importance. It is, therefore, not surprising that we estimate
very imperfectly the result of operations thus invisible to us; and that,
when analogous results of former epochs are presented to our inspection,
we cannot immediately recognise the analogy. He who has observed the
quarrying of stone from a rock, and has seen it shipped for some distant
port, and then endeavours to conceive what kind of edifice will be raised
by the materials, is in the same predicament as a geologist, who, while he
is confined to, the land, sees the decomposition of rocks, and the transpor-
tation of matter by rivers to the sea, and then endeavours to picture to
himself the new strata which Nature is building beneath the waters.
LYELL — PRINCIPLES OF GEOLOGY 283
Prejudices arising from our not seeing subterranean changes. — Nor
is his position less unfavourable when, beholding a volcanic eruption, he
tries to conceive what changes the column of lava has produced, in its
passage upwards, on the intersected strata; or what form the melted mat-
ter may assume at great depths on cooling; or what may be the extent of
the subterranean rivers and reservoirs of liquid matter far beneath the
surface. It should, therefore, be remembered that the task imposed on
those who study the earth's history requires no ordinary share of discre-
tion; for we are precluded from collating the corresponding parts of the
system of things as it exists now and as it existed at former periods. If we
were inhabitants of another element — if the great ocean were our domain,
instead of the narrow limits of the land — our difficulties would be consid-
erably lessened; while, on the other hand, there can be little doubt, al-
though the reader may, perhaps, smile at the bare suggestion of such an
idea, that an amphibious being, who should possess our faculties, would
still more easily arrive at sound theoretical opinions in geology, since he
might behold, on the one hand, the decomposition of rocks in the atmos-
phere or the transportation of matter by running water; and, on the other,
examine the deposition of sediment in the sea and the imbedding of ani-
mal and vegetable remains in new strata. He might ascertain, by direct
observation, the action of a mountain torrent as well as of a marine cur-
rent; might compare the products of volcanos poured out upon the land
with those ejected beneath the waters; and might mark, on the one hand,
the growth of the forest, and, on the other, that of the coral reef. Yet,
even with these advantages, he would be liable to fall into the greatest
errors, when endeavouring to reason on rocks of subterranean origin. He
would seek in vain, within the sphere of his observation, for any direct
analogy to the process of their formation, and would therefore be in
danger of attributing them, wherever they are upraised to view, to some
"primeval state of nature."
For more than two centuries the shelly strata of the Sub-Apennine
hills afforded matter of speculation to the early geologists of Italy, and
few of them had any suspicion that similar deposits were then forming in
the neighbouring sea. Some imagined that the strata, so rich in organic
remains, instead of being due to secondary agents, had been so created in
the beginning by the fiat of the Almighty. Others ascribed the imbedded
fossil bodies to some plastic power which resided in the earth in the early
ages of the world. In what manner were these dogmas at length ex-
ploded? The fossil relics were carefully compared with their living ana-
logues, and all doubts as to their organic origin were eventually dispelled.
So, also, in regard to the containing beds of mud, sand, and limestone:
those parts of the bottom of the sea were examined where shells are now
becoming annually entombed in new deposits. Donati explored the bed of
the Adriatic and found the closest resemblance between the strata there
forming and those which constituted hills above a thousand feet high in
various parts of the Italian peninsula. He ascertained by dredging that
living testacea were there grouped together in precisely the same manner
284 MASTERWQRKS OF SCIENCE
as were their fossil analogues in the inland strata; and while some of the
recent shells of the Adriatic were becoming incrusted with calcareous
rock, he discovered that others had been newly buried in sand and clay,
precisely as fossil shells occur in the Sub-Apennine hills.
The establishment, from time to time, of numerous points of identi-
fication drew at length from geologists a reluctant admission that there
was more correspondence between the condition of the globe at former
eras and now, and more uniformity in the laws which have regulated the
changes of its surface, than they at first imagined. If, in this state of the
science, they still despaired of reconciling every class of geological phe-
nomena to the operations of ordinary causes, even by straining analogy to
the utmost limits of credibility, we might have expected, at least, that the
balance of probability would now have been presumed to incline toward
the close analogy of the ancient and modern causes. But, after repeated
experience of the failure of attempts to speculate on geological monu-
ments, as belonging to a distinct order of things, new sects continued to
persevere in the principles adopted by their predecessors. They still began,
as each new problem presented itself, whether relating to the animate or
inanimate world, to assume an original and dissimilar order of nature;
and when at length they approximated, or entirely came round to an
opposite opinion, it was always with the feeling that they were conceding
what they had been justified a priori in deeming improbable. In a word,
the same men who, as natural philosophers, would have been most incred-
ulous respecting any deviations from the known course of nature, if
reported to have happened in their own time, were equally disposed, as
geologists, to expect the proofs of such deviation at every period of the
past.
Ill Doctrine of the Discordance of the Ancient and
Modern Causes of Change Controverted
Climate of the northern hemisphere formerly different. — Proofs of former
revolutions in climate, as deduced from fossil remains, have afforded one
of the most popular objections to the theory which endeavours to explain
all geological changes by reference to those now in progress on the earth.
The probable causes, - therefore, of fluctuations in climate may first be
treated of.
That the climate of the northern hemisphere has undergone an im-
portant change, and that its mean annual temperature must once have
more nearly resembled that now experienced within the tropics, was the
opinion of some of the first naturalists who investigated the contents of
the ancient strata. Their conjecture became more probable when the
shells and corals of the older tertiary and many secondary rocks were
LYELL — PRINCIPLES OF GEOLOGY 285
carefully examined; for the organic remains of these formations were
found to be intimately connected by generic affinity with species now
living in warmer latitudes. At a later period, many reptiles, such as turtles,
tortoises, and large saurian animals, were discovered in European forma-
tions in great abundance; and they supplied new and powerful arguments,
from analogy, in support of the doctrine that the heat of the climate had
been great when our secondary strata were deposited. Lastly, when the
botanist turned his attention to the specific determination of fossil plants,
the evidence acquired still further confirmation; for the flora of a country
is peculiarly influenced by temperature: and the ancient vegetation of
the earth 'might have been expected more readily than the forms of
animals to have afforded conflicting proofs, had the popular theory been
without foundation. When the examination of fossil remains was ex-
tended to rocks in the most northern parts of Europe and North America,
and even to the Arctic regions, indications of the same revolution in
climate were discovered.
Proofs -from -fossil shells in tertiary strata. — In Sicily, Calabria, and in
the neighbourhood of Naples, the fossil testaceaof the most modern tertiary
formations belong almost entirely to species now inhabiting the Mediter-
ranean; but as we proceed northwards in the Italian peninsula we find
in the strata called Sub-Apennine an assemblage of fossil shells departing
somewhat more widely from the type of the neighbouring seas. The pro-
portion of species identifiable with those now living in the Mediterranean
is still considerable; but it no longer predominates, as in the South of Italy
and part of Sicily, over the unknown species. Although occurring in
localities which are removed several degrees farther from the equator
(as at Siena, Parmi, Asti, &c.), the shells yield clear indications of a
warmer climate. This evidence is of great weight, and is not neutralized
by any facts of a conflicting character; such, for instance, as the association,
in the same group, of individuals referable to species now confined to
arctic regions.
On comparing the fossils of the tertiary deposits of Paris and London
with those of Bordeaux, and these again with the more modern strata
of Sicily, we should at first expect that they would each indicate a higher
temperature in proportion as they are situated farther to the south. But
the contrary is true; of the shells belonging to these several groups,
whether freshwater or marine, some are of extinct, others of living species.
Those found in the older, or Eocene, deposits of Paris and London,
although six or seven degrees to the north of the Miocene strata at
Bordeaux, afford evidence of a warmer climate; while those o£ Bordeaux
Imply that the sea In which they lived was of a higher temperature than
that of Sicily, where the shelly strata were formed six or seven degrees
nearer to the equator. In these cases the greater antiquity of the several
formations (the Parisian being the oldest and the Sicilian the newest) has
more than counterbalanced the Influence which latitude would otherwise
exert, and this phenomenon clearly points to a gradual and successive
refrigeration of climate.
286 MASTERWORKS OF SCIENCE
Siberian mammoths. — It will naturally be asked whether some recent
geological discoveries bringing evidence to light of a colder, or, as it has
been termed, "glacial epoch," towards the close of the tertiary periods
throughout the northern hemisphere, does not conflict with the theory
above alluded to, of a warmer temperature having prevailed in the eras
of the Eocene, Miocene, and Pliocene formations. In answer to this
enquiry, it may certainly be affirmed that an oscillation of climate has
occurred in times Immediately antecedent to the peopling of the earth
by man; but proof of the intercalation of a less genial climate at an era
when nearly all the marine and terrestrial testacea had already become
specifically the same as those now living by no means rebuts the con-
clusion previously drawn, in favour of a warmer condition of the globe,
during the ages which elapsed while the tertiary strata were deposited.
In some of the most superficial patches of sand, gravel, and loam, scat-
tered very generally over Europe, and containing recent shells, the remains
of extinct species of land quadrupeds have been found, especially in places
where the alluvial matter appears to have been washed into small lakes
or into depressions in the plains bordering ancient rivers. Among the
extinct mammalia thus entombed, we find species of the elephant, rhi-
noceros, hippopotamus, bear, hyaena, lion, tiger, monkey (macacus), and
many others; consisting partly of genera now confined to warmer regions.
It is certainly probable that when some of these quadrupeds abounded
in Europe, the climate was milder than that now experienced. The hip-
popotamus, for example. Is now only met with where the temperature of
the water Is warm and nearly uniform throughout the year, and where
the rivers are never frozen over. Yet when the great fossil species (Hip-
potamus major Cuv.) inhabited England, the testacea of our country were
nearly the same as those now existing, and the climate cannot be supposed
to have been very hot.
The mammoth also appears to have existed in England when the
temperature of our latitudes could not have been very different from
that which now prevails; for remains of this animal have been found
at North Cliff, In the county of York, in a lacustrine formation, in which
all the land and freshwater shells, thirteen in number, can be Identified
with species and varieties now existing in that county. Bones of the bison
also, an animal now inhabiting a cold or temperate climate, have been
found in the same place. That these quadrupeds, and the Indigenous
species of testacea associated with them, were all contemporary inhabi-
tants of Yorkshire has been established by unequivocal proof.
Recent investigations have placed beyond all doubt the important fact
that a species of tiger, identical with that of Bengal, is common in the
neighbourhood of Lake Aral, near Sussac, In the forty-fifth degree of
north latitude; and from time to time this animal is now seen in Siberia
in a latitude as far north as the parallel of Berlin and Hamburg.
Now, if the Indian tiger can range in our own times to the southern
borders of Siberia or skirt the snows of the Himalaya, and if the puma
can reach the fifty-third degree of latitude in South America, we may
LYELL — PRINCIPLES OF GEOLOGY 287
easily understand how large species of the same genera may once have
inhabited our temperate climate. The mammoth (E. primigenius) , already
alluded to,, as occurring fossil in England, was decidedly different from
the two existing species of elephants, one of which is limited to Asia,
south of the thirty-first degree of north latitude, the other to Africa, where
it extends as far south as the Cape of Good Hope.
Pallas and other writers describe the bones of the mammoth as
abounding throughout all the Lowland of Siberia, stretching in a direction
west and east, from the borders of Europe to the extreme point nearest
America, and south and north, from the base of the mountains of Central
Asia to tie shores of the Arctic Sea. Within this space, scarcely inferior in
area to the whole of Europe, fossil ivory has been collected almost every-
where, on the banks of the Irtish, Obi, Yenesei, and other rivers. But it is
not on the Obi nor the Yenesei, but on the Lena, farther to the east,
where, in the same parallels of latitude, the cold is far more intense, that
fossil remains have been found in the most wonderful state of preser-
vation. In 1772, Pallas obtained from Wiljuiskoi, in latitude 64°, from the
banks of the Wiijui, a tributary of the Lena, the carcass of a rhinoceros
(R. tichorhinus}, taken from the sand in which it must have remained
congealed for ages, the soil of that region being always frozen to within
a slight depth of the surface. This carcass was compared to a natural
mummy, and emitted an odour like putrid flesh, part of the skin being
still covered with black and grey hairs.
After more than thirty years, the entire carcass of a mammoth (or
extinct species of elephant) was obtained in 1803, by Mr. Adams, much
farther to the north. It fell from a mass of ice, in which it had been
encased, on the banks of the Lena, in latitude 70°; and so perfectly had
the soft parts of the carcass been preserved that the flesh, as it lay, was
devoured by wolves and bears. This skeleton is still in the museum of
St. Petersburg, the head retaining its Integument and many of the liga-
ments entire. The skin of the animal was covered, first, with black bristles,
thicker than horsehair, from twelve to sixteen inches in length; secondly,
with hair of a reddish-brown colour, about four inches long; and thirdly,
with wool of the same colour as the hair, about an inch in length. Of the
fur, upwards of thirty pounds' weight were gathered from the wet sand-
bank. The individual was nine feet high and sixteen feet long, without
reckoning the large curved tusks: a size rarely surpassed by the largest
living male elephants.
It is evident, then, that the mammoth, instead of being naked, like
the living Indian and African elephants, was enveloped in a thick shaggy
covering of fur, probably as impenetrable to rain and cold as that of the
musk ox. The species may have been fitted by nature to withstand the
vicissitudes of a northern climate; and it is certain that, from the moment
when the carcasses, both of the rhinoceros and elephant, above described,
were buried in Siberia, in latitudes 64° and 70° north, the soil must have
remained frozen and the atmosphere nearly as cold as at this day.
On considering all the facts above enumerated, it seems reasonable
288 MASTERWORKS OF SCIENCE
to Imagine that a large region in Central Asia, including, perhaps, the
southern half of Siberia, enjoyed, at no very remote period in the earth's
history, a temperate climate, sufficiently mild to afford food for numerous
herds of elephants and rhinoceroses, of species distinct from those now
living. But the age of this fauna was comparatively modern in the earth's
history. It appears that when the oldest or Eocene tertiary deposits were
formed, a warm temperature pervaded the European seas and lands. Shells
of the genus Nautilus and other forms characteristic of tropical latitudes;
fossil reptiles, such as the crocodile, turtle, and tortoise; plants, such as
palms, some of them allied to the cocoanut, the screw pine, the custard
apple, and the acacia, all lead to this conclusion. This flora and fauna were
followed by those of the Miocene formation, in which indications of a
southern, but less tropical, climate are detected. Finally, the Pliocene
deposits, which come next in succession, exhibit in their organic remains
a much nearer approach to the state of things now prevailing in corre-
sponding latitudes. It was towards the close of this period that the seas
of the northern hemisphere became more and more filled with floating
icebergs often charged with erratic blocks, so that the waters and the
atmosphere were chilled by the melting ice, and an arctic fauna enabled,
for a time, to invade the temperate latitudes both of North America and
Europe. The extinction of a considerable number of land quadrupeds and
aquatic mollusca was gradually brought about by the increasing severity of
the cold; but many species survived this revolution in climate, either by
their capacity of living under a variety of conditions, or by migrating for
a time to more southern lands and seas. At length, by modifications in the
physical geography of the northern regions, and the cessation of floating
ice on the eastern side of the Atlantic, the cold was moderated, and a
milder climate ensued, such as we now enjoy in Europe.
Proofs from fossils in secondary and still older strata. — A great inter-
val of time appears to have elapsed between the formation of the second-
ary strata, which constitute the principal portion of the elevated land in
Europe, and the origin of the Eocene deposits. If we examine the rocks
from the chalk to the new red sandstone inclusive, we find many distinct
assemblages of fossils entombed in them, all of unknown species, and
many of them referable to genera and families now most abundant be-
tween the tropics. Among the most remarkable are reptiles of gigantic
size; some of them herbivorous, others carnivorous, and far exceeding
in size any now known even in the torrid zone. The genera are for the
most part extinct, but some of them, as the crocodile and monitor, have
still representatives in the warmer parts of the earth. Coral reefs also were
evidently numerous in the seas of the same periods, composed of species
often belonging to genera now characteristic of a tropical climate. The
number of large chambered shells also, including the nautilus, leads us
to infer an elevated temperature; and the associated fossil plants, although
imperfectly known, tend to the same conclusion, the Cycadeae constituting
the most numerous family.
But it is from the more ancient coal deposits that the most extraordi-
LYELL — PRINCIPLES OF GEOLOGY 289
nary evidence has been supplied in proof of the former existence of a
very different climate, a climate which seems to have been moist, warm,
and extremely uniform, in those very latitudes which are now the colder,
and in regard to temperature the most variable regions of the globe. We
learn from the researches of Adolphe Brongniart, Goeppert, and other
botanists that in the flora of the Carboniferous era there was a great pre-
dominance of ferns, some of which were arborescent; as, for example,
Caulopteris, Protopteris, and Psarronius; nor can this be accounted for, as
some have supposed, by the greater power which ferns possess of resisting
maceration in water. This prevalence of ferns indicates a moist, equable,
and temperate climate, and the absence of any severe cold; for such are
the conditions which, at the present day, are found to be most favourable
to that tribe of plants. It is only in the islands of the tropical oceans, and
of the southern temperate zone, such as Norfolk Island, Otaheite, the
Sandwich Islands, Tristan d'Acunha, and New Zealand, that we find any
near approach to that remarkable preponderance of ferns which is charac-
teristic of the carboniferous flora. It has been observed that tree ferns and
other forms of vegetation which flourished most luxuriantly within the
tropics extend to a much greater distance from the equator in the south-
ern hemisphere than in the northern, being found even as far as 46° south
latitude in New Zealand. There is little doubt that this is owing to the
more uniform and moist climate occasioned by the greater proportional
area of sea. Next to ferns and pines, the most abundant vegetable forms
in the coal formation are the Calamites, Lepidodendra, Sigillariae, and
Stigmarise. These were formerly considered to be so closely allied to tropi-
cal genera, and to be so much greater in size than the corresponding tribes
now inhabiting equatorial latitudes, that they were thought to imply an
extremely hot as well as humid and equable climate. But recent discoveries
respecting the structure and relations of these fossil plants have shown
that they deviated so widely from all existing types in the vegetable world
that we have more reason to infer from this evidence a widely different
climate in the Carboniferous era, as compared to that now prevailing, than
a temperature extremely elevated. Palms, if not entirely wanting when
the strata of the carboniferous group were deposited, appear to have been
-exceedingly rare. The Coniferae, on the other hand, so abundantly met
with in the coal, resemble Araucariae in structure, a family of the fir tribe
characteristic at present of the milder regions of the southern hemisphere,
such as Chili, Brazil, New Holland, and Norfolk Island.
"In regard to the geographical extent of the ancient vegetation, it
was not confined/' says M. Brongniart, "to a small space, as to Europe,
for example; for the same forms are met with again at great distances.
Thus the coal plants of North America are, for the most part, identical
with those of Europe, and all belong to the same genera. Some specimens,
also, from Greenland, are referable to ferns, analogous to those of our
European coal mines."
To return, therefore, from this digression — the flora of the coal ap-
pears to indicate a uniform and mild temperature in the air, while the
290 MASTERWORKS OF SCIENCE
fossils of the contemporaneous mountain limestone, comprising abun-
dance of lamelllferous corals, large chambered cephalopods, and crinoidea,
naturally lead us to infer a considerable warmth in the waters of the
northern sea of the Carboniferous period. So also in regard to strata older
than the coal, they contain in high northern latitudes mountain masses of
corals which must have lived and grown on the spot, and large chambered
univalves, such as Orthocerata and Nautilus, all seeming to indicate, even
in regions bordering on the arctic circle, the former prevalence of a tem-
perature more elevated than that now prevailing.
The warmth and humidity of the air, and the uniformity of climate,
both in the different seasons of the year and in different latitudes, appear
to have been most remarkable when some of the oldest of the fossiliferous
strata were formed. The approximation to a climate similar to that now
enjoyed in these latitudes does not commence till the era of the formations
termed tertiary; and while the different tertiary rocks were deposited in
succession, from the Eocene to the Pliocene, the temperature seems to
have been lowered, and to have continued to diminish even after the ap-
pearance upon the earth of a considerable number of the existing species,
the cold reaching its maximum of intensity in European latitudes during
the glacial epoch, or the epoch immediately antecedent to that in which
all the species now contemporary with man were in being.
IV. Farther Examination of the Question as to the
Assumed Discordance of the Ancient and
Modern Causes of Change
Causes of vicissitudes in climate. — As the proofs enumerated in the last
chapter indicate that the earth's surface has experienced great changes of
climate since the deposition of the older sedimentary strata, we have next
to inquire how such vicissitudes can be reconciled with the existing order -
of nature. At first it was imagined that the earth's axis had been for ages
perpendicular to the plane of the ecliptic, so that there was a perpetual
equinox, and uniformity of seasons throughout the year; — that the planet
enjoyed this "paradisiacal" state until the era of the great flood; but in
that catastrophe, whether by the shock of a comet or some other convul-
sion, it lost its equal poise, and hence the obliquity of its axis, and with
that the varied seasons of the temperate zone and the long nights and
days of the polar circles.
When tie progress of astronomical science had exploded this theory,
it was assumed that the earth at its creation was in a state of fluidity and
red hot, and that ever since tHat era, it had been cooling down, contracting
its dimensions, and acquiring a solid crust — an hypothesis hardly less
LYELL — PRINCIPLES OF GEOLOGY 291
arbitrary, yet more calculated for lasting popularity; because, by referring
the mind directly to the beginning of things, it requires no support from
observation, nor from any ulterior hypothesis. But if, instead of forming
vague conjectures as to what might have been the state of the planet at
the era of its creation, we fix our thoughts on the connexion at present ex-
isting between climate and the distribution of land and sea, and then con-
sider what influence former fluctuations in the physical geography of the
earth must have had on superficial temperature, we may perhaps approxi-
mate to a true theory. If doubts and obscurities still remain, they should
be ascribed to our limited acquaintance with the laws of Nature, not to
revolutions in her economy; — they should stimulate us to farther research,
not tempt us to indulge our fancies respecting the imaginary changes of
internal temperature in an embryo world.
Diffusion of heat over the globe. — In considering the laws which
regulate the diffusion of heat over the globe, we must be careful, as Hum-
boldt well remarks, not to regard the climate of Europe as a type of the
temperature which all countries placed under the same latitude enjoy. For
the same reason, we may warn the geologist to be on his guard, and not
hastily to assume that the temperature of the earth in the present era is
a type of that which most usually obtains, since he contemplates far
mightier alterations in the position of land and sea, at different epochs,
than those which now cause the climate of Europe to differ from that of
other countries in the same parallels.
On comparing the two continents of Europe and America, it is found
that places in the same latitudes have sometimes a mean difference of
temperature amounting to 11°, or even in a few cases to 17° Fahrenheit;
and some places on the two continents, which have the same mean tem-
perature, differ from 7° to 17° in latitude. Thus, Cumberland House, in
North America, having the same latitude (54° north) as the city of York
in England, stands on the isothermal line of 32°, which in Europe rises to
the North Cape, in latitude 71°, but its summer heat exceeds that of
Brussels or Paris. The principal cause of greater intensity of cold in corre-
sponding latitudes of North America, as contrasted with Europe, is the
connexion of America with the polar circle, by a large tract of land, some
of which is from three to five thousand feet in height; and, on the other
hand, the separation of Europe from the arctic circle by an ocean. The
ocean has a tendency to preserve everywhere a mean temperature, which
it communicates to the contiguous land, so that it tempers the climate,
moderating alike an excess of heat or cold. The elevated land, on the other
hand, rising to the colder regions of the atmosphere, becomes a great
reservoir of ice and snow, arrests, condenses, and congeals vapour, and
communicates its cold to the adjoining country. For this reason, Green-
land, forming part of a continent which stretches northward to the 82d
degree of latitude, experiences under the 60 th parallel a more rigorous
climate than Lapland under the 72d parallel.
But if land be situated between the 40th parallel and the equator, it
produces, unless it be of extreme height, exactly the opposite effect; for
292 MASTERWORKS OF SCIENCE
it then warms the tracts of land or sea that intervene between it and the
polar circle. For the surface, being in this case exposed to the vertical,
or nearly vertical, rays of the sun, absorbs a large quantity of heat, which
it diffuses by radiation into the atmosphere. For this reason, the western
parts of the old continent derive warmth from Africa; "which, like an
immense furnace, distributes its heat to Arabia, to Turkey in Asia, and
to Europe." On the contrary, the northeastern extremity of Asia experi-
ences in the same latitude extreme cold; for it has land on the north
between the 6oth and ypth parallel, while to the south it is separated from
the equator by the Pacific Ocean.
Influence of currents on temperature. — Among other influential causes,
both of remarkable diversity in the mean annual heat, and of unequal
division of heat in the different seasons, are the direction of currents and
the accumulation and drifting of ice in high latitudes. The temperature
of the Lagullas current is 10° or 12° Fahrenheit above that of the sea at
the Cape of Good Hope; for it derives the greater part of its waters from
the Mozambique Channel, and southeast coast of Africa, and from regions
in the Indian Ocean much nearer the line, and much hotter than the Cape.
An opposite effect is produced by the "equatorial" current, which crosses
the Atlantic from Africa to Brazil, having a breadth varying from 160 to
450 nautical miles. Its waters are cooler by 3° or 4° Fahrenheit than those
of the ocean under the line, so that it moderates the heat of the tropics.
But the effects of the Gulf Stream on the climate of the North Atlan-
tic Ocean are far more remarkable. This most powerful of known currents
has its source in the Gulf or Sea of Mexico, which, like the Mediterranean
and other close seas in temperate or low latitudes, is warmer than the
open ocean in the same parallels. The temperature of the Mexican sea in
summer is 86° Fahrenheit, or at least 7° above that of the Atlantic in the
same latitude. From this great reservoir or caldron of warm water a con-
stant current pours forth through the Straits of Bahama at the rate of 3 or
4 miles an hour; it crosses the ocean in a northeasterly direction, skirting
the great bank of Newfoundland, where it still retains a temperature of
8° above that of the surrounding sea. It reaches the Azores in about 78
days, after flowing nearly 3000 geographical miles, and from thence it
sometimes extends its course a thousand miles farther, so as to reach the
Bay of Biscay, still retaining an excess of 5° above the mean temperature
of that sea. As it has been known to arrive there in the months of Novem-
ber and January, it may tend greatly to moderate the cold of winter in
countries on the west of Europe.
Difference of climate of the northern and southern hemispheres. —
When we compare the climate of the northern and southern hemispheres,
we obtain still more instruction in regard to the influence of the distri-
bution of land and sea on climate. The dry land in the southern hemi-
sphere is to that of the northern in the ratio only of one to three, excluding
from our consideration that part which lies between the pole and the 78°
of south latitude, which has hitherto proved inaccessible. And whereas
in the northern hemisphere, between the pole and the thirtieth parallel of
LYELL — PRINCIPLES OF GEOLOGY 293
north latitude, the land and sea occupy nearly equal areas, the ocean in
the southern hemisphere covers no less than fifteen parts in sixteen of the
entire space included between the antarctic circle and the thirtieth parallel
of south latitude.
This great extent of sea gives a particular character to climates south
of the equator, the winters being mild and the summers cool. Thus, in
Van Diemen's Land, corresponding nearly in latitude to Rome, the winters
are more mild than at Naples, and the summers not warmer than those
at Paris, which is 7° farther from the equator.
It has long been supposed that the general temperature of the south-
ern hemisphere was considerably lower than that of the northern, and
that the difference amounted to at least 10° Fahrenheit. Baron Humboldt,
after collecting and comparing a great number of observations, came to
the conclusion that even a much larger difference existed, but that none
was to be observed within the tropics, and only a small difference as far
as the thirty-fifth and fortieth parallel.
The description given by ancient as well as modern navigators of the
sea and land in high southern latitudes clearly attests the greater seventy
of the climate as compared to arctic regions. In Sandwich Land, in lati-
tude 59° south, or in nearly the same parallel as the north of Scotland,
Captain Cook found the whole country, from the summits of the moun-
tains down to the very brink of the sea cliffs, "covered many fathoms thick
with everlasting snow," and this on the ist of February, the hottest time
of the year. The permanence of snow in the southern hemisphere is in
this instance partly due to the floating ice, which chills the atmosphere
and condenses the vapour, so that in summer the sun cannot pierce
through the foggy air. But besides the abundance of ice which covers the
sea to the south of Georgia and Sandwich Land, we may also, as Hum-
boldt suggests, ascribe the cold of those countries in part to the absence of
land between them and the tropics.
If Africa and New Holland extended farther to the south, a dimi-
nution of ice would take place in consequence of the radiation of heat
from these continents during summer, which would warm the contiguous
sea and rarefy the air. The heated aerial currents would then ascend and
flow more rapidly towards the south pole, and moderate the winter. In
confirmation of these views, it is stated that the ice, which extends as far
as the 68° and 71° of south latitude, advances more towards the equator
whenever it meets an open sea; that is, where the extremities of the
present continents are not opposite to it; and this circumstance seems
explicable only on the principle above alluded to, of the radiation of heat
from the lands so situated.
The cold o£ the antarctic regions was conjectured by Cook to be due
to the existence of a large tract of land between the seventieth degree of
south latitude and the pole. The justness of these and other speculations
of that great navigator have since been singularly confirmed by the investi-
gation made by Sir James Ross in 1841. He found Victoria Land, extend-
ing from 71° to- 79° south latitude, skirted by a great barrier of ice, the
dp
55
MAP
SHOWING THE EXTENT OF SURFACE IN
EUROPE
WHICH HAS BEEN COVERED BY THE SEA
SINCE THE COMMENCEMENT OF THE
EOCENE PERIOD
'?&h£*^&z£&i%m
OBSERVATIONS
The space which is dotted comprehends the present sea, together wrth the
area which can be proved by geological evidence to have been covered by
the sea, since the earlier part of the Tertiary period, or since a portion of the
Eocene (or oldest Tertiary) strata were already formed.
It is not meant that the whole space which is dotted was eve^ submerged at
any one point of time within the period above mentioned, but that different
portions of the space have been under water in succession, or owing to oscil-
lations in the level of the ground, have been alternately sea and land, more
than once.
The space left white, is now dry tand, and has been always land, (unless
occupied by fresh water lakes) since the earlier part of the Eocene penod. The
geology however of some part of this area (Spain for example) is imperfectly
known. For a -more detailed description of the map with reference to author:
itie$ see Chapter 5
296 MASTERWORKS OF SCIENCE __
height of the land ranging from 4000 to 14,000 feet, the whole entirely
covered with snow, except a narrow ring of black earth surrounding the
huge crater of the active volcano of Mount Erebus, rising 12,400 feet above
the level of the sea.
Changes in the position of land and sea may give rise to vicissitudes
in climate. — Having offered these brief remarks on the diffusion of heat
over the globe in the present state of the surface, I shall now proceed to
speculate on the vicissitudes of climate, which must attend those endless
variations in the geographical features of our planet which are contem-
plated in geology. That our speculations may be confined within the
strict limits of analogy, I shall assume, ist, That the proportion of dry
land to sea continues always the same, adly. That the volume of the land
rising above the level of the sea is a constant quantity; and not only that
its mean, but that its extreme height, is liable only to trifling variations.
3dly, That both the mean and extreme depth of the sea are invariable;
and 4thly, It may be consistent with due caution to assume that the group-
ing together of the land in continents is a necessary part of the economy
of nature; for it is possible that the laws which govern the subterranean
forces, and which act simultaneously along certain lines, cannot but pro-
duce, at every epoch, continuous mountain chains; so that the subdivision
of the whole land into innumerable islands may be precluded.
Before considering the effect which a material change in the distri-
bution of land and sea must occasion, it may be well to remark how
greatly organic life may be affected by those minor variations, which need
not in the least degree alter the general temperature. «Thus, for example,
if we suppose, by a series of convulsions, a certain part of Greenland to
become sea, and, in compensation, a tract of land to rise and connect
Spitzbergen with Lapland — an accession not greater in amount than one
which the geologist can prove to have occurred in certain districts border-
ing the Mediterranean, within a comparatively modern period — this altered
form of the land might cause an interchange between the climate of
certain parts of North America and of Europe, which lie in corresponding
latitudes. Many European species of plants and animals would probably
perish in consequence, because the mean temperature would be greatly
lowered; and others would fail in America, because it would there be
raised. On the other hand, in places where the mean annual heat remained
unaltered, some species which flourish in Europe, where the seasons are
more uniform, would be unable to resist the greater heat of the North
American summer, or the intenser cold of the winter; while others, now
fitted by their habits for the great contrast of the American seasons, would
not be fitted for the insular climate of Europe.
If we now proceed to consider the circumstances required for a
general change of temperature, it will appear, from the facts and principles
already laid down, that whenever a greater extent of high land is collected
in the polar regions, the cold will augment; and the same result will be
produced when there is more sea between or near the tropics; while, on
the contrary, so often as the above conditions are reversed, the heat will
LYELL — PRINCIPLES OF GEOLOGY 297
be greater. (See Figs. 3 and 4.) If this be admitted, it will follow that
unless the superficial inequalities of the earth be fixed and permanent,
there must be never-ending fluctuations in the mean temperature of every
zone; and that the climate of one era can no more be a type of every other
than is one of our four seasons of all the rest.
Position of land and sea which might produce the extreme of cold
of which the earth's surface is susceptible. — To simplify our view of the
various changes in climate, which different combinations of geographical
circumstances may produce, we shall first consider the conditions neces-
sary for bringing about the extreme of cold, or what would have been
termed in the language of the old writers the winter of the "great year,"
or geological cycle, and afterwards, the conditions requisite to produce
the maximum of heat, or the summer of the same year.
To begin with the northern hemisphere. Let us suppose those hills
of the Italian peninsula and of Sicily, which are of comparatively modern
origin, and contain many fossil shells identical with living species, to sub-
side again into the sea, from which they have been raised, and that an
extent of land of equal area and height (varying from one to three thou-
sand feet) should rise up in the Arctic Ocean between Siberia and the
north pole. The alteration now supposed in the physical geography of the
northern regions would cause additional snow and ice to accumulate
where now there is usually an open sea; and the temperature of the
greater part of Europe would be somewhat lowered, so as to resemble
more nearly that of corresponding latitudes of North America: or, in
other words, it might be necessary to travel about 10° farther south in
order to meet with the same climate which we now enjoy. No compen-
sation would be derived from the disappearance of land in the Mediter-
ranean countries; but the contrary, since the mean heat of the soil in those
latitudes probably exceeds that which would belong to the sea, by which
we imagine it to be replaced.
But let the configuration of the surface be still farther varied, and let
some large district within or near the tropics, such as Brazil, with its
plains and hills of moderate height, be converted into sea, while lands
of equal elevation and extent rise up in the arctic circle. From this change
there would, in the first place, result a sensible diminution of temperature
near the tropic, for the Brazilian soil would no longer be heated by the
sun; so that the atmosphere would be less warm, as also the neighbouring
Atlantic. On the other hand, the whole of Europe, Northern Asia, and
North America would be chilled by the enormous quantity of ice and
snow thus generated on the new arctic continent. If, as we have already
seen, there are now some points in the southern hemisphere where snow
is perpetual down to the level of the sea, in latitudes as low as central
England, such might assuredly be the case throughout a great part of
Europe, under the change of circumstances above supposed; and if at
present the extreme range of drifted icebergs is the Azores, they might
easily reach the equator after the assumed alteration. But to pursue the
subject still further, let the Himalaya Mountains, with the whole of
298 MASTERWQRKS OF SCIENCE
Hindostan, sink down, and tlieir place be occupied by the Indian Ocean,
while an equal extent of territory and mountains, of the same vast height,
rise up between North Greenland and the Orkney Islands. It seems diffi-
cult to exaggerate the amount to which the climate of the northern hemi-
sphere would then be cooled.
But the refrigeration brought about at the same time in the southern
hemisphere would be nearly equal, and the difference of temperature be-
tween the arctic and equatorial latitudes would not be much greater than
at present; for no important disturbance can occur in the climate of a
particular region without its immediately affecting all other latitudes,
however remote. The heat and cold which surround the globe are in a
state of constant and universal flux and reflux. The heated and rarefied
air is always rising and flowing from the equator towards the poles in the
higher regions of the atmosphere; while in the lower, the colder air is
flowing back to restore the equilibrium.
That a corresponding interchange takes place in the seas is demon-
strated, according to Humboldt, by the cold which is found to exist at
great depths within the tropics; and, among other proofs, may be men-
tioned the mass of warmer water which the Gulf Stream is constantly
bearing northwards, while a cooler current flows from the north along the
coast of Greenland and Labrador and helps to restore the equilibrium.
To return to the state of the earth after the changes above supposed,
we must not omit to dwell on the important effects to which a wide ex-
panse of perpetual snow would give rise. It is probable that nearly the
whole sea, from the poles to the parallels of 45 °, would be frozen over;
for it is well known that the immediate proximity of land is not essential
to the formation and increase of field ice, provided there be in some part
of the same zone a sufficient quantity of glaciers generated on or near the
land, to cool down the sea. Captain Scoresby, in his account of the arctic
regions, observes that when the sun's rays "fall upon the snow-clad sur-
face of the ice or land, they are in a great measure reflected, without pro-
ducing any material elevation of temperature; but when they impinge on
the black exterior of a ship, the pitch on one side occasionally becomes
fluid while ice is rapidly generated at the other."
Now field ice is almost always covered with snow; and thus not only
land as extensive as our existing continents, but immense tracts of sea
in the frigid and temperate zones, might present a solid surface covered
with snow, and reflecting the sun's rays for the greater part of the year.
Within the tropics, moreover, where the ocean now predominates, the
sky would no longer be serene and clear, as in the present era; but masses
of floating ice would cause quick condensations of vapour, so that fogs
and clouds would deprive the vertical rays of the sun of half their power.
The whole planet, therefore, would receive annually a smaller proportion
D£ the solar influence, and the external crust would part, by radiation,
with some of the heat which had been accumulated in it during a differ-
ent state of the surface. This heat would be dissipated in the spaces sur-
LYELL— PRINCIPLES OF GEOLOGY 299
rounding our atmosphere, which, according to the calculations of M.
Fourier, have a temperature much inferior to that of freezing water.
After the geographical revolution above assumed, the climate of
equinoctial lands might be brought at last to resemble that of the present
temperate zone, or perhaps be far more wintry. They who should then
inhabit such small isles and coral reefs as are now seen in the Indian
Ocean and South Pacific would wonder that zoophytes of large dimen-
sions had once been so prolific in their seas; or if, perchance, they found
the wood and fruit of the cocoanut tree or the palm silicified by the
waters of some ancient mineral spring, or incrusted with calcareous mat-
ter, they would muse on the revolutions which had annihilated such gen-
era and replaced them by the oak, the chestnut, and the pine. With equal
admiration would they compare the skeletons* of their small lizards with
the bones of fossil alligators and crocodiles more than twenty feet in
length, which, at a former epoch, had multiplied between the tropics: and
when they saw a pine included in an iceberg, drifted from latitudes which
we now call temperate, they would be astonished at the proof thus
afforded that forests had once grown where nothing could be seen in their
own times but a wilderness of snow.
But we have still to contemplate the additional refrigeration which
might be effected by changes in the relative position of land and sea in
the southern hemisphere. If the remaining continents were transferred
from the equatorial and contiguous latitudes to the south polar regions,
the intensity of cold produced might, perhaps, render the globe uninhabit-
able. We are too ignorant of the laws governing the direction of subter-
ranean forces to determine whether such a crisis be within the limits of
possibility. At the same time, it may be observed that no distribution of
land can well be imagined more irregular, or, as it were, capricious, than
that which now prevails; for at present, the globe may be divided into
two equal parts, in such a manner that one hemisphere shall be almost
entirely covered with water, while the other shall contain less water than
land (see Figs, i and 2); and, what is still more extraordinary, on com-
paring the extratropical lands in the northern and southern hemispheres,
the lands in the northern are found to be to those in the southern in the
proportion of thirteen to one! To imagine all the lands, therefore, in high,
and all the sea in low latitudes, as delineated in Figs. 3 and 4, would
scarcely be a more anomalous state of the surface.
Position of land and sea which might give rise to the extreme of
heat. — Let us now turn from the contemplation of the winter of the
"great year," and consider the opposite train of circumstances which
would bring on the spring and summer. To imagine all the lands to be
collected together in equatorial latitudes, and a few promontories only to
project beyond the thirtieth parallel, as represented in the annexed map
(Fig. 3), would be undoubtedly to suppose an extreme result of geo-
logical change. But if we consider a mere approximation to such a state
of things, it would be sufficient to cause a general elevation of tempera-
ture. Nor can it be regarded as a visionary idea that amidst the revolu-
300
MASTERWORKS OF SCIENCE
FIG. i
FIG. 2
MAP SHOWING THE PRESENT UNEQUAL DISTRIBUTION OF LAND AND WATER ON THE
SURFACE OF THE GLOBE
FIG. i. Here London is taken as a centre and we behold the greatest quantity
of land existing in one hemisphere.
FIG. 2. Here the centre is the antipodal point to London and we see the
greatest quantity of water existing in one hemisphere.
LYELL — PRINCIPLES OF GEOLOGY 301
FIG. 3
EXTREME OF HEAT
FIG. 4
EXTREME OF COLD
MAPS SHOWING THE POSITION OF LAND AND SEA WHICH MIGHT PRODUCE THE EX-
TREMES OF HEAT AND COLD IN THE CLIMATES OF THE GLOBE
Observations: These maps are intended to show that continents and islands
having the same shape and relative dimensions as those now existing might be
placed so as to occupy either the equatorial or polar regions.
In FIG. 3 scarcely any of the land extends from the equator towards the poles
beyond the 3Oth parallel of latitude, and in FIG. 4 a very small proportion of it
extends from the poles towards the equator beyond the 40th parallel of latitude.
302 MASTERWQRKS OF SCIENCE
tions of the earth's surface the quantity of land should, at certain periods,
have been simultaneously lessened in the vicinity of both the ^ poles and
increased within the tropics. We must recollect that even now it is neces-
sary to ascend to the height of fifteen thousand feet in jJie Andes under
the line, and in the Himalaya Mountains, which are without the tropic,
to seventeen thousand feet, before we reach the limit of perpetual snow.
On the northern slope, indeed, of the Himalaya range, where the heat
radiated from a great continent moderates the cold, there are meadows
and cultivated land at an elevation equal to the height of Mont Blanc. If
then there were no arctic lands to chill the atmosphere and freeze the sea,
and if the loftiest chains were near the line, it seems reasonable to imag-
ine that the highest mountains might be clothed with a rich vegetation
to their summits, and that nearly all signs of frost would disappear from
the earth.
When the absorption of the solar rays was in no region impeded,
even in winter, by a coat of snow, the mean heat of the earth's crust would
augment to considerable depths, and springs, which we know to be in
general an index of the mean temperature of the climate, would be
warmer in all latitudes. The waters of lakes, therefore, and rivers, would
be much hotter in winter, and would be never chilled in summer by
melted snow and ice. A remarkable uniformity of climate would prevail
amid the archipelagos of the temperate and polar oceans, where the
tepid waters of equatorial currents would freely circulate. The genera]
humidity of the atmosphere would far exceed that of the present period,
for increased heat would promote evaporation in all parts of the globe.
The winds would be first heated in their passage over the tropical plains,
and would then gather moisture from the surface of the deep, till, charged
with vapour, they arrived at extreme northern and southern regions, and
there encountering a cooler atmosphere, discharged their burden in warm
rain. If, during the long night of a polar winter, the snows should whiten
the summits of some arctic islands, they would be dissolved as rapidly by
the returning sun as are the snows of Etna by the blasts of the sirocco.
We learn from those who have studied the geographical distribution
of plants that in very low latitudes, at present, the vegetation of small
islands remote from continents has a peculiar character; the ferns and
allied families, in particular, bearing a great proportion to the total num-
ber of other plants. Other circumstances being the same, the more remote
the isles are from the continents, the greater does this proportion become.
Thus, in the continent of India, and the tropical parts of New Holland,
the proportion of ferns to the phaenogamous plants is only as one to
twenty-six; whereas, in the South Sea Islands, it is as one to four, or even
as one to three.
We might expect, therefore, in the summer of the "great year," or
cycle of climate, that there would be a predominance of tree ferns and
plants allied to genera now called tropical, in the islands of the wide
ocean, while many forms now confined to arctic and temperate regions,
or only found near the equator on the summit of the loftiest mountains,
LYELL — PRINCIPLES OF GEOLOGY 303
would almost disappear from the earth. Then might those genera of
animals return, of which the memorials are preserved in the ancient rocks
of our continents. The pterodactyle might flit again through the air, the
huge iguanodon reappear in the woods, and the ichthyosaurs swarm once
more in the sea. Coral reefs might be prolonged again beyond the arctic
circle, where the whale and the narwal now abound; and droves of turtles
might begin again to wander through regions now tenanted by the walrus
and the seal.
But not to indulge too far in these speculations, I may observe, in
conclusion, that however great, during the lapse of ages, may be the vicis-
situdes of temperature in every zone, it accords with this theory that the
general climate should not experience any sensible change in the course
of a few thousand years; because that period is insufficient to affect the
leading features of the physical geography of the globe.
V. On Former Changes in Physical Geography and
Climate
I HAVE STATED the arguments derived from organic remains for conclud-
ing that in the period when the carboniferous strata were deposited, the
temperature of the ocean and the air was more uniform in the different
seasons of the year, and in different latitudes, than at present, and that
there was a remarkable absence of cold as well as great moisture in the
atmosphere. It was also shown that the climate had been modified more
than once since that epoch, and that it had been reduced, by successive
changes, more and more nearly to that now prevailing in the same lati-
tudes. Further, I endeavoured, in the last chapter, to prove that vicissi-
tudes in climate of no less importance may be expected to recur in future
if it be admitted that causes now active in nature have power, in the lapse
of ages, to produce considerable variations in the relative position of land
and sea. It remains to inquire whether the alterations, which the geologist
can prove to have actually ta\en place at former periods, in the geographi-
cal features of the northern hemisphere, coincide in their nature, and in
the time of their occurrence, with such revolutions in climate as might
naturally have resulted,t according to the meteorological principles already
explained.
Period of the primary fossiliferous roc%s. — The oldest system o£ strata
which afford by their organic remains any evidence as to climate, or the
former position of land and sea, are those formerly known as the transi-
tion roc1(s, or what have since been termed Lower Silurian or "primary
fossiliferous" formations. These have been found in England, France,
Germany, Sweden, Russia, and other parts of central and northern Europe,
as also in the Great Lake District of Canada and the United States. The
304 MASTERWORKS OF SCIENCE
multilocular or chambered univalves, including the Nautilus, and the
corals, obtained from the limestones of these ancient groups, have been
compared to forms now most largely developed in tropical seas. The
corals, however, have been shown by M. Milne Edwards to differ generally
from all living zoophytes; so that conclusions as to a warmer climate
drawn from such remote analogies must be received with caution. Hith-
erto, few, if any, contemporaneous vegetable remains have been noticed;
but such as are mentioned agree more nearly with the plants of the
Carboniferous era than any other, and would therefore imply a warm and
humid atmosphere entirely free from intense cold throughout the year.
This absence or great scarcity of plants as well as the freshwater shells
and other indications of neighbouring land, coupled with the wide extent
of marine strata of this age in Europe and North America, are facts which
imply such a state of physical geography (so far at least as regards the
northern hemisphere) as would, according to the principles before ex-
plained, give rise to such a moist and equable climate. (See Fig. 3.)
Carboniferous group. — This group comes next in the order of succes-
sion: and one of its principal members, the mountain limestone, was evi-
dently a marine formation, as is shown by the shells and corals which
it contains. That the ocean of that period was of considerable extent in
our latitudes, we may infer from the continuity of these calcareous strata
over large areas in Europe, Canada, and the United States. The same
group has also been traced in North America, towards the borders of the
arctic sea.
Since the time of the earlier writers, no strata have been more ex-
tensively investigated, both in Europe and North America, than those
of the ancient carboniferous group, and the progress of science has led
to a general belief that a large portion of the purest coal has been formed,
not, as was once imagined, by vegetable matter floated from a distance,
but by plants which grew on the spot, and somewhat in the manner of
peat on the spaces now covered by the beds of coal. The former existence
of land in some of these spaces has been proved, as already stated, by the
occurrence of numerous upright fossil trees, with their roots terminating
downwards in seams of coal; and still more generally by the roots of trees
(stigmariae) remaining in their natural position in the clays which under-
lie almost every layer of coal.
As some nearly continuous beds of such coal have of late years been
traced in North America, over areas 100 or 200 miles and upwards in
diameter, it may be asked whether the large tracts of ancient land implied
by this fact are not inconsistent with the hypothesis of the general preva-
lence of islands at the period under consideration. In reply, I may observe
that the coal fields must originally have been low alluvial grounds, resem-
bling in situation the cypress swamps of the Mississippi, or the sunder-
bunds of the Ganges, being liable like them to be inundated at certain
periods by a river or by the sea, if the land should be depressed a few
feet. All the phenomena, organic and inorganic, imply conditions nowhere
to be met with except in the deltas of large rivers. We have to account
LYELL — PRINCIPLES OF GEOLOGY 305
for an abundant supply of fluviatile sediment, carried for ages towards one
and the same region, and capable of forming strata of mud and sand thou-
sands of feet, or even fathoms, in thickness,, many of them consisting of
laminated shale, inclosing the leaves of ferns and other terrestrial plants.
We have also to explain the frequent intercalations of root beds, and the
interposition here and there of brackish and marine deposits, demonstrat-
ing the occasional presence of the neighbouring sea. But these forest-
covered deltas could only have been formed at die termination of large
hydrographical basins, each drained by a great river and its tributaries;
and the accumulation of sediment bears testimony to contemporaneous
denudation on a large scale, and, therefore, to a wide area of land, prob-
ably containing within it one or more mountain chains.
In the case of the great Ohio or Appalachian coal field, the largest
in the world, it seems clear that the uplands drained by one or more great
rivers were chiefly to the eastward, or they occupied a space now filled
by part of the Atlantic Ocean, for the mechanical deposits of mud and
sand increase greatly in thickness and coarseness of material as we ap-
proach the eastern borders of the coal figld, or the southeast flanks of the
Allegheny Mountains, near Philadelphia. In that region numerous beds of
pebbles, often of the size of a hen's egg, are seen to alternate with beds
of pure coal.
But the American coal fields are all comprised within the 30th and
50th degrees of north latitude; and there is no reason to presume that the
lands at the borders of which they originated ever penetrated so far or in,
such masses into the colder and arctic regions as to generate a cold
climate. In the southern hemisphere, where the predominance of sea over
land is now the distinguishing geographical feature, we nevertheless find
a large part of the continent of Australia, as well as New Zealand, placed
between the 30th and 5oth degrees of south latitude. The two islands of
New Zealand, taken together, are between 800 and 900 miles in length,
with a breadth in some parts of ninety miles, and they stretch as far south
as the 46th degree of latitude. They afford, therefore, a wide area for the
growth of a terrestrial vegetation, and the botany of this region is charac-
terised by abundance of ferns, one hundred and forty species of which
are already known, some of them attaining the size of trees. In this respect
the southern shores of New Zealand in the 46th degree of latitude almost
vie with tropical islands. Another point of resemblance between the Flora
of New Zealand and that of the ancient Carboniferous period is the preva-
lence of the fir tribe or of coniferous wood.
An argument of some weight in corroboration of the theory above
explained respecting the geographical condition of the temperate and
arctic latitudes of the northern hemisphere in the Carboniferous period
may also be derived from an examination of those groups of strata which
immediately preceded the coal. The fossils of the Devonian and Silurian
strata in Europe and North America have led to the conclusion that they
were formed for the most part in deep seas, far from land. In those older
strata land plants are almost as rare as they are abundant or universal in
306 MASTERWORKS OF SCIENCE
the coal measures. Those ancient deposits, therefore, may be supposed to
have belonged to an epoch when dry land had only just begun to be
upraised from the deep; a theory which would imply the existence during
the Carboniferous epoch of islands, instead of an extensive continent, in
the area where the coal was formed.
Such a state of things prevailing in the north, from the pole to the
3oth parallel of latitude, if not neutralized by circumstances of a contrary
tendency in corresponding regions south of the line, would give rise to a
general warmth and uniformity of climate throughout the globe.
Changes in physical geography between the formation of the car-
boniferous strata and the chalJ^. — We have evidence in England that the
strata of the ancient carboniferous group, already adverted to, were, in
many instances, fractured and contorted, and often thrown into a vertical
position, before the deposition of some even of the oldest known sec-
ondary rocks, such as the new red sandstone.
A freshwater deposit, called the Wealden, occurs in the upper part
of the secondary series of the south of England, which, by its extent and
fossils, attests the existence in that region of a large river draining a conti-
nent or island of considerable dimensions. We know that this land was
clothed with wood and inhabited by huge terrestrial reptiles and birds.
Its position so far to the north as the counties of Surrey and Sussex, at a
time when the mean temperature of the climate is supposed to have been
much hotter than at present, may at first sight appear inconsistent with
, the theory before explained, that the heat was caused by the gathering
together of all the great masses of land in low latitudes, while the north-
ern regions were almost entirely sea. But it must not be taken for granted
that the geographical conditions already described (see Fig. 3) as capa-
ble of producing the extreme of heat were ever combined at any geological
period of which we have as yet obtained information. It is more prob-
able, from what has been stated in the preceding chapters, that a slight
approximation to such an extreme state of things would be sufficient; in
other words, if most of the dry land were tropical, and scarcely any of it
arctic or antarctic, a prodigious elevation of temperature must ensue, even
though a part of some continents should penetrate far into the temperate
zones.
Changes during the tertiary periods. — The secondary and tertiary
formations of Europe, when considered separately, may be contrasted as
having very different characters; the secondary appearing to have been
deposited in open seas, the tertiary in regions where dry land, lakes, bays,
and perhaps inland seas, abounded. The secondary series is almost ex-
clusively marine; the tertiary, even the oldest part, contains lacustrine
strata, and not unfrequently freshwater and marine beds alternating. In
fact, there is evidence of important geographical changes having occurred
between the deposition of the cretaceous system, or uppermost of the
secondary series, and that of the oldest tertiary group, and still more be-
tween the era of the latter and that of the newer tertiary formations. This
change in the physical geography of Europe and North America was ac-
LYELL — PRINCIPLES OF GEOLOGY 307
companied by an alteration no less remarkable in organic life, scarcely
any species being common both to the secondary and tertiary rocks, and
the fossils of the latter affording evidence of a different climate.
On the other hand, when we compare the tertiary formations of suc-
cessive ages, we trace a gradual approximation in the imbedded fossils,
from an assemblage in which extinct species predominate to one where
the species agree for the most part with those now existing. In other
words, we find a gradual increase of animals and plants fitted for our
present climates, in proportion as the strata which we examine are more
modern. Now, during all these successive tertiary periods, there are signs
of a great increase of land in European and North American latitudes.
By reference to the map (pages 294 and 295), and its description, the
reader will see that about two thirds of the present European lands have
emerged since the earliest tertiary group originated. Nor is this the only
revolution which the same region has undergone within the period alluded
to, some tracts which were previously land having gained in altitude,
others, on the contrary, having sunk below their former level.
That the existing lands were not all upheaved at once into their pres-
ent position is proved by the most striking evidence. Several Italian
geologists, even before the time of Brocchi, had justly inferred that the
Apennines were elevated several thousand feet above the level of the
Mediterranean before the deposition of the modern Sub-Apennine beds
which flank them on either side. What now constitutes the central cal-
careous chain of the Apennines must for a long time have been a narrow
ridgy peninsula, branching off, at its northern extremity, from the Alps
near Savona. This peninsula has since been raised from one to two thou-
sand feet, by which movement the ancient shores, and, for a certain ex-
tent, the bed of the contiguous sea, have been laid dry, both on the side
of the Mediterranean and the Adriatic.
The nature of these vicissitudes will be explained by the accompany-
ing diagram, which represents a transverse section across the Italian penin-
sula. The inclined strata A are the disturbed formations of the Apennines
into which the ancient igneous rocks a are supposed to have intruded
themselves. At a lower level on each flank of the chain are the more
recent shelly beds b bt which often contain rounded pebbles derived from
the waste of contiguous parts of the older Apennine limestone. These, it
will be seen, are horizontal, and lie in what is termed "unconformable
stratification" on the more ancient series. They now constitute a line of
308 MASTERWORKS OF SCIENCE
hills of moderate elevation between the sea and the, Apennines, but never
penetrate to the higher and more ancient valleys of that chain.
The remarkable break between the most modern of the known sec-
ondary rocks and the oldest tertiary may be apparent only, and ascribable
to the present deficiency of our information. Already the marls and
greensand of Heers near Tongres, in Belgium, observed by M. Dumont.
and the "pisolitic limestone" of the neighbourhood of Paris, both inter-
mediate in age between the Maestricht chalk and the lower Eocene strata,
begin to afford us" signs of a passage from one state of things to another.
Nevertheless, it is far from impossible that the interval between the chalk
and tertiary formations constituted an era in the earth's history, when
the transition from one class of organic beings to another was, compara-
tively speaking, rapid. For if the doctrines above explained in regard to
vicissitudes of temperature are sound, it will follow that changes of equal
magnitude in the geographical features of the globe may at different
periods produce very unequal effects on climate; and, so far as the exist-
ence of certain animals and plants depends on climate, the duration of
species would be shortened or protracted, according to the rate at which
the change of temperature proceeded.
Map showing the extent of surface in Europe which has at one period
or another been covered by the sea since the commencement of the deposi-
tion of the older or Eocene tertiary strata. — The aforesaid map on pp. 294
and 295 will enable the reader to perceive at a glance the great extent of
change of the physical geography of Europe, which can be proved to have
taken place since some of the older tertiary strata began to be deposited.
The proofs of submergence, during some part or other of this period, in
all the dotted portions of the map, are of a most unequivocal character; for
the area thus described is now covered by deposits containing the fossil re-
mains of animals which could only have lived in salt water. The most
ancient part of the period referred to cannot be deemed very remote, con-
sidered geologically; because the deposits of the Paris and London basins,
and many other districts belonging to the older tertiary epoch, are newer
than the greater part of the sedimentary rocks (those commonly called
secondary and primary fossiliferous or paleozoic) of which the crust of
the globe is composed. The species, moreover, of marine testacea, of
which the remains are found in these older tertiary formations, are not
entirely distinct from such as now live. Yet, notwithstanding the com-
paratively recent epoch to which this retrospect is carried, the variations
in the distribution of land and sea depicted on the map form only a part
of those which must have taken place during the period under considera-
tion. Some approximation has merely been made to an estimate of the
amount of sea converted into land in parts of Europe best known to
geologists; but we cannot determine how much land has become sea dur-
ing the same period; and there may have been repeated interchanges of
land and water in the same places, changes of which no account is taken
in the map, and respecting the amount of which little accurate informa-
tion can ever be obtained.
LYELL — PRINCIPLES OF GEOLOGY 309
I have extended the sea In some instances beyond the limits of the
land now covered by tertiary formations and marine drift, because other
geological data have been obtained for inferring the submergence of these
tracts after the deposition of the Eocene strata had begun. Thus, for ex-
ample, there are good reasons for concluding that part of the chalk of
England (the North and South Downs, for example, together with the
intervening secondary tracts) continued beneath the sea until the oldest
tertiary beds had begun to accumulate.
A strait of the sea separating England and Wales has also been intro-
duced, on the evidence afforded by shells of existing species found in a
deposit of gravel, sand, loam, and clay, called the northern drift, by Sir R.
Murchison. And Mr. Trimmer has discovered similar recent marine shells
on the northern coast of North Wales, and on Moel Tryfane, near the
Menai Straits, at the height of 1392 feet above the level of the sea!
Some raised sea beaches, and drift containing marine shells, which
I examined in 1843, between Limerick and Dublin, and which have been
traced over other parts of Ireland by different geologists, have required
an extension of the dotted portions so as to divide that island into several.
In improving this part of my map I have been especially indebted to the
assistance of Mr. Oldham, who in 1843 announced to the British Associa-
tion at Cork the fact that at the period when the drift or glacial beds were
deposited, Ireland must have formed an archipelago such as is here de-
picted. A considerable part of Scotland might also have been represented
in a similar manner as under water when the drift originated.
I was anxious, even in the title of this map, to guard the reader
against the supposition that it was intended to represent the state of the
physical geography of part of Europe at any one point of time. The diffi-
culty, or rather the impossibility, of restoring the geography of the globe
as it may have existed at any former period, especially a remote one, con-
sists In this, that we can only point out where part of the sea has been
turned Into land, and are almost always unable to determine what land
may have become sea. All maps, therefore, pretending to represent the
geography of remote geological epochs must be ideal.
It may be proper to remark that the vertical movements to which the
land is subject in certain regions occasion alternately the subsidence and
the uprising of the surface; and that, by such oscillations at successive
periods, a great area may have been entirely covered with marine deposits,
although the whole may never have been beneath the waters at one time;
nay, even though the relative proportion of land and sea may have con-
tinued unaltered throughout the whole period. I believe, however, that
since the commencement of the tertiary period, the dry land in the
northern hemisphere has been continually on the increase, both because
it Is now greatly In excess beyond the average proportion which land
generally bears to water on the globe, and because a comparison of the
secondary and tertiary strata affords indications, as I have already shown,
of a passage from the condition of an ocean interspersed with islands to
that of a large continent.
310 MASTERWQRKS OF SCIENCE
But supposing it were possible to represent all the vicissitudes in the
distribution of land and sea that have occurred during the tertiary period,
and to exhibit not only the actual existence of land where there was once
sea, but also the extent of surface now submerged which may once have
been land, the map would still fail to express all the important revolutions
in physical geography which have taken place within the epoch under
consideration. For the oscillations of level, as was before stated, have not
merely been such as to lift up the land from below the water, but in some
cases to occasion a rise of many thousand feet above the sea. Thus the
Alps have acquired an additional altitude of 4000, and even in some places
10,000 feet; and the Apennines owe a considerable part of their present
height to subterranean convulsions which have happened within the
tertiary epoch.
Concluding remarks on changes in physical geography. — The fore-
going observations, it may be said, are confined chiefly to Europe, and
therefore merely establish the increase of dry land in a space which con-
stitutes but a small portion of the northern hemisphere; but it was stated
in the preceding chapter that the great Lowland of Siberia, lying chiefly
between the latitudes 55° and 75° north (an area nearly equal to all
Europe), is covered for the most part by marine strata, which, from the
account given by Pallas, and more recently by Sir R. Murchison, belongs
to a period when all or nearly all the shells were of a species still living
in the north. The emergence, therefore, of this area from the deep is,
comparatively speaking, a very modern event, and must, as before re-
marked, have caused a great increase of cold throughout the globe.
Upon a review, then, of all the facts above enumerated, respecting
the ancient geography of the globe as attested by geological monuments,
there appear good grounds for inferring that changes of climate coincided
with remarkable revolutions in the former position of sea and land. A
wide expanse of ocean, interspersed with islands, seems to have pervaded
the northern hemisphere at the periods when the Silurian and carbonifer-
ous rocks were formed, and a warm and very uniform temperature then
prevailed. Subsequent modifications in climate accompanied the deposi-
tion of the secondary formations, when repeated changes were effected
in the physical geography of our northern latitudes. Lastly, the refrigera-
tion became most decided, and the climate most nearly assimilated to that
now enjoyed, when the lands in Europe and northern Asia had attained
their full extension, and the mountain chains their actual height.
VI. Supposed Intensity of Aqueous Forces at Remote Periods
Intensity of aqueous causes. — The great problem considered in the pre-
ceding chapters, namely, whether the former changes of the earth made
known to us by geology resemble in kind and degree those now in daily
LYELL — PRINClFi.Jbb u±<
progress, may still be contemplated from several other points of view. We
may inquire, for example, whether there are any grounds for the belief
entertained by many that the intensity both of aqueous and of igneous
forces, in remote ages, far exceeded that which we witness in our own
times.
First, then, as to aqueous causes: it has been shown in our history of
the science that Woodward did not hesitate, in 1695, to teach that the
entire mass of fossiliferous strata contained in the earth's crust had been de-
posited in a few months; and, consequently, as their mechanical and deriva-
tive origin was already admitted, the reduction of rocky masses into mud,
sand, and pebbles, the transportation of the same to a distance, and their
accumulation elsewhere in regular strata were all assumed to have taken
place with a rapidity unparalleled in modern times. This doctrine was
modified by degrees, in proportion as different classes of organic remains,
such as shells, corals, and fossil plants, had been studied with attention.
Analogy led every naturalist to assume that each full-grown individual of
the animal or vegetable kingdom had required a certain number of
months or years for the attainment of maturity and the perpetuation of
its species by generation; and thus the first approach was made to the
conception of a common standard of time, without which there are no
means whatever of measuring the comparative rate at which any succes-
sion of events has taken place at two distinct periods. This standard con-
sisted of the average duration of the lives of individuals of the same
genera or families in the animal and vegetable kingdoms; and the multi-
tude of fossils dispersed through successive strata implied the continu-
ance of the same species for many generations. At length the idea that
species themselves had had a limited duration arose out of the observed
fact that sets of strata of different ages contained fossils of distinct species.
Finally, the opinion became general that in the course of ages one assem-
blage of animals and plants had disappeared after another again and
again, and new tribes had started into life to replace them.
Denudation. — In addition to the proofs derived from organic re-
mains, the forms of stratification led also, on a fuller investigation, to the
belief that sedimentary rocks had been slowly deposited; but it was still
supposed that denudation, or the power of running water, and the waves
and currents of the ocean, to strip off superior strata and lay bare the
rocks below, had formerly operated with an energy wholly unequalled
in our times. These opinions were both illogical and inconsistent, because
deposition and denudation are parts of the same process, and what is true
of the one must be true of the other. Their speed must be always limited
by the same causes, and the conveyance of solid matter to a particular
region can only keep pace with its removal from another, so that the
aggregate of sedimentary strata in the earth's crust can never exceed in
volume the amount of solid matter which has been ground down and
washed away by running water. How vast then must be the spaces which
this abstraction of matter has left vacant! How far exceeding in dimen-
sions all the valleys, however numerous, and the hollows, however vast,
312 MASTERWORKS OF SCIENCE
which we can prove to have been cleared out by aqueous erosion! The
evidences of the work of denudation are defective, because it is the na-
ture of every destroying cause to obliterate the signs of its own agency;
but the amount of reproduction in the form of sedimentary strata must
always afford a true measure of the minimum of denudation which the
earth's surface has undergone.
Supposed universality of ancient deposits. — The next fallacy which
has helped to perpetuate the doctrine that the operations of water were
on a different and grander scale in ancient times is founded on the indefi-
nite areas over which homogeneous deposits were supposed to extend. No
modern sedimentary strata, it is said, equally identical in mineral charac-
ter and fossil contents, can be traced continuously from one quarter of
the globe to another. But the first propagators of these opinions were very
slightly acquainted with the inconstancy in mineral composition of the
ancient formations, and equally so of the wide spaces over which the same
kind of sediment is now actually distributed by rivers and currents in the
course of centuries. The persistency of character in the older series was
exaggerated, its extreme variability in the newer was assumed without
proof.
In regard to the imagined universality of particular rocks of ancient
date, it was almost unavoidable that this notion, when once embraced,
should be perpetuated; for the same kinds of rock have occasionally been
reproduced at successive epochs: and when once the agreement or dis-
agreement in mineral character alone was relied on as the test of age, it
followed that similar rocks, if found even at the antipodes, were referred
to the same era, until the contrary could be shown.
Now it is usually impossible to combat such an assumption on geo-
logical grounds, so long as we are imperfectly acquainted with the
order of superposition and the organic remains of these same formations.
Thus, for example, a group of red marl and red sandstone, containing salt
and gypsum, being interposed in England between the Lias and the Coal,
all other red marls and sandstones, associated some of them with salt, and
others with gypsum, and occurring not only in different parts of Europe,
but in North America,_Peru, India, the salt deserts of Asia, those of Africa
— in a word, in every quarter of the globe — were referred to one and the
same period. The burden of proof was not supposed to rest with those
who insisted on the identity in age of all these groups — their identity in
mineral composition was thought sufficient. It was in vain to urge as an
objection the improbability of the hypothesis which implies that all the
moving waters on the globe were once simultaneously charged with sedi-
ment of a red colour.
But the rashness of pretending to identify, in age, all the red sand-
stones and marls in question has at length been sufficiently exposed by the
discovery that, even in Europe, they belong decidedly to many different
epochs. It is already ascertained that the red sandstone and red marl con-
taining the rock salt of Cardona in Catalonia is newer than the Oolitic,
if not more modern than the Cretaceous period. It is also known that cer-
LYELL-—PRINCIPLES OF GEOLOGY 313
tain red marls and variegated sandstones in Auvergne which are undis-
tinguishable in mineral composition from the New Red Sandstone of
English geologists belong, nevertheless, to the Eocene period: and, lastly,
the gypseous red marl of Aix, in Provence, formerly supposed to be a
marine secondary group, is now acknowledged to be a tertiary freshwater
formation. In Nova Scotia one great deposit of red marl, sandstone, and
gypsum, precisely resembling in mineral character the "New Red** of
England, occurs as a member of the carboniferous group, and in the
United States, near the Falls of Niagara, a similar formation constitutes
a subdivision of the Silurian series.
VII On the Supposed Former Intensity of the Igneous Forces
WHEN REASONING on the intensity of volcanic action at former periods, as
well as on the power of moving water, already treated of, geologists have
been ever prone to represent Nature as having been prodigal of violence
and parsimonious of time. Now, although it is less easy to determine the
relative ages of the volcanic than of the fossiliferous formations, it is un-
deniable that igneous rocks have been produced at all geological periods,
or as often as we find distinct deposits marked by peculiar animal and
vegetable remains. It can be shown that rocks 'commonly called trappean
have been injected into fissures and ejected at the surface, both before
and during the deposition of the carboniferous series, and at the time
when the Magnesian Limestone and when the Upper New Red Sandstone
were formed, or when the Lias, Oolite, Greensand, Chalk and the several
tertiary groups newer than the chalk originated in succession. Nor is this
all; distinct volcanic products may be referred to the subordinate divi-
sions of each period, such as the Carboniferous, as in the county of Fife,
in Scotland, where certain masses of contemporaneous trap are associated
with the Lower, others with the Upper Coal Measures. And if one of
these masses is more minutely examined, we find it to consist of the
products of a great many successive outbursts, by which scoriae and lava
were again and again emitted, and afterwards consolidated, then fissured,
and finally traversed by melted matter constituting what are called dikes.
As we enlarge, therefore, our knowledge of the ancient rocks formed by
subterranean heat, we find ourselves compelled to regard them as the
aggregate effects of innumerable eruptions, each of which may have been
comparable in violence to those now experienced in volcanic regions.
Gradual development of subterranean movements. — The extreme vio-
lence of the subterranean forces in remote ages has been often inferred
from the facts that the older rocks are more fractured and dislocated
than the newer. But what other result could we have anticipated if the
quantity of movement had been always equal in equal periods of time?
Time must, in that case, multiply the derangement of strata in the ratio
314 MASTERWORKS OF SCIENCE
of their antiquity. Indeed the numerous exceptions to the above rule
which we find in nature present at first sight the only objection to the
hypothesis of uniformity. For the more ancient formations remain in
many places horizontal, while in others much newer strata are curved
and vertical.
That the more impressive effects of subterranean power, such as the
upheaval of mountain chains, may have been due to multiplied convul-
sions of moderate intensity rather than to a few paroxysmal explosions
will appear the less improbable when the gradual and intermittent devel-
opment of volcanic eruptions in times past is once established. It is now
very generally conceded that these eruptions have their source in the same
causes as those which give rise to the permanent elevation and sinking
of land; the admission, therefore, that one of the two volcanic or subter-
ranean processes has gone on gradually draws with it the conclusion that
the effects of the other have been elaborated by successive and gradual
efforts.
Faults. — The same reasoning is applicable to great faults, or those
striking instances of the upthrow or downthrow of large masses of rock,
which have been thought by some to imply tremendous catastrophes
wholly foreign to the ordinary course of nature. Thus we have in England
faults in which the vertical displacement is between 600 and 3000 feet and
the horizontal extent thirty miles or more, the width of the fissures since
filled up with rubbish varying from ten to fifty feet. But when we inquire
into the proofs of the mass having risen or fallen suddenly on the one side
of these great rents, several hundreds or thousands of feet above or below
the rock with which it was once continuous on the other side, we find the
evidence defective. There are grooves, it is said, and scratches on the
rubbed and polished walls, which have often one common direction,
favouring the theory that the movement was accomplished by a single
stroke and not by a series of interrupted movements. But, in fact, the striae
are not always parallel in such cases, but often irregular, and sometimes
the stones and earth which are in the middle of the fault, or fissure, have
been polished and striated by friction in different directions, showing that
there have been slidings subsequent to the first introduction of the frag-
mentary matter. Nor should we forget that the last movement must always
tend to obliterate the signs of previous trituration, so that neither its in-
stantaneousness nor the uniformity of its direction can be inferred from
the parallelism of the striae that have been last produced.
When rocks have been once fractured, and freedom of motion com-
municated to detached portions of them, these will naturally continue to
yield in the same direction, if the process of upheaval or of undermining
be repeated again and again. The incumbent mass will always give way
along the lines of least resistance, or where it was formerly rent asunder.
Probably, the effects of reiterated movement, whether upward or down-
ward, in a fault, may be undistinguishable from those of a single and in-
stantaneous rise or subsidence; and the same may be said of the rising or
LYELL — PRINCIPLES OF GEOLOGY 315
falling of continental masses, such as Sweden or Greenland, which we
know to take place slowly and insensibly.
Slow upheaval and subsidence. — Recent observations have disclosed
to us the wonderful fact that not only the west coast of South America,
but also other large areas, some of them several thousand miles in circum-
ference, such as Scandinavia, and certain archipelagos in the Pacific, are
slowly and insensibly rising; while other regions, such as Greenland and
parts of the Pacific and Indian Oceans, in which atolls or circular coral
islands abound, are as gradually sinking. That all the existing continents
and submarine abysses may have originated in movements of this kind,
continued throughout incalculable periods of time, is undeniable, and the
denudation which the dry land appears everywhere to have suffered
favours the idea that it was raised from the deep by a succession of up-
ward movements, prolonged throughout indefinite periods. For the action
of waves and currents on land slowly emerging from the deep affords the
only power by which we can conceive so many deep valleys and wide
spaces to have been denuded as those which are unquestionably the
effects of running water.
But perhaps it may be said that there is no analogy between the slow
upheaval of broad plains or table lands and the manner in which we must
presume all mountain chains, with their inclined strata, to have origi-
nated. It seems, however, that the Andes have been rising century after
century, at the rate of several feet, while the Pampas on the east have been
raised only a few inches in the same time. Crossing from the Atlantic to
the Pacific, in a line passing through Mendoza, Mr. Darwin traversed a
plain 800 miles broad, the eastern part of which has emerged from be-
neath the sea at a very modern period. The slope from the Atlantic is at
first very gentle, then greater, until the traveller finds, on reaching Men-
doza, that he has gained, almost insensibly, a height of 4000 feet. The
mountainous district then begins suddenly, and its breadth from Mendoza
to the shores of the Pacific is 120 miles, the average height of the princi-
pal chain being from 15,000 to 16,000 feet, without including some promi-
nent peaks, which ascend much higher. Now all we require, to explain
the origin of the principal inequalities of level here described, is to
imagine, first, a zone of more violent movement to the west of Mendoza,
and, secondly, to the east of that place, an upheaving force, which died
away gradually as it approached the Atlantic. In short, we are only called
upon to conceive that the region of the Andes was pushed up four feet in
the same period in which the Pampas near Mendoza rose one foot and the
plains near the shores of the Atlantic one inch. In Europe we have learnt
that the land at the North Cape ascends about five feet in a century, while
farther to the south the movements diminish in quantity first to a foot,
and then, at Stockholm, to three inches in a century, while at certain
points still farther south there is no movement.
In conclusion, I may observe that one of the soundest objections to
the theory of the sudden upthrow or downthrow of mountain chains is
this, that it provides us with too much force of one kind, namely, that ot
316 MASTERWORKS OF SCIENCE _
subterranean movement, while it deprives us of another kind of mechani-
cal force, namely, that exerted by the waves and currents of the ocean,
which the geologist requires for the denudation of land during its slow
upheaval or depression. It may be safely affirmed that the quantity of
igneous and aqueous action — of volcanic eruption and denudation — of
subterranean movement and sedimentary deposition — not only of past
ages, but of one geological epoch, or even the fraction of an epoch, has
exceeded immeasurably all the fluctuations of the inorganic world which
have been witnessed by man. But we have still to inquire whether the
time to which each chapter or page or paragraph of the earth's auto-
biography relates was not equally immense when contrasted with a brief
era of 3000 or 5000 years. The real point on which the whole controversy
turns is the relative amount of work done by mechanical force in given
quantities of time, past and present. Before we can determine the relative
intensity of the force employed, we must have some fixed standard by
which to measure the time expended in its development at two distinct
periods. It is not the magnitude of the effects, however gigantic their pro-
portions, which can inform us in the slightest degree whether the opera-
tion was sudden or gradual, insensible or paroxysmal. It must be shown
that a slow process could never in any series of ages give rise to the same
results.
The advocate of paroxysmal energy might assume an uniform and
fixed rate of variation in times past and present for the animate world,
that is to say, for the dying-out and coming-in of species, and then en-
deavour to prove that the changes of the inanimate world have not gone
on in a corresponding ratio. But the adoption of such a standard of com-
parison would lead, I suspect, to a theory by no means favourable to the
pristine intensity of natural causes. That the present state of the organic
world is not stationary can be fairly inferred from the fact that some
species are known to have become extinct in the course even of the last
three centuries, and that the exterminating causes always in activity, both
on the land and in the waters, are very numerous; also, because man him-
self is an extremely modern creation; and we may therefore reasonably
suppose that some of the mammalia now contemporary with man, as well
as a variety of species of inferior classes, may have been recently intro-
duced into the earth, to supply the places of plants and animals which
have from time to time disappeared. But granting that some such secular
variation in the zoological and botanical worlds is going on, and is by no
means wholly inappreciable to the naturalist, still it is certainly far less
manifest than the revolution always in progress in the inorganic world.
Every year some volcanic eruptions take place, and a rude estimate might
be made of the number o£ cubic feet of lava and scoriae poured or cast out
of various craters. The amount of mud and sand deposited in deltas, and
the advance of new land upon the sea, or the annual retreat of wasting
sea cliffs, are changes the minimum amount of which might be roughly
estimated. The quantity of land raised above or depressed below the level
of the sea might also be computed, and the change arising from such
LYELL — PRINCIPLES OF GEOLOGY 317
movements in a century might be conjectured. Suppose the average rise
of the land in some parts of Scandinavia to be as much as five feet in a
hundred years, the present seacoast might be uplifted 700 feet in fourteen
thousand years; but we should have no reason to anticipate, from any
zoological data hitherto acquired, that the molluscous fauna of the north-
ern seas would in that lapse of years undergo any sensible amount of vari-
ation. We discover sea beaches in Norway 700 feet high, in which the
shells are identical with those now inhabiting the German Ocean; for the
rise of land in Scandinavia, however insensible to the inhabitants, has
evidently been rapid when compared to the rate of contemporaneous
change in the testaceous fauna of the German Ocean. Were we to wait
therefore until the mollusca shall have undergone as much fluctuation as
they underwent between the period of the Lias and the Upper Oolite for-
mations, or between the Oolite and Chalk, nay, even between any two of
eight subdivisions of the Eocene series, what stupendous revolutions in
physical geography ought we not to expect, and how many mountain
chains might not be produced by the repetition of shocks of moderate
violence, or by movements not even perceptible by man!
Or, if we turn from the mollusca to the vegetable kingdom, and ask
the botanist how many earthquakes and volcanic eruptions might be ex-
pected, and how much the relative level of land and sea might be altered,
or how far the principal deltas will encroach upon the ocean, or the sea
cliffs recede from the present shores, before the species of European forest
trees will die out, he would reply that such alterations in the inanimate
world might be multiplied indefinitely before he should have reason to
anticipate, by reference to any known data, that the existing species of
trees in our forests would disappear and give place to others. In a word,
the movement of the inorganic world is obvious and palpable, and might
be likened to the minute hand of a clock, the progress of which can be
seen and heard, whereas the fluctuations of the living creation are nearly
invisible and resemble the motion of the hour hand of a timepiece. It is
only by watching it attentively for some time, and comparing its relative
position after an interval, that we can prove the reality of its motion.
VIII Uniformity in the Series of Past Changes in the
Animate and Inanimate World
Origin of the doctrine of alternate periods of repose and disorder. —
It has been truly observed that when we arrange the fossiliferous forma-
tions in chronological order, they constitute a broken and defective series
of monuments: we pass without any intermediate gradations from sys-
tems of strata which are horizontal to other systems which are highly in-
clined, from rocks of peculiar mineral composition to others which have a
318 MASTERWORKS OF SCIENCE
character wholly distinct — from one assemblage of organic remains to an-
other, in which frequently all the species, and most of the genera, are dif-
ferent. These violations of continuity are so common as to constitute the
rule rather than the exception, and they have been considered by many
geologists as conclusive in favour of sudden revolutions in the inanimate
and animate world. According to the speculations of some writers, there
have been in the past history of the planet alternate periods of tranquillity
and convulsion, the former enduring for ages, and resembling that state
of things now experienced by man: the other brief, transient, and paroxys-
mal, giving rise to new mountains, seas, and valleys, annihilating one set
of organic beings and ushering in the creation of another.
It is true that in the solid framework of the globe, we have a chrono-
logical chain of natural records, and that many links in this chain are
wanting; but a careful consideration of all the phenomena will lead to the
opinion that the series was originally defective — that it has been rendered
still more so by time — that a great part of what remains is inaccessible to
man, and even of that fraction which is accessible, nine tenths are to this
day unexplored.
How the facts may be explained by assuming a uniform series of
changes. — The readiest way, perhaps, of persuading the reader that we
may dispense with great and sudden revolutions in the geological order of
events is by showing him how a regular and uninterrupted series of
changes in the animate and inanimate world may give rise to such breaks
in the sequence, and such unconformability of stratified rocks, as are
usually thought to imply convulsions and catastrophes. It is scarcely neces-
sary to state that the order of events thus assumed to occur, for the sake of
illustration, must be in harmony with all the conclusions legitimately
drawn by geologists from the structure of the earth, and must be equally
in accordance with the changes observed by man to be now going on in
the living as well as in the inorganic creation. It may be necessary in the
present state of science to supply some part of the assumed course of
nature hypothetically; but if so, this must be done without any violation
of probability, and always consistently with the analogy of what is known
both of the past and present economy of our system.
UNIFORMITY OF CHANGE CONSIDERED FIRST IN
REFERENCE TO THE LIVING CREATION
First, in regard to the vicissitudes of the living creation, all are agreed
that the sedimentary strata found in the earth's crust are divisible into a
variety of groups, more or less dissimilar in their organic remains and
mineral composition. The conclusion universally drawn from the study
and comparison of these fossiliferous groups is this, that at successive
periods, distinct tribes of animals and plants have inhabited the land and
waters, and that the organic types of the newer formations are more
analogous to species now existing than those of more ancient rocks. If we
LYELL — PRINCIPLES OF GEOLOGY 319
then turn to the present state of the animate creation, and inquire
whether it has now become fixed and stationary, we discover that, on the
contrary, it is in a state of continual flux — that there are many causes in
action which tend to the extinction of species, and which are conclusive
against the doctrine of their unlimited durability. But natural history has
been successfully cultivated for so short a period that a few examples only
of local, and perhaps but one or two of absolute, extirpation can as yet be
proved, and these only where the interference of man has been conspicu-
ous. It will nevertheless appear evident that man is not the only extermi-
nating agent; and that, independently of his intervention, the annihilation
of species is promoted by the multiplication and gradual diffusion of
every animal or plant.
Recent origin of man, and gradual approach in the tertiary fossils of
successive periods from an extinct to the recent fauna. — The geologist,
however, if required to advance some fact which may lend countenance to
the opinion that in the most modern times, that is to say, after the greater
part of the existing fauna and flora were established on the earth, there
has still been a new species superadded, may point to man himself as
furnishing the required illustration — for man must be regarded by the
geologist as a creature of yesterday, not merely in reference to the past
history of the organic world, but also in relation to that particular state
of the animate creation of which he forms a part. The comparatively
modern introduction of the human race is proved by the absence of the
remains of man and his works, not only from all strata containing a cer-
tain proportion of fossil shells of extinct species, but even from a large
part of the newest strata, in which all the fossil individuals are referable to
species still living.
To enable the reader to appreciate the full force of this evidence I
shall give a slight sketch of the information obtained from the newer
strata, respecting fluctuations in the animate world in times immediately
antecedent to the appearance of man.
In tracing the series of fossiliferous formations from the more ancient
to the more modern, the first deposits in which we meet with assemblages
of organic remains, having a near analogy to the fauna of certain parts of
the globe in our own time, are those commonly called tertiary. Even in
the Eocene, or oldest subdivision of these tertiary formations, some few of
the testacea belong to existing species, although almost all of them, and
apparently all the associated vertebrata, are now extinct. These Eocene
strata are succeeded by a great number of more modern deposits, which
depart gradually in the character of their fossils from the Eocene type,
and approach more and more to that of the living creation. In the pres-
ent state of science, it is chiefly by the aid of shells that we are enabled to
arrive at these results, for of all classes the testacea are the most generally
diffused in a fossil state, and may be called the medals principally em-
ployed by nature, in recording the chronology of past events. In the Mio-
cene deposits, which are next in succession to the Eocene, we begin^ to
find a considerable number, although still a minority, of recent species,
320 MASTERWORKS OF SCIENCE
Intermixed with some fossils common to the preceding epoch. We then
arrive at the Pliocene strata, in which species now contemporary with
man begin to preponderate, and in the newest o£ which nine tenths of the
fossils agree with species still inhabiting the neighbouring sea.
In thus passing from the older to the newer members of the tertiary
system we meet with many chasms, but none which separate entirely, by
a broad line of demarcation, one state of the organic world from another.
There are no signs of an abrupt termination of one fauna and flora, and
the starting into life of new and wholly distinct forms. Although we are
far from being able to demonstrate geologically an insensible transition
from the Eocene to the Miocene, or even from the latter to the recent
fauna, yet the more we enlarge and perfect our general survey, the more
nearly do we approximate to such a continuous series, and the more grad-
ually are we "conducted from times when many of the genera and nearly
all the species were extinct to those in which scarcely a single species
flourished which we do not know to exist at present.
It had often been objected that the evidence of fossil species occur-
ring in two consecutive formations was confined to the testacea or zoo-
phytes, the characters of which are less marked and decisive than those
afforded by the vertebrate animals. But Mr. Owen has lately insisted on
the important fact that not a few of the quadrupeds which now inhabit
cur island, and among others the horse, the ass, the hog, the smaller wild
ox, the goat, the red deer, the roe, the beaver, and many of the diminutive
rodents, are the same as those which once co-existed with the mammoth,
the great northern hippopotamus, two kinds of rhinoceros, and other
mammalia long since extinct. "A part," he observes, "and not the whole of
the modern tertiary fauna has perished, and hence we may conclude that
the cause of their- destruction has not been a violent and universal catas-
trophe from which none could escape."
Had we discovered evidence that man had come into the earth at a
period as early as that when a large number of the fossil quadrupeds now
living, and almost all the recent species of land, freshwater, and marine
shells were in existence, we should have been compelled to ascribe a much
higher antiquity to our species than even the boldest speculations of the
ethnologist require, for no small part of the great physical revolution de-
picted on the map of Europe before described took place very gradually
after the recent testacea abounded almost to the exclusion of the extinct.
Thus, for example, in the deposits called the "northern drift," or the
glacial formation of Europe and North America, the fossil marine shells
can easily be identified with species either now inhabiting the neighbour-
ing sea or living in the seas of higher latitudes. Yet they exhibit no memo-
rials of the human race, or of articles fabricated by the hand of man.
There are other post-tertiary formations of fluviatile origin, in the
centre of Europe, in which the absence of human remains is perhaps still
more striking, because, when formed, they must have been surrounded by
dry land. I allude to the silt or loess of the basin of the Rhine, which must
lave gradually filled up the great valley of that river since the time when
LYELL — PRINCIPLES OF GEOLOGY 321
its" waters, and the contiguous lands, were inhabited by the existing spe-
cies of freshwater and terrestrial mollusks. Showers of ashes, thrown out
by some of the last eruptions of the Eifel volcanos, fell during the deposi-
tion of this fluviatile silt, and were interstratified with it. But these vol-
canos became exhausted, the valley was re-excavated through the silt, and
again reduced to its present form before the period of human history.
The study, therefore, of this shelly silt reveals to us the history of a long
series of events, which occurred after the testacea now living inhabited
the land and rivers of Europe, and the whole terminated without any
signs of the coming of man into that part of the globe.
To conclude, it appears that, in going back from the recent to the
Eocene period, we are carried by many successive steps from the fauna
now contemporary with man to an assemblage of fossil species wholly dif-
ferent from those now living. In this retrospect we have not yet succeeded
in tracing back a perfect transition from the recent to an extinct fauna;
but there are usually so many species in common to the groups which
stand next in succession as to show that there is no great chasm, no signs
of a crisis when one class of organic beings was annihilated to give place
suddenly to another. This analogy, therefore, derived from a period of the
earth's history which can best be compared with the present state of
things, and more thoroughly investigated than any other, leads to the con-
clusion that the extinction and creation of species has been and is the
result of a slow and gradual change in the organic world.
UNIFORMITY OF CHANGE CONSIDERED, SECONDLY, IN
REFERENCE TO SUBTERRANEAN MOVEMENTS
Certain countries have, from time immemorial, been rudely shaken
again and again, while others, comprising by far the largest part of the
globe, have remained to all appearance motionless. In the regions of con-
vulsion rocks have been rent asunder, the surface has been forced up into
ridges, chasms have opened, or the ground throughout large spaces has
been permanently lifted up above or let down below its former level. In
the regions of tranquillity some areas have remained at rest, but others
have been ascertained by a comparison of measurements, made at differ-
ent periods, to have risen by an insensible motion, as in Sweden, or to
have subsided very slowly, as in Greenland. That these same movements,,
whether ascending or descending, have continued for ages in the same
direction has been established by geological evidence. Thus we find both
on the east and west coast of Sweden that ground which formerly consti-
tuted the bottom of the Baltic and of the ocean has been lifted up to an
elevation of several hundred feet above high-water mark. The rise within
the historical period has not amounted to many yards, but the greater
extent of antecedent upheaval is proved by the occurrence in inland spots^
several hundred feet high, of deposits filled with fossil shells of species
now living either in the ocean or the Baltic.
322 MASTERWORKS OF SCIENCE
To detect proofs of slow and gradual subsidence must in general be
more difficult; but the form of circular coral reefs and lagoon islands will
satisfy the reader that there are spaces on the globe, several thousand
miles in circumference, throughout which the downward movement has
predominated for ages, and yet the land has never, in a single instance,
gone down suddenly for several hundred feet at once. Yet geology demon-
strates that the persistency of subterranean movements in one direction
has not been perpetual throughout all past time. There have been great
oscillations of level by which a surface of dry land has been submerged to
a depth of several thousand feet, and then at a period long subsequent
raised again and made to emerge. Nor have the regions now motionless
been always at rest; and some of those which are at present the theatres of
reiterated earthquakes have formerly enjoyed a long continuance of tran-
quillity. But although disturbances have ceased after having long pre-
vailed, or have recommenced after a suspension for ages, there has been
no universal disruption of the earth's crust or desolation of the surface
since times the most remote. The non-occurrence of such a general con-
vulsion is proved by the perfect horizontality now retained by some of
the most ancient fossiliferous strata throughout wide areas.
Inferences derived -from unconjormable strata. — That the subterra-
nean forces have visited different parts of the globe at successive periods
is inferred chiefly from the unconformability of strata belonging to groups
of different ages. Thus, for example, on the borders of Wales and Shrop-
shire we find the slaty beds of the ancient Silurian system curved and ver-
tical, while the beds of the overlying carboniferous shale and sandstone
are horizontal. All are agreed that in such a case the older set of strata had
suffered great dislocation before the deposition of the newer or carbonif-
erous beds, and that these last have never since been convulsed by any
movements of excessive violence. But the strata of the inferior group suf-
fered only a local derangement, and rocks of the same age are by no means
found everywhere in a curved or vertical position. In various parts of
Europe, and particularly near Lake Wener in the south of Sweden, and in
many parts of Russia, beds of the same Silurian system maintain the most
perfect horizontality; and a similar observation may be made respecting
limestones and shales of the like antiquity in the Great Lake District of
Canada and the United States. They are still as flat and horizontal as
when first formed; yet since their origin not only have most of the actual
mountain chains been uplifted, but the very rocks of which those moun-
tains are composed have been formed.
UNIFORMITY OF CHANGE CONSIDERED, THIRDLY, IN
REFERENCE TO SEDIMENTARY DEPOSITION
If we survey the surface of the globe we immediately perceive that it
is divisible into areas of deposition and non-deposition, or, in other
words, at any given time there are spaces which are the recipients, others
LYELL — PRINCIPLES OF GEOLOGY 323
which are not the recipients, of sedimentary matter. No new strata, for
example, are thrown down on dry land, which remains the same from
year to year; whereas, in many parts of the bottom of seas and lakes, mud,
sand, and pebbles are annually spread out by rivers and currents. There
are also great masses of limestone growing in some seas, or in mid-ocean,
chiefly composed of corals and shells.
No sediment deposited on dry land. — As to the dry land, so far from
being the receptacle of fresh accessions of matter, it is exposed almost
everywhere to waste away. Forests may be as dense and lofty as those of
Brazil, and may swarm with quadrupeds, birds, and insects, yet at the end
of ten thousand years one layer of black mould, a few inches thick, may
be the sole representative of those myriads of trees, leaves, flowers, and
fruits, those innumerable bones and skeletons of birds, quadrupeds, and
reptiles, which tenanted the fertile region. Should this land be at length
submerged, the waves of the sea may wash away in a few hours the scanty
covering of mould, and it may merely impart a darker shade of colour to
the next stratum of marl, sand, or other matter newly thrown down. So
also at the bottom of the ocean where no sediment is accumulating, sea-
weed, zoophytes, fish, and even shells, may multiply for ages and decom-
pose, leaving no vestige of their form or substance behind. Their decay,
in water, although more slow, is as certain and eventually as complete as
in the open air. Nor can they be perpetuated for indefinite periods in a
fossil state, unless imbedded in some matrix which is impervious to water
or which at least does not allow a free percolation of that fluid, impreg-
nated as it usually is, with a slight quantity of carbonic or other acid.
Such a free percolation may be prevented either by the mineral nature of
the matrix itself, or by the superposition of an impermeable stratum: but
if unimpeded the fossil shell or bone will be dissolved and removed, par-
ticle after particle, and thus entirely effaced, unless petrifaction or the
substitution of mineral for organic matter happen to take place.
That there has been land as well as sea at all former geological peri-
ods, we know from the fact that fossil trees and terrestrial plants are im-
bedded in rocks of every age. Occasionally lacustrine and fluviatile shells,
insects, or the bones of amphibious or land reptiles point to the same con-
clusion. The existence of dry land at all periods of the past implies, as
before mentioned, the partial deposition of sediment, or its limitation to
certain areas; and the next point to which I shall call the reader's attention
is the shifting of these areas from one region to another.
First, then, variations in the site of sedimentary deposition are
brought about independently of subterranean movements. There is always
*a slight change from year to year/ or from century to century. The sedi-
ment of the Rhone, for example, thrown into the Lake of Geneva, is now
conveyed to a spot a mile and a half distant from that where it accumu-
lated in the tenth century, and six miles from the point where the delta
began originally to form. We may look forward to the period when this
lake will be filled up, and then the distribution of the transported matter
will be suddenly altered, for the mud and sand brought down from the
324 MASTERWORKS OF SCIENCE
Alps will thenceforth, instead of being deposited near Geneva, be carried
nearly 200 miles southwards, where the Rhone enters the Mediterranean.
But, secondly, all these causes of fluctuation in the sedimentary areas
are entirely subordinate to those great upward or downward movements
of land which have been already described as prevailing over large tracts
of the globe. By such elevation or subsidence certain spaces are gradually
submerged, or made gradually to emerge: — in the one case sedimentary
deposition may be suddenly renewed after having been suspended for
ages, in the other as suddenly made to cease after having continued for an
indefinite period.
Causes of variation in mineral character of successive sedimentary
groups. — If deposition be renewed after a long interval, the new strata
will usually differ greatly from the sedimentary rocks previously formed
in the same place, and especially if the older rocks have suffered derange-
ment, which implies a change in the physical geography of the district
since the previous conveyance of sediment to the same spot. It may hap-
pen, however, that, even when the inferior group is horizontal and con-
formable to the upper strata, these last may still differ entirely in mineral
character, because since the origin of the older formation the geography
of some distant country has been altered. In that country rocks before
concealed may have become exposed by denudation; volcanos may have
burst out and covered the surface with scoriae and lava, or new lakes may
have been formed by subsidence; and other fluctuations may have oc-
curred, by which the materials brought down feom thence by rivers to the
sea have acquired a distinct mineral character.
It is well known that the stream of the Mississippi is charged with
sediment of a different colour from that of the Arkansas and Red Rivers,
which are tinged with red mud, derived from rocks of porphyry in "the
far west." The waters of the Uruguay, says Darwin, draining a granitic
country, are clear and black, those of the Parana, red. The mud with
which the Indus is loaded, says Burnes, is of a clayey hue, that of the
Chenab, on the other hand, is reddish, that of the Sudej is more pale. The
same causes which make these several rivers, sometimes situated at no
great distance the one from the other, to differ greatly in the character of
their sediment will make the waters draining the same country at differ-
ent epochs, especially before and after great revolutions in physical geog-
raphy, to be entirely dissimilar.
Why successive sedimentary groups contain distinct -fossils. — If, in
the next place, we assume, for reasons before stated, a continual extinction
of species and introduction of others into the globe, it will then follow
that the fossils of strata formed at two distant periods on the same spot*
will differ even more certainly than the mineral composition of the same.
For rocks of the same kind have sometimes been reproduced in the same
district after a long interval of time, whereas there are no facts leading to
the opinion that species which have once died out have ever been repro-
duced. The submergence then of land must be often attended by the com-
mencement of a new class of sedimentary deposits, characterized by a new
LYELL — PRINCIPLES OF GEOLOGY 325
set of fossil animals and plants, while the reconversion of the bed of the
sea into land may arrest at once and for an indefinite time the formation
of geological monuments. Should the land again sink, strata will again be
formed; but one or many entire revolutions in animal or vegetable life
may have been completed in the interval.
Conditions requisite for the original completeness of a jossiliferous
series. — If we infer, for reasons before explained, that fluctuations in the
animate world are brought about by the slow and successive removal and
creation of species, we shall be convinced that a rare combination of cir-
cumstances alone can give rise to such a series of strata as will bear testi-
mony to a gradual passage from one state of organic life to another. To
produce such strata nothing less will be requisite than the fortunate co-
incidence of the following conditions: first, a never-failing supply of sedi-
ment in the same region throughout a period of vast duration; secondly,,
the fitness of the deposit in every part for the permanent preservation o£
imbedded fossils; and, thirdly, a gradual subsidence to prevent the sea or
lake from being filled up and converted into land.
In certain parts of the Pacific and Indian Oceans, most of these condi-
tions, if not all, are complied with, and the constant growth of coral, keep-
ing pace with the sinking of the bottom of the sea, seems to have gone on
so slowly, for such indefinite periods, that the signs of a gradual change in
organic life might probably be detected in that quarter of the globe, if we
could explore its submarine geology. Instead of the growth of coralline
limestone, let us suppose, in some other place, the continuous deposition
of fluviatile mud and sand, such as the Ganges and Brahmapootra have
poured for thousands of years into the Bay of Bengal. Part of this bay,,
although of considerable depth, might at length be filled up before an ap-
preciable amount of change was effected in the fish, mollusca, and other
inhabitants of the sea and neighbouring land. But, if the bottom be low-
ered by sinking at the same rate that it is raised by fluviatile mud, the bay
can never be turned into dry land. In that case one new layer of matter
may be superimposed upon another for a thickness of many thousand feet,
and the fossils of the inferior beds may differ greatly from those en-
tombed in the uppermost, yet every intermediate gradation may be indi-
cated in the passage from an older to a newer assemblage of species.
Granting, however, that such an unbroken sequence of monuments may
thus be elaborated in certain parts of the sea, and that the strata happen to
be all of them well adapted to preserve the included fossils from decom-
position, how many accidents must still concur before these submarine
formations will be laid open to our investigation! The whole deposit must
first be raised several thousand feet, in order to bring into view the very
foundation; and during the process of exposure the superior beds must
not be entirely swept away by denudation.
In the first place, the chances are as three to one against the mere
emergence of the mass above the waters, because three fourths of the
globe are covered by the ocean. But if it be upheaved and made to consti-
tute part of the dry land, it must also, before it can be available for our
326 MASTERWORKS OF SCIENCE
instruction, become part of that area already surveyed by geologists; and
this area comprehends perhaps less than a tenth of the whole earth. In
this small fraction of land already explored, and still very imperfectly
known, we are required to find a set of strata, originally of limited extent,
and probably much lessened by subsequent denudation.
Yet it is precisely because we do not encounter at every step the evi-
dence of such gradations from one state of the organic world to another
that so many geologists embrace the doctrine of great and sudden revolu-
tions in the history of the animate world. Not content with simply avail-
ing themselves, for the convenience of classification, of those gaps and
chasms which here and there interrupt the continuity of the chronological
series, as at present known, they deduce, from the frequency of these
breaks in the chain of records, an irregular mode of succession in the
events themselves both in the organic and inorganic world. But, besides
that some links of the chain which once existed are now clearly lost and
others concealed from view, we have good reason to suspect that it was
never complete originally. It may undoubtedly be said that strata have
been always forming somewhere, and therefore at every moment of past
time nature has added a page to her archives; but, in reference to this
subject, it should be remembered that we can never hope to compile a
consecutive history by gathering together monuments which were origi-
nally detached and scattered over the globe. For as the species of organic
beings contemporaneously inhabiting remote regions are distinct, the fos-
sils of the first of several periods which may be preserved in any one
country, as in America, for example, will have no connection with those of
a second period found in India, and will therefore no more enable us to
trace the signs of a gradual change in the living creation than a fragment
of Chinese history will fill up a blank in the political annals of Europe.
How far some of the great violations of continuity which now exist
in the chronological table of fossiliferous rocks will hereafter be removed
or lessened must at present be mere matter of conjecture. The hiatus
which exists in Great Britain between the fossils of the Lias and those of
the Magnesian Limestone is supplied in Germany by the rich fauna and
flora of the Muschelkalk, Keuper, and Bunter Sandstein, which we know
to be of a date precisely intermediate; those three formations being inter-
posed in Germany between others which agree perfectly in their organic
remains with our Lias and Magnesian Limestone. Still we must expect,
for reasons before stated, that some such chasms will forever continue to
occur in some parts of our sedimentary series.
Consistency of the theory of gradual change, with the existence of
great breads in the series. — To return to the general argument pursued in
this chapter, it is assumed, for reasons above explained, that a slow change
of species is in simultaneous operation everywhere throughout the habit-
able surface of sea and land; whereas the fossilization of plants and ani-
mals is confined to those areas where new strata are produced. These
areas, as we have seen, are always shifting their position; so that the fos-
silizing process, by means of which the commemoration of the particular
LYELL— -PRINCIPLES OF GEOLOGY 327
state of the organic world, at any given time, is affected, may be said to
move about, visiting and revisiting different tracts in succession.
To make still more clear the supposed working of this machinery, I
shall compare it to a somewhat analogous case that might be imagined to
occur in the history of human affairs.
Suppose we had discovered two buried cities at the foot of Vesuvius,
immediately superimposed upon each other, with a great mass of tuff and
lava intervening, just as Portici and Resina, if now covered with ashes,
would overlie Herculaneum. An antiquary might possibly be entitled to
infer, from the inscriptions on public edifices, that the inhabitants of the
inferior and older city were Greeks, and those of the modern towns Ital-
ians. But he would reason very hastily if he also concluded from these
data that there had been a sudden change from "the Greek to the Italian
language in Campania. But if he afterwards found three buried cities, one
above the other, the intermediate one being Roman, while, as in the for-
mer example, the lowest was Greek and the uppermost Italian, he would
then perceive the fallacy of his former opinion, and would begin to sus-
pect that the catastrophes, by which the cities were inhumed, might have
no relation whatever to the fluctuations in the language of the inhabitants:
and that, as the Roman tongue had evidently intervened between the
Greek and Italian, so many other dialects may have been spoken in suc-
cession, and the passage from the Greek to the Italian may have been very
gradual; some terms growing obsolete, while others were introduced from
time to time.
If this antiquary could have shown that the volcanic paroxysms of
Vesuvius were so governed as that cities should be buried one above the
other, just as often as any variation occurred in the language of the in-
habitants, then, indeed, the abrupt passage from a Greek to a Roman, and
from a Roman to an Italian city, would afford proof of fluctuations no less
sudden in the language of the people.
So, in Geology, if we could assume that it is part of the plan of Na-
ture to preserve, in every region of the globe, an unbroken series of monu-
ments to commemorate the vicissitudes of the organic creation, we might
infer the sudden extirpation of species, and the simultaneous introduction
of others, as often as two formations in contact are found to include dis-
similar organic fossils. But we must shut our eyes to the whole economy
of the existing causes, aqueous, igneous, and organic, if we fail to perceive
that such is not the -plan of Nature.
Concluding remarks on the identity of the ancient and present system
of terrestrial changes. — I shall now conclude the discussion of whether
there has been any interruption, from the remotest periods, of one uni-
form system of change in the animate and inanimate world. We were in-
duced to enter into that inquiry by reflecting how much the progress of
opinion in Geology had been influenced by the assumption that the anal-
ogy was slight in kind, and still more slight in degree, between the causes
which produced the former revolutions of the globe and those now in
everyday operation.
328 MASTERWORKS OF SCIENCE
Never was there a dogma more calculated to foster. indolence, and to-
blunt the keen edge of curiosity, than this assumption of the discordance
between the ancient and existing causes of change. It produced a state of
mind unfavourable in the highest degree to the candid reception of the
evidence of those minute but incessant alterations which every part of the
earth's surface is undergoing, and by which the condition of its living in-
habitants is continually made to vary. The student, instead of being en-
couraged with the hope of interpreting the enigmas presented to him in
the earth's structure, — instead of being prompted to undertake laborious
inquiries into the natural history of the organic world, and the compli-
cated effects of the igneous and aqueous causes now in operation, was
taught to despond from the first. Geology, it was affirmed, could never
rise to the rank of an exact science — the greater number of phenomena
must forever remain inexplicable, or only be partially elucidated by ingen-
ious conjectures. Even the mystery which invested the subject was said
to constitute one of its principal charms, affording, as it did, full scope to
the fancy to indulge in a boundless field of speculation.
The course directly opposed to this method of philosophizing con-
sists in an earnest and patient inquiry, how far geological appearances are
reconcilable with the effect of changes now in progress, or which may be
in progress in regions inaccessible to us, and of which the reality is at-
tested by volcano s and subterranean movements. It also endeavours to es-
timate the aggregate result of ordinary operations multiplied by time, and
cherishes a sanguine hope that the resources to be derived from observa-
tion and experiment, or from the study of nature such as she now is, are
very far from being exhausted. For this reason all theories are rejected
which involve the assumption of sudden and violent catastrophes and rev-
olutions of the whole earth, and its inhabitants — theories which are re-
strained by no reference to existing analogies, and in which a desire is
manifested to cut, rather than patiently to untie, the Gordian knot.
We have now, at least, the advantage of knowing, from experience,
that an opposite method has always put geologists on the road that leads
to truth — suggesting views which, although imperfect at first, have been
found capable of improvement, until at last adopted by universal consent;
while the method of speculating on a former distinct state of things and
causes has led invariably to a multitude of contradictory systems, which
have been overthrown one after the other — have been found incapable of
modification — and which have often required to be precisely reversed.
THE ORIGIN OF SPECIES
by
CHARLES DARWIN
CONTENTS
The Origin of Species
Introduction
I. Variation under Domestication
II. Variation under Nature
III. Struggle for Existence
IV. Natural Selection; or The Survival of the Fittest
V. Laws of Variation
VI. Difficulties of the Theory
VII. Miscellaneous Objections to the Theory of Natural Selection
VIII. Instinct
IX. On the Imperfection of the Geological Record
X, On the Geological Succession of Organic Beings
XL Geographical Distribution
XII. - Geographical Distribution— con tinned
XIII. Mutual Affinities of Organic Beings: Morphology: Embryology:
Rudimentary Organs
XIV, Conclusion
CHARLES DAR WIN
1809-1882
BORN on February 12, 1809, in Shrewsbury, the fifth child of
Dr. Robert Darwin, Charles Darwin was descended on his
mother's side from the great ceramic manufacturer, Josiah
Wedgwood, and on his father's from Erasmus Darwin, the
naturalist and poet. He was a docile, amiable child, much
given to daydreaming, and, after his mother's death when he
was five, to long, solitary cross-country walks. He had a quite
undistinguished residence at a boarding school, then at Edin-
burgh, where he displayed small interest In the medical lec-
tures he had gone to attend, then at Cambridge, where he
showed no more aptitude for theology than he had for medi-
cine. When he left Cambridge In 1831, his friends and his
family knew him as a generous, energetic lad who enjoyed
shooting, riding, gambling, and gay dinner parties; who had
dabbled a bit in chemistry and had barely survived his various
scholastic examinations; who had haphazardly collected coins,
minerals, and beetles. Once, after hearing Adam Sedgwick
lecture on geology, he had made a holiday geological expedi-
tion into North Wales. Once, after reading Alexander von
Humboldt's Personal Narrative, he had become sufficiently en-
thusiastic for a naturalist's journeys and life to study Spanish
in the hope of making a naturalist's expedition to Teneriffe.
Of these half-developed tastes, his Cambridge lecturer in bot-
any, John Stevens Henslow, knew. In 1831 he secured for
young Darwin an appointment as unsalaried naturalist for the
Beagle, a 25O-ton brig which was about to sail on a long sur-
vey of South America and to make chronometrical measure-
ments round the world. On December 2.7, 1831, the Beagle
sailed, carrying the unknown Darwin on an expedition which
lasted almost five years.
For his work as naturalist, Darwin was assigned as office
and shop a space in the chartroom so narrow that he was
332 MASTERWORKS OF SCIENCE
forced to develop habits of order. The Beagle visited, in turn,
the Cape Verde Islands, the coasts of South America, the
Galapagos, Tahiti, New Zealand, Australia, Tasmania, Mauri-
tius, Ascension, the Azores. Gradually Darwin made himself
a first-rate collector, an observant, shrewd geologist. He
puzzled over the fossils of the South American continent,
over the birds of Galapagos; he faced the vexed problem of
the origin of species.
On the return of the Beagle to England in 1836, Darwin
busied himself for several years in Cambridge and London
with his collections, some geological reports, and with the
writing of his Journal. In 1839 he married his cousin, Emma
Wedgwo.od, and three years later they went to live in Down,
a village fifteen miles from London. Darwin's health had de-
clined almost from the time of the Beagle's return; during his
remaining forty years he was almost constantly ill. He devel-
oped a routine of working very hard for so long as his consti-
tution allowed, then taking a brief holiday rest, then plunging
again into work. Except for these brief holiday jaunts and for
short trips to such meetings as those of the British Society, he
spent these forty years almost wholly in his own house and
garden at Down.
Before moving to Down, Darwin had given his fossil col-
lection to the College of Surgeons; with the aid of a Treasury
grant he had published the quarto volumes Zoology of the
Voyage of the Beagle; he had read several papers to the Geo-
logical Society and had served three years as the Society's sec-
retary. In the early years at Down (1842-46) he wrote Vol-
canic Islands and Geology of South America, propounded a
theory — immediately accepted by other geologists — on the
origin of coral reefs, and prepared a second edition of his
Journal. Then he devoted eight years to the preparation for
the Paleontological Society and the Royal Society (1851, 1854)
of his definitive monograph on the cirripides. During this
long labor he learned taxonomy and morphology, thus com-
pleting the education of a naturalist begun on the Beagle.
Though Darwin had pondered the problem of the origin
of species while he was aboard the Beagle, it was the reading
of Malthus's theories on population which crystallized his
own ideas. In 1842 he set these ideas down in a sketch thirty-
five pages long (unpublished) and two years later expanded
the sketch into an essay of 220 pages. Convinced that his
theory was revolutionary, he now settled to an arduous course
to prepare himself for writing a developed book on the sub-
ject. For fourteen years he read books of travel, books on
natural history, horticulture, animal husbandry; he read whole
files of journals. Always he took copious notes, constantly or-
DARWIN — ORIGIN OF SPECIES 333
ganizing and filing them. He prepared skeletons o£ domesti-
cated birds in order to compare their bones with those of wild
species. He kept pigeons and did experiments in crossbreed-
ing. He corresponded voluminously with Charles Lyell, Asa
Gray, and William Jackson Hooker about disputed points of
geology, about the geographical distribution of species, about
the transportation of seeds. Finally, in 1856, Lyell persuaded
him that he had undertaken an endless task of study and that
he should publish a book on his findings and theorizings so
far. Two years later, when he had just completed ten chapters
of the projected book, he received from Alfred Russel Wallace,
then in Malaysia, an essay for his criticism. It expressed in
detail Darwin's own theory.
Darwin's first inclination was to publish Wallace's paper
at once, withdrawing all claim to priority in conceiving his
theory of the origin of species. Lyell and Hooker counseled
differently. On their advice, Wallace's essay and some por-
tions of Darwin's 1844 essa-y were presented to the Linnaean
Society for publication in its Journal in 1858. Immediately
abandoning his great book, Darwin began preparing an "ab-
stract" of it. This was ready in a year and appeared in 1859:
On the Origin of Species by Means of Natural Selection, or the
Preservation of Favoured Races in the Struggle for Life.
Partly because of the great exciting phrases in its title,
partly because the topic of evolution — advanced earlier by
Lamarck and temperately discussed by Lyell — was already in
the air, the first edition (1,200 copies) of this book sold out
on the day of publication. Two months later a second edition
(3,000 copies) sold almost as rapidly. Its early chapters (I-IV)
explain the operations of artificial selection by man, and of
natural selection occasioned by the struggle for existence.
Then it presents (Chapter V) the laws of variation and causes
of modification other than natural selection, exposes fully
(Chapters VI— X) the difficulties in believing in evolution and
natural selection, and closes with three masterly chapters
(XI-XIII) marshaling athe evidence for evolution. The theory
of natural selection is primarily an explanation of the phe-
nomenon of adaptation. But the explanation makes easy the
acceptance of the theory of evolution. Further, it provides a
mechanical explanation for what had hitherto required the
special-creation hypothesis. Pedantic religious men took the
theory to be a denial of God as the creator. Bishop Wilber-
force in particular fulminated against Darwin. Huxley came
to the defense of the new theory, and a furious contention de-
veloped, culminating in the famous Oxford debate of 1860.
Darwin was slow in controversy. He left the defense of
his position largely to his polemical friends; but in a scholar's
334 MASTERWORKS OF SCIENCE
way lie busied himself in consolidating it. In 1868 he pub-
lished the work of eight years, The Variation of Animals and
Plants Under Domestication, which is really an elaboration of
a part of the Origin. In 1871 he published Descent of Man,
really a continuation of the Variation. Much more shocking
from an orthodox religious point of view than the Origin, the
Descent roused little bitter hostility. In the preceding twelve
years the scientific and intellectual world had almost univer-
sally accepted the Darwinian theses.
In the tremendous success he attained, Darwin remained
unostentatious. Convinced of the importance of his interpre-
tation of accumulated data, he was sometimes unjust to his
predecessors. But he never wearied of observing and collect-
ing facts, of reflecting over any subject patiently in order the
better to theorize, of abandoning hypotheses which experi-
ment, common sense, and observation proved untenable, and
of clinging pertinaciously to doctrines no matter how radical
when experiment, common sense, and observation insured
their value.
Darwin's remarkable studies, On the British Orchids
(1862), On Climbing Plants (1864), Expression of the Emo-
tions in Man and Animals (1872) — all the results of his om-
nivorous reading and his enthusiastic experimentation — con-
tributed to the acceptance of his theory. They did more. They
revolutionized the work of the natural historian — who thence-
forth busied himself retracing zoological history, and of the
embryologist — who became a reader of phylogeny in ontogeny,
and of the comparative anatomist — who concentrated now on
the effect of function and environment in molding bodily form.
It is hardly possible, furthermore, to say how much the optimis-
tic nineteenth-century doctrine of progress owed to the theory
of organic evolution. The greatest single contribution of the
nineteenth century to the world's intellectual history is
summed up in the term Darwinism,
.THE ORIGIN OF SPECIES
INTRODUCTION
WHEN on board H.M.S. Beagle, as naturalist, I was much struck with
certain facts in the distribution of the organic beings inhabiting South
America, and in the geological relations of the present to the past inhabit-
ants of that continent. These facts, as will be seen in the latter chapters
of this volume, seemed to throw some light on the origin of species — that
mystery of mysteries, as it has been called by one of our greatest philoso-
phers. On my return home, it occurred to me, in 1837, tnat something
might perhaps be made out on this question by patiently accumulating
and reflecting on all sorts of facts which could possibly have any bearing
on it. After five years' work I allowed myself to speculate on the subject,
and drew up some short notes; these I enlarged in 1844 into a sketch of
the conclusions, which then seemed to me probable: from that period to
the present day I have steadily pursued the same object. I hope that I
may be excused for entering on these personal details, as I give them to
show that I have not been hasty in coming to a decision.
This Abstract, which I now publish, must necessarily be imperfect. I
cannot here give references and authorities for my several statements; and
I must trust to the reader reposing some confidence in my accuracy. No
doubt errors wrill have crept in, though I hope I have always been cautious
in trusting to good authorities alone. I can here give only the general con-
clusions at which I have arrived, with a few facts in illustration, but^which,
I hope, in most cases will suffice. No one can feel more sensible than I
do of the necessity of hereafter publishing in detail all the facts, with
references, on which my conclusions have been grounded; and I hope in
a future work to do this. For I am well aware that scarcely a single
point is discussed in this volume on which facts cannot be adduced, often
apparently leading to conclusions directly opposite to those at which I
have arrived. A fair result can be obtained only by fully stating and
balancing the facts and arguments on both sides of each question; and
this is here impossible.
No one ought to feel surprise at much remaining as yet unexplained
in regard to the origin of species and varieties, ,if he make due allowance
for our profound ignorance in regard to the mutual relations of the many
beings which live around us. Who can explain why one species ranges
336 MASTERWORKS OF SCIENCE
widely and is very numerous, and why another allied species has a narrow
range and is rare? Yet these relations are of the highest importance, for
they determine the present welfare and, as I believe, the future success
and modification of every inhabitant of this world. Still less do we know
of the mutual relations of the innumerable inhabitants of the world during
the many past geological epochs in its history. Although much remains
obscure, and will long remain obscure, I can entertain no doubt, after the
most deliberate study and dispassionate judgment of which I am ca-
pable, that the view which most naturalists until recently entertained, and
which I formerly entertained — namely, that each species has been inde-
pendently created — is erroneous. I am fully convinced that species are not
immutable; but that those belonging to what are called the same genera
are lineal descendants of some other and generally extinct species, in the
same manner as the acknowledged varieties of any one species are the de-
scendants of that species. Furthermore, I am convinced that Natural
Selection has been the most important, but not the exclusive, means of
modification.
7. VARIATION UNDER DOMESTICATION
Causes of Variability
WHEN we compare the individuals of the same variety or sub-variety of
our older cultivated plants and animals, one of the first points which
strikes us is that they generally differ more from each other than do the
individuals of any one species or variety in a state of nature. And if we
reflect on the vast diversity of the plants and animals which have been
cultivated, and which have varied during all ages under the most different
climates and treatment, we are driven to conclude that this great vari-
ability is due to our domestic productions having been raised under con-
ditions of life not so uniform as, and somewhat different from, those to
which the parent species had been exposed under nature.
As far as I am able to judge, after long attending to the subject, the
conditions of life appear to act in two ways — directly on the whole organ-
isation or on certain parts alone, and indirectly by affecting the repro-
ductive system. With respect to the direct action, we must bear in mind
that in every case there are two factors: namely, the nature of the or-
ganism, and the nature of the conditions. The former seems to be much
the more important; for nearly similar variations sometimes arise under,
as far as we can judge, dissimilar conditions; and, on the other hand,
dissimilar variations arise under conditions which appear to be nearly
uniform. The effects on the offspring are either definite or indefinite.
They may be considered as definite when all or nearly all the offspring
of individuals exposed to certain conditions during several generations
are modified in the same manner.
Indefinite variability is a much more common result of changed con-
DARWIN — ORIGIN OF SPECIES 337
ditions than definite variability, and has probably played a more important
part in the formation of our domestic races. We see indefinite variability
in the endless slight peculiarities which distinguish the individuals of the
same species, and which cannot be accounted for by inheritance from
either parent or from some more remote ancestor. Even strongly marked
differences occasionally appear in the young of the same litter and in seed-
lings from the same seed capsule. All such changes of structure, whether
extremely slight or strongly marked, which appear amongst many indi-
viduals living together, may be considered as the indefinite effects of the
conditions of life on each individual organism, in nearly the same manner
as the chili affects different men in an indefinite manner, according to
their state of body or constitution, causing coughs or colds, rheumatism,
or inflammation of various organs.
With respect to what I have called the indirect action of changed con-
ditions, namely, through the reproductive system being affected, we
may infer that variability is thus induced, pardy from the fact of this
system being extremely sensitive to any change in the conditions, and
partly from the similarity, as Kolreuter and others have remarked, be-
tween the variability which follows from the crossing of distinct species
and that which may be observed with plants and animals when reared
under new or unnatural conditions. Many facts clearly show how emi-
nently susceptible the reproductive system is to very slight changes in the
surrounding conditions. Nothing is more easy than to tame an animal,
and few things more difficult than to get it to breed freely under confine-
ment, even when the male and female unite. Carnivorous animals, even
from the tropics, breed in this country pretty freely under confinement,
with the exception of the plantigrades or bear family, which seldom pro-
duce young; whereas carnivorous birds, with the rarest exceptions, hardly
ever lay fertile eggs. Many exotic pknts have pollen utterly worthless, in
the same condition as in the most sterile hybrids. When, on the one hand,
we see domesticated animals and plants, though often weak and sickly,
breeding freely under confinement; and when, on the other hand, we see
individuals, though taken young from a state of nature, perfectly tamed,
long-lived and healthy (of which I could give numerous instances), yet
having their reproductive system so seriously affected by unperceived
causes as to fail to act, we need not be surprised at this system, when it
does act under confinement, acting irregularly, and producing offspring
somewhat unlike their parents.
Effects of Habit and of the Use or Disuse of Parts; Correlated
Variation; Inheritance
Changed habits produce an inherited effect, as in the period of the
flowering of plants when transported from one climate to another. With
animals the increased use or disuse of parts has had a more marked
influence; thus I find in the domestic duck that the bones of the wing
338 MASTERWORKS OF SCIENCE
weigh less and the bones of the leg more, in proportion to the whole
skeleton, than do the same bones in the wild duck; and this change may
be safely attributed to the domestic duck flying much less, and walking
more, than its wild parents. Not one of our ^domestic animals can be
named which has not in some country drooping ears; and the view which
has been suggested, that the drooping is due to disuse of the muscles of
the ear, from the animals being seldom much alarmed, seems probable.
Many laws regulate variation, some few of which can be dimly seen,
and will hereafter be briefly discussed. I will here only allude to what
may be called correlated variation. Breeders believe that long limbs are
almost always accompanied by an elongated head. Some instances of cor-
relation are quite whimsical: thus cats which are entirely white and have
blue eyes are generally deaf; but it has been lately stated by Mr. Tait that
this is confined to the males. Colour and constitutional peculiarities go
together, of which many remarkable cases could be given amongst animals
and plants. From facts collected by Heusinger, it appears that white sheep
and pigs are injured by certain plants, whilst dark-coloured individuals
escape: Professor Wyman has recently communicated to me a good illus-
tration of this fact; on asking some farmers in Virginia how it was that
all their pigs were black, they informed him that the pigs ate the paint-
root (Lachnanthes), which coloured their bones pink, and which caused
the hoofs of all but the black varieties to drop off; and one of the
"crackers" (i.e. Virginia squatters) added, "we select the black members
of a litter for raising, as they alone have a good chance of living." Hairless
dogs have imperfect teeth; long-haired and coarse-haired animals are apt
to have, as is asserted, long or many horns; pigeons with feathered feet
have skin between their outer toes; pigeons with short beaks have small
feet, and those with long beaks large feet. Hence if man goes on selecting,
and thus augmenting, any 'peculiarity, he will almost certainly modify
unintentionally other parts of the structure, owing to the mysterious laws
of correlation.
Any variation which is not inherited is unimportant for us. But the
number and diversity of inheritable deviations of structure, both those of
slight and those of considerable physiological importance, are endless. No
breeder doubts how strong is the tendency to inheritance; that like pro-
duces like is his fundamental belief: doubts have been thrown on this
principle only by theoretical writers. When any deviation of structure often
appears, and we see it in the father and child, we cannot tell whether it may
not be due to the same cause having acte'd on both; but when amongst indi-
viduals, apparently exposed to the same conditions, any very rare devi-
ation, due to some extraordinary combination of circumstances, appears
in the parent — say, once amongst several million individuals — and it reap-
pears in the child, the mere doctrine of chances almost compels us to
attribute its reappearance to inheritance. Everyone must have heard of
cases of albinism, prickly skin, hairy bodies, &c.? appearing in several
members of the same family. If strange and rare deviations of structure
are really inherited, less strange and commoner deviations may be freely
DARWIN — ORIGIN OF SPECIES 339
admitted to be Inheritable. Perhaps the correct way of viewing the whole
subject would be to look at the inheritance o£ every character whatever
as the rule, and non-Inheritance as the anomaly.
Character of Domestic Varieties; difficulty of distinguishing between Va-
rieties and Species; origin of Domestic Varieties from one or more
Species
When we look to the hereditary varieties or races of our domestic
animals and plants, and compare them with closely allied species, we
generally perceive In each domestic race, as already remarked, less uni-
formity of character than in true species.
It has often been assumed that man has chosen for domestication
animals and plants having an extraordinary Inherent tendency to vary, and
likewise to withstand diverse climates. I do not dispute that these capaci-
ties have added largely to the value of most of our domesticated produc-
tions: but how could a savage possibly know, when he first tamed an
animal, whether It would vary In succeeding generations, and whether It
would endure other climates? Has the little variability of the ass and
goose, or the small power of endurance of warmth by the reindeer, or of
cold by the common camel, prevented their domestication? I cannot doubt
that if other animals and plants, equal in number to our domesticated
productions, and belonging to equally diverse classes and countries, were
taken from a state of nature, and could be made to breed for an equal
number of generations under domestication, they would on an average
vary as largely as the parent species of our existing domesticated produc-
tions have varied.
The doctrine of the origin of our several domestic races from several
aboriginal stocks has been carried to an absurd extreme by some authors.
They believe that every race which breeds true, let the distinctive charac-
ters be ever so slight, has had Its wild prototype. At this rate there must
have existed at least a score of species of wild cattle, as many sheep, and
several goats, In Europe alone, and several even within Great Britain.
Even in the case of the breeds of the domestic dog throughout the world,
which I admit are descended from several wild species, it cannot be
doubted that there has been an immense amount of Inherited variation;
for who will believe that animals closely resembling the Italian greyhound,
the bloodhound, the bulldog, pug dog, or Blenheim spaniel, &c. — so unlike
all wild Canidse — ever existed in a state of nature? It has often been
loosely said that all our races of dogs have been produced by the crossing
of a few aboriginal species; but by crossing we can only get forms in
some degree intermediate between their parents; and if we account for
our several domestic races by this process, we must admit the former
existence of the most extreme forms, as the Italian greyhound, blood-
hound, bulldog, &c., in the wild state. Moreover, the possibility of making
distinct races by crossing has been greatly exaggerated. Many cases are on
340 MASTERWORKS OF SCIENCE
record, showing that a race may be modified by occasional crosses, if
aided by the careful selection of the individuals which present the desired
character; but to obtain a race intermediate between two quite distinct
races would be very difficult. Sir J. Sebright expressly experimented with
this object and failed. The offspring from the first cross between two pure
breeds is tolerably and sometimes (as I have found with pigeons) quite
uniform in character, and everything seems simple enough; but when
these mongrels are crossed one with another for several generations,
hardly two of them are alike, and then the difficulty of the task becomes
manifest.
Breeds of the Domestic Pigeon, their Differences and Origin
Believing that it is always best to study some special group, I have,
after deliberation, taken up domestic pigeons. The diversity of the breeds
is something astonishing. Compare the English carrier and the short-faced
tumbler, and see the wonderful difference in their beaks, entailing cor-
responding differences in their skulls. The carrier, more especially the
male bird, is also remarkable from the wonderful development of the
carunculated skin about the head; and this is accompanied by greatly
elongated eyelids, very large external orifices to the nostrils, and a wide
gape of mouth. The short-faced tumbler has a beak in outline almost like
that of a finch; and the common tumbler has the singular inherited habit of
flying at a great height in a compact flock, and tumbling in the air head
over heels. The runt is a bird of great size, with long massive beak and
large feet; some of the sub-breeds of runts have very long necks, others
very long wings and tails, others singularly short tails. The barb is allied
to the carrier, but, instead of a long beak, has a very short and broad one.
The pouter has a much elongated body, wings, and legs; and its enor-
mously developed crop, which it glories in inflating, may well excite
astonishment and even laughter. The turbit has a short and conical beak,
with a line of reversed feathers down the breast; and it has the habit of
continually expanding slightly the upper part of the oesophagus. The
Jacobin has the feathers so much reversed along the back of the neck that
they form a hood; and it has, proportionally to its size, elongated wing
and tail feathers. The trumpeter and laugher, as their names express, utter
a very different coo from the other breeds. The fantail has thirty or even
forty tail feathers, instead of twelve or fourteen — the normal number in all
the members of the great pigeon family: these feathers are kept expanded,
and are carried so erect that in good birds the head and tail touch: the
oil gland is quite aborted.
Altogether at least a score of pigeons might be chosen, which, if
shown to an ornithologist, and he were told that they were wild birds,
would certainly be ranked by him as well-defined species. Moreover, I do
not believe that any ornithologist would in this case place the English
carrier, the short-faced tumbler, the runt, the barb, pouter, and fantail in
DARWIN — ORIGIN OF SPECIES 341
the same genus; more especially as In each of these breeds several truly
inherited sub-breeds, or species, as he would call them, could be shown
him.
Great as are the differences between the breeds of the pigeon, I am
fully convinced that the common opinion of naturalists is correct, namely,
that all are descended from the rock pigeon (Columba livia), including
under this term several geographical races or sub-species, which differ
from each other in the most trifling respects. As several of the reasons
which have led me to this belief are in some degree applicable in other
cases, I will here briefly give them. If the several breeds are not varieties,
and have not proceeded from the rock pigeon, they must have descended
from at least seven or eight aboriginal stocks; for it is impossible to make
the present domestic breeds by the crossing of any lesser number: how,
for instance, could a pouter be produced by crossing two breeds unless
one of the parent stocks possessed the characteristic enormous crop? The
supposed aboriginal stocks must all have been rock pigeons, that is, they
did not breed or willingly perch on trees. But besides C. livia, with its
geographical sub-species, only two or three other species of rock pigeons
are known; and these have not any of the characters of the domestic
breeds. Hence the supposed aboriginal stocks must either still exist in the
countries where they were originally domesticated, and yet be unknown
to ornithologists; and this, considering their size, habits, and remarkable
characters, seems improbable; or they must have become extinct in the
wild state. But birds breeding on precipices, and good fliers, are unlikely
to be exterminated; and the common rock pigeon, which has the same
habits with the domestic breeds, has not been exterminated even on
several of the smaller British islets, or on the shores of the Mediterranean.
Hence the supposed extermination of so many species having similar
habits with the rock pigeon seems a very rash assumption. Moreover, the
several above-named domesticated breeds have been transported to all
parts of the world, and, therefore, some of them must have been carried
back again into their native country; but not one has become wild or feral,
though the dovecot pigeon, which is the rock pigeon in a very slightly
altered state, has become feral in several places.
Some facts in regard to the colouring of pigeons well deserve con-
sideration. The rock pigeon is of a slaty-blue, with white loins; but the
Indian sub-species, C. intermedia of Strickland, has this part bluish. The
tail has a terminal dark bar, with the outer feathers externally edged at
the base with white. The wings have two black bars. Some semi-domestic
breeds, and some truly wild breeds, have, besides the two black bars, the
wings chequered with black. These several marks do not occur together in
any other species of the whole family. Now, in every one of the domestic
breeds, taking thoroughly well-bred birds, all the above marks, even to
the white edging of the outer tail feathers, sometimes concur perfectly
developed. Moreover, when birds belonging to two or more distinct breeds
are crossed, none of which are blue or have any of the above-specified
marks, the mongrel offspring are very apt suddenly to acquire these
342 MASTERWORKS OF SCIENCE
characters. To give one instance out of several which I have observed: — I
crossed some white fantails, which breed very true, with some black barbs
— and it so happens that blue varieties of barbs are so rare that I never
heard of an instance in England; and the mongrels were black, brown,
and mottled. I also crossed a barb with a spot, which is a white bird with
a red tail and red spot on the forehead, and which notoriously breeds very
true; the mongrels were dusky and mottled. I then crossed one of the
mongrel barb fantails with a mongrel barb spot, and they produced a bird
of as beautiful a blue colour, with the white loins, double black wing bar,
and barred and white-edged tail feathers, as any wild rock pigeon! We
can understand these facts, on the well-known principle of reversion to
ancestral characters, if all the domestic breeds are descended from the
rock pigeon. But if we deny this, we must make one of the two following
highly improbable suppositions. Either, first, that all the several imagined
aboriginal stocks were coloured and marked like the rock pigeon, although
no other existing species is thus coloured and marked, so that in each
separate breed there might be a tendency to revert to the very same
colours and markings. Or, secondly, that each breed, even the purest, has
within a dozen, or at most within a score, of generations been crossed by
the rock pigeon: I say within a dozen or twenty generations, for no in-
stance is known of crossed descendants reverting to an ancestor of foreign
blood, removed by a greater number of generations. In a breed which has
been crossed only once, the tendency to revert to any character derived
from such a cross will naturally become less and less, as in each succeeding
generation there will be less of the foreign blood; but when there has
been no cross, and there is a tendency in the breed to revert to a character
which was lost during some former generation, this tendency, for all that
we can see to the contrary, may be transmitted undiminished for an in-
definite number of generations. These two distinct cases of reversion are
often confounded together by those who have written on inheritance.
From these several reasons, namely — the improbability of man having
formerly made seven or eight supposed species of pigeons to breed freely
under domestication; — these supposed species being quite unknown in a
wild state, and their not having become anywhere feral; — these species
presenting certain very abnormal characters, as compared with all other
Columbidae, though so like the rock pigeon in most respects; — the oc-
casional reappearance of the blue colour and various black marks in all
the breeds, both when kept pure and when crossed; — and lastly, the mon-
grel offspring being perfectly fertile; — from these several reasons taken
together* we may safely conclude that all our domestic breeds are de-
scended from the rock pigeon or Columba livia with its geographical
sub-species.
In favour of this view, I may add, firstly, that the wild C. livia has
been found capable of domestication in Europe and in India; and that it
agrees in habits and in a great number of points of structure with all the
domestic breeds. Secondly, that, although an English carrier or a short-
faced tumbler differs immensely in certain characters from the rock
DARWIN — ORIGIN OF SPECIES 345
pigeon, yet that, by comparing the several sub-breeds of these two races,
more especially those brought from distant countries, we can make, be-
tween them and the rock pigeon, an almost perfect series; so we can in
some other cases, but not with all the breeds. Thirdly, those characters
which are mainly distinctive of each breed are in each eminently variable,
for instance, the wattle and length of beak of the carrier, the shortness of
that of the tumbler, and the number of tail feathers in the fantail; and the
explanation of this fact will be obvious when we treat of Selection.
Fourthly, pigeons have been watched and tended with the utmost care,
and loved by many people. They have been domesticated for thousands of
years in several quarters of the world; the earliest known record of pigeons
is in the fifth ^Egyptian dynasty, about 3000 B.C., as was pointed out to
me by Professor Lepsius; but Mr. Birch informs me that pigeons are
given in a bill of fare in the previous dynasty. In the time of the Romans,
as we hear from Pliny, immense prices were given for pigeons; "nay,
they are come to this pass, that they can reckon up their pedigree and
race." Pigeons were much valued by Akber Khan in India, about the
year 1600; never less than 20,000 pigeons were taken with the court. "The
monarchs of Iran and Turan sent him some very rare birds," and, con-
tinues the courtly historian, "His Majesty, by crossing the breeds, which
method was never practised before, has improved them astonishingly."
About this same period the Dutch were as eager about pigeons as were
the old Romans. The paramount importance of these considerations, in
explaining the immense amount of variation which pigeons have under-
gone, will likewise be obvious when we treat of Selection. We shall then,
also, see how it is that the several breeds so often have a somewhat mon-
strous character.
I have discussed the probable origin of domestic pigeons at some, yet
quite insufficient, length; because when I first kept pigeons and watched
the several kinds, well knowing how truly they breed, I felt fully as much
difficulty in believing that since they had been domesticated they had all
proceeded from a common parent, as any naturalist could in coming to a
similar conclusion in regard to the many species of finches, or other
groups of birds, in nature. One circumstance has struck me much; namely,
that nearly all the breeders of the various domestic animals and the culti-
vators of plants, with whom I have conversed, or whose treatises I have
read, are firmly convinced that the several breeds to which each has
attended are descended from so many aboriginally distinct species. Ask,
as I have asked, a celebrated raiser of Hereford cattle whether his cattle
might not have descended from Longhorns, or both from a common parent
stock, and he will laugh you to scorn. I have never met a pigeon, or
poultry, or duck, or rabbit fancier who was not fully convinced that each
main breed was descended from a distinct species. Van Mons, in his
treatise on pears and apples, shows how utterly he disbelieves that the
several sorts, for instance, a Ribston pippin or Codlin apple, could ever
have proceeded from the seeds of the same tree. Innumerable other
examples could be given. The explanation, I think, is simple: from long-
344 MASTERWORKS OF SCIENCE
continued study they are strongly impressed with the differences between
the several races; and though they well know that each race varies slightly,
for they win their prizes by selecting such slight differences, yet they
ignore all general arguments, and refuse to sum up in their minds slight
differences accumulated during many successive generations. May not
those naturalists who, knowing far less of the laws of inheritance than does
the breeder, and knowing no more than he does of the intermediate links
in the long lines of descent, yet admit that many of our domestic races are
descended from the same parents — may they not learn a lesson of caution,
when they deride the idea of species in a state of nature being lineal
descendants of other species?
Principles of Selection anciently followed, and their Effects
Let us now briefly consider the steps by which domestic races have
been produced, either from one or from several allied species. Some effect
may be attributed to the direct and definite action of the external condi-
tions of life, and some to habit; but he would be a bold man who would
account by such agencies for the differences between a dray and race
horse, a greyhound and bloodhound, a carrier and tumbler pigeon. One of
the most remarkable features in our domesticated races is that we see in
them adaptation, not indeed to the animal's or plant's own good, but to
man's use or fancy. Some variations useful to him have probably arisen
suddenly, or by one step; many botanists, for instance, believe that the
fuller's teasel, with its hooks, which cannot be rivalled by any mechanical
contrivance, is only a variety of the wild Dipsacus; and this amount of
change may have suddenly arisen in a seedling. So it has probably been
with the turnspit dog; and this is known to have been the case with the
ancon sheep. But when we compare the dray horse and race horse, the
dromedary and camel, the various breeds of sheep fitted either for culti-
vated land or mountain pasture, with the wool of one breed good for one
purpose, and that of another breed for another purpose; when we compare
the many breeds of dogs, each good for man in different ways; when we
compare the gamecock, so pertinacious in battle, with other breeds so
little quarrelsome, with "everlasting layers" which never desire to sit, and
with the bantam so small and elegant; when we compare the host of agri-
cultural, culinary, orchard, and flower-garden races of plants, most useful
to man at different seasons and for different purposes, or so, beautiful in
his eyes, we must, I think, look further than to mere variability. We can-
not suppose that all the breeds were suddenly produced as perfect and as
useful as we now see them; indeed, in many cases, we know that this has
not been their history. The key is man's power of accumulative selection:
nature gives successive variations; man adds them up in certain directions
useful to him. In this sense he may be said to have made for himself use-
ful breeds.
The great power of this principle of selection is not hypothetical.
DARWIN — ORIGIN OF SPECIES 345
What English breeders have actually effected is proved by the enormous
prices given for animals with a good pedigree; and these have been ex-
ported to almost every quarter of the world. The improvement is by no
means generally due to crossing different breeds; all the best breeders are
strongly opposed to this practice, except sometimes amongst closely allied
sub-breeds. And when a cross has been made, the closest selection Is far
more indispensable even than in ordinary cases. If selection consisted
merely in separating some very distinct variety, and breeding from it, the
principle would be so obvious as hardly to be worth notice; but its im-
portance consists in the great effect produced by the accumulation in one
direction, during successive generations, of differences absolutely inap-
preciable by an uneducated eye — differences which I for one have vainly
attempted to appreciate. Not one man in a thousand has accuracy of eye
and judgment sufficient to become an eminent breeder. If gifted with
these qualities, and he studies his subject for years, and devotes his life-
time to it with indomitable perseverance, he will succeed, and may make
great improvements; if he wants any of these qualities, he will assuredly
fail. Few would readily believe in the natural capacity and years of prac-
tice requisite to become even a skilful pigeon fancier.
It may be objected that the principle of selection has been reduced to
methodical practice for scarcely more than three quarters of a century;
it has certainly been more attended to of late years, and many treatises
have been published on the subject; and the result has been, in a corre-
sponding degree, rapid and important. But it is very far from true that the
principle is a modern discovery. The principle of selection I find dis-
tinctly given in an ancient Chinese encyclopaedia. Explicit rules are laid
down by some of the Roman classical writers. From passages in Genesis,
it is clear that the colour of domestic animals was at that early period
attended to. Savages now sometimes cross their dogs with wild canine
animals, to improve the breed, and they formerly did so, as Is attested by
passages In Pliny. The savages in South Africa match their draught cattle
by colour, as do some of the Esquimaux their teams of dogs. Livingstone
states that good domestic breeds are highly valued by the Negroes in the
interior of Africa who have not associated with Europeans. Some of these
facts do not show actual selection, but they show that the breeding of
domestic animals was carefully attended to in ancient times, and is now
attended to by the lowest savages. It would, indeed, have been a strange
fact had attention not been paid to breeding, for the inheritance of good
and bad qualities is so obvious.
Unconscious Selection
At the present time, eminent breeders try by methodical selection,
with a distinct object in view, to make a new strain or sub-breed, superior
to anything of the kind in the country. But, for our purpose, a form of
Selection, which may be called Unconscious, and which results from every-
346 MASTERWQRKS OF SCIENCE
one trying to possess and breed from the best individual animals, is more
important. Thus, a man who intends keeping pointers naturally tries to
.get as good dogs as he can, and afterwards breeds from his own best dogs,
but he has no wish or expectation of permanently altering the breed.
Nevertheless we may infer that this process, continued during centuries,
would improve and modify any breed. Some highly competent authorities
are convinced that the setter is directly derived from the spaniel, and has
probably been slowly altered from it. It is known that the English pointer
has been greatly changed within the last century, and in this case the
change has, it is believed, been chiefly effected by crosses with the fox-
hound; but what concerns us is that the change has been effected uncon-
sciously and gradually, and yet so effectually that, though the old Spanish
pointer certainly came from Spain, Mr. Borrow has not seen, as I am
Informed by him, any native dog in Spain like our pointer.
On the view here given of the important part which selection by man
has played, it becomes at once obvious how it is that our domestic races
show adaptation in their structure or in their habits to man's wants or
fancies. We can, I think, further understand the frequently abnormal
characters of our domestic races, and likewise their differences being so
great in external characters and relatively so slight in internal parts or
organs. Man can hardly select, or only with much difficulty, any deviation
of structure excepting such as is externally visible; and indeed he rarely
-cares for what is internal. He can never act by selection, excepting on vari-
ations which are first given to him in some slight degree by nature. No
man would ever try to make a fantail till he saw a pigeon with a tail
developed in some slight degree in an unusual manner, or a pouter till he
saw a pigeon with a crop of somewhat unusual size; and the more abnor-
mal or unusual any character was when it first appeared, the more likely
It would be to catch his attention. But to use such an expression as trying
to make a fantail Is, I have no doubt, in most cases utterly Incorrect.
The man who first selected a pigeon writh a slightly larger tail never
dreamed what the descendants of that pigeon would become through long-
continued, partly unconscious and partly methodical, selection. Perhaps
the parent bird of all fantaiis had only -fourteen tail feathers somewhat
expanded, like the present Java fantail, or like individuals of other and
distinct breeds, in which as many as seventeen tail feathers have been
counted. Perhaps the first pouter pigeon did not inflate its crop much
more than the turbit now does the upper part of its oesophagus — a habit
which Is disregarded by all fanciers, as it Is not one of the points of the
breed.
Nor let it be thought that some great deviation of structure would be
necessary to catch the fancier's eye: he perceives extremely small differ-
ences, and It is in human nature to value any novelty, however slight, in
one's own possession. Nor must the value which would formerly have
been set on any slight differences in the Individuals of the same species be
judged of by the value which is now set on them, after several breeds have
fairly been established. It is known that with pigeons many slight varia-
DARWIN — ORIGIN OF SPECIES 347
tions now occasionally appear, but these are rejected as faults or devia-
tions from the standard of perfection in each breed. The common goose
has not given rise to any marked varieties; hence the Toulouse and the
common breed, which differ only in colour, that most fleeting of charac-
ters, have lately been exhibited as distinct at our poultry shows.
These views appear to explain what has sometimes been noticed —
namely, that we know hardly anything about the origin or history of any
of our domestic breeds. But, in fact, a breed, like a dialect of a language^
can hardly be said to have a distinct origin. A man preserves and breeds,
from an individual with some slight deviation of structure, or takes more
care than usual in matching his best animals, and thus improves them,
and the improved animals slowly spread in the immediate neighbourhood.
But they will as yet hardly have a distinct name, and from being only
slightly valued, their history will have been disregarded. When further
improved by the same slow and gradual process, they will spread more
widely, and will be recognised as something distinct and valuable, and
will then probably first receive a provincial name. In semi-civilised coun-
tries, with little free communication, the spreading of a new sub-breed
would be a slow process. As soon as the points of value are once acknowl-
edged, the principle, as I have called it, of unconscious selection will al-
ways tend — perhaps more at one period than at another, as the breed
rises or falls in fashion — perhaps more in one district than in another,
according to the state of civilisation of the inhabitants — slowly to add
to the characteristic features of the breed, whatever they may be. But the
chance will be infinitely small of any record having been preserved o£
such slow, varying, and insensible changes.
Circumstances favourable to Man's Power of Selection
I will now say a few words on the circumstances favourable, or the
reverse, to man's power of selection. A high degree of variability is obvi-
ously favourable, as freely giving the materials for selection to work on;
not that mere individual differences are not amply sufficient, with extreme
care, to allow of the accumulation of a large amount of modification in
almost any desired direction. But as variations manifestly useful or pleas-
ing to man appear only occasionally, the chance of their appearance will
be much increased by a large number of individuals being kept. Hence.,
number is of the highest importance for success. Nurserymen, from keep-
ing large stocks of the same plant, are generally far more successful than
amateurs in raising new and valuable varieties. A large number of indi-
viduals of an animal or plant can be reared only where the conditions for
its propagation are favourable. When the individuals are scanty, all will
be allowed to breed, whatever their quality may be, and this will effectu-
ally prevent selection. But probably the most important elemejit is that
the animal or plant should be so highly valued by man that the closest
attention is paid to even the slightest deviations in its qualities or struc-
348 MASTERWORKS OF SCIENCE
ture. Unless such attention be paid nothing can be effected. I have seen
It gravely remarked that it was most fortunate that the strawberry began
to vary just when gardeners began to attend to this plant. No doubt the
strawberry had always varied since it was cultivated, but the slightest
varieties had been neglected. As soon, however, as gardeners picked out
individual plants with slightly larger, earlier, or better fruit, and raised
seedlings from them, and again picked out the best seedlings and bred
from them, then (with some aid by crossing distinct species) those many
admirable varieties of the strawberry were raised which have appeared
during the last half century.
With animals, facility in preventing crosses is an important element
in the formation of new races — at least, in a country which is already
stocked with other races. In this respect enclosure of the land plays a part.
Wandering savages or the inhabitants of open plains rarely possess more
than one breed of the same species. Pigeons can be mated for life, and
this is a great convenience to die fancier, for thus many races may be im-
proved and kept true, though mingled in the same aviary; and this cir-
cumstance must have largely favoured the formation of new breeds.
Pigeons, I may add, can be propagated in great numbers and at a very
quick rate, and inferior birds may be freely rejected, as when killed they
serve for food. On the other hand, cats, from their nocturnal rambling
habits, cannot be easily matched, and, although so much valued by women
and children, we rarely see a distinct breed long kept up; such breeds as
we do sometimes see are almost always imported from some other coun-
try. Although I do not doubt that some domestic animals vary less than
others, yet the rarity or absence of distinct breeds of the cat, the donkey,
peacock, goose, &c., may be attributed in main part to selection not hav-
ing been brought into play: in cats, from the difficulty in pairing them;
in donkeys, from only a few being kept by poor people, and little atten-
tion paid to their breeding; for recently in certain parts of Spain and of
the United States this animal has been surprisingly modified and im-
proved by careful selection.
To sum up on the origin of our domestic races of animals and plants.
Changed conditions of life are of the highest importance in causing vari-
ability, both by acting directly on the organisation and indirectly by affect-
ing the reproductive system. It is not probable that variability is an in-
herent and necessary contingent, under all circumstances. The greater or
less force of inheritance and reversion determine whether variations shall
endure. Variability is governed by many unknown laws, of which corre-
lated growth is probably the most important. Something, but how much
we do not know, may be attributed to the definite action of the conditions
of life. Some, perhaps a great, effect may be attributed to the increased
use or disuse of parts. Over all these causes of Change, the accumulative
action of Selection, whether applied methodically and quickly or uncon-
sciously a%d slowly but more efficiently, seems to have been the predomi-
nant Power.
DARWIN — ORIGIN OF SPECIES 349
//. VARIATION UNDER NATURE
BEFORE applying the principles arrived at in the last chapter to organic
beings in the state of nature, we must briefly discuss whether these latter
are subject to any variation. To treat this subject properly, a long cata-
logue of dry facts ought to be given; but these I shall reserve for a future
work. Nor shall I here discuss the various definitions which have been
given of the term species. No one definition has satisfied all naturalists;
yet every naturalist knows vaguely what he means when he speaks of a
species. Generally the term includes the unknown element of a distant act
of creation. The term "variety" is almost equally difficult to define; but
here community of descent is almost universally implied, though it can
rarely be proved.
Individuals of the same species often present, as is known to everyone,.
great differences of structure, independently of variation, as in the two
sexes of various animals, in the two or three castes of sterile females or
workers amongst insects, and in the immature and larval states of many
of the lower animals. There are, also, cases of dimorphism and trirnor-
phism, both with animals and plants. Thus, Mr. Wallace, who has lately
called attention to the subject, has shown that the females of certain spe-
cies of butterflies, in the Malayan archipelago, regularly appear under two-
or even three conspicuously distinct forms, not connected by intermediate
varieties.
The many slight differences which appear in the offspring from the
same parents, or which it may be presumed have thus arisen, from being
observed in the individuals of the same species inhabiting the same con-
fined locality, may be called individual differences. No one supposes that
all the individuals of the same species are cast in the same actual mould,
These individual differences are of the highest importance for us, for they
are often inherited, as must be familiar to everyone; and they thus afford
materials for natural selection to act on and accumulate, in the same man-
ner as man accumulates in any given direction individual differences ia
his domesticated productions. These individual differences generally affect
what naturalists consider unimportant parts; but I could show by a long
catalogue of facts that parts which must be called important, whether
viewed under a physiological or classificatory point of view, sometimes
vary in the individuals of the same species. It certainly at first appears a
highly remarkable fact that the same female butterfly should have the
power of producing at the same time three distinct female forms and a
male; and that an hermaphrodite plant should produce from the same
seed capsule three distinct hermaphrodite forms, bearing three different
kinds of females and three or even six different kinds of males. Neverthe-
less these cases are only exaggerations of the common fact that the female
produces offspring of two sexes which sometimes differ from each other
in a wonderful manner.
350 MASTERWORKS OF SCIENCE
The forms which possess in some considerable degree the character
o£ species, but which are so closely similar to other forms, or are so closely
linked to them by intermediate gradations, that naturalists do not like to
xank them as distinct species, are in several respects the most important
for us. We have every" reason to believe that many of these doubtful and
closely allied forms have permanently retained their characters for a long
time; for as long, as far as we know, as have good and true species. Prac-
tically, when a naturalist can unite by means of intermediate links any
two forms, he treats the one as a variety of the other; ranking the most
common, but sometimes the one first described, as the species, and the
•other as the variety.
Many years ago, when comparing, and seeing others compare, the
"birds from the closely neighbouring islands of the Galapagos archipelago,
one with another, and with those from the American mainland, I was
much struck how entirely vague and arbitrary is the distinction between
species and varieties. On the islets of the little Madeira group there are
many insects which are characterised as varieties in Mr. Wollaston's ad-
mirable \vork, but which would certainly be ranked as distinct species by
many entomologists. Even Ireland has a few animals, now generally re-
garded as varieties, but which have been ranked as species by some zoolo-
gists. Several experienced ornithologists consider our British red grouse
as only a strongly marked race of a Norwegian species, whereas the
greater number rank it as an undoubted species peculiar to Great Britain.
A wide distance between the homes of two doubtful forms leads many
naturalists to rank them as distinct species; but what distance, it has been
well asked, will suffice; if that between America and Europe is ample, will
that between Europe and the Azores, or Madeira, or the Canaries, or be-
tween the several islets of these small archipelagos, be sufficient?
Certainly no clear line of demarcation has as yet been drawn between
species and sub-species — that is, the forms which in the opinion of some
naturalists come very near to, but do not quite arrive at, the rank of spe-
cies: or, again, between sub-species and well-marked varieties, or between
lesser varieties and individual differences. These differences blend into
each other by an insensible series; and a series impresses the mind with
the idea of an actual passage.
Hence I look at individual differences, though of small interest to the
•systematist, as of the highest importance for us, as being the first steps
towarcfs such slight varieties as are barely thought worth recording in
•works on natural history. And I look at varieties which are in any degree
more distinct and permanent as steps towards more strongly marked and
permanent varieties; and at the latter as leading to sub-species, and then
to species. The passage from one stage of difference to another may, in
many cases, be the simple result of the nature of the organism and of the
different physical conditions to which it has long been exposed; but with
respect to the more important and adaptive characters, the passage from
one stage of difference to another may be safely attributed to the cumula-
tive action of natural selection, hereafter to be explained, and to the effects
DARWIN — ORIGIN OF SPECIES 351
of the increased use or disuse of parts. A well-marked variety may there-
fore be called an Incipient species; but whether this belief is justifiable
must be judged by the weight of the various facts and considerations to
be given throughout this work.
From these remarks it will be seen that I look at the term species as
one arbitrarily given, for the sake of convenience, to a set of Individuals
closely resembling each other, and that It does not essentially differ from
the term variety, which is given to less distinct and more fluctuating
forms. The term variety, again, in comparison with mere individual dif-
ferences. Is also applied arbitrarily, for convenience' sake.
Wide-ranging, much diffused, and common Species vary most
Alphonse de Candolle and others have shown that plants which have
very wide ranges generally present varieties; and this might have been
expected, as they are exposed to diverse physical conditions, and as they
come into competition (which, as we shall hereafter see, is an equally or
more Important circumstance) with different sets of organic beings. But
my tables further show that, In any limited country, the species which are
the most common, that Is, abound most In individuals, and the species
which are most widely diffused within their own country (and this is a
different consideration from wide range, and to a certain extent from com-
monness) oftenest give rise to varieties sufficiently well marked to have
been recorded in botanical works. Hence it is the most flourishing, or, as
they may be called, the dominant species — those which range widely, are
the most diffused In their own country, and are the most numerous In
individuals — which oftenest produce well-marked varieties, or, as I con-
sider them, incipient species. And this, perhaps, might have been antici-
pated; for, as varieties, in order to become in any degree permanent, neces-
sarily have to struggle with the other Inhabitants of the country, the
species which are already dominant will be the most likely to yield off-
spring which, though in some slight degree modified, still inherit those
advantages that enabled their parents to become dominant over their com-
patriots. In these remarks on predominance, it should be understood that
reference Is made only to the forms which come into competition with
each other, and more especially to the members of the same genus or
class having nearly similar habits of life. With respect to the number of
Individuals or commonness of species, the comparison of course relates
only to the members of the same group. One of the higher plants may be
said to be dominant if it be more numerous in individuals and more
widely diffused than the other plants of the same country, which live
under nearly the same conditions. A plant of this kind is not the less
dominant because some conferva inhabiting the water or some parasitic
fungus is Infinitely more numerous in individuals and more widely dif-
fused. But if the conferva or parasitic fungus exceeds its allies in the
above respects, it will then be dominant within its own class.
352 MASTERWORKS OF SCIENCE
Species of the Larger Genera in each Country vary more frequently than
the Species of the Smaller Genera
From looking at species as only strongly marked and well-defined
varieties, I was led to anticipate that the species of the larger genera in
each country would oftener present varieties than the species of the smaller
genera; for wherever many closely related species (i.e., species of the
same genus) have been formed, many varieties or incipient species ought,
as a general rule, to be now forming. Where many large trees grow, we
expect to find saplings. Where many species of a genus have been formed
through variation, circumstances have been favourable for variation; and
hence we might expect that the circumstances would generally be still
favourable to variation. On the other hand, if we look at each species as
a special act of creation, there is no apparent reason why more varieties
should occur in a group having many species than in one having few.
To test the truth of this anticipation I have arranged the plants of
twelve countries, and the coleopterous insects of two districts, into two
nearly equal masses, the species of the larger genera on one side and those
of the smaller genera on the other side, and it has invariably proved to
be the case that a larger proportion of the species on the side of the larger
genera presented varieties than on the side of the smaller genera. More-
over, the species of the large genera which present any varieties invari-
ably present a larger average number of varieties than do the species of
the small genera. Both these results follow when another division is
made, and when all the least genera, with from only one to four species,
are altogether excluded from the tables. These facts are of plain significa-
tion on the view that species are only strongly marked and permanent
•varieties; for wherever many species of the same genus have been formed,
or where, if we may use the expression, the manufactory of species has
teen active, we ought generally to find the manufactory still in action,
more especially as we have every reason to believe the process of manufac-
turing new species to be a slow one. And this certainly holds true if varie-
ties be looked at as incipient species; for my tables clearly show as a gen-
eral rule that, wherever many species of a genus have been formed, the
species of that genus present a number of varieties, that is of incipient spe-
cies, beyond the average. It is not that all large genera are now varying
much, and are thus increasing in the number of their species, or that no
small genera are now varying and increasing; for if this had been so, it
would have been fatal to my theory; inasmuch as geology plainly tells us
that small genera have in the lapse of time often increased greatly in size;
and that large genera have often come to their maxima, decline, and dis-
appeared. All that we want to show is that, when many species of a genus
have been formed, on an average many are still forming; and this cer-
tainly holds good.
DARWIN — ORIGIN OF SPECIES 353
^ of the Species included within the Larger Genera resemble Varie-
ties in being very closely, but unequally, related to each other, and in
having restricted ranges
There are other relations between the species of large genera and their
recorded varieties which deserve notice. We have seen that there is no
infallible criterion by which to distinguish species and well-marked varie-
ties; and when intermediate links have not been found between doubt-
ful forms, naturalists are compelled to come to a determination by the
amount of difference between them, judging by analogy whether or not
the amount suffices to raise one or both to the rank of species. Hence the
amount of difference is one very important criterion in settling whether
two forms should be ranked as species or varieties. Now Fries has re-
marked in regard to plants, and Westwood in regard to insects, that in
large genera the amount of difference between the species is often exceed-
ingly small. I have endeavoured to test this numerically by averages, and,
as far as my imperfect results go? they confirm the view. I have also con-
sulted some sagacious and experienced observers, and, after deliberation,
they concur in this view. In this respect, therefore, the species of the
larger genera resemble varieties more than do the species of the smaller
genera. Or the case may be put in another way, and it may be said that
In the larger genera, in which a number of varieties or incipient species
greater than the average are now manufacturing, many of the species al-
ready manufactured still to a certain extent resemble varieties, for they
differ from each other by less than the usual amount of difference.
Moreover, the species of the larger genera are related to each other,
in the same manner as the varieties of any one species are related to each
other. No naturalist pretends that all the species of a genus are equally
distinct from each other; they may generally be divided into sub-genera,
or sections, or lesser groups. As Fries has well remarked, little groups of
species are generally clustered like satellites around other species. And
what are varieties but groups of forms, unequally related to each other,
and clustered round certain forms — that is, round their parent species?
///. STRUGGLE FOR EXISTENCE
BEFORE entering on the subject of this chapter, I must make a few prelimi-
nary remarks, to show how the struggle for existence bears on Natural
Selection. It has been seen in the last chapter that amongst organic beings
in a state of nature there is some individual variability: indeed I am not
aware that this has ever been disputed. It is immaterial for us whether a
multitude of doubtful forms be called species or sub-species or varieties;
what rank, for instance, the two or three hundred doubtful forms of Brit-
ish plants are entitled to hold, if the existence of any well-marked varie-
354 MASTERWORKS OF SCIENCE
ties be admitted. But the mere existence of Individual variability ^and of
some few well-marked varieties, though necessary as the foundation for
the work, helps us but little in understanding how species arise in nature.
How have all those exquisite adaptations of one part of the organisation
to another part, and to the conditions of life, and of one organic being to
another being, been perfected? We see these beautiful co-adaptations
most plainly in the woodpecker and the mistletoe; and only a little less
plainly in the humblest parasite which clings to the hairs of a quadruped
or feathers of a bird; in the structure of the beetle which dives through
the water; In the plumed seed which is wafted by the gentlest breeze; in
shorty we see beautiful adaptations everywhere and in every part of the
organic world.
Again, It may be asked, how is it that varieties, which I have called
incipient species, become ultimately converted into good and distinct spe-
cies which in most cases obviously differ from each other far more than do
the varieties of the same species? How do those groups of species, which
constitute what are called distinct genera, and which differ from each
other more than do the species of the same genus, arise? All these results,
as we shall more fully see in the next chapter, follow from the struggle for
life. Owing to this struggle, variations, however slight and from whatever
cause proceeding, if they be in any degree profitable to the individuals of
a spe.cies, In their infinitely complex relations to other organic beings and
to- their physical conditions of life, will tend to the preservation of such
individuals, and will generally be inherited by the offspring. The off-
spring, also, will thus have a better chance of surviving, for, of the many
individuals of any species which are periodically born, but a small number-
can survive. I have called this principle, by which each slight variation, If
useful, is preserved, by the term Natural Selection, in order to mark its
relation to man's power of selection. But the expression often used by
Mr. Herbert Spencer of the Survival of the Fittest is more accurate, and
is sometimes equally convenient. We have seen that man by selection can
certainly produce great results, and can adapt organic beings to his own
uses, through the accumulation of slight but useful variations, given to
him by the hand of Nature. But Natural Selection, as we shall hereafter
see, is a power Incessantly ready for action, and is as immeasurably supe-
rior to man's feeble efforts as the works of Nature are to those of Art.
Nothing is easier than to admit in words the truth of the universal
struggle for life, or more difficult — at least I have found it so — than con-
stantly to bear this conclusion in mind. Yet unless it be thoroughly en-
grained in the mind, the whole economy of nature, with every fact on
distribution, rarity, abundance, extinction, and variation, will be dimly
seen or quite misunderstood. We behold the face of nature bright with
gladness, we often see superabundance of food; we do not see, or we
forget, that the birds which are idly singing round us mostly live on
insects or seeds, and are thus constantly destroying life; or we forget how
largely these songsters, or their eggs, or their nestlings, are destroyed by
birds and beasts of prey; we do not always bear in mind that, though
DARWIN — ORIGIN OF SPECIES 355
food may be now superabundant, it Is not so at all seasons of each recur-
ring year.
The Term, Struggle -for Existence, used in a large sense
I should premise that I use this term in a large and metaphorical
sense including dependence of one being on another, and including (which
is more Important) not only the life o£ the individual, but success in leav-
ing progeny. Two canine animals, in a time of dearth, may be truly said
to struggle with each other which shall get food and live. But a plant on
the edge of a desert is said to struggle for life against the drought, though
more properly it should be said to be dependent on the moisture. A plant
which annually produces a thousand seeds, of which only one of an aver-
age comes to maturity, may be more truly said to struggle with the plants
of the same and other kinds which already clothe the ground. The mistle-
toe Is dependent on the apple and a few other trees, but can only in a far-
fetched sense be said to struggle with these trees, for, If too many of these
parasites grow on the same tree, It languishes and dies. But several seed-
ling mistletoes, growing close together on the same branch, may more
truly be said to struggle with each other. As the mistletoe is disseminated
by birds, Its existence depends on them; and It may methodically be said
to struggle with other fruit-bearing plants, in tempting the birds to de-
vour and thus disseminate Its seeds. In these several senses, which pass
Into each other, I use for convenience* sake the general term of Struggle
for Existence.
Geometrical Ratio of Increase
A struggle for existence inevitably fellows from the high rate at which
all organic beings tend to Increase. Every being, which during its natural
lifetime produces several eggs or seeds, must suffer destruction during
some period of its life, and during some season or occasional year, other-
wise, on the principle of geometrical increase, Its numbers would quickly
become so inordinately great that no country could support the product.
Hence, as more Individuals are produced than can possibly survive, there f
must In every case be a struggle for existence, either one individual with
another of the same species, or with the individuals of distinct species, or
with the physical conditions of life. It Is the doctrine of Malthus applied
with manifold force to the whole animal and vegetable kingdoms; for In
this case there can be no artificial Increase of food, and no prudential
restraint from marriage. Although some species may be now Increasing,
more or less rapidly, in numbers, all cannot do so, for the world would not
hold them.
There is no exception to the rule that every organic being naturally
Increases at so high a rate that, If not destroyed, the earth would soon be
covered by the progeny of a single pair. Even slow-breeding man has
356 MASTERWORKS OF SCIENCE
doubled In twenty-five years, and at this rate, In less than a thousand
years, there would literally not be standing room for his progeny. Linnaeus
has calculated that if an annual plant produced only two seeds — and there
Is no plant so unproductive as this — and their seedlings next year pro-
duced two, and so on, then in twenty years there should be a million
plants. The elephant Is reckoned the slowest breeder of all known anij
mals, and I have taken some pains to estimate its probable minimum rate
of natural increase; it will be safest to assume that it begins breeding
when thirty years old, and goes on breeding till ninety years old, bringing
forth six young In the interval, and surviving till one hundred years old;
If this be so, after a period of from 740 to 750 years there would be nearly
nineteen million elephants alive, descended from the first pair.
The only difference between organisms which annually produce eggs
or seeds by the thousand and those which produce extremely few is that
the slow breeders would require a few more years to people, under favour-
able conditions, a whole district, let it be ever so large. The condor lays a
couple of eggs and the ostrich a score, and yet in the same country the
condor may be the more numerous of the two; the Fulmar petrel lays but
one egg, yet It Is believed to be the most numerous bird in the world. One
fly deposits hundreds of eggs, and another, like the hippobosca, a single
one; but this difference does not determine how many individuals of the
two species can be supported In a district. A large number of eggs is of
some importance to those species which depend on a fluctuating amount
of food, for It allows them rapidly to Increase in number. But the real Im-
portance of a large number of eggs or seeds is to make up for much de-
struction at some period of life; and this period in the great majority of
cases Is an early one. If an animal can in any way protect Its own eggs or
young, a small number may be produced, and yet the average stock be
fully kept up; but if many eggs or young are destroyed, many must be
produced, or the species will become extinct. It would suffice to keep up
the full number of a tree, which lived on an average for a thousand years,
if a single seed were produced once In a thousand years, supposing that
this seed were never destroyed, and could be ensured to germinate in a
fitting place. So that, In all cases, the average number of any animal or
plant depends only indirectly on the number of its eggs or seeds.
In looking at Nature, it is most necessary to keep the foregoing con-
siderations always in mind — never to forget that every single organic being
may be said to be striving to the utmost to increase in numbers; that each
lives by a struggle at some period of its life; that heavy destruction inevi-
tably falls either on the young or old, during each generation or at recur-
rent intervals. Lighten any check, mitigate the destruction ever so little,
and the number of the species will almost instantaneously increase to any
amount.
DARWIN — ORIGIN OF SPECIES 357
Complex Relations of all Animals and Plants to each other in the Struggle
for Existence
Many cases are on record showing how complex and unexpected are
the checks and relations between organic beings, which have to struggle
together In the same country. I will give only a single instance, which,
though a simple one, interested me. In Staffordshire, on the estate of a
relation, where I had ample means of investigation, there was a large and
extremely barren heath, which had never been touched by the hand of
man; but several hundred acres of exactly the same nature had been en-
closed twenty-five years previously and planted with Scotch fir. The change
in the native vegetation of the planted part of the heath was most remark-
able, more than is generally seen In passing from one quite different soil
to another: not only the proportional numbers of the heath plants were
wholly changed, but twelve species of plants (not counting grasses and
carices) flourished In the plantations, which could not be found on the
heath. The effect on the insects must have been still greater, for six Insec-
tivorous birds were very common in the plantations, which were not to
be seen on the heath; and the heath was frequented by two or three dis-
tinct insectivorous birds. Here we see how potent has been the effect of
the introduction of a single tree, nothing whatever else having been done,
with the exception of the land having been enclosed, so that cattle could
not enter. But how Important an element enclosure is, I plainly saw near
Farnham, in Surrey. Here there are extensive heaths, with a few clumps
of old Scotch firs on the distant hilltops: within the last ten years large
spaces have been enclosed, and self-sown firs are now springing up in mul-
titudes, so close together that all cannot live. When I ascertained that
these young trees had not been sown or planted, I was so much surprised
at their numbers that I went to several points of view, whence I could
examine hundreds of acres of the unenclosed heath, and literally I could
not see a single Scotch fir, except the old planted clumps. But on looking:
closely between the stems of the heath, I found a multitude of seedlings
and little trees which had been perpetually browsed down by the cattle.
In one square yard, at a point some hundred yards distant from one of
the old clumps, I counted thirty-two little trees; and one of them, with
twenty-six rings of growth, had, during many years, tried to raise Its head
above the stems of the heath, and had failed. No wonder that, as soon as
the land was enclosed, it became thickly clothed with vigorously growing
young firs. Yet the heath was so extremely barren and so extensive that
no one would ever have imagined that cattle would have so closely and
effectually searched It for food.
Here we see that cattle absolutely determine the existence of the
Scotch fir; but In several parts of the world Insects determine the exist-
ence of cattle. Perhaps Paraguay offers the most curious instance of this;
for here neither cattle nor horses nor dogs have ever run wild, though
358 MASTERWORKS OF SCIENCE
they swarm southward and northward in a feral state; and Azara and
Rengger have shown that this is caused by the greater number in Para-
guay of a certain fly, which lays its eggs in the navels of these animals
when first born. The increase of these flies, numerous as they are, must be
habitually checked by some means, probably by other parasitic insects.
Hence, if certain insectivorous birds were to decrease in Paraguay, the
parasitic insects would probably increase; and this would lessen the num-
ber of the navel-frequenting flies — then cattle and horses would become
feral, and this would certainly greatly alter (as indeed I have observed in
parts of South America) the vegetation: this again would largely affect
the insects; and this, as we have just seen In Staffordshire, the insectivo-
rous birds, and so onwards in ever-increasing circles of complexity. Not
that under nature the relations will ever be as simple as this. Battle within
battle must be continually recurring with varying success; and yet in the
long run the forces are so nicely balanced that the face of nature remains
for long periods of time uniform, though assuredly the merest trifle would
give the victory to one organic being over .another. Nevertheless, so pro-
found is our ignorance, and so high our presumption, that we marvel
when we hear of the extinction of an organic being; and as we do not see
the cause, we invoke cataclysms to desolate the world, or invent laws on
the duration of the forms of life!
The dependency of one organic being on another, as of a parasite on
its prey, lies generally between beings remote in the scale of nature. This
is likewise sometimes the case with those which may be strictly said to
struggle with each other for existence, as in the case of locusts and grass-
feeding quadrupeds. But the struggle will almost invariably be most severe
between the individuals of the same species, for they frequent the same
districts, require the same food, and are exposed to the same dangers.
In the case of varieties of the same species, the struggle will generally be
almost equally severe, and we sometimes see the contest soon decided:
for instance, if several varieties of wheat be sown together, and the mixed
seed be resown, some of the varieties which best suit the soil or climate,
or are naturally the most fertile, will beat the others and so yield more
seed, and will consequently in a few years supplant the other varieties.
As the species of the same genus usually have, though by no means in-
variably, much similarity in habits and constitution, and always in struc-
ture, the struggle will generally be more severe between them, if they
come into competition with each other, than between the species of dis-
tinct genera. We see this in the recent extension over parts of the United
States of one species of swallow having caused the decrease of another
species. The recent increase of the missel thrush in parts of Scotland has
caused the decrease of the song thrush. How frequently we hear of one
species of rat taking the place of another species under the most different
climates! In Russia the small Asiatic cockroach has everywhere driven
before it its great congener. In Australia the imported hive bee is rapidly
exterminating the small, stingless native bee. One species of charlock has
been known to supplant another species; and so in other cases. We can
DARWIN — ORIGIN OF SPECIES 359
dimly see why the competition should be most severe between allied
forms, which fill nearly the same place in the economy of nature; but
probably in no one case could we precisely say why one species has been
victorious over another in the great battle of life.
IV. NATURAL SELECTION; OR THE SURVIVAL
OF THE FITTEST
How will the struggle for existence, briefly discussed in the last chapter,
act in regard to variation? Can the principle of selection, which we have
seen is so potent in the hands of man, apply under nature? I think we
shall see that it can act most efficiently. Let the endless number of slight
variations and individual differences occurring in our domestic produc-
tions, and, in a lesser degree, in those under nature, be borne in mind; as
well as the strength of the hereditary tendency. Under domestication, it
may be truly said that the whole organisation becomes in some degree
plastic. But the variability, which we almost universally meet with in our
domestic productions, is not directly produced, as Hooker and Asa Gray
"have well remarked, by rnan; he can neither originate varieties nor pre-
vent their occurrence; he can preserve and accumulate such as do occur.
Unintentionally he exposes organic beings to new and changing condi-
tions of life, and variability ensues; but similar changes of conditions
might and do occur under nature. Let it also be borne in mind how in-
finitely complex and close-fitting are the mutual relations of all organic
beings to each other and to their physical conditions of life; and conse-
quently what infinitely varied diversities of structure might be of use to
each being under changing conditions of life. Can it, then, be thought im-
probable, seeing that variations useful to man have undoubtedly occurred,
that other variations useful in some way to each being in the great and
complex battle of life should occur in the course of many successive gen-
erations? If such do occur, can we doubt (remembering that many more
individuals are born than can possibly survive) that individuals having
any advantage, however slight, over others, would have the best chance
of surviving and of procreating their kind? On the other hand, we may
feel sure that any variation in the least degree injurious would be rigidly
destroyed. This preservation of favourable individual differences and vari-
ations, and the destruction of those which are injurious, I have called
Natural Selection, or the Survival of the Fittest.
We shall best understand the probable course of natural selection by
taking the case of a country undergoing some slight physical change, for
instance, of climate. The proportional numbers of its inhabitants will al-
most immediately undergo a change, and some species will probably be-
come extinct. We may conclude, from what we have seen of the intimate
and complex manner in which the inhabitants of each country are bound
together, that any change in the numerical proportions of the inhabitants,
independently of the change of climate itself, would seriously affect the
360 MASTERWORKS OF SCIENCE
others. If the country were open on its borders, new forms would cer-
tainly immigrate, and this would likewise seriously disturb the relations
of some of the former inhabitants. Let it be remembered how powerful
the influence of a single introduced tree or mammal has been shown to be.
But in the case of an island, or of a country partly surrounded by bar-
riers, into which new and better adapted forms could not freely enter, we
should then have places in the economy of nature which would assuredly
be better filled up, if some of the original Inhabitants were in some man-
ner modified; for, had the area been open to immigration, these same
places would have been seized on by intruders. In such cases, slight modi-
fications, which in any way favoured the individuals of any species, by
better adapting them to their altered conditions, would tend to be pre-
served; and natural selection would have free -scope for the work of im-
provement.
As man can produce, and certainly has produced, a great result by his
methodical and unconscious means of selection, what may not natural
selection effect? Man selects only for his own good: Nature only for that
of the being which she tends. Every selected character is fully exercised
by her, as is implied by the fact of their selection. Man keeps the natives
of many climates in the same country; he seldom exercises each selected
character in some peculiar and fitting manner; he feeds a long- and a
short-beaked pigeon on the same food; he does not exercise a long-backed
or long-legged quadruped in any peculiar manner; he exposes sheep with
long and short wool to the same climate. He does not allow the most
vigorous males to struggle for the females. He does not rigidly destroy
all inferior animals, but protects during each varying season, as far as lies
in his power, all his productions. He often begins his selection by some
half -monstrous form; or at least by some modification prominent enough
to catch the eye or to be plainly useful to him. Under nature, the slightest
differences of structure or constitution may well turn the nicely balanced
scale in the struggle for life, and so be preserved. How fleeting are the
wishes and efforts of man! how short his time! and consequently how
poor will be his results, compared with those accumulated by Nature
during whole geological periods! Can we wonder, then, that Nature's pro-
ductions should be far "truer" in character than man's productions; that
they should be infinitely better adapted to the most complex conditions
of life, and should plainly bear the stamp of far higher workmanship?
It may metaphorically be said that natural selection Is daily and hourly
scrutinising, throughout the world, the slightest variations; rejecting
those that are bad, preserving and adding up all that are good; silently
and insensibly working, whenever and wherever opportunity offers, at the
Improvement of each organic being in relation to its organic and inorganic
conditions of life. We see nothing of these slow changes in progress, until
the hand of time has marked the lapse of ages, and then so imperfect i&
our view Into long-past geological ages that we see only that the forms
of life are now different from what they formerly were.
Although natural selection can act only through and for the good of
DARWIN — ORIGIN OF SPECIES 361
each being, yet characters and structures, which we are apt to consider as
of very trifling importance, may thus be acted on. When we see leaf-eating
insects green, and bark feeders mottled grey; the alpine ptarmigan white
in winter, the red grouse the colour of heather, we must believe that these
tints are of service to these birds and insects in preserving them from
danger. Grouse, if not destroyed at some period of their lives, would
increase in countless numbers; they are known to suffer largely from
birds of prey; and hawks are guided by eyesight to their prey — so much
so that on parts of the Continent persons are warned not to keep white
pigeons, as being the most liable to destruction. Hence natural selection
might be effective in giving the proper colour to each kind of grouse, and
in keeping that colour, when once acquired, true and constant. Nor ought
we to think that the occasional destruction of an animal of any particular
colour would produce little effect: we should remember how essential it is
in a flock of white sheep to destroy a lamb with the faintest trace of
black. We have seen how the colour of the hogs, which feed on the "paint-
root" in-Virginia, determines whether they shall live or die.
As we see that those variations which, under domestication, appear at
any particular period of life tend to reappear in the offspring at the same
period; — for instance, in the shape, size, and flavour of the seeds of the
many varieties of our culinary and agricultural plants; in the caterpillar
and cocoon stages of the varieties of the silkworm; in the eggs of poultry,
and in the colour of the down of their chickens; in the horns of our sheep
and cattle when nearly adult; — so in a state of nature natural selection
will be enabled to act on and modify organic beings at any age, by the
accumulation of variations profitable at that age, and by their inheritance
at a corresponding age. If it profit a plant to have its seeds more and more
widely disseminated by the wind, I can see no greater difficulty in this
being effected through natural selection than in the cotton planter increas-
ing and improving by selection the down in the pods on his cotton trees.
Natural selection may modify and adapt the larva of an insect to a score
of contingencies, wholly different from those which concern the mature in-
sect; and these modifications may effect, through correlation, the structure
of the adult. So, conversely, modifications in the adult may affect the struc-
ture of the larva; but in all cases natural selection will ensure that they shall
not be injurious: for if they were so, the species would become extinct.
Natural selection will modify the structure of the young in relation
to the parent, and of the parent in relation to the young. In social animals
it will adapt the structure of each individual for the benefit of the whole
community; if the community profits by the selected change. What natu-
ral selection cannot do is to modify the structure of one species, without
giving it any advantage, for the good of another species; and though state-
ments to this effect may be found in works of natural history, I cannot
find one case which will bear investigation. A structure used only once
in an animal's life, if of high importance to it, might be modified to any
extent by natural selection; for instance, the great jaws possessed by cer-
tain insects, used exclusively for opening the cocoon — or the hard tip to
362 MASTERWORKS OF SCIENCE
the beak of unhatched birds, used for breaking the egg. It has been as-
serted that of the best short-beaked tumbler pigeons a greater number
perish in the egg than are able to get out of it; so that fanciers assist in
the act of hatching. Now if nature had to make the beak of a full-grown
pigeon very short for the bird's own advantage, the process of modifica-
tion would be very slow, and there would be simultaneously the most rig-
orous selection of all the young birds within the egg, which had the most
powerful and hardest beaks, for all with weak beaks would inevitably
perish; or, more delicate and more easily broken shells might be selected,
the thickness of the shell being known to vary like every other structure.
Illustrations of the Action of Natural Selection, or the
Survival of the Fittest
In order to make it clear how, as I believe, natural selection acts, I
must beg permission to give one or two imaginary illustrations* Let us
take the case of a wolf, which preys on various animals, securing some by
craft, some by strength, and some by fleetness; and let us suppose that
the fleetest prey, a deer for instance, had from any change in the country
increased in numbers, or that other prey had decreased in numbers, dur-
ing that season of the year when the wolf was hardest pressed for food.
Under such circumstances the swiftest and slimmest wolves would have
the best chance of surviving and so be preserved or selected — provided
always that they retained strength to master their prey at this or some
other period of the year, when they were compelled to prey on other ani-
mals. I can see no more reason to doubt that this would be the result thaa
that man should be able to improve the fleetness of his greyhounds by
careful and methodical selection, or by that kind of unconscious selection
which follows from each man trying to keep the best dogs without any
thought of modifying the breed. I may add that, according to Mr. Pierce,
there are two varieties of the wolf inhabiting the Catskill Mountains, in
the United States, one with a light greyhound-like form, which pursues
deer, and the other more bulky, with shorter legs, which more frequently
attacks the shepherd's flocks.
It may be worth while to give another and more complex illustration
of the action of natural selection. Certain plants excrete sweet juice, appar-
ently for the sake of eliminating something injurious from the sap: this is
effected, for instance, by glands at the base of the stipules in some Legu-
minosae, and at the backs of the leaves of the common laurel. This juice,
though small in quantity, is greedily sought by insects; but their visits do-
not in any way benefit the plant. Now, let us suppose that the juice or
nectar was excreted from the inside of the flowers of a certain number of
plants of any species. Insects in seeking the nectar would get dusted with
pollen, and would often transport it from one flower to another. The flow-
ers of two distinct individuals of the same species would thus get crossed;
and the act of crossing, as can be fully proved, gives rise to vigorous seed-
DARWIN — ORIGIN OF SPECIES 363
lings which consequently would have the best chance of flourishing and
surviving. The plants which produced flowers with the largest glands or
nectaries, excreting most nectar, would oftenest be visited by insects, and
would oftenest be crossed; and so in the long run would gain the upper
hand and form a local variety. The flowers, also, which had their stamens
and pistils placed, in relation to the size and habits of the particular in-
sects which visited them, so as to favour in any degree the transportal of
the pollen, would likewise be favoured.
Let us now turn to the nectar-feeding insects; we may suppose the
plant, of which we have been slowly increasing the nectar by continued
selection, to be a common plant; and that certain insects depended in
main part on its nectar for food. I could give many facts showing how
anxious bees are to save time: for instance, their habit of cutting holes
and sucking the nectar at the bases of certain flowers, which, with a very
little more trouble, they can enter by the mouth. Bearing such facts in
mind, it may be believed that under certain circumstances individual dif-
ferences in the curvature or length o£ the proboscis, &c., too slight to be
appreciated by us, might profit a bee or other insect, so that certain indi-
viduals would be able to obtain their food more quickly than others; and
thus the communities to which they belonged would flourish and throw
off many swarms inheriting the same peculiarities. The tubes of the
corolla of the common red and incarnate clovers (Trifolium pratense and
incarnatum) do not on a hasty glance appear to differ in length; yet the
hive bee can easily suck the nectar out of the incarnate clover, but not
out of the common red clover, which is visited by bumblebees alone; so
that %vhole fields of red clover offer in vain an abundant supply of precious
nectar to the hive bee. That this nectar is much liked by the hive bee is
certain; for I have repeatedly seen, but only in the autumn, many hive
bees sucking the flowers through holes bitten in the base of the tube by
bumblebees. Thus, in a country where this kind of clover abounded, it
might be a great advantage to the hive bee to have a slightly longer or
differently constructed proboscis. On the other hand, as the fertility of
this clover absolutely depends on bees visiting the flowers, if bumblebees
were to become rare in any country, it might be a great advantage to the
plant to have a shorter or more deeply divided corolla, so that the hive
bees should be enabled to suck its flowers. Thus I can understand how a
flower and a bee might slowly become, either simultaneously or one after
the other, modified and adapted to each other in the most perfect manner,
by the continued preservation of all the individuals which presented slight
deviations of structure mutually favourable to each other.
I am well aware that this doctrine of natural selection, exemplified In
the above imaginary instances, is open to the same objections which were
first urged against Sir Charles Lyell's noble views on "the modern changes
of the earth, as illustrative of geology"; but we now seldom hear the agen-
cies which we see still at work, spoken of as trifling or insignificant, when
used in explaining the excavation of the deepest valleys or the formation
of long lines of inland cliffs. Natural selection acts only by the preserva-
364 MASTERWQRKS OF SCIENCE
tion and accumulation of small Inherited modifications, each profitable to
the preserved being; and as modern geology has almost banished such
views as the excavation of a great valley by a single diluvial wave, so will
natural selection banish the belief of the continued creation of new or-
ganic beings, or of any great and sudden modification in their structure.
Circumstances jav our able for the production of new forms through
Natural Selection
This Is an extremely intricate subject. A great amount of variability,
under which term individual differences are always included, will evi-
dently be favourable. A large number of individuals, by giving a better
chance within any given period for the appearance of profitable varia-
tions, will compensate for a lesser amount of variability In each individual,
and Is, I believe, a highly Important element of success. Though Nature
grants long periods of time for the work of natural selection, she does not
grant an indefinite period; for as all organic beings are striving to seize
on each place in the economy of nature, if any one species does not be-
come modified and improved in a corresponding degree with its competi-
tors, It will be exterminated. Unless favourable variations be inherited by
some at least of the offspring, nothing can be effected by natural selection.
The tendency to reversion may often check or prevent the work; but as
this tendency has not prevented man from forming by selection numerous
domestic races, why should It prevail against natural selection?
Intercrossing will chiefly affect those animals which unite for each
birth and wander much, and which do not breed at a very quick rate.
Hence with animals of this nature, for instance, birds, varieties will gener-
ally be confined to separated countries; and this I find to be the case.
With hermaphrodite organisms which cross only occasionally, and like-
wise with animals which unite for each birth, but which wander little and
can Increase at a rapid rate, a new and improved variety might be quickly
formed on any one spot, and might there maintain Itself in a body and
afterwards spread, so that the individuals of the new variety would chiefly
cross together. On this principle, nurserymen always prefer saving seed
from a large body of plants, as the chance of intercrossing is thus lessened.
Isolation, also, is an important element In the modification of species
through natural selection. In a confined or isolated area, if not very large,
the organic and inorganic conditions of life will generally be almost uni-
form; so that natural selection will tend to modify all the varying individ-
uals of the same species In the same manner. Intercrossing with the in-
habitants of the surrounding districts will, also, be thus prevented. The
importance o£ Isolation Is likewise great in preventing, after any physical
change In the" conditions, such as of climate, elevation of the land, &c., the
Immigration of better adapted organisms; and thus new places in the
natural economy of the district will be left open to be filled up by the
modification of the old inhabitants. Lastly, isolation will give time for a
DARWIN — ORIGIN OF SPECIES 365
new variety to be Improved at a slow rate; and this may sometimes be of
much importance.
Although isolation is of great importance in the production of new
species, on the whole I am inclined to believe that largeness of area Is still
more important, especially for the production of species which shall prove
capable of enduring for a long period, and of spreading widely. Through-
out a great and open area, not only will there be a better chance of favour-
able variations, arising from the large number of individuals of the same
species there supported, but the conditions of life are much more com-
plex from the large number of already existing species; and if some of
these many species become modified and Improved, others will have to be
improved In a corresponding degree, or they will be exterminated. Each
new form, also, as soon as it has been much improved, will be able to
spread over the open and continuous area, and will thus come into compe-
tition with many other forms. Moreover, great areas, though now continu-
ous, will often, owing to former oscillations of level, have existed in a
broken condition; so that the good effects of isolation will generally, to a
certain extent3 have concurred.
To sum up, as far as the extreme intricacy of the subject permits, the
circumstances favourable and unfavourable for the production of new
species through natural selection. I conclude that for terrestrial produc-
tions a large continental area, which has undergone many oscillations of
levelj will have been the most favourable for the production of many new
forms of life, fitted to endure for a long time and to spread widely. Whilst
the area existed as a continent, the inhabitants will have been numerous
In individuals and kinds, and will have been subjected to severe competi-
tion. When converted by subsidence into large separate islands, there will
still have existed many individuals of the same species on each island: in-
tercrossing on the confines of the range of each new species will have been
checked: after physical changes of any kind, Immigration will have been
prevented, so that new places In the polity of each island will have had to
be filled up by the modification of the old Inhabitants; and time will have
been allowed for the varieties In each to become well modified and per-
fected. When, by renewed elevation, the islands were reconverted Into a
continental area, there will again have been very severe competition: the
most favoured or Improved varieties will have been enabled to spread:
there will have been much extinction of the less Improved forms, and the
relative proportional numbers of the various inhabitants of the reunited
continent will again have been changed; and again there will have been a
fair field for natural selection§ to improve still further the Inhabitants, and
thus to produce new species.
Slow though the process of selection may be, If feeble man can do
much by artificial selection, I can see no limit to the amount of change, to
the beauty and complexity of the coadaptations between all organic
beings, one with another and with their physical conditions of life, which
may have been effected in the long course of time- through nature's power
of selection, that is, by the survival of the fittest.
366 MASTERWORKS OF SCIENCE
Divergence of Character
The principle, which I have designated by this term, is of high im-
portance, and explains, as I believe, several important facts. In the first
place, varieties, even strongly marked ones, though having somewhat of
the character of species — as is shown by the hopeless doubts in many
cases how to rank them — yet certainly differ far less from each other than
do good and distinct species. Nevertheless, according to my view, varie-
ties are species in the process of formation, or are, as I have called them,
incipient species. How, then, does the lesser difference between varieties
become augmented into the greater difference between species? That this
does habitually happen, we must infer from most of the innumerable
species throughout nature presenting well-marked differences; whereas
varieties, the supposed prototypes and parents of future well-marked
species, present slight and ill-defined differences. Mere chance, as we may
call it, might cause one variety to differ in some character from its par-
ents, and the offspring of this variety again to differ from its parent in
the very same character and in a greater degree; but this alone would
never account for so habitual and large a degree of difference as that
between the species of the same genus.
As has always been my practice, I have sought light on this head
from our domestic productions. We shall here find something analogous.
It will be admitted that the production of races so different as Shorthorn
and Hereford cattle, race and cart horses, the several breeds of pigeons,
&c., could never have been effected by the mere chance accumulation of
similar variations during many successive generations. In practice, a fan-
cier is, for instance, struck by a pigeon having a slightly shorter beak;
another fancier is struck by a pigeon having a rather longer beak; and on
the acknowledged principle that "fanciers do not and will not admire a
medium standard, but like extremes," they both go on (as has actually
occurred with the sub-breeds of the tumbler pigeon) choosing and breed-
ing from birds with longer and longer beaks, or with shorter and shorter
beaks. Again, we may suppose that at an early period of history, the men
of one nation or district required swifter horses, whilst those of another
required stronger and bulkier horses. The early differences would be very
slight; but, in the course of time, from the continued selection of swifter
horses in the one case, and of stronger ones in the other, the differences
would become greater, and would be noted as forming two sub-breeds.
Ultimately, after the lapse of centuries, these sub-breeds would become
converted into two well-established and distinct breeds. As the differences
became greater, the inferior animals with intermediate characters, being
neither swift nor very strong, would not have been used for breeding, and
will thus have tended to disappear. Here, then, we see in man's produc-
tions the action of what-may be called the principle of divergence, causing
differences, at first barely appreciable, steadily to increase, and the breeds
DARWIN — ORIGIN OF SPECIES 367
to diverge in character, both from each other and from their common
parent.
But how, it may be asked, can any analogous principle apply in na-
ture? I believe it can and does apply most efficiently (though it was a
long time before I saw how), from the simple circumstance that the more
diversified the descendants from any one species become in structure,
constitution, and habits, by so much will they be better enabled to seize
on many and widely diversified places in the polity of nature, and so be
enabled to increase in numbers.
We can clearly discern this in the case of animals with simple habits.
Take the case of a carnivorous quadruped, of which the number that can
be supported in any country has long ago arrived at its full average. If its
natural power of increase be allowed to act, it can succeed in increasing
(the country not undergoing any change in conditions) only by its vary-
ing descendants seizing on places at present occupied by other animals:
some of them, for instance, being enabled to feed on new kinds of prey,
either dead or alive; some inhabiting new stations, climbing trees, fre-
quenting water, and some perhaps becoming less carnivorous. The more
diversified in habits and structure the descendants of our carnivorous ani-
mals become, the more places they will be enabled to occupy.
The advantage of diversification of structure in the inhabitants of the
same region is, in fact, the same as that of the physiological division of
labour in the organs of the same individual body — a subject so well eluci-
dated by Milne Edwards. No physiologist doubts that a stomach adapted
to digest vegetable matter alone, or flesh alone, draws most nutriment
from these substances. So in the general economy of any land, the more
widely and perfectly the animals and plants are diversified for different
habits of life, so will a greater number of individuals be capable of there
supporting themselves. A set of animals, with their organisation but little
diversified, could hardly compete with a set more perfectly diversified in
structure. It may be doubted, for instance, whether the Australian mar-
supials, which are divided into groups differing but little from each other,
and feebly representing, as Mr, Waterhouse and others have remarked,
our carnivorous, ruminant, and rodent mammals, could successfully com-
pete with these well-developed orders. In the Australian mammals, we see
the process of diversification in an early and incomplete stage of devel-
opment.
The Probable Effects of the Action of Natural Selection through Diver-
gence of Character and Extinction, on the Descendants of a Common
Ancestor.
After the foregoing discussion, which has been much compressed, we
may assume that the modified descendants of any one species will succeed
so much the better as they become more diversified in structure, and are
thus enabled to encroach on places occupied by other beings. Now let us
368 MASTERWQRKS OF SCIENCE
see how this principle of benefit being derived from divergence of charac-
ter, combined with the principles o£ natural selection and o£ extinction,
tends to act.
The accompanying diagram will aid us in understanding this rather
perplexing subject. Let A to L represent the species of a genus large in its
own country; these species are supposed to resemble each other in un-
equal degrees, as is so generally the case In nature, and as is represented
in the diagram by the letters, standing at unequal distances. I have said a
large genus because, as we saw in the second chapter, on an average more
species vary in large genera than in small genera; and the varying species
of the large genera present a greater number of varieties. We have, also,
seen that the species which are the commonest and the most widely
diffused vary more than do the rare and restricted species. Let (A) be a
common, widely diffused, and varying species, belonging to a genus large
in its own country. The branching and diverging dotted lines of unequal
lengths proceeding from (A) may represent its varying offspring. The
variations are supposed to be extremely slight, but of the most diversified
nature; they are not supposed all to appear simultaneously, but often after
long intervals of time; nor are they all supposed to endure for equal
periods. Only those variations which are in some way profitable will be
preserved or naturally selected. And here the importance of the principle
of benefit derived from divergence of character comes in; for this will
generally lead to the most different or divergent variations (represented
by the outer dotted lines) being preserved and accumulated by natural
selection. When a dotted line reaches one of the horizontal lines, and is
there marked by a small numbered letter, a sufficient amount of variation
is supposed to have been accumulated to form it into a fairly well-marked
variety, such as would be thought worthy of record in a systematic work.
The intervals between the horizontal lines in the diagram may repre-
sent each a thousand or more generations. After a thousand generations,
species (A) is supposed to have produced two fairly well-marked varie-
ties, namely a1 and m*. These two varieties will -generally still be exposed
to the same conditions which made their parents variable, and the tend-
ency to variability is in itself hereditary; consequently they will likewise
tend to vary, and commonly in nearly the same manner as did their par-
ents. Moreover, these two varieties, being only slightly modified forms,
will tend to inherit those advantages which made their parent (A) more
numerous than most of the other inhabitants of the same country; they
will also partake of those more general advantages which made the genus
to which the parent species belonged a large genus in its own country.
And all these circumstances are favourable to the production of new
varieties.
If, then, these two varieties be variable, the most divergent of their
variations will generally be preserved during the next thousand genera-
tions. And after this interval, variety a1 is supposed in the diagram to
have produced variety ^j2, which will, owing to the principle of diver-
gence, differ more from (A) than did variety a1. Variety ml is supposed
*
K
*<
^
"M —
$
370 MASTERWORKS OF SCIENCE
to have produced two varieties, namely m2 and s2, differing from each
other, and more considerably from their common parent (A). We may
continue the process by similar steps for any length of time; some of the
varieties, after each thousand generations, producing only a single variety,
but in a more and more modified condition, some producing two or three
varieties, and some failing to produce any. Thus the varieties or modified
descendants of the common parent (A) will generally go on increasing in
number and diverging in character. In the diagram the process is rep-
resented up to the ten thousandth generation, and under a condensed and
simplified form up to the fourteen thousandth generation.
As all the modified descendants from a common and widely diffused
species, belonging to a large genus, will tend to partake of the same ad-
vantages which made their parent successful in life, they will generally go
on multiplying in number as well as diverging in character: this is repre-
sented in the diagram by the several divergent branches proceeding from
(A). The modified offspring from the later and more highly improved
branches in the lines of descent will, it is probable, often take the place
of, and so destroy, the earlier and less improved branches: this is repre-
sented in the diagram by some of the lower branches not reaching to the
upper horizontal lines. In some cases no doubt the process of modification
will be confined to a single line of descent and the number of modified
descendants will not be increased; although the amount of divergent
modification may have been augmented. This case would be represented
in the diagram, if all the lines proceeding from (A) were removed, ex-
cepting that from a1 to aw. In the same way the English race horse and
English pointer have apparently both gone on slowly diverging in charac-
ter from their original stocks, without either having given off any fresh
branches or races.
After ten thousand generations, species (A) is supposed to have pro-
duced three forms, aw, /10, and m10, which, from having diverged in char-
acter during the successive generations, will have come to differ largely,
but perhaps unequally, from each other and from their common parent. If
we suppose the amount of change between each horizontal line in our
diagram to be excessively small, these three forms may still be only well-
marked varieties; but we have only to suppose the steps in the process of
modification to be more numerous or greater in amount, to convert these
three forms into doubtful or at least into well-defined species. Thus the
diagram illustrates the steps by which the small differences distinguishing
varieties are increased into the larger differences distinguishing species.
By continuing the same process for a greater number of generations (as
shown in the diagram in a condensed and simplified manner), we get
eight species, marked by the letters between #14 and m14, all descended
from (A). Thus, as I believe, species are multiplied and genera are
formed.
In a large genus it is probable that more than one species would vary.
In the diagram I have assumed that a second species (I) has produced, by
analogous steps, after ten thousand generations, either two well-marked
DARWIN — ORIGIN OF SPECIES 371
varieties (wig and zlQ) or two species, according to the amount of change
supposed to be represented between the horizontal lines. After fourteen
thousand generations, six new species, marked by the letters n^ to jsr14,
are supposed to have been produced. In any genus, the species which are
already very different in character from each other will generally tend to
produce the greatest number of modified descendants; for these will have
the best chance of seizing on new and widely different places in the polity
of nature: hence in the diagram I have chosen the extreme -species (A),
and the nearly extreme species (I), as those which have largely varied
and have given rise to new varieties and species. The other nine species
(marked by capital letters) of our original genus may for long but un-
equal periods continue to transmit unaltered descendants; and this is
shown in the diagram by the dotted lines unequally prolonged upwards.
But during the process of modification, represented in the diagram,
another of our principles, namely that of extinction, will have played an
important part. As in each fully stocked country natural selection neces-
sarily acts by the selected form having some advantage in the struggle for
life over other forms, there will be a constant tendency in the improved
descendants of any one species to supplant and exterminate in each stage
of descent their predecessors and their original progenitor. For it should
be remembered that the competition will generally be most severe be-
tween those forms which are most nearly related to each other in habits,
constitution, and structure. Hence all the intermediate forms between the
earlier and later states, that is between the less and more improved states
of the same species, as well as the original parent species itself, will gen-
rally tend to become extinct. So it probably will be with many whole col-
lateral lines of descent, which will be conquered by later and improved
lines. If, however, the modified offspring of a species get into some dis-
tinct country, or become quickly adapted to some quite new station, in
which offspring and progenitor do not come into competition, both may
continue to exist.
If, then, our diagram be assumed to represent a considerable amount
of modification, species (A) and all the earlier varieties will have become
extinct, being replaced by eight new species (a14 to m14); and species (I)
will be replaced by six (n14 to z14) new species.
But we may go further than this. The original species of our genus
were supposed to resemble each other in unequal degrees, as is so gener-
ally the case in nature; species (A) being more nearly related to B, C,
and D than to the other species; and species (I) more to G, H, K, L,
than to the others. These two species (A) and (I) were also supposed to
be very common and widely diffused species, so that they must originally
have had some advantage over most of the other species of the genus.
Their modified descendants, fourteen in number at the fourteen thou-
sandth generation, will probably have inherited some of the same advan-
tages: they have also been modified and improved in a diversified manner
at each stage of descent, so as to have become adapted to many related
places in the natural economy of their country. It seems, therefore, ex-
372 MASTERWORKS OF SCIENCE
tremely probable that they will have taken the places of, and thus exter-
minated not only their parents (A) and (I), but likewise some of the
original species which were most nearly related to their parents. Hence
very few of the original species will have transmitted offspring to the
fourteen thousandth generation. We may suppose that only one, (F), of
the two species (E and F) which were least closely related to the other
nine original species has transmitted descendants to this late stage of
descent.
The new species in our diagram descended from the original eleven
species will now be fifteen in number. Owing to the divergent tendency
of natural selection, the extreme amount of difference in character be-
tween species ali and #14 will be much greater than that between the most
distinct of the original eleven species. The new species, moreover, will be
allied to each other in a widely different manner. Of the eight descend-
ants from (A) the three marked au, q14, pu, will be nearly related from
having recently branched off from a10; £14 and /14, from having diverged
at an earlier period from <z5, will be In some degree distinct from the three
first-named species; and lastly, o14, tf14, and m14 will be nearly related one
to the other, but, from having diverged at the first commencement of the
process of modification, will be widely different from the other five
species, and may constitute a sub-genus or a distinct genus.
The six descendants from (I) will form two sub-genera or genera.
But as the original species (I) differed largely from (A), standing nearly
at the extreme end of the original genus, the six descendants from (I)
will, owing to Inheritance alone, differ considerably from the eight de-
scendants from (A); the two groups, moreover, are supposed to, have gone
on diverging In different directions. The Intermediate species, also (and
this is a very Important consideration), which connected the original
species (A) and (I), have all become, excepting (F), extinct, and have left
no descendants. Hence the six new species descended from (I), and the
eight descendants from (A), will have to be ranked as very distinct
genera, or even as distinct sub-families.
Thus it is, as I believe, that two or more genera are produced by de-
scent with modification from two or more species of the same genus. And
the two or more parent species are supposed to be descended from some
one species of an earlier genus. In our diagram, this is indicated by the
broken lines, beneath the capital letters, converging In sub-branches
downwards towards a single point; this point represents a species, the
supposed progenitor of our several new sub-genera and genera.
We have seen that In each country it is the species belonging to the
larger genera which oftenest present varieties or incipient species. This,
Indeed, might have been expected; for, as natural selection acts through
one form having some advantage over other forms in the struggle for ex-
istence, it will chiefly act on those which already have some advantage;
and the largeness of any group shows that its species have inherited from
a common ancestor some advantage in common. Hence, the struggle for
the production of new and modified descendants will mainly lie between
DARWIN — ORIGIN OF SPECIES 373
the larger groups which are all trying to increase in number. One large
group will slowly conquer another large group, reduce its numbers, and
thus lessen its chance of further variation and improvement. Within the
same large group, the later and more highly perfected sub-groups, from
branching out and seizing on many new places in the polity of Nature,
will constantly tend to supplant and destroy the earlier and less improved
sub-groups. Small and broken groups and sub-groups will finally disap-
pear. Looking to the future, we can predict that the groups of organic
beings which are now large and triumphant, and which are least broken
ups that is, which have as yet suffered least extinction, will, for a Jong
period, continue to increase. But which groups will ultimately prevail, no
man can predict; for we know that many groups formerly most exten-
sively developed have now become extinct. Looking still more remotely ^to
the future, we may predict that, owing to the continued and ^ steady in-
crease of the larger groups, a multitude of smaller groups will become
utterly extinct, and leave no modified descendants; and consequently that,
of the species living at any one period, extremely few will transmit de-
scendants to a remote futurity.
On the Degree to which Organisation tends to advance
Natural Selection acts exclusively by the preservation and accumula-
tion of variations, which are beneficial under the organic and inorganic
conditions to which each creature is exposed at all periods of life. The
ultimate result is that each creature tends to become more and more im-
proved in relation to its conditions. This improvement inevitably leads to
the gradual advancement of the organisation of the greater number of
living beings throughout the world. But here we enter on a very intricate
subject, for naturalists have not defined to each other's satisfaction what
is meant by an advance in organisation. Amongst the vertebrata the de-
gree of intellect and an approach in structure to man clearly come into
play. It might be thought that the amount of change which the various
parts and organs pass through in their development from the embryo to
maturity would suffice as a standard of comparison; but there are cases,
as with certain parasitic crustaceans, in which several parts of the struc-
ture become less perfect, so that the mature animal cannot be called
higher than its larva. Von Baer's standard seems the most widely applica-
ble and the best, namely, the amount of differentiation of the parts of the
same organic being, in the adult state as I should be inclined to add, and
their specialisation for different functions; or, as Milne Edwards would
express it, the completeness of the division of "physiological labour. ^
But it may be objected that if all organic beings thus tend to rise in
the scale, how is it that throughout the world a multitude of the lowest
forms still exist; and how is it that in each great class some forms are far
more highly developed than others? Why have not the more highly devel-
oped forms everywhere supplaitted and exterminated the lower? Lamarck,
374 MASTERWORKS OF SCIENCE ^
who believed in an innate and inevitable tendency towards perfection in
all organic beings, seems to have felt this difficulty so strongly that he was
led to suppose that new and simple forms are continually being produced
by spontaneous generation. Science has not as yet proved the truth of this
belief, whatever the future may reveal. On our theory the continued exist-
ence of lowly organisms offers no difficulty; for natural selection, or the
survival of the fittest, does not necessarily include progressive develop-
ment— it only takes advantage of such variations as arise and are bene-
ficial to each creature under its complex relations of life. And it may be
asked what advantage, as far as we can see, would it be to an infusorian
animalcule — to an intestinal worm — or even to an earthworm, to be highly
organised. If it were no advantage, these forms would be left, by natural
selection, unimproved or but little improved, and might remain for indefi-
nite ages in their present lowly condition. And geology tells us that some
of the lowest forms, as the infusoria and rhizopods, have remained for an
enormous period in nearly their present state.
Looking to the first dawn of life, when all organic beings, as we may
believe, presented the simplest structure, how, it has been asked, could
the first steps in the advancement or differentiation of parts have arisen?
Mr. Herbert Spencer would probably answer that, as soon as simple uni-
cellular organism came by growth or division to be compounded of
several cells, or became attached to any supporting surface, his law "that
homologous units of any order become differentiated in proportion as
their relations to incident forces become different" would come into
action. But as we have no facts to guide us, speculation on the subject is
almost useless. It is, however, an error to suppose that there would be no
struggle for existence, and, consequently, no natural selection, until many
forms had been produced: variations in a single species inhabiting an
isolated station might be beneficial, and thus the whole mass of individ-
uals might be modified, or two distinct forms might arise. But, as I re-
marked towards the close of the Introduction, no one ought to feel sur-
prise at much remaining as yet unexplained on the origin of species, if we
make due allowance for our profound ignorance on the mutual relations
of the inhabitants of the world at the present time, and still more so
during past ages.
The affinities of all the beings of the same class have sometimes been
represented by a great tree. I believe this simile largely speaks the truth.
The green and budding twigs may represent existing species; and those
produced during former years may represent the long succession of ex-
tinct species. At each period of growth all the growing twigs have tried
to branch out on all sides, and to overtop and kill the surrounding twigs
and branches, in the same manner as species and groups of species have
at all times overmastered other species in the great battle for life. The
limbs divided into great branches, and these into lesser and lesser
branches, were themselves once, when the tree was young, budding twigs,
and this connection of the former and present buds by ramifying branches
may-well represent the classification of all extinct and living species in
DARWIN — ORIGIN OF SPECIES 375
groups subordinate to groups. Of the many twigs which flourished when
the tree was a mere bush, only two or three, now grown into great
branches, yet survive and bear the other branches; so with the species
which lived during long-past geological periods, very few have left living
and modified descendants. From the first growth of the tree, many a limb
and branch has decayed and dropped off; and these fallen branches of
various sizes may represent those whole orders, families, and genera
which have now no living representatives, and which are known to us
only in a fossil state. As we here and there see a thin straggling branch
springing from a fork low down in a tree, and which by some chance has
been favoured and is still alive on its summit, so we occasionally see an
animal like the Ornithorhynchus or Lepidosiren, which in some small de-
gree connects by its affinities two large branches of life, and which has
apparently been saved from fatal competition by having 'inhabited a pro-
tected station. As buds give rise by growth to fresh buds, and these, if
vigorous, branch out and overtop on all sides many a feebler branch, so by
generation I believe it has been with the great Tree of Life, which fills
with its dead and broken branches the crust of the earth, and covers the
surface with its ever-branching and beautiful ramifications.
V. LAWS OF VARIATION
I HAVE hitherto sometimes spoken as if the variations — so common and
multiform with organic beings under domestication, and in a lesser de-
gree with those under nature — were due to chance. This, of course, is a
wholly incorrect expression, but it serves to acknowledge plainly our igno-
rance of the cause of each particular variation. Some authors believe it to
be as much the function of the reproductive system to produce individual
differences, or slight deviations of structure, as to make the child like its
parents. But the fact of variations and monstrosities occurring much more
frequently under domestication than under nature, and the greater varia-
bility of species having wider ranges than of those with restricted ranges,
leads to the conclusion that variability is generally related to the condi-
tions of life to which each species has been exposed during several suc-
cessive generations. In the first chapter I attempted to show that changed
conditions act in two ways, directly on the whole organisation or on cer-
tain parts alone, and indirectly through the reproductive system. In aE
cases there are two factors, the nature of the organism, which is much the
most important of the two, and the nature of the conditions. The direct
action of changed conditions leads to definite or indefinite results. In the
latter case the organisation seems to become plastic, and we have much
fluctuating variability. In the former case the nature of the organism is
such that it yields readily, when subjected to certain conditions, and all,
or nearly all, the individuals become modified in the same way.
It is very difficult to decide how far changed conditions, such as of
climate, food, &c., have acted in a definite manner. There is reason to be-
376 MASTERWORKS OF SCIENCE
lieve that in the course of time the effects have been greater than can be
proved by clear evidence. But we may safely conclude that the innumer-
able complex coadaptations of structure, which we see throughout nature
between various organic beings, cannot be attributed simply to such
action.
When a variation is of the slightest use to any being, we cannot tell
how much to attribute to the accumulative action of natural selection and
how much to the definite action of the conditions of life. Thus, it is well
known to furriers that animals of the same species have thicker and better
fur the further north they live; but who can tell how much of this differ-
ence may be due to the warmest-clad individuals having been favoured
and preserved during many generations, and how much to the action of
the severe climate? for it would appear that climate has some direct
action on the hair of our domestic quadrupeds.
In one sense the conditions of life may be said, not only to cause vari-
ability, either directly or indirectly, but likewise to include natural selec-
tion, for the conditions determine whether this or that variety shall
survive. But when man is the selecting agent, we clearly see that the two
elements of change are distinct; variability is in some manner excited, but
it is the will of man which accumulates the variations in certain direc-
tions; and it is this latter agency which answers to the survival of the
fittest under nature.
Effects of the increased Use and Disuse of Parts, as controlled by Natural
Selection
From the facts alluded to in the first chapter, I think there can be no
doubt that use in our domestic animals has strengthened and enlarged
certain parts, and disuse diminished them; and that such modifications
are inherited. Under free nature, we have no standard of comparison, by
which to judge of the effects of long-continued use or disuse, for we know
not the parent forms; but many animals possess structures which can be
best explained by the effects of disuse.
It is well known that several animals, belonging to the most different
classes, which inhabit the caves of Carniola and of Kentucky, are blind.
In some of the crabs the footstalk for the eye remains, though the eye is
gone; — the stand for the telescope is there, though the telescope with its
gksses has been lost. As it is difficult to imagine that eyes, though useless,
could be in any way injurious to animals living in darkness, their loss may
be attributed to disuse. In one of the blind animals, namely, the cave rat
(Noetoma), two of which were captured by Professor Silliman at above
half a mile distance from the mouth of the cave, and therefore not in the
profoundest depths, the eyes were lustrous and of large size; and these
animals, as I am informed by Professor Silliman, after having been ex-
posed for about a month to a graduated light, acquired a dim perception
of objects.
DARWIN — ORIGIN OF SPECIES 377
It is difficult to imagine conditions of life more similar than deep
limestone caverns under a nearly similar climate; so that, in. accordance
with the old view of the blind animals having been separately created for
the American and European caverns, very close similarity in their organi-
sation and affinities might have been expected. This is certainly not the
case if we look at the two whole faunas. On my view we must suppose
that American animals, having in most cases ordinary powers of vision,
slowly migrated by successive generations from the outer wrorld into the
deeper and deeper recesses of the Kentucky caves, as did European
animals into the caves of Europe. By the time that an animal had reached,
after numberless generations, the deepest recesses, disuse will on this
view have more or less perfectly obliterated its eyes, and natural selection
will often have effected other changes, such as an increase in the length of
the antennae or palpi, as a compensation for blindness. Notwithstanding
such modifications, we might expect still to see, in the cave animals of
America, affinities to the other inhabitants of that continent, and in those
of Europe to the inhabitants of the European continent. And this is the
case with some of the American cave animals, as I hear from Professor
Dana; and some of the European cave insects are very closely allied to
those of the surrounding country. It would be difficult to give any rational
explanation of the affinities of the blind cave animals to the other inhabit-
ants of the two continents on the ordinary view of their independent
creation.
Correlated Variation
I mean by this expression that the whole organisation is so tied to-
gether during its growth and development that when slight variations in
any one part occur, and are accumulated through natural selection, other
parts become modified. This is a very important subject, most imperfectly
understood, and no doubt wholly different classes of facts may be here
easily confounded together. We shall presently see that simple inheritance
often gives the false appearance of correlation. One of the most obvious
real cases is that variations of structure arising in the young or larvae
naturally tend to affect the structure of the mature animal. The several
parts of the body which are homologous, and which, at an early embry-
onic period^ are identical in structure, and which are necessarily exposed
to similar conditions, seem eminently liable to vary in a like manner: we
see this in the right and left sides of the body varying in the same man-
ner; in the front and hind legs, and even in the jaws and limbs, varying
together, for the lower jaw is believed by some anatomists to be homolo-
gous with the limbs. These tendencies, I do not doubt, may be mastered
more or less completely by natural selection; thus a family of stags once
existed with an antler only on one side; and if this had been of any great
use to the breed, it might probably have been rendered permanent by
selection.
We may often falsely attribute to correlated variation structures
378 MASTERWORKS OF SCIENCE
which are common to whole groups of species, and which in truth are
simply due to inheritance; for an ancient progenitor may have acquired
through natural selection some one modification in structure, and, after
thousands of generations, some other and independent modification; and
these two modifications, having been transmitted to a whole group of
descendants with diverse habits, would naturally be thought to be in some
necessary manner correlated. Some other correlations are apparently due
to the manner in which natural selection can alone act. For instance,
Alphonse de Candolle has remarked that winged seeds are never found in
fruits which do not open; I should explain this rule by the impossibility
of seeds gradually becoming winged through natural selection, unless the
capsules were open; for in this case alone could the seeds, which were a
little better adapted to be wafted by the wind, gain an advantage over
others less well fitted for wide dispersal
When we see any part or organ developed in a remarkable degree or
manner in a species, the fair presumption is that it is of high importance
to that species: nevertheless it is in this case eminently liable to variation.
Why should this be so? On the view that each species has been independ-
ently created, with all its parts as we now see them, I can see no explana-
tion. But on the view that groups of species are descended from some
other species, and have been modified through natural selection, I think
we can obtain some light.
When a part has been developed in an extraordinary manner in any
one species, compared with the other species of the same genus, we may
conclude that this part has undergone an extraordinary amount of modifi-
cation since the period when the several species branched off from the
common progenitor of the genus. This period will seldom be remote in
any extreme degree, as species rarely endure for more than one geological
period. An extraordinary amount of modification implies an unusually
large and long-continued amount of variability, which has continually
been accumulated by natural selection for the benefit of the species. But as
the variability of the extraordinarily developed part or organ has been so
great and long-continued within a period not excessively remote, we
might, as a general rule, still expect to find more variability in such parts
than in other parts of the organisation which have remained for a much
longer period nearly constant. And this, I am convinced, is the case. That
the struggle between natural selection, on the one hand, and the tend-
ency to reversion and variability, on the other hand, will in the course of
time cease; and that the most abnormally developed organs may be made
constant, I see no reason to doubt. Hence, when an organ, however ab-
normal it may be, has been transmitted in approximately the same condi-
tion to many modified descendants, as in the case of the wing of the bat,
it must have existed, according to our theory, for an immense period in
nearly the same state; and thus it has come not to be more variable than
any other structure.
DARWIN — ORIGIN OF SPECIES 379
Specific Characters more Variable than Generic Characters
It Is notorious that specific characters are more variable than generic.
To explain by a simple example what is meant: if in a large genus of
plants some species had blue flowers and some had red, the colour would
be only a specific character, and no one would be surprised at one of the
blue species varying into red, or conversely; but if all the species had blue
flowers, the colour would become a generic character, and its variation
would be a more unusual circumstance.
On the ordinary view of each species having been independently cre-
ated, why should that part of the structure which differs from the same
part in other independently created species of the same genus be more
variable than those parts which are closely alike in the several species? I
do not see that any explanation can be given. But on the view that species
are only strongly marked and fixed varieties, we might expect often to
find them still continuing to vary in those parts of their structure which
have varied within a moderately recent period, and which have thus come
to differ. Or to state the case in another manner: — the points in which all
the species of a genus resemble each other, and in which they differ from
allied genera, are called generic characters; and these characters may be
attributed to inheritance from a common progenitor, for it can rarely
have happened that natural selection will have modified several distinct
species, fitted to more or less widely different habits, in exactly the same
manner: and as these so-called generic characters have been inherited
from before the period when the several species first branched off from
their common progenitor, and subsequently have not varied or come to
differ in any degree, or only in a slight degree, it is not probable that they
should vary at the present day. On the other hand, the points in which
species differ from other species of the same genus are called specific
characters; and as these specific characters have varied and come to differ
since the period when the species branched off from a common progeni-
tor, it is probable that they should still often be in some degree variable —
at least more variable than those parts of the organisation which have for
a very long period remained constant.
Distinct Species present analogous Variations, so that a Variety of
one Species often assumes a Character proper to an allied Species, or re-
verts to some of the Characters of an early Progenitor. — These proposi-
tions will be most readily understood by looking to our domestic races.
The most distinct breeds of the pigeon, in countries widely apart, present
sub-varieties with reversed feathers on the head, and with feathers on the
feet — characters not possessed by the aboriginal rock pigeon; these then
are analogous variations in two or more distinct races. The frequent pres-
ence of fourteen or even sixteen tail feathers in the pouter may be consid-
ered as a variation representing the normal structure of another race, the
fantail. I presume that no one will doubt that all such analogous varia-
380 MASTERWQRKS OF SCIENCE
dons are due to the several races of the pigeon having inherited from a
common parent the same constitution and tendency to variation, when
acted on by similar unknown influences.
With pigeons, however, we have another case, namely, the occasional
appearance in all the breeds of slaty-blue birds with two black bars on the
wings, white loins, a bar at the end of the tail, with the outer feathers
externally edged near their basis with white. As all these marks are char-
acteristic of the parent rock pigeon, I presume that no one will doubt
that this is a case of reversion, and not of a new yet analogous variation
appearing in the several breeds. We may, I think, confidently come to this
conclusion, because, as we have seen, these coloured marks are eminently
liable to appear in the crossed offspring of two distinct and differently
coloured breeds; and in this case there is nothing in the external condi-
tions of life to cause the reappearance of the slaty-blue, with the several
marks, beyond the influence of the mere act of crossing on the laws of
inheritance.
I will give one curious and complex case, not indeed as affecting any
important character, but from occurring in several species of the same
genus, partly under domestication and partly under nature. It is a case
almost certainly of reversion. The ass sometimes has very distinct trans-
verse bars on its legs, like those on the legs of the zebra: it has been as-
serted that these are plainest in the foal, and, from inquiries which I have
made, I believe this to be true. The stripe on the shoulder is sometimes
double, and is very variable in length and outline. A white ass, but not an
albino, has been described without either spinal or shoulder stripe: and
these stripes are sometimes very obscure, or actually quite lost, in dark-
coloured asses. The koulan of Pallas is said to have been seen with a
double shoulder stripe. Mr. Blyth has seen a specimen of the hemionus
with a distinct shoulder stripe, though it properly has none; and I have
been informed by Colonel Poole that the foals of this species are gener-
ally striped on the legs, and faindy on the shoulder. The quagga, though
so plainly barred like a zebra over the body, is without bars on the legs;
but Dr. Gray has figured one specimen with very distinct zebra-like bars
on the hocks.
With respect to the horse, I have collected cases in England of the
spinal stripe in horses of the most distinct breeds, and of all colours:
transverse bars on the legs are not rare in duns, mouse duns, and in one
instance in a chestnut: a faint shoulder stripe may sometimes be seen in
duns, and I have seen a trace in a bay horse. My son made a careful ex-
amination and sketch for me of a dun Belgian cart horse with a double
stripe on each shoulder and with leg stripes; I have myself seen a dun
Devonshire pony, and a small dun Welsh pony has been carefully de-
scribed to me, both with three parallel stripes on each shoulder.
Now let us turn to the effects of crossing the several species of the
horse genus. Rollin asserts that the common mule from the ass and horse
is particularly apt to have bars on its legs; according to Mr. Gosse, in
certain parts of the United States about nine out of ten mules have
DARWIN — ORIGIN OF SPECIES 381
striped legs. I once saw a mule with its legs so much striped that anyone
might have thought that it was a hybrid zebra; and Mr. W. C. Martin,
in his excellent treatise on the horse, has given a figure of a similar mule.
In four coloured drawings, which I have seen, of hybrids between the ass
and zebra, the legs were much more plainly barred than the rest of the
body; and in one of them there was a double shoulder stripe. In Lord
Morton's famous hybrid, from a chestnut mare and male quagga, the
hybrid and even the pure offspring subsequently produced from the same
mare by a black Arabian sire were much more plainly barred across the
legs than is even the pure quagga- Lastly, and this is another most re-
markable case, a hybrid has been figured by Dr. Gray (and he informs
me that he knows of a second case) from the ass and the hemionus; and
this hybrid, though the ass only occasionally has stripes on its legs and
the hemionus has none and has not even a shoulder stripe, nevertheless
had all four legs barred, and had three short shoulder stripes, like those
on the dun Devonshire and Welsh ponies, and even had some zebra-like
stripes on the sides of its face.
What now are we to say to these several facts? We see several dis-
tinct species of the horse genus becoming, by simple variation, striped on
the legs like a zebra, or striped on the shoulders like an ass. In the horse
we see this tendency strong whenever a dun tint appears — a tint which
approaches to that of the general colouring of the other species of the
genus. The appearance of the stripes is not accompanied by any change of
form or by any other new character. We see this tendency to become
striped most strongly displayed in hybrids from between several of the
most distinct species. Now observe the case of the several breeds of
pigeons: they are descended from a pigeon (including two or three sub-
species or geographical races) of a bluish colour, with certain bars and
other marks; and when any breed assumes by simple variation a bluish
tint, these bars and other marks invariably reappear; but without any
other change of form or character. When the oldest and truest breeds of
various colours are crossed, we see a strong tendency for the blue tint and
bars and marks to reappear in the mongrels. I have stated that the most
probable hypothesis to account for the reappearance of very ancient char-
acters is — that there is a tendency in the young of each successive genera-
tion to produce the long-lost character, and that this tendency, from un-
known causes, sometimes prevails. And we have just seen that in several
species of the horse genus the stripes are either plainer or appear more
commonly in the young than in the old. Call the breeds of pigeons, some
of which have bred true for centuries, species; and how exactly parallel is
the case with that of the species of the horse genus! For myself, I venture
confidently to look back thousands on thousands of generations, and I see
an animal striped like a zebra, but perhaps otherwise very differently con-
structed, the common parent of our domestic horse (whether or not it be
descended from one or more wild stocks), of the ass, the hemionus,
quagga, and zebra.
382 MASTERWORKS OF SCIENCE
VI. DIFFICULTIES OF THE THEORY
LONG BEFORE the reader has arrived at this part of my work, a crowd of
difficulties will have occurred to him. Some of them are so serious that
to this day I can hardly reflect on them without being in some degree
staggered; but, to the best of my judgment, the greater number are only
apparent, and those that are real are not, I think, fatal to the theory.
These difficulties and objections may be classed tinder the following
heads: — First, why, if species have descended from other species by fine
gradations, do we not everywhere see innumerable transitional forms?
Why is not all nature in confusion, instead of the species being, as we see
them, well defined?
Secondly, is it possible that an animal having, for instance, the struc-
ture and habits of a bat could have been formed by the modification of
some other animal with widely different habits and structure? Can we
believe that natural selection could produce, on the one hand, an organ of
trifling importance, such as the tail of a giraffe, which serves as a fly
flapper, and, on the other hand, an organ so wonderful as the eye?
Thirdly, can instincts be acquired and modified through natural
selection?
On the Absence or Rarity of Transitional Varieties. — As natural se-
lection acts solely by the preservation of profitable modifications, each
new form will tend in a fully stocked country to take the place of, and
finally to. exterminate, its own less improved parent form and other less
favoured forms with which it comes into competition. Thus extinction
and natural selection go hand in hand. Hence, if we look at each species
as descended from some unknown form, both the parent and all the tran-
sitional varieties will generally have been exterminated by the very
process of the formation and perfection of the new form.
But it may be urged that when several closely allied species inhabit
the same territory, we surely ought to find at the present time many tran-
sitional forms. Let us take a simple case: in travelling from north to south
over a continent, we generally meet at successive intervals with closely
allied or representative species, evidently filling nearly the same place in
the natural economy of the land. These representative species often meet
and interlock; and as the one becomes rarer and rarer, the other becomes
more and more frequent, till the one replaces the other. But if we com-
pare these species where they intermingle, they are generally as absolutely
distinct from each other in every detail of structure as are specimens
taken from the metropolis inhabited by each. By my theory these allied
species are descended from a common parent; and during the process of
modification, each has become adapted to the conditions of life of its own
region, and has supplanted and exterminated its original parent form and
all the transitional varieties between its past and present states. Hence we
ought not to expect at the present time to meet with numerous transi-
DARWIN — ORIGIN OF SPECIES 383
tional varieties in each region, though they must have existed there, and
may be embedded there in a fossil condition. But in the intermediate
region, having intermediate conditions of life, why do we not now find
closely linking intermediate varieties? This difficulty for a long time quite
confounded me. But I think it can be in large part explained.
As allied or representative species, when inhabiting a continuous
area, are generally distributed in such a manner that each has a wide
range, with a comparatively narrow neutral territory between them, in
which they become rather suddenly rarer and rarer; then, as varieties do
not essentially differ from species, the same rule will probably apply to
both; and if we take a varying species inhabiting a very large area, we
shall have to adapt two varieties to two large areas, and a third variety to
a narrow intermediate zone. The intermediate variety, consequently, will
exist in lesser numbers from inhabiting a narrow and lesser area; and
practically, as far as I can make out, this rule holds good with varieties
in a state of nature. Now, if varieties linking two other varieties together
generally have existed in lesser numbers than the forms which they con-
nect, then we can understand why intermediate varieties should not
endure for very long periods: — why, as a general rule, they should be
exterminated and disappear sooner than the forms which they originally
linked together.
For any form existing in lesser numbers would, as already remarked,
run a greater chance of being exterminated than one existing in large
numbers; and in this particular case the intermediate form would be
eminently liable to the inroads of closely allied forms existing on both
sides of it. Hence, the more common forms, in the race for life, will tend
to beat and supplant the less common forms, for these will be more slowly
modified and improved. It is the same principle which, as I believe,
accounts for the common species in each country, as shown in the second
chapter, presenting on an average a greater number of well-marked va-
rieties than do the rarer species. I may illustrate what I mean by sup-
posing three varieties of sheep to be kept, one adapted to an extensive
mountainous region; a second to a comparatively narrow, hilly tract; and
a third to the wide plains at the base; and that the inhabitants are all
trying with equal steadiness and skill to improve their stocks by selection;
the chances in this case will be strongly in favour of the great holders on
the mountains or on the plains improving their breeds more quickly than
the small holders on the intermediate narrow, hilly tract; and consequently
the improved mountain or plain breed will soon take the place of the less
improved hill breed; and thus the two breeds, which originally existed in
greater numbers, will come into close contact with each other, without the
interposition of the supplanted, intermediate hill variety.
To sum up, I believe that species come to be tolerably well-defined
objects, and do not at any one period present an inextricable chaos of vary-
ing and intermediate links; first, because new varieties are very slowly
formed, for variation is a slow process, and natural selection can do
nothing until favourable individual differences or variations occur, and
384 MASTERWORKS OF SCIENCE
until a place in the natural polity of the country can be better filled by
some modification of some one or more of its inhabitants. And such new
places will depend on slow changes of climate, or on the occasional im-
migration of new inhabitants,, and, probably, in a still more important
degree, on some of the old inhabitants becoming slowly modified, with
the new forms thus produced, and the old ones acting and reacting on
each other. So that, in any one region and at any one time, we ought to
see only a few species presenting slight modifications of structure in some
degree permanent; and this assuredly we do see.
Secondly, areas now continuous must often have existed within the
recent period as isolated portions, in which many forms, more especially
amongst the classes which unite for each birth and wander much, may
have separately been rendered sufficiently distinct to rank as representative
species. In this case, intermediate varieties between the several representa-
tive species and their common parent must formerly have existed within
each isolated portion of the land, but these links during the process of
natural selection will have been supplanted and exterminated, so that they
will no longer be found in a living state.
Thirdly, when two or more varieties have been formed in different
portions of a strictly continuous area, intermediate varieties will, it is
probable, at first have been formed in the intermediate zones, but they
will generally have had a short duration. For these intermediate varieties
will, from reasons already assigned (namely from what we know of the
actual distribution of closely allied or representative species, and likewise
of acknowledged varieties), exist in the intermediate zones in lesser num-
bers than the varieties which they tend to connect. From this cause alone
the intermediate varieties will be liable to accidental extermination; and
during the process of further modification through natural selection, they
will almost certainly be beaten and supplanted by the forms which they
connect; for these, from existing in greater numbers, will, in the aggregate,
present more varieties, and thus be further improved through natural
selection and gain further advantages.
Lastly, looking not to any one time, but to all time, if my theory be
true, numberless intermediate varieties, linking closely together all the
species of the same group, must assuredly have existed; but the very proc-
ess of natural selection constantly tends, as has been so often remarked,
to exterminate the parent forms and the intermediate links. Consequently
evidence of their former existence could be found only amongst fossil
remains, which are preserved, as we shall attempt to show in a future
chapter, in an extremely imperfect and intermittent record.
On the Origin and Transitions of Organic Beings with peculiar Habits
and Structure. — It has been asked by the opponents of such views as I
hold how, for instance, could a land carnivorous animal have been con-
verted into one with aquatic habits; for how could the animal in its
transitional state have subsisted ? It would be easy to show that there now
exist carnivorous animals presenting close intermediate grades from
strictly terrestrial to aquatic habits; and as each exists by a struggle for
DARWIN — ORIGIN OF SPECIES 385
life, it is clear that each must be well adapted to its place in nature. Look
at the Mustek vison of North America, which has webbed feet, and
which resembles an otter in its fur, short legs, and form of tail. During the
summer this animal dives for and preys on fish, but during the long
winter it leaves the frozen waters, and preys, like other polecats, on mice
and land animals.
Look at the family of squirrels; here we have the finest gradation
from animals with their tails only slightly flattened, and from others, as
Sir }. Richardson has remarked, with the posterior part of their bodies
rather wide and with the skin on their flanks rather full, to the so-called
flying squirrels; and flying squirrels have their limbs and even the base
of the tail united by a broad expanse of skin, which serves as a parachute
and allows them to glide through the air to an astonishing distance from.
tree to tree. We cannot doubt that each structure is of use to each kind of
squirrel in its own country," by enabling it to escape birds or beasts of
prey, to collect food more quickly, or, as there is reason to believe, to
lessen the danger from occasional falls. But it does not follow from this fact
that the structure of each squirrel is the best that it is possible to conceive
under ail possible conditions. Let the climate and vegetation change, let
other competing rodents or new beasts of prey immigrate, or old ones
become modified, and all analogy would lead us to believe that some at
least of the squirrels would decrease in numbers or become exterminated,
unless they also become modified and improved in structure in a cor-
responding manner. Therefore, I can see no difficulty, more especially
under changing conditions of life, in the continued preservation of indi-
viduals with fuller and fuller flank membranes, each modification being
useful, each being propagated, until, by the accumulated effects of this
process of natural selection, a perfect so-called flying squirrel was pro-
duced.
Now look at the Galeopithecus or so-called flying lemur, which
formerly was ranked amongst bats, but is now believed to belong to the
Insectivora. An extremely wide flank membrane stretches from the corners
of the jaw to the tail, and includes the limbs with the elongated fingers.
This flank membrane is furnished with an extensor muscle. Although no
graduated links of structure, fitted for gliding through the air, now con-
nect the Galeopithecus with the other Insectivora, yet there is no difficulty
in supposing that such links formerly existed, and that each was developed
in the same manner as with the less perfectly gliding squirrels; each grade
of structure having been useful to its possessor. Nor can I see any insuper-
able difficulty in further believing that the membrane connected fingers
and forearm of the Galeopithecus might have been greatly lengthened by
natural selection; and this, as far as the organs of flight are concerned,
would have converted the animal into a bat. In certain bats in which the
wing membrane extends from the top of the shoulder to the tail and
Includes the hind legs, we perhaps see traces of an apparatus originally
fitted for gliding through the air rather than for flight.
It is, however, difficult to decide, and immaterial for us, whether
386 MASTERWORKS OF SCIENCE
"habits generally change first and structure afterwards; or whether slight
modifications of structure lead to changed habits; both probably often
occurring almost simultaneously. Of cases of changed habits it will suffice
merely to allude to that of the many British insects which now feed on
exotic plants, or exclusively on artificial substances. Of diversified habits
innumerable instances could be given: I have often watched a tyrant fly-
catcher (Saurophagus sulphuratus) in South America, hovering over one
.spot and then proceeding to another, like a kestrel, and at other times
.-standing stationary on the margin of water, and then dashing into it like
.a kingfisher at a fish. In our own country the larger titmouse (Parus
major) may be seen climbing branches, almost like a creeper; it some-
times, like a shrike, kills small birds by blows on the head; and I have
many times seen and heard it hammering the seeds of the yew on a
branch, and thus breaking them like a nuthatch. In North America the
Hack bear was seen by Hearne swimming for hours with widely open
mouth, thus catching, almost like a whale, insects in the water.
He who believes in separate and innumerable acts of creation may
say that in these cases it has pleased the Creator to cause a being of one
type to take the place of one belonging to another type; but this seems
to me only restating the fact in dignified language. He who believes in the
struggle for existence and in the principle of natural selection will ac-
knowledge that every organic being is constantly. endeavouring to increase
in numbers; and that if any one being varies ever so little, either in habits
«or structure, and thus gains an advantage over some other inhabitant of
the same country, it will seize on the place of that inhabitant, however
•different that may be from its own place. Hence it will cause him no sur-
prise that there should be geese and frigate birds with webbed feet living
-on the dry land and rarely alighting on the water, that there should be
long-toed, corn crakes living in meadows instead of in swamps; that there
should be woodpeckers where hardly a tree grows; that there should be
diving thrushes and diving Hymenoptera, and petrels with the habits of
auks.
Organs of extreme Perfection and Complication
To suppose that the eye, with all its inimitable contrivances for ad-
justing the focus to different distances, for admitting different amounts of
light, and for the correction of spherical and chromatic aberration, could
have been formed by natural selection seems, I freely confess, absurd in
the highest degree. When it was first said that the sun stood still and the
world turned round, the common sense of mankind declared the doctrine
false; but the old saying of Vox populi, vox Dei, as every philosopher
knows, cannot be trusted in science. Reason tells me that if numerous
gradations from a simple and imperfect eye to one complex and perfect
can be shown to exist, each grade being useful to its possessor, as is
certainly the case; if, further, the eye ever varies and the variations be
inherited, as is likewise certainly the case; and if such variations should be
DARWIN — ORIGIN OF SPECIES 387
useful to any animal under changing conditions of life, then the difficulty
of believing that a perfect and complex eye could be formed by natural
selection, though insuperable by our imagination, should not be con-
sidered as subversive of the theory.
In searching for the gradations through which an organ in any species
has been perfected, we ought to look exclusively to its lineal progenitors;,
but this is scarcely ever possible, and we are forced to look to other
species and genera of the same group, that is to the collateral descendants,
from the same parent form, in order to see what gradations are possible,,
and for the chance of some gradations having been transmitted in an
unaltered or little altered condition. But the state of the same organ in
distinct classes may incidentally throw light on the steps by which it has
been perfected.
The simplest organ which can be called an eye consists of an optic
nerve, surrounded by pigment cells and covered by translucent skin, but
without any lens or other refractive body. We may, however, according
to M. Jourdain, descend even a step lower and find aggregates of pigment
cells, apparently serving as organs of vision, without any nerves, and
resting merely on sarcodic tissue. Eyes of the above simple nature are
not capable of distinct vision, and serve only to distinguish light from
darkness. In certain star fishes, small depressions in the layer of pigment
which surrounds the nerve are filled, as described by the author just
quoted, with transparent gelatinous matter, projecting with a convex
surface, like the cornea in the higher animals. He suggests that this serves
not to form an image, but only to concentrate the luminous rays and
render their perception more easy. In this concentration of the rays we
gain the first and by far the most important step towards the formation
of a true, picture-forming eye; for we have only to place the naked ex-
tremity of the optic nerve, which in some of the lower animals lies deeply
buried in the body, and in some near the surface, at the right distance
from the concentrating apparatus, and an image will be formed on it.
Within the highest division of the animal kingdom, namely, the
Vertebrata, we can start from an eye so simple that it consists, as in the
lancelet, of a little sack of transparent skin, furnished with a nerve and
lined with pigment, but destitute of any other apparatus. In fishes and
reptiles, as Owen has remarked, "the range of gradations of dioptric
structures is very great." It is a significant fact that even in man, accord-
ing to the high authority of Virchow, the beautiful crystalline lens is
formed in the embryo by an accumulation of epidermic cells, lying in a
sack-like fold of the skin; and the vitreous body is formed from embryonic
subcutaneous tissue. To arrive, however, at a just conclusion regarding
the formation of the eye, with all its marvellous yet not absolutely perfect
characters, it is indispensable that the reason should conquer the imagi-
nation; but I have felt the difficulty far too keenly to be surprised at others
hesitating to extend the principle of natural selection to so startling a
length.
It is scarcely possible to avoid comparing the eye with a telescope. We
388 MASTERWORKS OF SCIENCE
know that this Instrument has been perfected by the long-continued
efforts of the highest human intellects; and we naturally infer that the eye
has been formed by a somewhat analogous process. But may not this
inference be presumptuous? Have we any right to assume that the Creator
works by intellectual powers like those of man? If we must compare the
eye to an optical instrument, we ought in imagination to take a thick
layer o£ transparent tissue, with spaces filled with fluid, and with a nerve
sensitive to light beneath, and then suppose every part of this layer to be
continually changing slowly in density, so as to separate into layers of
different densities and thicknesses, placed at different distances from each
other, and with the surfaces of each layer slowly changing in form. Further
we must suppose that there is a power, represented by natural selection
or the survival of the fittest, always intently watching each slight alter-
ation in the transparent layers; and carefully preserving each which, under
varied circumstances, in any way or in any degree, tends to- produce a
distincter image. We must suppose each new state of the instrument
to be multiplied by the million; each to be preserved until a better one
is produced, and then the old ones to be all destroyed. In living bodies,
variation will cause the slight alterations, generation will multiply them
almost infinitely, and natural selection will pick out with unerring skill
each improvement. Let this process go on for millions of years; and during
each year on millions of individuals of many kinds; and may we not
believe that a living optical instrument might thus be formed as superior
to one of glass, as the works of the Creator are to those of man?
Modes of Transition
If it could be demonstrated that any complex organ existed which
could not possibly have been formed by numerous, successive, slight modi-
fications, my theory would absolutely break down. But I can find out no
such case. No doubt many organs exist of which we do not know the
transitional grades, more especially if we look to much-isolated species,
round rwhich, according to the theory, there has been much extinction.
Or again, if we take an organ common to all the members of a class, for
in this latter case the organ must have been originally formed at a remote
period, since which all the many members of the class have been de-
veloped; and in order to discover the early transitional grades through
which the organ has passed, we should have to look to very ancient
ancestral forms, long since become extinct.
We should be extremely cautious in concluding that an organ could
not have been formed by transitional gradations of some kind. Numerous
cases could be given amongst the lower animals of the same organ per-
forming at the same time wholly distinct functions; thus in the larva of
the dragonfly and in the fish Cobites the alimentary canal respires, digests,
and excretes. In the Hydra, the animal may be turned inside out, and the
exterior surface will then digest and the stomach respire. In such cases
DARWIN — ORIGIN OF SPECIES 389
natural selection might specialise, if any advantage were thus gained, the
whole or part of an organ, which had previously performed two functions,
for one function alone, and thus by insensible steps greatly change its
nature.
The illustration of the swim bladder in fishes is a good one, because
it shows us clearly the highly important fact that an organ originally con-
structed for one purpose, namely, flotation, may be converted into one
for a widely different purpose, namely, respiration. The swim bladder has,
also, been worked in as an accessory to the auditory organs of certain
fishes. All physiologists admit that the swim bladder is homologous, or
"ideally similar" in position and structure with the lungs of the higher
vertebrate animals: hence there is no reason to doubt that the swim blad-
der has actually been converted into lungs, or an organ used exclusively
for respiration.
According to this view it may be inferred that all vertebrate animals
with true lungs are descended by ordinary generation from an ancient
and unknown prototype, which was furnished with a floating apparatus
or swim bladder. We can thus, as I infer from Owen's interesting descrip-
tion of these parts, understand the strange fact that every particle of food
and drink which we swallow has to pass over the orifice of the trachea,
with some risk of falling into the lungs, notwithstanding the beautiful
contrivance by which the glottis is closed. In the higher Vertebrate the
branchiae have wholly disappeared — but in the embryo the slits on the
sides of the neck and the loop-like course of the arteries still mark their
former position.
It is a common rule throughout nature that the same end should be
gained, even sometimes in the case of closely related beings, by the most
diversified means. How differently constructed is the feathered wing of a
bird and the membrane-covered wing of a bat; and still more so the four
wings of a butterfly, the two wings of a fly, and the two wings with the
elytra of a beetle. Bivalve shells are made to open and shut, but on what
a number of patterns is the hinge constructed — from the long row of
neatly interlocking teeth in a Nucula to the simple ligament of a Mussel!
With plants having separated sexes, and with those in which, though
hermaphrodites, the pollen does not spontaneously fall on the stigma,
some aid is necessary for their fertilisation. With several kinds this is
effected by the pollen grains, which are light and incoherent, being blown
by the wind through mere chance on to the stigma; and this is the simplest
plan which can well be conceived. An almost equally simple, though very
different, plan occurs in many plants in which a symmetrical flower
secretes a few drops of nectar, and is consequently visited by insects; and
these carry the pollen from the anthers to the stigma.
From this simple stage we may pass through an inexhaustible num-
ber of contrivances, all for the same purpose and effected in essentially
the same manner, but entailing changes in every part of the flower. The
nectar may be stored in variously shaped receptacles, with the stamens
and pistils modified in many ways, sometimes forming trap-like contriv-
390 MASTERWORKS OF SCIENCE
ances, and sometimes capable of neatly adapted movements through irri-
tability or elasticity. From such structures we may advance till we come
to such a case of extraordinary adaptation as that lately described by Dr.
Criiger in the Coryanthes. This orchid has part of its labellum or lower lip
hollowed out into a great bucket, into which drops of almost pure water
continually fall from two secreting horns which stand above it; and when
the bucket is half full, the water overflows by a spout on one side. The
basal part of the labellum stands over the bucket, and is itself hollowed
out into a sort of chamber with two lateral entrances; within this chamber
there are curious fleshy ridges. The most Ingenious man, if he had not
witnessed what takes place, could never have imagined what purpose all
these parts serve. But Dr. Cruger saw crowds of large humblebees visiting
the gigantic flowers of this orchid, not In order to suck nectar, but to
gnaw off the ridges within the chamber above the bucket; in doing this
they frequently pushed each other into the bucket, and their wings being
thus wetted they could not fly away, but were compelled to crawl out
through the passage formed by the spout or overflow. Dr. Cruger saw a
"continual procession" of bees thus crawling out of their involuntary bath.
The passage is narrow, and is roofed over by the column, so that a bee,
In forcing Its way out, first rubs its back against the viscid stigma and
then against the viscid glands of the pollen masses. The pollen masses are
thus glued to the back of the bee which first happens to crawl out through
the passage of a lately expanded flower, and are thus carried away. Dr.
Cruger sent me a flower in spirits of wine, with a bee which he had killed
before it had quite crawled out with a pollen mass still fastened to its
back. When the bee, thus provided, flies to another flower, or to the same
flower a second time, and Is pushed by its comrades into the bucket and
then crawls out by the passage, the pollen mass necessarily comes first into
contact with the viscid stigma, and adheres to it, and the flower is ferti-
lised. Now at last we see the full use of every part of the flower, of the
water-secreting horns, of the bucket half full of water, which prevents the
bees from flying away, and forces them to crawl out through the spout, and
rub against the properly placed viscid pollen masses and the viscid stigma.
How, it may be asked, in the foregoing and in innumerable other
instances, can we understand the graduated scale of complexity and the
multifarious means for gaining the same end? The answer no doubt Is, as
already remarked, that when two forms vary, which already differ from
each other in some slight degree, the variability will not be of the same
-exact nature, and consequently the results obtained through natural selec-
tion for the same general purpose will not be the same. We should also
bear in mind that every highly developed organism has passed through
many changes; and that each modified structure tends to be inherited, so
that each modification will not readily be quite lost, but may be again and
again further altered. Hence the structure of each part of each species,
for whatever purpose it may serve, is the sum of many inherited changes,
through which the species has passed during its successive adaptations to
changed habits and conditions of life.
__ DARWIN — ORIGIN OF SPECIES 391
Finally then, although In many cases it is most difficult even to con-
jecture by what transitions organs have arrived at their present state; yet,
considering how small the proportion of living and known forms is to the
extinct and unknown, I have been astonished how rarely an organ can be
named, towards which no transitional grade is known to lead. It certainly
is true that new organs appearing as if created for some special purpose
rarely or never appear in any being; — as indeed is shown by that old, but
somewhat exaggerated, canon in natural history of "Natura non facit
saltum." We meet with this admission in the writings of almost every
experienced naturalist; or, as Milne Edwards has well expressed it, Nature
is prodigal in variety, but niggard in innovation. Why, on the theory of
Creation, should there be so much variety and so little real novelty? Why
should all the parts and organs of many independent beings, each sup-
posed to have been separately created for its proper place in nature, be so
commonly linked together by graduated steps? Why should not Nature
take a sudden leap from structure to structure? On the theory of natural
selection, we can clearly understand why she should not; for natural selec-
tion acts only by taking advantage of slight successive variations; she
can never- take a great and sudden leap, but must advance by short and
sure, though slow, steps.
Natural selection cannot possibly produce any modification in a spe-
cies exclusively for the good of another species; though throughout nature
one species incessantly takes advantage of, and profits by, the structures of
others. But natural selection can and does often produce structures for
the direct injury of other animals, as we see in the fang of the adder, and
in the ovipositor of the ichneumon, by which its eggs are deposited in
the living bodies of other insects. If it could be proved that any part of
the structure of any one species had been formed for the exclusive good of
another species, it would annihilate my theory, for such could not have
been produced through natural selection. Although many statements may
be found in works on natural history to this effect, I cannot find even one
which seems to me of any weight. It is admitted that the rattlesnake has
a poison fang for its own defence, and for the destruction of its prey; but
some authors suppose that at the same time it is furnished with a rattle
for its own injury, namely, to warn its prey. I would almost as soon believe
that the cat curls the end of its tail when preparing to spring, in order to
warn the doomed mouse. It Is a much more probable view that the rattle-
snake uses its rattle, the cobra expands its frill, and the puf! adder swells
whilst hissing so loudly and harshly, in order to alarm the many birds and
beasts which are known to attack even the most venomous species.
Natural selection tends only to make each organic being as perfect as,
or slightly more perfect than, the other inhabitants of the same country
with which it comes into competition. And we see that this is the standard
of perfection attained under nature. The endemic productions of New
Zealand, for instance, are perfect one compared with another; but they
are now rapidly yielding before the advancing legions of plants and ani-
mals introduced from Europe. Natural selection will not produce absolute
392 MASTERWORKS OF SCIENCE
perfection, nor do we always meet, as far as we can judge, with this high
standard under nature. The correction for the aberration of light is said
by Muller not to be perfect even in that mosc perfect organ, the human
eye. If our reason leads us to admire with enthusiasm a multitude of inimi-
table contrivances in nature, this same, reason tells us, though we may
easily err on both sides, that some other contrivances are less perfect. Can
we consider the sting of the bee as perfect, which, when used against
many kinds of enemies, cannot be withdrawn, owing to the backward
serratures, and thus inevitably causes the death of the insect by tearing
out its viscera?
If we look at the sting of the bee, as having existed in a remote pro-
genitor, as a boring and serrated instrument, like that in so many members
of the same great order, and that it has since been modified but not per-
fected for Its present purpose, with the poison originally adapted for
some other object, such as to produce galls, since intensified, we can
perhaps understand how it is that the use of the sting should so often
cause the insect's own death: for if on the whole the power of stinging
be useful to the social community, it will fulfil all the requirements of
natural selection, though it may cause the death of some few members.
If we admire the several ingenious contrivances, by which orchids and
many other plants are fertilised through insect agency, can we consider as
equally perfect the elaboration of dense clouds of pollen by our fir trees,
so that a few granules may be wafted by chance on to the ovules?
Summary: the Law of Unity of Type and of the Conditions of Existence
embraced by the Theory of Natural Selection
We have seen in this chapter how cautious we should be in concluding
that the most different habits of life could not graduate into each other;
that a bat, for instance, could not have been formed by natural selection
from an animal which at first only glided through the air.
We have seen that a species under new conditions of life may change
Its habits; or it may have diversified habits, with some very unlike those
of Its nearest congeners. Hence we can understand, bearing in mind that
each organic being is trying to live wherever it can live, how it has arisen
that there are upland geese with webbed feet, ground woodpeckers, diving
thrushes, and petrels with the habits of auks.
Although the belief that an organ so perfect as the eye could have
been formed by natural selection is enough to stagger anyone; yet in the
case o£ any organ, if we know of a long series of gradations in complexity,
each good for its possessor, then, under changing conditions of life, there
is no logical impossibility In the acquirement of any conceivable degree
of perfection through natural selection. In the cases in which we know
of no intermediate or transitional states, we should be extremely cautious
in concluding that none can have existed, for the metamorphoses of many
organs show what wonderful changes in function are at least possible. For
DARWIN — ORIGIN OF SPECIES 393
instance, a swim bladder has apparently been converted into an air-
breathing lung.
VII. MISCELLANEOUS OBJECTIONS TO THE THEORY OF
NATURAL SELECTION
A DISTINGUISHED ZOOLOGIST, Mr. St. George Mivart, has recently collected
all the objections which have ever been advanced by myself and others
against the theory of natural selection, as propounded by Mr. Wallace
and myself, and has illustrated them with admirable art and force. When
thus marshalled, they make a formidable array; and as it forms no part
of Mr. Mivart's plan to give the various facts and considerations opposed
to his conclusions, no slight effort of reason and memory is left to the
reader, who may wish to weigh the evidence on both sides.
All Mr. Mivart's objections will be, or have been, considered in the
present volume. The one new point which appears to have struck many
readers is, "that natural selection is incompetent to account for the incipi-
ent stages of useful structures." This subject is intimately connected with
that of the gradation of characters, often accompanied by a change of
function — for instance, the conversion of a swim bladder into lungs —
points which were discussed in the last chapter. Nevertheless, I will here
consider in some detail several of the cases advanced by Mr. Mivart, se-
lecting those which are the most illustrative, as want of space prevents me
from considering all.
The giraffe, by its lofty stature, much elongated neck, forelegs, head
and tongue, has its whole frame beautifully adapted for browsing on the
higher branches of trees. It can thus obtain food beyond the reach of the
other Ungulata or hoofed animals inhabiting the same country; and this
must be a great advantage to it during dearths. Before coming to Mr.
Mivart's objections, it may be well to explain once again how natural
selection will act in all ordinary cases. Man has modified some of his
animals, without necessarily having attended to special points of structure,
by simply preserving and breeding from the fleetest individuals, as with
the race horse and greyhound, or as with the gamecock, by breeding from
the victorious birds. So under nature with the nascent giraffe the indi-
viduals which were the highest browsers, and were able during dearths
to reach even an inch or two above the others, will often have been
preserved; for they will have roamed over the whole country in search of
food. That the individuals of the same species often differ slightly in the
relative lengths of all their parts may be seen in many works of natural
history, in which careful measurements are given. These slight propor-
tional differences, due to the laws of growth and variation, are not of the
slightest use or importance to most species. But it will have been other-
wise with the nascent giraffe, considering its probable habits of life; for
those individuals which had some one part or several parts of their bodies
rather more elongated than usual would generally have survived. These
394 MASTERWORKS OF SCIENCE
will have intercrossed and left offspring, either inheriting the same bodily
peculiarities or with a tendency to vary again in the^ same manner; whilst
the individuals, less favoured in the same respects, will have been the most
liable to perish.
We here see that there is no need to separate single pairs, as man
does, when he methodically improves a breed: natural selection will pre-
serve and thus separate all the superior individuals, allowing them freely
to intercross, and will destroy all the inferior individuals. By this process
long-continued, which exactly corresponds with what I have called un-
conscious selection by man, combined no doubt in a most important man-
ner with the inherited effects of the increased use of parts, it seems to me
almost certain that an ordinary hoofed quadruped might be converted
into a giraffe.
To this conclusion Mr. Mivart brings forward two objections. One is
that the increased size of the body would obviously require an increased
supply of food, and he considers it as "very problematical whether the
disadvantages thence arising would not, in times of scarcity, more than
counterbalance the advantages." But as the giraffe does actually exist in
large numbers in South Africa, and as some of the largest antelopes in the
world, taller than an ox, abound there, why should we doubt that, as far
as size is concerned, intermediate gradations could formerly have existed
there, subjected as now to severe dearths? Assuredly the being able to
reach, at each stage of increased size, to a supply of food, left untouched
by the other hoofed quadrupeds of the country, would have been of some
advantage to the nascent giraffe. Nor must we overlook the fact that in-
creased bulk would act as a protection against almost all beasts of prey
excepting the lion; and against this animal, its tall neck— and the taller
the better — would, as Mr. Chauncey Wright has remarked, serve as a
watchtower. It is from this cause, as Sir Samuel Baker remarks, that no
animal is more difficult to stalk than the giraffe. This animal also uses its
long neck as a means of offence or defence, by violently swinging his head
armed with stump-like horns. The preservation of each species can rarely
be determined by any one advantage, but by the union of all, great and
small.
Mr. Mivart then asks (and this is his second objection), if natural se-
lection be so potent, and if high browsing be so great an advantage, why
has not any other hoofed quadruped acquired a long neck and lofty stat-
ure, besides the giraffe, and, in a lesser degree, the camel, guanaco, and
macrauchenia? Or, again, why has not any member of the group acquired
a long proboscis? With respect to South Africa, which was formerly in-
habited by numerous herds of the giraffe, the answer is not difficult, and
can best be given by an illustration. In every meadow in England in which
trees grow, we see the lower branches trimmed or planed to an exact level
by the browsing of the horses or cattle; and what advantage would it be,
for instance, to sheep, if kept there, to acquire slightly longer necks? In
every district some one kind of animal will almost certainly be able to
browse higher than the others; and it is almost equally certain that this
DARWIN — ORIGIN OF SPECIES 395
one kind alone could have its neck elongated for this purpose, through
natural selection and the effects of increased use. In South Africa the
competition for browsing on the higher branches of the acacias and other
trees must be between giraffe and giraffe, and not with the other ungulate
animals.
Why, in other quarters of the world, various animals belonging to
this same order have not acquired either an elongated neck or a proboscis
cannot be distinctly answered; but it is as unreasonable to expect a dis-
tinct answer to such a question as why some event in the history of man-
kind did not occur in one country whilst it did in another. We are igno-
rant with respect to the conditions which determine the numbers and
range of each species; and we cannot even conjecture what changes of
structure wrould be favourable to its increase in some new country. We
can, however, see in a general manner that various causes might have in-
terfered with the development of a long neck or proboscis. To reach the
foliage at a considerable height (without climbing, for which hoofed ani-
mals are singularly ill-constructed) implies greatly increased bulk of body;
and we know that some areas support singularly few large quadrupeds,
for instance South America, though it is so luxuriant; whilst South Africa
abounds with them to an unparalleled degree. Why this should be so, we
do not know; nor why the later tertiary periods should have been so much
more favourable for their existence than the present time. Whatever the
causes may have been, we can see that certain districts and times would
have been- much more favourable than others for the development of so
large a quadruped as the giraffe.
The mammary glands are common to the whole class of mammals,
and are indispensable for their existence; they must, therefore, have been
-developed at an extremely remote period, and we can know nothing posi-
tively about their manner of development. Mr. Mivart asks: "Is it con-
ceivable that the young of any animal was ever saved from destruction
by accidentally sucking a drop of scarcely nutritious fluid from an acci-
dentally hypertrophied cutaneous gland of its mother? And even if one
was so, what chance was there of the perpetuation of such a variation?"
But the case is not here put fairly. It is admitted by most evolutionists
that mammals are descended from a marsupial form; and if so, the mam-
mary glands will have been at first developed within the marsupial sack.
In the case of the fish (Hippocampus) the eggs are hatched, and the
young are reared for a time, within a sack of this nature; and an Ameri-
can naturalist, Mr. Lockwood, believes from what he has seen of the de-
velopment of the young, that they are nourished by a secretion from the
cutaneous glands of the sack. Now with the early progenitors of mam-
mals, almost before they deserved to be thus designated, is it not at least
possible that the young might have been similarly nourished? And in this
case, the individuals which secreted a fluid, in some degree or manner the
most nutritious, so as to partake of the nature of milk, would in the long
run have reared a larger number of well-nourished offspring, than would
the individuals which secreted a poorer fluid; and thus the cutaneous
396 MASTERWORKS OF SCIENCE
glands, which are the homologues of the mammary glands, would have
been improved or rendered more effective. It accords with the widely ex-
tended principle of specialisation that the glands over a certain space of
the sack should have become more highly developed than the remainder;
and they would then have formed a breast, but at first without a nipple,
as we see in the -Ornithorhyncus, at the base of the mammalian series.
Through what agency the glands over a certain space became more highly
specialised than the others, I will not pretend to decide, whether in part
through compensation of growth, the effects of use, or of natural selection.
The development of the mammary glands would have been of no
service, and could not have been effected through natural selection, unless
the young at the same time were able to partake of the secretion. There is
no greater difficulty in understanding how young mammals have instinc-
tively learnt to suck the breast than in understanding how unhatched
chickens have learnt to break the eggshell by tapping against it with
their specially adapted beaks; or how a few hours after leaving the shell
they have learnt to pick up grains of food. In such cases the most prob-
able solution seems to be that the habit was at first acquired by practice
at a more advanced age, and afterwards transmitted to the offspring at an
earlier age.
In the vegetable kingdom Mr. Mivart only alludes to two cases,
namely the structure of the flowers of orchids, and the movements of
climbing plants. With respect to the former, he says, "the explanation of
their origin is deemed thoroughly unsatisfactory — utterly insufficient to
explain the incipient, infinitesimal beginnings of structures which are of
utility only when they are considerably developed." I have fully treated
this subject in another work.
We will now turn to climbing plants. These can be arranged in a long
series, from those which simply twine round a support, to those which I
have called leaf climbers, and to those provided with tendrils. In these
two latter classes the stems have generally, but not always, lost the power
of twining, though they retain the power of revolving, which the tendrils
likewise possess. The gradations from leaf climbers to tendril bearers are
wonderfully close, and certain plants may be indifferently placed in either
class. But in ascending the series from simple twiners to leaf climbers,
an important quality is added, namely sensitiveness to a touch, by which
means the footstalks of the leaves or flowers, or these modified and con-
verted into tendrils, are excited to bend round and clasp the touching ob-
ject. He who will read my memoir on these plants will, I think, admit that
all the many gradations in function and structure between simple twiners
and tendril bearers are in each case beneficial in a high degree to the spe-
cies. For instance, it is clearly a great advantage to a twining plant to be-
come a leaf climber; and it is probable that every twiner which possessed
leaves with long footstalks would have been developed into a leaf climber
if the footstalks had possessed in any slight degree the requisite sensi-
tiveness to a touch.
As twining is the simplest means of ascending a support, and forms
DARWIN — ORIGIN OF SPECIES 397
the basis of our series, it may naturally be asked how did plants acquire
this power in an incipient degree, afterwards to be improved and in-
creased through natural selection? The power of twining depends, firstly,
on the stems whilst young being extremely flexible (but this is a character
common to many plants which are not climbers); and, secondly, on their
continually bending to all points of the compass, one after the other in
succession, in the same order. By this movement the stems are inclined to
all sides, and are made to move round and round. As soon as the lower
part of a stem strikes against any object and is stopped, the upper part
still goes on bending and revolving, and thus necessarily twines round and
up the support. The revolving movement ceases after the early growth ^of
each shoot. As in many widely separated families of plants, single species
and single genera possess the power of revolving, and have thus become
twiners, they must have Independently acquired it, and cannot have in-
herited it from a common progenitor. Hence I was led to predict that
some slight tendency to a movement of this kind would be found^to be
far from uncommon with plants which did not climb; and that this had
afforded the basis for natural selection to work on and improve. When
I made this prediction, I knew of only one imperfect case, namely, of the
young flower peduncles of a Maurandia which revolved slightly and ir-
regularly, like the stems of twining plants, but without making any use of
this habit. Soon afterwards Fritz Miiller discovered that the young stems
of an Alisma and of a Linum — plants which do not climb and are widely
separated in the natural system — revolved plainly, though irregularly;
and he states that he has reason to suspect that this occurs with some
other plants. These slight movements appear to be of no service to the
plants in question; anyhow, they are not of the least use in the way of
climbing, which is the point that concerns us. Nevertheless we can see
that if the stems of these plants had been flexible, and if under the condi-
tions to which they are exposed it had profited them to ascend to a height,
then the habit of slightly and irregularly revolving might have been in-
creased and utilised through natural selection, until they had become con-
verted into well-developed twining species.
Mr. Mivart is further inclined to believe, and some naturalists agree
with him, that new species manifest themselves "with suddenness and by
modifications appearing at once." For instance, he supposes that the dif-
ferences between the extinct three-toed Hipparion and the horse arose
suddenly. He thinks it difficult to believe that the wing of a bird "was de-
veloped in any other way than by a comparatively sudden modification of
a marked and important kind"; and apparently he would extend the same
view to the wings of bats and pterodactyles. This conclusion, which im-
plies great breaks or discontinuity in the series, appears to me improbable
in the highest degree.
My reasons for doubting whether natural species have changed as ab-
ruptly as have occasionally domestic races, and for entirely disbelieving
that they have changed in the wonderful manner indicated by Mr.
Mivart, are as follows. According to our experience, abrupt and strongly
398 MASTERWORKS OF SCIENCE
marked variations occur In our domesticated productions, singly and at
rather long intervals of time. If such occurred under nature, they would
be liable, as formerly explained, to be lost by accidental causes of destruc-
tion and by subsequent intercrossing; and so it is known to be under do-
mestication, unless abrupt variations of this kind are specially preserved
and separated by the care of man. Hence in order that a new species
should suddenly appear in the manner supposed by Mr, Mivart, It is al-
most necessary to believe, in opposition to all analogy, that several won-
derfully changed individuals appeared simultaneously within the same
district. This difficulty, as in the case of unconscious selection by man, is
avoided on the theory of gradual evolution, through the preservation of a
large number of individuals, which varied more or less in any favourable
direction, and of the destruction of a large number which varied in an
opposite manner.
VIII. INSTINCT
MANY INSTINCTS are so wonderful that their development will probably
appear to the reader a difficulty sufficient to overthrow my whole theory.
I may here premise that I have nothing to do with the origin of the men-
tal powers, any more than I have with that of life itself. We are concerned
only with the diversities of Instinct and of the other mental faculties in
animals of the same class.
I will not attempt any definition of instinct. It would be easy to show
that several distinct mental actions are commonly embraced by this term;
but everyone understands what is meant when it is said that instinct
impels the cuckoo to migrate and to lay her eggs in other birds' nests.
An action which we ourselves require experience to enable us to perform,
when performed by an animal, more especially by a very young one, with-
out experience, and when performed by many individuals in the same
way, without their knowing for what purpose it is performed, is usually
said to be instinctive.
It will be universally admitted that instincts are as important as cor-
poreal structures for the welfare of each species, under its present condi-
tions of life. Under changed conditions of life, it is at least possible that
slight modifications of instinct might be profitable to a species; and if it
can be shown that instincts do vary ever so little, then I can see no diffi-
culty in natural selection preserving and continually accumulating varia-
tions of instinct to any extent that was profitable. It is thus, as I believe,
that all the most complex and wonderful instincts have originated. As
modifications of corporeal structure arise from, and are increased by, use
or habit, and are diminished or lost by disuse, so I do not doubt it has
been with instincts. But I believe that the effects of habit are in many
cases of subordinate importance to the effects of the natural selection of
what may be called spontaneous variations of instincts; — that is of vari-
ations produced by the same unknown causes which produce slight devia-
tions of bodily structure.
DARWIN — ORIGIN OF SPECIES 399
No complex instinct can possibly be produced through natural selec-
tion, except by the slow and gradual accumulation o£ numerous slight, yet
profitable, variations. Hence, as in the case of corporeal structures, we
ought to find in nature, not the actual transitional gradations by which
each complex instinct has been acquired — for these could be found only
in the lineal ancestors of each species — but we ought to find in the collat-
eral lines of descent some evidence of such gradations; or we ought at
least to be able to show that gradations of some kind are possible; and this
we certainly can do. I have been surprised to find, making allowance for
the instincts of animals having been but little observed except in Europe
and North America, and for no instinct being known amongst extinct
species, how very generally gradations, leading to the most complex In-
stincts, can be discovered.
Again, as in the case of corporeal structure, and conformably to my
theory, the instinct of each species is good for itself, but has never, as far
as we can judge, been produced for the exclusive good of others. One of
the strongest instances of an animal apparently performing an action for
the sole good of another, with which I am acquainted, is that of aphides
voluntarily yielding, as was first observed by Huber, their sweet excretion
to ants: that they do so voluntarily, the following facts show. I removed
all the ants from a group of about a dozen aphides on a dock plant, and
prevented their attendance during several hours. After this interval, I felt
sure that the aphides would want to excrete. I watched them for some
time through a lens, but not one excreted; I then tickled and stroked
them with a hair in the same manner, as well as I could, as the ants do
with their antennae; but not one excreted. Afterwards I allowed an ant to
visit them, and it immediately seemed, by its eager way of running about,
to be well aware what a rich flock it had discovered; it then began to play
with its antennae on the abdomen first of one aphis and then of another;
and each, as soon as it felt the antennae, immediately lifted up its abdo-
men and excreted a limpid drop of sweet juice, which was eagerly de-
voured by the ant. Even the quite young aphides behaved in this manner,
showing that the action was instinctive, and not the result of experience.
It is certain, from the observations of Huber, that the aphides show no
dislike to the ants: if the latter be not present they are at last compelled
to eject their excretion. But as the excretion is extremely viscid, it is no
doubt a convenience to the aphides to have it removed; therefore proba-
bly they do not excrete solely for the good of the ants.
As some degree of variation in instincts under a state of nature, and
the inheritance of such variations, is indispensable for the action of natural
selection, as many instances as possible ought to be given; but want of
space prevents rne. I can only assert that instincts certainly do vary — for
Instance, the migratory instinct, both in extent and direction, and in Its
total loss. So it is with the nests of birds, which vary partly in dependence
on the situations chosen, and on the nature and temperature of the coun-
try inhabited, but often from causes wholly unknown to us: Audubon has
400 MASTERWQRKS OF SCIENCE
given several remarkable cases of differences in the nests of the same spe-
cies in the northern and southern United States.
Inherited Changes of Habit or Instinct in Domesticated Animals
The possibility, or even probability, of inherited variations of instinct
in a state of nature will be strengthened by briefly considering a few cases
under domestication. We shall thus be enabled to see the part which habit
and the selection of so-called spontaneous variations have played in modi-
fying the mental qualities of our domestic animals. It is notorious how
much domestic animals vary in their mental qualities. With cats, for in-
stance, one naturally takes to catching rats, and another mice, and these
tendencies are known to be inherited. But let us look to the familiar case
of the breeds of the dogs: it cannot be doubted that young pointers (I
have myself seen a striking instance) will sometimes point and even back
other dogs the very first time that they are taken out; retrieving is cer-
tainly in some degree inherited by retrievers; and a tendency to run
round, instead of at, a flock of sheep, by shepherd dogs. I cannot see that
these actions, performed without experience by the young, and in nearly
the same manner by each individual, performed with eager delight by
each breed, and without the end being known — for the young pointer can
no more know that he points to aid his master than the white butterfly
knows why she lays her eggs on the leaf of the cabbage — I cannot see that
these actions differ essentially from true instincts. If we were to behold
one kind of wolf, when young and without any training, as soon as it
scented its prey, stand motionless like a statue, and then slowly crawl
forward with a peculiar gait; and another kind of wolf rushing round,
instead of at, a herd of deer, and driving them to a distant point, we
should assuredly call these actions instinctive. Domestic instincts, as they
may be called, are certainly far less fixed than natural instincts; but they
have been acted on by far less rigorous selection, and have been trans-
mitted for an incomparably shorter period, under less fixed conditions
of life.
Natural instincts are lost under domestication: a remarkable instance
of this is seen in those breeds of fowls which very rarely or never become
"broody," that is, never wish to sit on their eggs. Familiarity alone pre-
vents our seeing how largely and how permanently the minds of our do-
mestic animals have been modified. It is scarcely possible to doubt that
the love of man has become instinctive in the dog. All "wolves, foxes, jack-
als, and species of the cat genus, when kept tame, are most eager to attack
poultry, sheep, and pigs; and this tendency has been found incurable in
dogs which have been brought home as puppies from countries such as
Tierra del Fuego and Australia, where the savages do not keep these do-
mestic animals. How rarely, on the other hand, do our civilised dogs, even
when quite young, require to be taught not to attack poultry, sheep, and
pigs! No doubt they occasionally do make an attack, and are then beaten;
DARWIN — ORIGIN OF SPECIES 401
and if not cured, they are destroyed; so that habit and some degree of
selection have probably concurred in civilising by inheritance our dogs.
Hence we may conclude that under domestication instincts have been
acquired, and natural instincts have been lost, partly by habit, and partly
by man selecting and accumulating, during successive generations, pecul-
iar mental habits and actions, which at first appeared from what we must
in our ignorance call an accident. In some cases compulsory habit alone
has sufficed to produce inherited mental changes; in other cases, compul-
sory habit has done nothing, and all has been the result of selection, pur-
sued both methodically and unconsciously: but in most cases habit and
selection have probably concurred.
Special Instincts
We shall, perhaps, best understand how instincts in a state of nature
have become modified by considering the slave-making instinct of certain
ants. This remarkable instinct was first discovered in the Formica (Poly-
erges) rufescens by Pierre Huber, a better observer even than his cele-
brated father. This ant is absolutely dependent on its slaves; without
their aid, the species would certainly become extinct in a single year. The
males and fertile females do no work of any kind, and the workers or
sterile females, though most energetic and courageous in capturing slaves,
do no other work. They are incapable of making their own nests, or of
feeding their own larvae. When the old nest is found inconvenient, and
they have to migrate, it is the slaves which determine the migration, and
actually carry their masters -in their jaws. So utterly helpless are the mas-
ters that when Huber shut up thirty of them without a slave, but with
plenty of the food which they like best, and with their own larvae and
pupae to stimulate them to work, they did nothing; they could not even
feed themselves, and many perished of hunger. Huber then introduced a
single slave (F. fusca), and she instantly set to work, fed and saved the
survivors; made some cells and tended the larvae, and put all to rights.
What can be more extraordinary than these well-ascertained facts? If we
had not known of any other slave-making ant, it would have been hope-
less to speculate how so wonderful an instinct could have been perfected.
Another species, Formica sanguinea, was likewise first discovered by
P. Huber to be a slave-making ant. This species is found in the southern
parts of England, and its habits have been attended to by Mr. F. Smith,
of the British Museum, to whom I am much indebted for information
on this and other subjects. Although fully trusting to the statements of
Huber and Mr. Smith, I tried to approach the subject in a sceptical frame
of mind, as anyone may well be excused for doubting the existence of so
extraordinary an instinct as that of making slaves. Hence, I will give the
observations which I made in some little detail. I opened fourteen nests
of F. sanguinea, and found a few slaves in all. Males and fertile females
of the slave species (F. fusca) are found only in their own proper com-
402 MASTERWORKS OF SCIENCE _^
munities, and have never been observed in the nests of F. sanguinea. The
slaves are black and not above half the size of their red masters, so that
the contrast in their appearance is great. When the nest is slightly dis-
turbed, the slaves occasionally come out, and like their masters are much
agitated and defend the nest: when the nest is much disturbed, and the
larvae and pupae are exposed, the slaves work energetically together with
their masters in carrying them away to a place of safety. Hence it is clear
that the slaves feel quite at home.
One day I fortunately witnessed a migration of F. sanguinea from one
nest to another, and it was a most interesting spectacle to behold the mas-
ters carefully carrying their slaves in their jaws instead of being carried
by them, as in the case of F. rufescens. Another day my attention was
struck by about a score of the slave makers haunting the same spot, and
evidently not in search of food; they approached and were vigorously
repulsed by an independent community of the slave species (F. fusca);
sometimes as many as three of these ants clinging to the legs of the slave-
making F. sanguinea. The latter ruthlessly killed their small opponents,
and carried their dead bodies as food to their nest, twenty-nine yards dis-
tant; but they were prevented from getting any pupae to rear as slaves.
I then dug up a small parcel of the pupse of F. fusca from another nest,
and put them down on a bare spot near the place of combat; they were
eagerly seized and carried off by the tyrants, who perhaps fancied that,
after all, they had been victorious in their late combat.
One evening I visited another community of F. sanguinea, and found
a number of these ants returning home and entering their nests, carrying
the dead bodies of F. fusca (showing that it was not a migration) and
numerous pupae. I traced a long file of ants burthened with booty, for
about forty yards back, to a very thick clump of heath, whence I saw the
last individual of F. sanguinea emerge, carrying a pupa; but I was not
able to find the desolated nest in the thick heath. The nest, however, must
have been close at hand, for two or three individuals of F. fusca were rush-
ing about in the greatest agitation, and one was perched motionless with
its own pupa in its mouth on the top of a spray of heath, an image of
despair over its ravaged home.
Such are the facts, though they did not need confirmation by me, in
regard to the wonderful instinct of making slaves. Let it be observed what
a contrast the instinctive habits of F. sanguinea present with those of the
continental F. rufescens. The latter does not build its own nest, does not
determine its own migrations, does not collect food for itself or its young,
and cannot even feed itself: it is absolutely dependent on its numerous
slaves. Formica sanguinea, on the other hand, possesses much fewer
slaves, and in the early part of the summer extremely few: the masters de-
termine when and where a new nest shall be formed, and when they mi-
grate, the masters carry the slaves. Both in Switzerland and England the
slaves seem to have the exclusive care of the larvse, and the masters alone
go on slave-making expeditions. In Switzerland the slaves and masters
work together, making and bringing materials for the nest; both, but
DARWIN — ORIGIN OF SPECIES 403
chiefly the slaves, tend, and milk, as it may be called, their aphides; and
thus both collect food for the community. In England the masters alone
usually leave the nest to collect building materials and food for them-
selves, their slaves and larvae. So that the masters in this country receive
much less service from their slaves than they do in Switzerland.
By what steps the instinct of F. sanguinea originated I will not pre-
tend to conjecture. But as ants which are not slave makers will, as I have
seen, carry off the pupa? of other species, if scattered near their nests, it is
possible that such pupae originally stored as food might become devel-
oped; and the foreign ants thus unintentionally reared would then follow
their proper instincts, and do what work they could. If their presence
proved useful to the species which had seized them — if it were more
advantageous to this species to capture workers than to procreate them —
the habit of collecting pupae, originally for food, might by natural selection
be strengthened and rendered permanent for the very different purpose
of raising slaves. When the instinct was once acquired, if carried out to a
much less extent even than in our British F. sanguinea, which, as we have
seen, is less aided by its slaves than the same species in Switzerland, nat-
ural selection might increase and modify the instinct — always supposing
each modification to be of use to the species — until an ant was formed as
abjectly dependent on its' slaves as is the Formica rufescens.
No doubt many instincts of very difficult explanation could be op-
posed to the theory of natural selection — cases in which we cannot see
how an instinct could have originated; cases in which no intermediate
gradations are known to exist; cases of instincts of such trifling importance
that they could hardly have been acted on by natural selection; cases of
instincts almost identically the same in animals so remote in the scale
of nature that we cannot account for their similarity by inheritance from
a common progenitor, and consequently must believe that they were inde-
pendently acquired through natural selection. I will not here enter on
these several cases, but will confine myself to one special difficulty, which
at first appeared to me insuperable, and actually fatal to the whole theory,
I allude to the neuters or sterile females in insect communities; for these
neuters often differ widely in instinct and in structure from both the
males and fertile females, and yet, from being sterile, they cannot propa-
gate their kind.
The subject well deserves to be discussed at great length, but I will
here take only a single case, that of working or sterile ants. How the
workers have been rendered sterile is a difficulty; but not much greater
than that of any other striking modification of structure; for it can be
shown that some insects and other articulate animals in a state of nature
occasionally become sterile; and if such insects had been social, and it had
been profitable to the community that a number should have been an-
nually born capable of work, but incapable of procreation, I can see no
especial difficulty in this having been effected through natural selection.
But I must pass over this preliminary difficulty. The great difficulty Jies
in the working ants differing widely from both the males and the fertile
404 MASTERWORKS OF SCIENCE
females in structure, as in the shape of the thorax, and in being destitute
of wings and sometimes of eyes, and in instinct. As far as instinct alone
is concerned, the wonderful difference in this respect between the work-
ers and the perfect females would have been better exemplified by the
hive bee. If a working ant or other neuter insect had been an ordinary
animal, I should have unhesitatingly assumed that all its characters had
been slowly acquired through natural selection; namely, by individuals
having been born with slight profitable modifications, which were in-
herited by the offspring; and that these again varied and again were
selected, and so onwards. But with the working ant we have an insect
differing greatly from its parents, yet absolutely sterile; so that it could
never have transmitted successively acquired modifications of structure
or instinct to its progeny. It may well be asked how is it possible to
reconcile this case with the theory of natural selection?
First, let it be remembered that we have innumerable instances, both
in our domestic productions and in those in a state of nature, of all sorts
of differences of inherited structure which are correlated with certain
ages, and with either sex. We have differences correlated not only with
one sex, but with that short period when the reproductive system is active,
as in the nuptial plumage of many birds, and in the hooked jaws of the
male salmon. We have even slight differences -in the horns of different
breeds of cattle in relation to an artificially imperfect state of the male
sex; for oxen of certain breeds have longer horns than the oxen of other
breeds, relatively to the length of the horns in both the bulls and cows of
these same breeds. Hence I can see no great difficulty in any character
becoming correlated with the sterile condition of certain members of in-
sect communities: the difficulty lies in understanding how such correlated
modifications of structure could have been slowly accumulated by natural
selection.
This difficulty, though appearing insuperable, is lessened, or, as I be-
lieve, disappears, when it is remembered that selection may be applied to
the family, as well as to the individual, and may thus gain the desired end.
Breeders of cattle wish the flesh and fat to be well marbled together: an
animal thus characterised has been slaughtered, but the breeder has gone
with confidence to the same stock and has succeeded. Such faith may be
placed in the power of selection that a breed of cattle, always yielding
oxen with extraordinarily long horns, could, it is probable, be formed by
carefully watching which individual bulls and cows, when matched, pro-
duced oxen with the longest horns; and yet no ox would ever have propa-
gated its kind. Here is a better and real illustration: according to M. Ver-
lot, some varieties of the double annual stock, from having been long and
carefully selected to the right degree, always produce a large proportion of
seedlings bearing double and quite sterile flowers; but they likewise yield
some single and fertile plants. These latter, by which alone the variety
can be propagated, may be compared with the fertile male and female
ants, and the double sterile plants with the neuters of the same commu-
nity. As with the varieties of the stock, so with social insects, selection has
DARWIN — ORIGIN OF SPECIES 405
been applied to the family, and not to the individual, for the sake of gam-
ing a serviceable end. Hence we may conclude that slight modifications
of structure or of instinct, correlated with the sterile condition of certain
members of the community, have proved advantageous: consequently the
fertile males and females have flourished, and transmitted to their fertile
offspring a tendency to produce sterile members with the same modifica-
tions. This process must have been repeated many times, until that pro-
digious amount of difference between the fertile and sterile females of the
same species has been produced which we see in many social insects.
* But we have not as yet touched on the acme of the difficulty; namely,
the fact that the neuters of several ants differ, not only from the fertile
females and males, but from each other, sometimes to an almost incredible
degree, and are thus divided into two or even three castes. The castes,
moreover, do not commonly graduate into each other, but are perfectly
well defined; being as distinct from each other as are any two species of
the same genus, or rather as any two genera of the same family. Thus in
Eciton, there are working and soldier neuters, with jaws and instincts
extraordinarily different: in Cryptocerus, the workers of one caste alone
carry a wonderful sort of shield on their heads, the use of which is quite
unknown: in the Mexican Myrmecocystus, the workers of one caste never
leave the nest; they are fed by the workers of another caste, and they
have an enormously developed abdomen which secretes a sort of honey,
supplying the place of that excreted by the aphides, or the domestic cattle
as they may be called, which our European ants guard and imprison.
It will indeed be thought that I have an overweening confidence in
the principle of natural selection, when I do not admit that such wonder-
ful and well-established facts at once annihilate the theory. In the simpler
case of neuter insects all of one caste, which, as I believe, have been ren-
dered different from the fertile males and females through natural selec-
tion, we may conclude from the analogy of ordinary variations that the suc-
cessive, slight, profitable modifications did not first arise in all the neuters
in the same nest, but in some few alone; and that by the survival of the
communities with females which produced most neuters having the ad-
vantageous modifications, all the neuters ultimately came to be thus char-
acterised. According to this view we ought occasionally to find in the
same nest neuter insects, presenting gradations of structure; and this we
do find, even not rarely, considering how few neuter insects out of Europe
have been carefully examined, Mr. F. Smith has shown that the neuters of
several British ants differ surprisingly from each other in size and some-
times in colour; and that the extreme forms can be linked together by
individuals taken out of the same nest: I have myself compared perfect
gradations of this kind. It sometimes happens that the larger or the
smaller sized workers are the most numerous; or that both large and small
are numerous, whilst those of an intermediate size are scanty in numbers. "
Formica flava has larger and smaller workers, with some few of inter-
mediate size; and, in this species, as Mr. F. Smith has observed, the larger
workers have simple eyes (ocelli), which though small can be plainly dis-
406 MASTERWORKS OF SCIENCE _^
tinguished, whereas the smaller workers have their ocelli rudimentary.
Having carefully dissected several specimens of these workers, I can
affirm that the eyes are far more rudimentary in the smaller workers than
can be accounted for merely by their proportionately lesser size; and I
fully believe, though I dare not assert so positively, that the workers of
intermediate size have their ocelli in an exactly intermediate condition.
So that here we have two bodies of sterile workers in the same nest, dif-
fering not only in size, but in their organs of vision, yet connected by
some few members in an intermediate condition.
I may give one other case: so confidently did I expect occasionally
to find gradations of important structures between the different castes of
neuters in the same species that I gladly availed myself of Mr'. F. Smith's
offer of numerous specimens from the same nest of the driver ant (An-
omma) of West Africa. The reader will perhaps best appreciate the
amount of difference in these workers by my giving not the actual meas-
urements, but a strictly accurate illustration: the difference was the same
as if we were to see a set of workmen building a house, of whom many
were five feet four inches high and many sixteen feet high; but we must
in addition suppose that the larger workmen had heads four instead of
three times as big as those of the smaller men, and jaws nearly five times
as big. The jaws, moreover, of the working ants of the several sizes dif-
fered wonderfully in shape and in the form and number of the teeth. But
the important fact for us is that, though the workers can be grouped into
castes of different size, yet they graduate insensibly into each other, as
does the widely different structure of their jaws. I speak confidently on
this latter point, as Sir J. Lubbock made drawings for me, with the camera
lucida, of the jaws which I dissected from the workers of the several
sizes. Mr. Bates, in his interesting Naturalist on the Amazons, has de-
scribed analogous cases.
With these facts before me, I believe that natural selection, by acting
on the fertile ants or parents, could form a species which should regularly
produce neuters, all of large size with one form of jaw, or all of small size
with widely different jaws; or lastly, and this is the greatest difficulty, one
set of workers of one size and structure, and simultaneously another set
of workers of a different size and structure; — a graduated series having
first been formed, as in the case of the driver ant, and then the extreme
forms having been produced in greater and greater numbers, through the
survival of the parents which generated them, until none with an inter-
mediate structure were -produced.
I do not pretend that the facts given in this chapter strengthen in any
great degree my theory; but none of the cases of difficulty, to the best of
my judgment, annihilate it. On the other hand, the fact that instincts are
not always absolutely perfect and are liable to mistakes: — that no instinct
can be shown to have been produced for the good of other animals,
though animals take advantage of the instincts of others; — that the canon
in natural history, of "Natura non facit saltum," is applicable to instincts
as well as to corporeal structure, and is plainly explicable on the foregoing
DARWIN — ORIGIN OF SPECIES 407
views, but is otherwise inexplicable — all tend to corroborate the theory
of natural selection.
This theory is alsq strengthened by some few other facts in regard
to instincts; as by that common case of closely allied but distinct species,
when inhabiting distant parts of the world and living under considerably
different conditions of life, yet often retaining nearly the same instincts.
For instance, we can understand, on the principle of inheritance, how it is
that the thrush of tropical South America lines its nest with mud, in the
same peculiar manner as does our British thrush; how it is that the horn-
bills of Africa and India have the same extraordinary instinct of plaster-
ing up and imprisoning the females in a hole in a tree, with only a small
hole left in the plaster through which the males feed them and their
young when hatched; how it is that the male wrens (Troglodytes) of
North America build "cock nests," to roost in, like the males of our
kitty-wrens — a habit wholly unlike that of any other known bird. Finally,
it may not be a logical deduction, but to my imagination it is far more
satisfactory to look at such instincts as the young cuckoo ejecting its fos-
ter brothers — ants making slaves — the larvae of ichneumonidae feeding
within the live bodies of caterpillars — not as specially endowed or created
instincts, but as small consequences of one general law leading to the
advancement of all organic beings — namely, multiply, vary, let the strong-
est live and the weakest die.
IX. ON THE IMPERFECTION OF THE GEOLOGICAL RECORD
THE MAIN CAUSE of innumerable intermediate links not now occurring
everywhere throughout nature depends on the very process of natural se-
lection, through which new varieties continually take the places of and
supplant their parent forms. But just in proportion as this process of ex-
termination has acted on an enormous scale, so must the number of inter-
mediate varieties, which have formerly existed, be truly enormous. Why
then is not every geological formation and every stratum full of such in-
termediate links? Geology assuredly does not reveal any such finely grad-
uated organic chain; and this, perhaps, is the most obvious and serious
objection which can be urged against the theory. The explanation lies, as
I believe, in the extreme imperfection of the geological record.
In the first place, it should always be borne in mind what sort of in-
termediate forms must, on the theory, have formerly existed. I have found
it difficult, when looking at any two species, to avoid picturing to myself
forms directly intermediate between them. But this is a wholly false view;
we should always look for forms intermediate between each species and
a common but unknown progenitor; and the progenitor will generally
have differed in some respects from all its modified descendants. To give
a simple illustration: If we look to forms very distinct for instance, to
the horse and tapir, we have no reason to suppose that links directly
intermediate between them ever existed, but between each and an un-
408 MASTERWORKS OF SCIENCE
known common parent. The common parent will have had In its whole
organisation much general resemblance to the tapir and to the horse; but
in some points o£ structure may have differed considerably from both,
even perhaps more than they differ from each other. Hence, in all such
cases, we should be unable to recognise the parent form of any two or
more species, even if we closely compared the structure of the parent with
that of its modified descendants, unless at the same time we had a nearly
perfect chain of the intermediate links.
On the Poorness of Palceontological Collections
Now let us turn to our richest geological museums, and what a paltry
display we behold! That our collections are imperfect is admitted by
everyone. The remark of that admirable palaeontologist, Edward Forbes,
should never be forgotten, namely, that very many fossil species are
known and named from single and often broken specimens, or from a few
specimens collected on some one spot. Only a small portion of the surface
of the earth has been geologically explored, and no part with sufficient
care, as the important discoveries made every year in Europe prove. No
organism wholly soft can be preserved. Shells and bones decay and disap-
pear when left on the bottom of the sea, where sediment is not accumu-
lating. In regard to "mammiferous remains, a glance at the historical table
published in LyelPs Manual will bring home the truth, how accidental
and rare is their preservation, far better than pages of detail. Nor Is their
rarity surprising, when we remember how large a proportion of the bones
of tertiary mammals have been discovered either in caves or In lacustrine
deposits; and that not a cave or true lacustrine bed Is known belonging to
the age of our secondary or palaeozoic formations.
But the imperfection in the geological record largely results from
another and more important cause than any of the foregoing; namely,
from the several formations being separated from each other by wide in-
tervals of time. This doctrine has been emphatically admitted by many
geologists and palaeontologists, who, like E. Forbes, entirely disbelieve in
the change of species. When we see the formations tabulated in written
works, or when we follow them In nature, it is difficult to avoid believing
that they are closely consecutive. But we know, for instance, from Sir R.
Murchison's great work on Russia, what wide gaps there are in that coun-
try between the superimposed formations; so it is in North America, and
in many other parts of the world. The most skilful geologist, if his atten-
tion had been confined exclusively to these large territories, would never
have suspected that, during the periods which were blank and barren in
his own country, great piles of sediment, charged with new and peculiar
forms of life, had elsewhere been accumulated. And if, in each separate
territory, hardly any idea can be formed of the length of time which has
elapsed between the consecutive formations, we may infer that this could
nowhere be ascertained. The frequent and great changes in the mineral-
DARWIN — ORIGIN OF SPECIES 409
ogical composition of consecutive formations, generally implying great
changes in the geography of the surrounding lands, whence the sediment
was derived, accord with the belief of vast intervals of time having
elapsed between each formation.
We may, I think, conclude that sediment must be accumulated in ex-
tremely thick, solid, or extensive masses, in order to withstand the inces-
sant action of the waves, when first upraised and during successive oscilla-
tions of level as well as the subsequent subaerial degradation. Such thick
and extensive accumulations of sediment may be formed in two ways;
either in profound depths of the sea, in which case the bottom will not be
inhabited by so many and such varied forms of life, as the more shallow
seas; and the mass when upraised will give an imperfect record of the
organisms which existed in the neighbourhood during the period of its
accumulation. Or sediment may be deposited to any thickness and extent
over a shallow bottom, if it continue slowly to subside. In this latter case,
as long as the rate of subsidence and the supply of sediment nearly bal-
ance each other, the sea will remain shallow and favourable for many and
varied forms, and thus a rich fossiliferous formation, thick enough, when
upraised, to resist a large amount of denudation, may be formed.
I am convinced that nearly all our ancient formations, which are
throughout the greater part of their thickness rich in jossils, have thus
been formed during subsidence.
All geological facts tell us plainly that each area has undergone slow
oscillations of level, and apparently these oscillations have affected wide
spaces. Consequently, formations rich in fossils, and sufficiently thick and
extensive to resist subsequent degradation, will have been formed over
wide spaces during periods of subsidence, but only where the supply of
sediment was sufficient to keep the sea shallow and to embed and preserve
the remains before they had time to decay. On the other hand, as long as
the bed of the sea remains stationary, thic^ deposits cannot have been
accumulated in the shallow parts, which are the most favourable to life.
Still less can this have happened during the alternate periods of elevation;
or, to speak more accurately, the beds which were then accumulated will
generally have been destroyed by being upraised and brought within the
limits of the coast action.
One remark is here worth a passing notice. During periods of eleva-
tion the area of the land and of the adjoining shoal parts of the sea will be
increased, and new stations will often be formed: — all circumstances fa-
vourable for the formation of new varieties and species; but during such
periods there will generally be a blank in the geological record. On the
other hand, during subsidence, the inhabited area and number of in-
habitants will decrease (excepting on the shores of a continent when first
broken up into an archipelago), and consequently during subsidence,
though there will be much extinction, few new varieties or species will
be formed; and it is during these very periods of subsidence that the de-
posits which are richest in fossils have been accumulated.
410 MASTERWORKS OF SCIENCE
On the Absence of Numerous Intermediate Varieties in any Single
Formation
From these several considerations, it cannot be doubted that the geo-
logical record, viewed as a whole, is extremely imperfect; but if we con-
fine our attention to any one formation, it becomes much more difficult to
understand why we do not therein find closely graduated varieties be-
tween the allied species which lived at its commencement and at its close.
Several cases are on record of the same species presenting varieties in the
upper and lower parts of the same formation; thus, Trautschold gives a
number of instances with Ammonites; and Hilgendorf has described a
most curious case of ten graduated forms of Planorbis multiformis in the
successive beds of a fresh-water formation in Switzerland.
We shall, perhaps, best perceive the improbability of our being en-
abled to connect species by numerous fine, intermediate, fossil links by
asking ourselves whether, for instance, geologists at some future period
will be able to prove that our different breeds of cattle, sheep, horses, and
dogs are descended from a single stock or from several aboriginal stocks;
or, again, whether certain sea shells inhabiting the shores of North Amer-
ica, which are ranked by some conchologists as distinct species from their
European representatives, and by other conchologists as only varieties, are
really varieties, or are, as it is called, specifically distinct. This could be
effected by the future geologist only by his discovering in a fossil state
numerous intermediate gradations; and such success is improbable in the
highest degree.
It has been asserted over and over again, by writers who believe in
the immutability of species, that geology yields no linking forms. This
assertion, as we shall see in the next chapter, is certainly erroneous. As
Sir J. Lubbock has remarked, "Every species is a link between other allied
forms." If we take a genus having a score of species, recent and extinct,
and destroy four fifths of them, no one doubts that the remainder will
stand much more distinct from each other. If the extreme forms in the
genus happen to have been thus destroyed, the genus itself will stand
more distinct from other allied genera. What geological research has not
revealed is the former existence of infinitely numerous gradations, as fine
as existing varieties, connecting together nearly all existing and extinct
species. But this ought not to be expected; yet this has been repeatedly
advanced as a most serious objection against my views.
On the sudden Appearance of whole Groups of allied Species
The abrupt manner in which whole groups of species suddenly ap-
pear in certain formations has been urged by several palaeontologists — for
instance, by Agassiz, Pictet, and Sedgwick — as a fatal objection to the be-
DARWIN — ORIGIN OF SPECIES 411
lief in the transmutation of species. If numerous species, belonging to the
same genera or families, have really started into life at once, the fact
would be fatal to the theory of evolution through natural selection. For
the development by this means of a group of forms, all of which are de-
scended from some one progenitor, must have been an extremely slow
process; and the progenitors must have lived long before their modified
descendants. But we continually overrate the perfection of the geological
record, and falsely infer, because certain genera or families have not beea
found beneath a certain stage, that they did not exist before that stage.
In all cases positive palseontological evidence may be implicitly trusted;
negative evidence is worthless, as experience has so often shown. We con-
tinually forget how large the world is, compared with the area over which
our geological formations have been carefully examined; we forget that
groups of species may elsewhere have long existed, and have slowly multi-
plied, before they invaded the ancient archipelagoes of Europe and the
United States. We do not make due allowance for the intervals of time
which have elapsed between our consecutive formations — longer perhaps
in many cases than the time required for the accumulation of each forma-
tion. These intervals will have given time for the multiplication of species
from some one parent form: and in the succeeding formation, such
groups or species will appear as if suddenly created.
I may recall the well-known fact that in geological treatises, pub-
lished not many years ago, mammals were always spoken of as having:
abruptly come in at the commencement of the tertiary series. And now
one of the richest known accumulations of fossil mammals belongs to the
middle of the secondary series; and true mammals have been discovered
in the new red sandstone at nearly the commencement of this great series.
Cuvier used to urge that no monkey occurred in any tertiary stratum; but
now extinct species have been discovered in India, South America, and in
Europe, as far back as the miocene stage. Had it not been for the rare
accident of the preservation of the footsteps in the new red sandstone of
the United States, who would have ventured to suppose that no less than
at least thirty different bird-like animals, some of gigantic size, existed
during that period? Not a fragment of bone has been discovered in these
beds. Not long ago, palaeontologists maintained that the whole class of
birds came suddenly into existence during the eocene period; but now we
know, on the authority of Professor Owen, that a bird certainly lived dur-
ing the deposition of the upper greensand; and, still more recently, that
strange bird, the Archeopteryx, with a long lizard-like tail, bearing a pair
of feathers on each joint, and with its wings" furnished with two free
claws, has been discovered in the oolitic slates of Solenhofen. Hardly any
recent discovery shows more forcibly than this how little we as yet know
of the former inhabitants of the world.
From these considerations, from our ignorance of the geology of
other countries beyond the confines of Europe and the United States, and
from the revolution in our palaeontological knowledge effected by the dis-
coveries of the last dozen years, it seems to me to be about as rash to
412 MASTERWQRKS OF SCIENCE
dogmatize on the succession of organic forms throughout the world as it
would be for a naturalist to land for five minutes on a barren point in
Australia and then to discuss the number and range of its productions.
On the sudden Appearance of Groups of allied Species in the lowest
\nown Fossiliferous Strata
There is another and allied difficulty, which is much more serious. I
allude to the manner in which species belonging to several of the main
divisions of the animal kingdom suddenly appear in the lowest known
fossiliferous rocks. Most of the arguments which have convinced me that
all the existing species of the same group are descended from a single
progenitor apply with equal force to the earliest known species. For in-
stance, it cannot be doubted that all the Cambrian and Silurian trilobites
are descended from some one crustacean, which must have lived long be-
fore the Cambrian age, and which probably differed greatly from any
known animal. Some of the most ancient animals, as the Nautilus, Lin-
gula, &c., do not differ much from living species; and it cannot on our
theory be supposed that these old species were the progenitors of all the
species belonging to the same groups which have subsequently appeared,
for they are not in any degree intermediate in character.
Consequently, if the theory be true, it is indisputable that before the
lowest Cambrian stratum was deposited long periods elapsed, as long as,
or probably far longer than, the whole interval from the Cambrian age to
the present day; and that during these vast periods the world swarmed
with living creatures.
To the question why we do not find rich fossiliferous deposits be-
longing to these assumed earliest periods prior to the Cambrian system, I
can give no satisfactory answer. Several eminent geologists, with Sir R.
Murchison at their head, were until recently convinced that we beheld in
the organic remains of the lowest Silurian stratum the first dawn of life.
Other highly competent judges, as Lyell and E. Forbes, have disputed this
conclusion. We should not forget that only a small portion of the world is
known with accuracy. Not very long ago M. Barrande added another and
lower stage, abounding with new and peculiar species, beneath the then
known Silurian system; and now, still lower down in the Lower Cam-
brian formation, Mr. Hicks has found in South Wales beds rich in trilo-
bites and . containing various molluscs and annelids. The presence of
phosphatic nodules and bituminous matter, even in some of the lowest
azoic rocks, probably indicates life at these periods; and the existence of
the Eozoon in the Laurentian formation of Canada is generally admitted.
There are three great series of strata beneath the Silurian system in Can-
ada, in the lowest of which the Eozoon is found. Sir W. Logan states that
their "united thickness may possibly far surpass that of all the succeeding
rocks, from the base of the palaeozoic series to the present time. We are
thus carried back to a period so remote that the appearance of the so-
DARWIN — ORIGIN OF SPECIES 413
called Primordial fauna (of Barrande) may by some be considered as a
comparatively modern event." The Eozoon belongs to the most lowly or-
ganised of all classes of animals, but is highly organised for its class; it
existed in countless numbers, and, as Dr. Dawson has remarked, certainly
preyed on other minute organic beings, which must have lived in great
numbers.
The several difficulties here discussed, namely — that, though we find
in our geological formations many links between the species which now
exist and which formerly existed, we do not find infinitely numerous fine
transitional forms closely joining them all together; — the sudden manner
in which several groups of species first appear in our European forma-
tions;— the almost entire absence, as at present known, of formations rich
in fossils beneath the Cambrian strata — are all undoubtedly of the most
serious nature. We see this in the fact that the most eminent palaeontolo-
gists, namely, Cuvier, Agassiz, Barrande, Pictet, Falconer, E. Forbes, &c.,
and all our greatest geologists, as Lyell, Murchison, Sedgwick, &c., have
unanimously, often vehemently, maintained the immutability of species.
But Sir Charles Lyell now gives the support of his high authority to the
opposite side; and most geologists and palaeontologists are much shaken
in their former belief. Those who believe that the geological record is in
any degree perfect will undoubtedly at once reject the theory. For my
part, following out Lyell's metaphor, I look at the geological record as a
history of the world imperfectly kept, and written in a changing dialect;
of this history we possess the last volume alone, relating only to two or
three countries. Of this volume, only here and there a short chapter has
been preserved; and of each page, only here and there a few lines. Each
word of the slowly changing language, more or less different in the suc-
cessive chapters, may represent the forms of life, which are entombed in
our consecutive formations, and which falsely appear to have been ab-
ruptly introduced. On this view, the difficulties above discussed are
greatly diminished, or even disappear.
X. ON THE GEOLOGICAL SUCCESSION OF ORGANIC
BEINGS
LET us NOW SEE whether the several facts and laws relating to the geologi-
cal succession of organic beings accord best with the common view of the
immutability of species or with that of their slow and gradual modifica-
tion, through variation and natural selection.
New species have appeared very slowly, one after another, both on
the land and in the waters. Lyell has shown that it is hardly possible to
resist the evidence on this head.
Species belonging to different genera and classes have not changed at
the same rate, or in the same degree. In the older tertiary beds a few
living shells may still be found in the midst of a multitude of extinct
forms. Falconer has given a striking instance of a similar fact, for an ex-
414 MASTERWQRKS OF SCIENCE
isting crocodile is associated with many lost mammals and reptiles in the
sub-Himalayan deposits. Yet if we compare any but the most closely re-
lated formations, all the species will be found to have undergone some
change. When a species has once disappeared from the face of the earth,
we" have no reason to believe that the same identical form ever reappears.
These several facts accord well with our theory, which includes no
fixed law of development, causing all the inhabitants of an area to change
abruptly, or simultaneously, or to an equal degree. The process of modifi-
cation must be slow, and will generally affect only a few species at the
same time; for the variability of each species is independent of that of all
others. Whether such variations or individual differences as may arise will
be accumulated through natural selection in a greater or less degree, thus
causing a greater or less amount of permanent modification, will depend
on many complex contingencies — on the variations being of a beneficial
nature, on the freedom of intercrossing, on the slowly changing physical
conditions of the country, on the immigration of new colonists, and on
the nature of the other inhabitants with which the varying species come
into competition. Hence it is by no means surprising that one species
should retain the same identical form much longer than others; or, if
changing, should change in a less degree. When many of the inhabitants
of any area have become modified and improved, we can understand, on
the principle of competition, and from the all-important relations of or-
ganism to organism in the struggle for life, that any form which did not
become in some degree modified and improved would be liable to exter-
mination. Hence we see why all the species in the same region do at last,
if we look to long enough intervals of time, become modified, for other-
wise they would become extinct.
On Extinction
We have as yet only spoken incidentally of the disappearance of
species and of groups of species. On the theory of natural selection, the
extinction of old forms and the production of new and improved forms
are intimately connected together. The old notion of all the inhabitants of
the earth having been swept away by catastrophes at successive periods is
very generally given up, even by those geologists, as Elie de Beaumont,
Murchison, Barrande, &c., whose general views would naturally lead them
to this conclusion. On the contrary, we have every reason to believe, from
the study of the tertiary formations, that species and groups of species
gradually disappear, one after another, first from one spot, then from an-
other, and finally from the world. In some few cases, however, as by the
breaking of an isthmus and the consequent irruption of a multitude of
new inhabitants into an adjoining sea, or by the final subsidence of an
island, the process of extinction may have been rapid. Both single species
and whole groups of species last for very unequal periods; some groups,
as we have seen, have endured from the earliest known dawn of life to
DARWIN — ORIGIN OF SPECIES 415
the present day; some have disappeared before the close of the palaeozoic
period. No fixed law seems to determine the length of time during which
any single species or any single genus endures. There is reason to believe
that the extinction of a whole group of species is generally a slower-
process than their production: if their appearance and disappearance be
represented by a vertical line of varying thickness, the line is found to
taper more gradually at its upper end, which marks the progress of exter-
mination, than at its lower end, which marks the first appearance and the
early increase in number of the species.
The theory of natural selection is grounded on the belief that each
new variety ,-and ultimately each new species, is produced and maintained
by having some advantage over those with which it comes into competi-
tion; and the consequent extinction of the less-favoured forms almost in-
evitably follows. It is the same with our domestic productions; when a
new and slightly improved variety has been raised, it at first supplants the
less improved varieties in the same neighbourhood; when much improved
it is transported far and near, like our Shorthorn cattle, and takes the
place of other breeds in other countries. Thus the appearance of new
forms and the disappearance of old forms, both those naturally and those
artificially produced, are bound together. In flourishing groups, the num-.
ber of new specific forms which have been produced within a given time
has at some periods probably been greater than the number of the old
specific forms which have been exterminated; but we know that species
have not gone on indefinitely increasing, at least during the later geologi-
cal epochs, so that, looking to later times, we may believe that the pro-
duction of new forms has caused the extinction of about the same number
of old forms.
Thus, as it seems to me, the manner in which single species and
whole groups of species become extinct accords well with the theory of
natural selection. We need not marvel at extinction; if we must marvel, let
it be at our own presumption in imagining for a moment that we under-
stand the many complex contingencies on which the existence of each
species depends. If we forget for an instant that each species tends to in-
crease inordinately, and that some check is always in action, yet seldom
perceived by us, the whole economy of nature will be utterly obscured.
Whenever we can precisely say why this species is more abundant in in-
dividuals than that; why this species and not another can be naturalised
in a given country; then, and not until then, we may justly feel surprise
why we cannot account for the extinction of any particular species or
group of species.
On the Forms of Life changing almost simultaneously throughout
the World
Scarcely any palaeontological discovery is more striking than the fac£
that the forms of life change almost simultaneously throughout the world *
416 MASTERWORKS OF SCIENCE
Thus our European Chalk formation can be recognised in many distant
regions, under the most different climates, where not a fragment of the
mineral chalk itself can be found; namely in North America, in equato-
rial South America, in Tierra del Fuego, at the Cape of Good Hope, and
in the peninsula of India. For at these distant points, the organic remains
in certain beds present an unmistakable resemblance to those of the
Chalk. It is not that the same species are met with; for in some cases not
one species is identically the same, but they belong to the same families,
genera, and sections of genera, and sometimes are similarly characterised
in such trifling points as mere superficial sculpture. Moreover, other
forms, which are not found in the Chalk of Europe, but which occur in
the formations either above or below, occur in the same order at these
distant points of the world. In the several successive palaeozoic formations
of Russia, Western Europe, and North America, a similar parallelism in
the forms of life has been observed by several authors; so it is, according
to Lyell, with the European and North American tertiary deposits.
This great fact of the parallel succession of the forms of life through-
out the world is explicable on the theory of natural selection. New species
are formed by having some advantage over older forms; and the forms,
which are already dominant, or have some advantage over the other forms
in their own country, give birth to the greatest number of new varieties
or incipient species. We have distinct evidence on this head, in the plants
which are dominant, that is, which axe commonest and most widely dif-
fused, producing the greatest number of new varieties. It is also natural
that the dominant, varying, and far-spreading species, which have already
invaded to a certain extent the territories of other species, should be those
which would have the best chance of spreading still further, and of giving
rise in new countries to other new varieties and species. The process of
diffusion would often be very slow, depending on climatal and geographi-
cal changes, on strange accidents, and on the gradual acclimatisation of
new species to the various climates through which they might have to
pass, but in the course of time the dominant forms would generally suc-
ceed in spreading and would ultimately prevail. The diffusion would, it is
probable, be slower with the terrestrial inhabitants of distinct continents
lhan with the marine inhabitants of the continuous sea. We might there-
fore expect to find, as we do find, a less strict degree of parallelism in the
succession of the productions of the land than with those of the sea.
On the Affinities of Extinct Species to each other, and to Living Forms
Let us now look to the mutual affinities of extinct and living species.
All fall into a few grand classes; and this fact is at once explained on the
principle of descent. The more ancient any form is, the more, as a general
rule, it differs from living forms. -But, as Buckland long ago remarked,
extinct species can all be classed either in still existing groups or between
them. That the extinct forms of life help to fill up the intervals between
DARWIN — ORIGIN OF SPECIES 417
existing genera, families, and orders is certainly true. If we confine our
attention either to the living or to the extinct species of the same class,
the series is far less perfect than if we combine both into one general
system.
Cuvier ranked the Ruminants and Pachyderms as two of the most
distinct orders of mammals: but so many fossil links have been disen-
tombed that Owen has had to alter the whole classification, and has
placed certain pachyderms in the same sub-order with ruminants; for ex-
ample, he dissolves by gradations the apparently wide interval between
the pig and the camel. The Ungulata or hoofed quadrupeds are now
divided into the even-toed or odd-toed divisions; but the Macrauchenia
of South America connects to a certain extent these two grand divisions.
No one will deny that the Hipparion is intermediate between the ex-
isting horse and certain older ungulate forms.
Let us see how far these several facts and inferences accord with the
theory of descent with modification. As the subject is somewhat complex,
I must request the reader to turn to the diagram in the fourth chapter.
We may suppose that the numbered letters in italics represent genera;
and the dotted lines diverging from~them the species in each genus. The
diagram is much too simple, too few genera and too few species being
given, but this is unimportant for us. The horizontal lines may represent
successive geological formations, and all the forms beneath the uppermost
line may be considered as extinct. The three existing genera, <214, q14, pl4y
will form a small family; £14 and fu a closely allied family or sub-family;
and o14, tf14, m14, a third family. These three families, together with the
many extinct genera on the several lines of descent diverging from the
parent form (A) will form an order, for all will have inherited something
in common from their ancient progenitor. On the principle of the con-
tinued tendency to divergence of character, which was formerly illustrated
by this diagram, the more recent any form is, the more it will generally
differ from its ancient progenitor. Hence we can understand the rule that
the most ancient fossils differ most from existing forms. We must not,
however, assume that divergence of character is a necessary contingency;
it depends solely on the descendants from a species being thus enabled to
seize on many and different places in the economy of nature. Therefore it
is quite possible, as we have seen in the case of some Silurian forms, that
a species might go on being slightly modified in relation to its slightly
altered conditions of life, and yet retain throughout a vast period the
same general characteristics. This is represented in the diagram by the
letter F14.
All the many forms, extinct and recent, descended from (A) make, as
before remarked, one order; and this order, from the continued effects of
extinction and divergence of character, has become divided into several
sub-families and families, some of which are supposed to have perished at
different periods, and some to have endured to the present day.
By looking at the diagram we can see that if many of the extinct
forms supposed to be embedded in the successive formations were dis-
418 MASTERWORKS OF SCIENCE
covered at several points low down In the series, the three existing fami-
lies on the uppermost line would be rendered less distinct from each
other. If, for instance, the genera al^a?} aw, /8, mz, m®, m® were disin-
terred, these three families would be so closely linked together that they
probably would have to be united into one great family, in nearly the
same manner as has occurred with ruminants and certain pachyderms. Yet
he who objected to consider as intermediate the extinct genera, which
thus link together the living genera of three families, would be partly
justified, for they are intermediate, not directly, but only by a long and
circuitous course through many widely different forms.
Under nature the process will be far more complicated than is repre-
sented in the diagram; for the groups will have been more numerous;
they will have endured for extremely unequal lengths of time, and will
have been modified in various degrees. As we possess only the last vol-
ume of the geological record, and that in a very broken condition, we
have no right to expect, except in rare cases, to fill up the wide intervals
in the natural system, and thus to unite distinct families or orders. All
that we have a right to expect is that those groups which have, within
known geological periods, undergone much modification should in the
older formations make some slight approach to each other; so that the
older members should differ less from each other in some of their char-
acters than do the existing members of the same groups; and this, by the
concurrent evidence of our best palaeontologists, is frequently the case.
Thus, on the theory of descent with modification, the main facts with
respect to the mutual affinities of the extinct forms of life to each other
and to living forms are explained in a satisfactory manner. And they are
wholly inexplicable on any other view.
On the Succession of the same Types within the same Areas, during the
later Tertiary Periods
Mr. Clift many years ago showed that the fossil mammals from the
Australian caves were closely allied to the living marsupials of that con-
tinent. In South America a similar relationship is manifest, even to an
uneducated eye, in the gigantic pieces of armour, like those of the arma-
dillo, found in several parts of La Plata; and Professor Owen has shown
In the most striking manner that most of the fossil mammals, buried there
in such numbers, are related to South American types,.
Now what does this remarkable law of the succession of the same
types within the same areas mean? He would be a bold man who, after
comparing the present climate of Australia and of parts of South America,
under the same latitude, would attempt to account, on the one hand
through dissimilar physical conditions, for the dissimilarity of the inhab-
itants of these two continents; and, on the other hand, through similarity
of conditions, for the uniformity of the same types in each continent
during the later tertiary periods. Nor can it be pretended that it is an
DARWIN — ORIGIN OF SPECIES 419
immutable law that marsupials should have been chiefly or solely pro-
duced in Australia; or that Edentata and other American types should
have been solely produced in South America. For we know that Europe in
ancient times was peopled by numerous marsupials.
On the theory of descent with modification, the great law of the long
enduring, but not immutable, succession of the same types within the
same areas is at once explained; for the inhabitants of each quarter of the
world will obviously tend to leave in that quarter, during the next suc-
ceeding period of time, closely allied though in some degree modified
descendants. If the inhabitants of one continent formerly differed greatly
from those of another continent, so will their modified descendants still
differ in nearly the same manner and degree. But after very long intervals
of time, and after great geographical changes, permitting much inter-
migration, the feebler will yield to the more dominant forms, and there
will be nothing immutable in the distribution of organic beings.
XL GEOGRAPHICAL DISTRIBUTION
IN CONSIDERING the distribution of organic beings over the face of the
globe, the first great fact which strikes us is that neither the similarity
nor the dissimilarity of the inhabitants of various regions can be wholly
accounted for by climatal and other physical conditions. Of late, almost
every author who has studied the subject has come to this conclusion.
The case of America alone would almost suffice to prove its truth; for if
we exclude the arctic and northern temperate parts, all authors agree that
one of the most fundamental divisions in geographical distribution is that
between the New and Old Worlds; yet if we travel over the vast Ameri-
can continent, from the central parts of the United States to its extreme
southern point, we meet with the most diversified conditions : humid dis-
tricts, arid deserts, lofty mountains, grassy plains, forests, marshes, lakes,
and great rivers, under almost every temperature. There is ha'rdly a cli-
mate or condition in the Old World which cannot be paralleled in the
New — at least as closely as the same species generally require. No doubt
small areas can be pointed out in the Old World hotter than any in the
New World; but these are not inhabited by a fauna different from that of
the surrounding districts; for it is rare to find a group of organisms con-
fined to a small area, of which the conditions are peculiar in only a slight
degree. Notwithstanding this general parallelism in the conditions of the
Old and New Worlds, how widely different are their living productions!
A second great fact which strikes us in our general review is that bar-
riers of any kind, or obstacles to free migration, are related in a close and
important manner to the differences between the productions of various
regions. We see this in the great difference in nearly all the terrestrial
productions of the New and Old Worlds, excepting in the northern parts,
where the land almost joins, and where, under a slightly different climate,
there might have been free migration for the northern temperate forms*
420 MASTERWORKS OF SCIENCE
as there now is for the strictly arctic productions. We see the same fact in
the great difference between the inhabitants of Australia, Africa, and
South America under the same latitude; for these countries are almost as
much isolated from each other as is possible. On each continent, also, we
see the same fact; for on the opposite sides of lofty and continuous moun-
tain ranges, of great deserts and even of large rivers, we find different
productions; though as mountain chains, deserts, &c., are not as impassa-
ble, or likely to have endured so long, as the oceans separating continents,
the differences are very inferior in degree to those characteristic of dis-
tinct continents.
A third great fact, partly included in the foregoing statement, is the
affinity of the productions of the same continent or of the same sea,
though the species themselves are distinct at different points and stations.
It is a law of the widest generality, and every continent offers innumer-
able instances. Nevertheless the naturalist, in travelling, for instance, from
north to south, never fails to be struck by the manner in which successive
groups of beings, specifically distinct, though nearly related, replace each
other. He hears from closely allied, yet distinct kinds of birds notes nearly
similar, and sees their nests similarly constructed, but not quite alike,
with eggs coloured in nearly the same manner. The plains near the Straits
of Magellan are inhabited by one species of Rhea (American ostrich), and
-northward the plains of La Plata by another species of the same genus;
and not by a true ostrich or emu, like those inhabiting Africa and Aus-
tralia under the same latitude. On these same plains of La Plata we see
the agouti and bizcacha, animals having nearly the same habits as our
hares and rabbits, and belonging to the same order of Rodents, but they
plainly display an American type of structure. We ascend the lofty peaks
of the Cordillera, and we find an alpine species of bizcacha; we look to
the waters, and we do not find the beaver or muskrat, but the coypu and
capybara, rodents of the South American type. Innumerable other in-
stances could be given. If we look to the islands off the American shore,
however much they may differ in geological structure, the inhabitants are
essentially American, though they may be all peculiar species. We may
look back to past ages, as shown in the last chapter, and we find American
types then prevailing on the American continent and in the American
seas. We see in these facts some deep organic bond, throughout space and
time, over the same areas of land and water, independently of physical
conditions. The naturalist must be dull who is not led to enquire what
this bond is.
The bond is simply inheritance, that cause which alone, as far as we
positively know, produces organisms quite like each other, or, as we see in
the case of varieties, nearly alike. The dissimilarity of the inhabitants of
different regions may be attributed to modification through variation and
natural selection, and probably in a subordinate degree to the definite in-
fluence of different physical conditions. The degrees of dissimilarity will
depend on the migration of the more dominant forms of life from one re-
gion into another having been more or less effectually prevented^ at peri-
DARWIN — ORIGIN OF SPECIES 421
ods more or less remote; — on the nature and number of the former immi-
grants;— and on the action of the inhabitants on each other in leading to
the preservation of different modifications; the relation of organism to
organism in the struggle for life being, as I have already often remarked,
the most important of all relations. Thus the high Importance of barriers
comes into play by checking migration; as does time for the slow process
of modification through natural selection.
According to these views, it is obvious that the several species of the
same genus, though inhabiting the most distant quarters of the world,
must originally have proceeded from the same source, as they are de-
scended from the same progenitor. In the case of those species which have
undergone during the whole geological periods little modification, there
is not much difficulty in believing that they have migrated from the same
region; for during the vast geographical and climatal changes which have
supervened since ancient times, almost any amount of migration is pos-
sible. But in many other cases, in which we have reason to believe that
the species of a genus have been produced within comparatively recent
times, there is great difficulty on this head. It is also obvious that the in-
dividuals of the same species, though now inhabiting distant and isolated
regions, must have proceeded from one spot, where their parents were
first produced: for, as has been explained, it is incredible that individuals
identically the same should have been produced from parents specifically
distinct.
Single Centres of supposed Creation. — We are thus brought to the
question which has been largely discussed by naturalists, namely, whether
species have been created at one or more points of the earth's surface.
Undoubtedly there are many cases of extreme difficulty in understanding
how the same species could possibly have migrated from some one point
to the several distant and isolated points, where now found. Nevertheless
the simplicity of the view that each species was first produced within a
single region captivates the mind. He who rejects it rejects the vera causa
of ordinary generation with subsequent migration, and calls in the agency
of a miracle. It is universally admitted that in most cases the area inhab-
ited by a species is continuous; and that when a plant or animal inhabits
two points so distant from each other, or with an interval of such a nature
that the space could not have been easily passed over by migration, the
fact is given as something remarkable and exceptional. The incapacity of
migrating across a wide sea is more clear in the case of terrestrial mam-
mals than perhaps with any other organic beings; and, accordingly, we
find no inexplicable instances of the same mammals inhabiting distant
points of the world.
Hence it seems to me, as it has to many other naturalists, that the
view of each species having been produced in one area alone, and having
subsequently migrated -from that area as far as its powers of migration and
subsistence under past and present conditions permitted, is the most
probable. Undoubtedly many cases occur, in which we cannot explain how
the same species could have passed from one point to the other. But the
422 MASTERWORKS OF SCIENCE
geographical and climatal changes which have certainly occurred within
recent geological times must have rendered discontinuous the formerly
continuous range of many species. So that we are reduced to consider
whether the exceptions to continuity of range are so numerous and of so
grave a nature that we ought to give up the belief, rendered probable by
general considerations, that each species has been produced within one
area, and has migrated thence as far as it could. If the existence of the
same species at distant and isolated points of the earth's surface can in
many instances be explained on the view of each species having migrated
from a single birthplace; then, considering our ignorance with respect to
former climatal and geographical changes and to the various occasional
means of transport, the belief that a single birthplace is the law seems to
me incomparably the safest.
In botanical works, this or that plant is often stated to be ill adapted
for wide dissemination; but the greater or less facilities for transport
across the sea may be said to be almost wholly unknown. Until I tried,
with Mr. Berkeley's aid, a few experiments, it was not even known how
far seeds could resist the injurious action of sea water. To my surprise I
found that out of 87 kinds, 64 germinated after an immersion of 28 days
and a few survived an immersion of 137 days. It is well known what a
difference there is in the buoyancy of green and seasoned timber; and it
occurred to me that floods would often wash into the sea dried plants or
branches with seed capsules or fruit attached to them. Hence I was led to
dry the stems and branches of 94 plants with ripe fruit, and to place them
on sea water. The majority sank rapidly, but some which, whilst green,
floated for a short time, when dried floated much longer; for instance,
ripe hazelnuts sank immediately, but when dried they floated for 90 days,
and afterwards, when planted, germinated; an asparagus plant with ripe
berries floated for 23 days, when dried it floated for 85 days, and the seeds
afterwards germinated; the ripe seeds of Helosciadium sank in two days,
when dried they floated for above 90 days, and afterwards germinated.
Altogether, out of the 94 dried plants, 18 floated for above 28 days; and
some of the 18 floated for a very much longer period. So that as 6%7
kinds of seeds germinated after an immersion of 28 days; and as 1%4
distinct species with ripe fruit (but not all the same species as in the
foregoing experiment) floated, after being dried, for above 28 days, we
may conclude, as far as anything can be inferred from these scanty facts,
that the seeds of ^-fioo kinds of plants of any country might be floated
By sea currents during 28 days and would retain their power of germina-
tion. In Johnston's Physical Atlas, the average rate of the several Atlantic
currents is 33 miles per diem (some currents running at the rate of 60
miles per diem); on this average, the seeds of 1%0o plants belonging to
one country might be floated across 924 miles of sea to another country,
and when stranded, if blown by an inland gale to a favourable spot, would
germinate.
Living birds can hardly fail to be highly effective agents in the trans-
portation of seeds. I could give many facts showing how frequently birds
DARWIN — ORIGIN OF SPECIES 423
of many kinds are blown by gales to vast distances across the ocean. We
may safely assume that under such circumstances their rate of flight
would often be 35 miles an hour; and some authors have given a far
higher estimate. I have never seen an instance of nutritious seeds passing
through the intestines of a bird; but hard seeds of fruit pass uninjured
through even the digestive organs of a turkey. In the course of two
months, I picked up in my garden 12 kinds of seeds, out of the excrement
of small birds, and these seemed perfect, and some of them, which were
tried, germinated. But the following fact is more important: the crops of
birds do not secrete gastric juice, and do not, as I know by trial, injure in
the least the germination of seeds; now, after a bird has found and de-
voured a large supply of food, it is positively asserted that all the grains
do not pass into the gizzard for twelve or even eighteen hours. A bird in
this interval might easily be blown to the distance of 500 miles, and
hawks are known to look out for tired birds, and the contents of their
torn crops might thus readily get scattered.
Although the beaks and feet of birds are generally clean, earth some-
times adheres to them: in one case I removed sixty-one grains, and in
another case twenty-two grains of dry argillaceous earth from the foot of
a partridge, and in the earth there was a pebble as large as the seed of a
vetch.
Considering that these several means of transport, and that other
means, which without doubt remain to be discovered, have been in action
year after year for tens of thousands of years, it would, I think, be a mar-
vellous fact if many plants had not thus become widely transported. It
should be observed that scarcely any means of transport would carry
seeds for very great distances: for seeds do not retain their vitality when
exposed for a great length of time to the action of sea water; nor could
they be long carried in the crops or intestines of birds. These means, how-
ever, would suffice for occasional transport across tracts of sea some hun-
dred miles in breadth, or from island to island, or from a continent to a
neighbouring island, but not from one distant continent to another. The
floras of distant continents would not by such means become mingled; but
would remain as distinct as they now are. The currents, from their course,
would never bring seeds from North America to Britain, though they
might and do bring seeds from the West Indies to our western shores,
where, if not killed by their very long immersion in salt water, they could
not endure our climate.
But it would be a great error to argue that because a well-stocked
island, like Great Britain, has not, as far as is known (and it would be
very difficult to prove this), received within the last few centuries,
through occasional means of transport, immigrants from Europe or any
other continent, that a poorly stocked island, though standing more re-
mote from the mainland, would not receive colonists by similar means.
Out of a hundred kinds of seeds or animals transported to an island, even
if far less well-stocked than Britain, perhaps not more than one would be
so well fitted to its new home as to become naturalised. But this is no
SCIENCE
valid argument against what would be effected by occasional means of
transport, during the long lapse of geological time, whilst the island was
being upheaved, and before it had become fully stocked with inhabitants.
On almost bare land, with few or no destructive insects or birds living
there, nearly every seed which chanced to arrive, if fitted for the climate,
would germinate and survive.
Dispersal during the Glacial Period
The identity of many plants and animals, on mountain summits, sep-
arated from each other by hundreds of miles of lowlands, where Alpine
species could not possibly exist, is one of the most striking cases known of
the same species living at distant points without the apparent possibility
of their having migrated from one point to the other. It is indeed a re-
markable fact to see so many plants of the same species living on the
snowy regions of the Alps or Pyrenees and in the extreme northern parts
of Europe; but it is far more remarkable that the plants on the White
Mountains, in the United States of America, are all the same with those
o£ Labrador, and nearly all the same, as we hear from Asa Gray, with
those on the loftiest mountains of Europe. Even as long ago as 1747, such
facts led Gmelin to conclude that the same species must have been inde-
pendently created at many distinct points; and we might have remained
in this same belief had not Agassiz and others called vivid attention to
the Glacial period, which, as we shall immediately see, affords a simple
explanation of these facts. We have evidence of almost every conceivable
kind, organic and inorganic, that, within a very recent geological period,
central Europe and North America suffered under an arctic climate. The
rains of a house burnt by fire do not tell their tale more plainly than do
the mountains of Scotland and Wales, with their scored flanks, polished
surfaces, and perched boulders, of the icy streams with which their valleys
were lately filled. So greatly has the climate of Europe changed that in
Northern Italy gigantic moraines, left by old glaciers, are now clothed by
the vine and maize. Throughout a large part of the United States, erratic
boulders and scored rocks plainly reveal a former cold period.
The former influence of the glacial climate on the distribution of the
inhabitants of Europe, as explained by Edward Forbes, is substantially as
follows. But we shall follow the changes more readily, by supposing a
new Glacial period slowly to come on, and then pass away, as formerly
occurred. As the cold came on, and as each more southern zone became
fitted for the inhabitants of the north, these would take the places of the
former inhabitants of the temperate regions. The latter, at the same time,
would travel further and further southward, unless they were stopped by
barriers, in which case they would perish. The mountains would become
covered with snow and ice, and their former Alpine inhabitants would
descend to the plains. By the time that the cold had reached its maximum,
we should have an arctic fauna and flora, covering the central parts of
DARWIN — ORIGIN OF SPECIES 425
Europe, as far south as the Alps and Pyrenees, and even stretching into
Spain. The now temperate regions of the United States would likewise be
covered by arctic plants and animals, and these would be nearly the same
with those of Europe; for the present circumpolar inhabitants, which we
suppose to have everywhere travelled southward, are remarkably uniform
round the world.
As the warmth returned, the arctic forms would retreat northward,
closely followed up in their retreat by the productions of the more tem-
perate regions. And as the snow melted from the bases of the mountains,
the arctic forms would seize on the cleared and thawed ground, always
ascending, as the warmth increased and the snow still further disappeared,
higher and higher, whilst their brethren were pursuing their northern
journey. Hence, when the warmth had fully returned, the same species,
which had lately lived together on the European and North American
lowlands, would again be found in the arctic regions of the Old and New
Worlds, and on many isolated mountain summits far distant from each
other.
Thus we can understand the identity of many plants at points so im-
mensely remote as the mountains of the United States and those of Eu-
rope. We can thus also understand the fact that the Alpine plants of each
mountain range are more especially related to the arctic forms living due
north or nearly due north of them: for the first migration when the cold .
came on, and the remigration on the returning warmth, would generally
have been due south and north. The Alpine plants, for example, of Scot-
land, as remarked by Mr. H. C. Watson, and those of the Pyrenees, as re-
marked by Raymond, are more especially allied to the plants of Northern
Scandinavia; those of the United States to Labrador; those of the moun-
tains of Siberia to the arctic regions of that country. These views,
grounded as they are on the perfectly well-ascertained occurrence of a for-
mer Glacial period, seem to me to explain in so satisfactory a manner the
present distribution of the Alpine and Arctic productions of Europe and
America that when in other regions we find the same species on distant
mountain summits, we may almost conclude, without other evidence, that
a colder climate formerly permitted their migration across the intervening
lowlands, now become too warm for their existence.
XII. GEOGRAPHICAL DISTRIBUTION— Continued ,
Fresh-water Productions
As LAKES and river systems are separated from each other by barriers of
land, it might have been thought that fresh-water productions would not
have ranged widely within the same country, and as the sea is apparently
a still more formidable barrier, that they would never have extended to
distant countries. But the case is exactly the reverse. Not only have many
fresh-water species, belonging to different classes, an enormous range, but
426 MASTERWQRKS OF SCIENCE
allied species prevail in a remarkable manner throughout the world.
When first collecting in the fresh waters of Brazil, I well remember feel-
ing much surprise at the similarity of the fresh-water insects, shells, &c.,
and at the dissimilarity of the surrounding terrestrial beings compared
with those of Britain.
But the wide ranging power of fresh-water productions can, I think,
in most cases be explained by their having become fitted, in a manner
highly useful to them, for short and frequent migrations from pond to
pond, or from stream to stream", within their own countries; and liability
to wide dispersal would follow from this capacity as an almost necessary
consequence. We can here consider only a few cases; of these, some of the
most difficult to explain are presented by fish. It was formerly believed
that the same fresh-water species never existed on two continents distant
from each other. But Dr. Giinther has lately shown that the Galaxias at-
tenuatus inhabits Tasmania, New Zealand, the Falkland Islands, and the
mainland of South America. This is a wonderful case, and probably indi-
cates dispersal from an Antarctic centre during a former warm period.
This case, however, is rendered in some degree less surprising by the
species of this genus having the power of crossing by some unknown
means considerable spaces of open ocean: thus there is one species com-
mon to New Zealand and to the Auckland Islands, though separated by
.a distance of about 230 miles. On the same continent fresh-water fish
often range widely, and as if capriciously; for in two adjoining river
systems some of the species may be the same and some wholly different.
It is probable that they are occasionally transported by what may be
called accidental means. Thus fishes still alive are not very rarely dropped
at distant points by whirlwinds; and it is known that the ova retain their
vitality for a considerable time after removal from the water. Their dis-
persal may, however, be mainly attributed to changes in the level of the
land within the recent period, causing rivers to flow into each other. In-
stances, also, could be given of this having occurred during floods, with-
out any change of level.
With respect to plants, it has long been known what enormous ranges
many fresh-water and even marsh species have, both over continents and
to the most remote oceanic islands. This is strikingly illustrated, ac-
cording to Alphonse de Candolle, in those large groups of terrestrial
plants which have very few aquatic members; for the latter seem immedi-
ately to acquire, as if in consequence, a wide range. I think favourable
means of dispersal explain this fact. I have before mentioned that earth oc-
casionally adheres in some quantity to the feet and beaks of birds. Wading
birds, which frequent the muddy edges of ponds, if suddenly flushed,
would be the most likely to have muddy feet. Birds of this order wander
more than those of any other; and they are occasionally found on the most
remote and barren islands of the open ocean; they would not be likely to
alight on the surface of the sea, so that any dirt on their feet would not be
washed off; and when gaming the land, they would be sure to fly to their
natural fresh-water haunts.
DARWIN — ORIGIN OF SPECIES 427
The species of all kinds which inhabit oceanic islands are few in
number compared with those on equal continental areas: Alphonse de
Candolle admits this for plants, and Wollaston for insects. New Zealand,
for instance, with its lofty mountains and diversified stations, extending
over 780 miles of latitude, together with the outlying islands of Auckland,
Campbell, and Chatham, contain altogether only 960 kinds of flowering
plants; if we comparer this moderate number with the species which
swarm over equal areas in Southwestern Australia or at the Cape of Good
Hope, we must admit that some cause, independently of different physi-
cal conditions, has given rise to so great a difference in number. Even the
uniform county of Cambridge has 847 plants, and the little island of
Anglesea 764, but a few ferns and a few introduced plants are included
in these numbers, and the comparison in some other respects is not quite
fair. We have evidence that the barren island of Ascension aboriginally
possessed less than half-a-dozen flowering plants; yet many species have
now become naturalised on it, as they have in New Zealand and on every
other oceanic island which can be named. In St. Helena there is reason to
believe that the naturalised plants and animals have nearly or quite exter-
minated many native productions. He who admits the doctrine of the
creation of each separate species will have to admit that a sufficient num-
ber of the best adapted plants and animals were not created for .oceanic
islands; for man has unintentionally stocked them far more fully and per-
fectly than did nature.
Although in oceanic islands the species are few in number, the pro-
portion of endemic kinds (/. e., those found nowhere else in the world) is
often extremely large. If we compare, for instance, the number of endemic
land shells in Madeira, or of endemic birds in the Galapagos Archipelago,
with the number found on any continent, and then compare the area of
the island with that of the continent, we shall see that this is true. This
fact might have been theoretically expected, for, as already explained,
species occasionally arriving after long intervals of time in the new and
isolated district, and having to compete with new associates, would be
eminently liable to modification, and would often produce groups of mod-
ified descendants. But it by no means follows that, because in an island
nearly all the species of one class are peculiar, those of another class, or of
another section of the same class, are peculiar; and this difference seems
to depend partly on the species which are not modified having immi-
grated in a body, so that their mutual relations have not been much dis-
turbed; and partly on the frequent arrival of unmodified immigrants
from the mother country, with which the insular forms have intercrossed.
It should be borne in mind that the offspring of such crosses would cer-
tainly gain in vigour; so that even an occasional cross would produce
more effect than might have been anticipated. I will give a few illustra-
tions of the foregoing remarks: in the Galapagos Jslands there are 26
land birds; of these 21 (or perhaps 23) are peculiar, whereas of the n
marine birds only 2 are peculiar; and it is obvious that marine birds could
arrive at these islands much more easily and frequently than land birds.
428 MASTERWORKS OF SCIENCE
Bermuda, on the other hand, which lies at about the same distance from
North America as the Galapagos Islands do from South America, and
which has a very peculiar soil, does not possess a single endemic land
bird, and we know from Mr. J. M. Jones's admirable account of Bermuda
that very many North American birds occasionally or even frequently
visit this island. Almost every year, as I am informed by Mr. E. V.
Harcourt, many European and African birds are*blown to Madeira; this
island is inhabited by 99 kinds, of which one alone is peculiar, though
very closely related to a European form; and three or four other species
are confined to this island and to the Canaries. So that the islands of
Bermuda and Madeira have been stocked from the neighbouring conti-
nents with birds, which for long ages have there struggled together and
have become mutually coadapted. Hence, when settled in their new
homes, each kind will have been kept by the others to its proper place
and habits, and will consequently have been but little liable to modifica-
tion. Any tendency to modification will also have been checked by inter-
crossing with the unmodified immigrants, often arriving from the mother
country.
Absence of Batrachians and Terrestrial Mammals on Oceanic Islands
With respect to the absence of whole orders of animals on oceanic
islands, Bory St. Vincent long ago remarked that Batrachians (frogs,
toads, newts) are never found on any of the many islands with which the
great oceans are studded. I have taken pains to verify this assertion, and
have found it true, with the exception of New Zealand, New Caledonia,
the Andaman Islands, and perhaps the Solomon Islands and the Sey-
chelles. But k is doubtful whether New Zealand and New Caledonia
ought to be classed as oceanic islands; and this is still more doubtful with
respect to the Andaman and Solomon groups and the Seychelles. This
general absence of frogs, toads, and newts on so many true oceanic islands
cannot be accounted for by their physical conditions: indeed it seems that
islands are peculiarly fitted for these animals; for frogs have been intro-
duced into Madeira, the Azores, and Mauritius, and have multiplied so as
to become a nuisance. But as these animals and their spawn are immedi-
ately killed (with the exception, as far as known, of one Indian species)
by sea water, there would be great difficulty in their transportal across the
sea, and therefore we can see why they do not exist on strictly oceanic
islands. But why, on the theory of creation, they should not have been
created there, it would be very difficult to explain.
Mammals offer another and similar case. I have carefully searched the
oldest voyages and have not found a single instance, free from doubt, of
a terrestrial mammal (excluding domesticated animals kept by the na-
tives) inhabiting an island situated above 300 miles from a continent or
great continental island; and many islands situated at a much less dis-
tance are equally barren. The Falkland Islands, which are inhabited by
DARWIN — ORIGIN OF SPECIES 429
a wolf-like fox, come nearest to an exception; but this group cannot be
considered as oceanic, as it lies on a bank in connection with the main-
land at the distance of about 280 miles; moreover, icebergs formerly
brought boulders to its western shores, and they may have formerly trans-
ported foxes, as now frequently happens in the arctic regions. Yet it can-
not be said that small islands will not support at least small mammals, for
they occur in many parts of the world on very small islands, when lying
close to a continent; and hardly an island can be named on which our
smaller quadrupeds have not become naturalised and greatly multiplied.
On the Relations of the Inhabitants of Islands to those of the nearest
Mainland
The most striking and important fact for us is the affinity of the spe-
cies which inhabit islands to those of the nearest mainland, without being
actually the same. Numerous instances could be given. The Galapagos
Archipelago, situated under the equator, lies at the distance of between
500 and 600 miles from the shores of South America. Here almost every
product of the land and of the water bears the unmistakable stamp of the
American continent. There are twenty-six land birds; of these, twenty-
one, or perhaps twenty-three, are ranked as distinct species, and would
commonly be assumed to have been here created; yet the close affinity of
most of these birds to American species is manifest in every character, in
their habits, gestures, and tones of voice. So it is with the other animals,
and with a large proportion of the plants, as shown by Dr. Hooker in his
admirable Flora of this archipelago. The naturalist, looking at the inhabit-
ants of these volcanic islands in the Pacific, distant several hundred
miles from the continent, feels that he is standing on American land. Why
should this be so? Why should the species which are supposed to have
been created in the Galapagos Archipelago, and nowhere else, bear so
plainly the stamp of affinity to those created in America? There is nothing
in the conditions of life, in the geological nature of the islands, in their
height or -climate, or in the proportions in which the several classes are
associated together, which closely resembles the conditions of the South
American coast: in fact, there is a considerable dissimilarity in all these
respects. On the other hand, there is a considerable degree of resemblance
in the volcanic nature of the soil, in the climate, height, and size of the
islands, between the Galapagos and Cape Verde Archipelagoes: but what
an entire and absolute difference In their inhabitants! The inhabitants of
the Cape Verde Islands are related to those of Africa, like those of the
Galapagos to America. Facts such as these admit of no sort of explanation
on the ordinary view of Independent creation; whereas on the view here
maintained, it is obvious that the Galapagos Islands would be likely to
receive colonists from America, whether by occasional means of transport
or (though I do not believe in this doctrine) by formerly continuous land,
and the Cape Verde Islands from Africa; such colonists would be liable
430 MASTERWORKS OF SCIENCE
to modification — the principle of inheritance still betraying their original
birthplace.
The same principle which governs the general character of the inhabit-
ants of oceanic islands, namely, the relation to the source whence colo-
nists could have been most easily derived, together with their subsequent
modification, is of the widest application throughout nature. We see this
on every mountain summit, in every lake and marsh. For Alpine species,
excepting in so far as the same species have become widely spread during
the Glacial epoch, are related to those of the surrounding lowlands; thus
we have in South America, Alpine hummingbirds, Alpine rodents, Alpine
plants, &c., all strictly belonging to American forms; and it is obvious that
a mountain, as it became slowly upheaved, would be colonised from the
surrounding lowlands. So it is with the inhabitants of lakes and marshes,
excepting in so far as great facility of transport has allowed the same forms
to prevail throughout large portions of the world. We see this same princi-
ple in the character of most of the blind animals inhabiting the caves of
America and of Europe. Other analogous facts could be given. It will, I
believe, be found universally true that wherever in two regions, let them
be ever so distant, many closely allied or representative species occur,
there will likewise be found some identical species; and wherever many
closely allied species occur, there will be found many forms which some
naturalists rank as distinct species, and others as mere varieties; these
doubtful forms showing us the steps in the progress of modification.
XIII. MUTUAL AFFINITIES OF ORGANIC BEINGS:
MORPHOLOGY: EMBRYOLOGY
Classification
FROM the most remote period in the history of the world organic beings
have been found to resemble each other in descending degrees, so that
they can be classed in groups under groups. This classification is not arbi-
trary like the grouping of the stars in constellations. The existence of
groups would have been of simpler significance if one group had been ex-
clusively fitted to inhabit the land and another the water; one to feed on
flesh, another on vegetable matter, and so on; but the case is widely
different, for it is notorious how commonly members of even the same
sub-group have different habits. In the second and fourth chapters, on
Variation and on Natural Selection, I have attempted to show that within
each country it is the widely ranging, the much diffused and common,
that is the dominant species, belonging to the larger genera in each class,
which vary most. The varieties, or incipient species, thus produced ulti-
mately become converted into new and distinct species; and these, on the
principle of inheritance, tend to produce other new and dominant species.
Consequently the groups which are now large, and which generally in-
clude many dominant species, tend to go on increasing in size. I further
DARWIN — ORIGIN OF SPECIES 431
attempted to show that from the varying descendants of each species try-
ing to occupy as many and as different places as possible in the economy
of nature, they constantly tend to diverge in character. This latter con-
clusion is supported by observing the great diversity of forms which, in
any small area, come into the closest competition, and by certain facts
in naturalisation.
I attempted also to show that there is a steady tendency, in the forms
which are increasing in number and diverging in character, to supplant
and exterminate the preceding less divergent and less improved forms. I
request the reader to turn to the diagram illustrating the action, as
formerly explained, of these several principles; and he will see that the
inevitable result is that the modified descendants proceeding from one
progenitor become broken up into groups subordinate to groups.
Naturalists, as we have seen, try to arrange the species, genera, and
families in each class on what is called the Natural System. But what is
meant by this system? Some authors look at it merely as a scheme for
arranging together those living objects which are most alike and for sepa-
rating those which are most unlike; or as an artificial method of enunci-
ating, as briefly as possible, general propositions — that is, by one sentence
to give the characters common, for instance, to all mammals, by another
those common to all carnivora, by another those common to the dog
genus, and then, by adding a single sentence, a full description is given
of each kind of dog. The ingenuity and utility of this system are indispu-
table. But many naturalists think that something more is meant by the
Natural System; they believe that it reveals the plan of the Creator; but
unless it be specified whether order in time or space, or both, or what else
is meant by the plan of the Creator, it seems to me that nothing is thus
added to our knowledge. Expressions such as that famous one by Linnaeus,
which we often meet with in a more or less concealed form, namely, that
the characters do not make the genus but that the genus gives the charac-
ters, seem to imply that some deeper bond is included in our classifi-
cations than mere resemblance. I believe that this is the case, and that
community of descent — the one known cause of close similarity in organic
beings — is the bond which, though observed by various degrees of modifi-
cation, is partially revealed to us by our classifications.
That the mere physiological importance of an organ does not de-
termine its classificatory value is almost proved by the fact that in allied
groups in which the same organ, as we have every reason to suppose, has
nearly the same physiological value, its classificatory value is widely dif-
ferent. No naturalist can have worked long at any group without being
struck with this fact; and it has been fully acknowledged in the writings
of almost every author. To give an example amongst insects: in one great
division of the Hymenoptera, the antennae, as Westwood has remarked,
are most constant in structure; in another division they differ much, and
the differences are of quite subordinate value in classification; yet no
one will say that the antennae in these two divisions of the same order are
of unequal physiological importance.
432 MASTERWORKS OF SCIENCE
Numerous instances could be given o£ characters derived from parts
which must be considered of very trifling physiological importance but
which are universally admitted as highly serviceable in the definition of
whole groups. For instance, whether or not there is an open passage from
the nostrils to the mouth, the only character, according to Owen, which
absolutely distinguishes fishes and reptiles — the inflection of the angle of
the lower jaw in Marsupials — the manner in which the wings of insects
are folded — mere colour in certain Alga: — mere pubescence ^ on parts of
the flower in grasses — the nature of the dermal covering, as hair or feathers
in the Vertebrata, If the Ornithorhyncus had been covered with feathers
instead of hair, this external and trifling character would have been con-
sidered by naturalists as an important aid in determining the degree of
affinity of this strange creature to birds.
The importance, for classification, of trifling characters mainly de-
pends on their being correlated with many other characters of more or less
importance. The value indeed of an aggregate of characters is very evident
in natural history. Hence, as has often been remarked, a species may
depart from its allies in several characters, both of high physiological im-
portance and of almost universal prevalence, and yet leave us in no doubt
where it should be ranked. Hence, also, it has been found that a classifi-
cation founded on any single character, however important that may be,
has always failed; for no part of the organisation is invariably constant.
The importance of an aggregate of characters, even when none are impor-
tant, alone explains the aphorism enunciated by Linnseus, namely, that
the characters do not give the genus, but the genus gives^the characters;
for this seems founded on the appreciation of many trifling points of
resemblance, too slight to be defined.
We can see why characters derived from the embryo should be of
equal importance with those derived from the adult, for a natural classifi-
cation of course includes all ages. But it is by no means obvious, on the
ordinary view, why the structure of the embryo should be more important
for this purpose than that of the adult, which alone plays its full part in
the economy of nature. Yet It has been strongly urged by those great
naturalists, Milne Edwards and Agassiz, that embryological characters are
the most important of all; and this doctrine has very generally been ad-
mitted as true. Thus the main divisions of flowering plants are founded on
differences in the embryo — on the number and position of the cotyledons,
and on the mode of development of the plumule and radicle.^ We shall
immediately see why these characters possess so high a value in classifi-
cation, namely, from the natural system being genealogical in its arrange-
ment.
Our classifications are often plainly Influenced by chains of affinities.
Nothing can be easier than to define a number of characters common to
all birds; but with crustaceans, any such definition has hitherto been
found impossible. There are crustaceans at the opposite ends of the series,
which have hardly a character in common; yet the species at lioth ends,
from being plainly allied to others, and these to others, and so onwards,
DARWIN — ORIGIN OF SPECIES 433
can be recognised as unequivocally belonging to this and to no other class
of the Articulata.
All the foregoing rules and aids and difficulties in classification may
be explained, if I do not greatly deceive myself, on the view that the
Natural System is founded on descent with modification; — that the charac-
ters which naturalists consider as showing true affinity between any two
or more species are those which have been inherited from a common
parent, all true classification being genealogical; — that community of de-
scent is the hidden bond which naturalists have been unconsciously seek-
ing, and not some unknown plan of creation, or the enunciation of general
propositions, and the mere putting together and separating objects more
or less alike.
But I must explain my meaning more fully. I believe that the arrange-
ment of the groups within each class, in due subordination and relation to
each other, must be strictly genealogical in order to be natural; but that
the amount of difference in the several branches or groups, though allied
in the same degree in blood to their common progenitor, may differ
gready, being due to the different degrees of modification which they
have undergone; and this is expressed by the forms being ranked under
different genera, families, sections, or orders. The reader will best under-
stand wiiat is meant if he will take the trouble to refer to the diagram
in the fourth chapter. We will suppose the letters A to L to represent
allied genera existing during the Silurian epoch, and descended from
some still earlier form. In three of these genera (A, F, and I), a species
has transmitted modified descendants to the present day, represented by
the fifteen genera (#14 to js*14) on the uppermost horizontal line. Now all
these modified descendants from a single species are related in blood or
descent in the same degree; they may metaphorically be called cousins to
the same millionth degree; yet they differ widely and in different degrees
from each other. The forms descended from A, now broken up into two
or three families, constitute a distinct order from those descended from
I, also broken up into two families. Nor can the existing species, de-
scended from A, be ranked in the same genus with the parent A; or
those from I, with the parent L But the existing genus F14 may be sup-
posed to have been but slightly modified; and it will then rank with the
parent genus F; just as some few still living organisms belong to Silurian
genera. So that the comparative value of the differences between these
organic beings, which are all related to each other in the same degree in
blood, has come to be widely different. Nevertheless their genealogical
arrangement remains strictly true, not only at the present time, but at
each successive period of descent. All the modified descendants from A
will have inherited something in common from their common parent, as
will all the descendants from I; so will it be with each subordinate branch
of descendants, at each successive stage. If, however, we suppose any
descendant of A, or of I, to have become so much modified as to have lost
all traces of its parentage, in this case, its place in the natural system will
be lost, as seems to have occurred with some few existing organisms. All
434 MASTERWORKS OF SCIENCE
the descendants of the genus F, along its whole line of descent, are sup-
posed to have been but little modified, and they form a single genus. But
this genus, though much isolated, will still occupy its proper intermediate
position.
As descent has universally been used in classing together the indi-
viduals of the same species, though the males and females and larvse are
sometimes extremely different; and as it has been used in classing varieties
which have undergone a certain, and sometimes a considerable amount
of modification, may not this same element of descent have been un-
consciously used in grouping species under genera, and genera under
higher groups, all under the so-called natural system? I believe it has been
unconsciously used; and thus only can I understand the several rules and
guides which have been followed by our best systematists. As we have
no written pedigrees, we are forced to trace community of descent by
resemblances of any kind. Therefore we chose those characters which are
the least likely to have been modified, in relation to the conditions of life to
which each species has been recently exposed. Rudimentary structures on
this view are as good as, or even better than, other parts of the organi-
sation. We care not how trifling a character may be — let it be the mere
inflection of the angle of the jaw, the manner in which an insect's wing
is folded, whether the skin be covered by hair or feathers — if it prevail
throughout many and different species, especially those having very dif-
ferent habits of life, it assumes high value; for we can account for its pres-
ence in so many forms with such different habits only by inheritance from a
common parent. We may err in this respect in regard to single points of
structure, but when several characters, let them be ever so trifling, concur
throughout a large group of beings having different habits, we may feel
almost sure, on the theory of descent, that these characters have been
inherited from a common ancestor; and we know that such aggregated
characters have especial value in classification.
On the principle of the multiplication and gradual divergence in
character of the species descended from a common progenitor, together
with their retention by inheritance of some characters in common, we can
understand the excessively complex and radiating affinities by which all
the members of the same family or higher group are connected together.
For the common progenitor of a whole family, now broken up by extinc-
tion into distinct groups and sub-groups, will have transmitted some of its
characters, modified in various ways and degrees, to all the species; and
they will consequently be related to each other by circuitous lines of
affinity of various lengths (as may be seen in the diagram so often
referred to), mounting up through many predecessors. As it is difficult
to show the blood relationship between the numerous kindred of any
ancient and noble family even by the aid of a genealogical tree, and almost
impossible to do so without this aid, we can understand the extraordinary
difficulty which naturalists have experienced in describing, without the
aid of a diagram, the various affinities which they perceive between the
many living and extinct members of the same great natural class.
DARWIN — ORIGIN OF SPECIES 435
Extinction has played an important part in defining and widening
the intervals between the several groups in each class. We may thus
account for the distinctness of whole classes from each other — for instance,
of birds from all other vertebrate animals — by the belief that many ancient
forms of life have been utterly lost, through which the early progenitors
of birds were formerly connected with the early progenitors of the other
and at that time less differentiated vertebrate classes. There has been
much less extinction of the forms of life which once connected fishes with
batrachians. There has been still less within some whole classes, for In-
stance the Crustacea, for here the most wonderfully diverse forms are still
linked together by a long and only partially broken chain of affinities.
Extinction has only defined the groups: it has by no means made them;
for if every form which has ever lived on this earth were suddenly to
reappear, though it would be quite impossible to give definitions by
which each group could be distinguished, still a natural classification, or
at least a natural arrangement, would be possible.
Morphology
We have seen that the members of the same class, independently of
their habits of life, resemble each other in the general plan of their organ-
isation. This resemblance is often expressed by the term "unity of type,"
or by saying that the several parts and organs in the different species of
the class are homologous. The whole subject is included under the general
term of Morphology. This is one of the most interesting departments of
natural history, and may almost be said to be its very soul. What can be
more curious than that the hand of a man, formed for grasping, that of a
mole for digging, the leg of the horse, the paddle of the porpoise, and the
wing of the bat should all be constructed on the same pattern, and should
include similar bones, in the same relative positions? How curious it is, to
give a subordinate though striking instance, that the hind feet of the
kangaroo, which are so well fitted for bounding over the open plains —
those of the climbing, leaf-eating koala, equally wrell fitted for grasping
the branches of trees — those of the ground-dwelling, insect or root-eating,
bandicoots — and those of some other Australian marsupials — should all be
constructed on the same extraordinary type, namely with the bones of the
second and third digits extremely slender and enveloped within the same
skin, so that they appear like a single toe furnished with two claws. Not-
withstanding this similarity of pattern, it is obvious that the hind feet of
these several animals are used for as widely different purposes as it is pos-
sible to conceive. The case is rendered all the more striking by the Ameri-
can opossums, which follow nearly the same habits of life as some of their
Australian relatives, having feet constructed on the ordinary plan.
The explanation is to a large extent simple on the theory of the selec-
tion of successive slight modifications — each modification being profitable
in some way to the modified form, but often affecting by correlation
436 MASTERWORKS OF SCIENCE __^
other parts of the organisation. -In changes of this nature, there will be
little or no tendency to alter the original pattern or to transpose the
parts. The bones of a limb might be shortened and flattened to any extent,
becoming at the same time enveloped in thick membrane, so as to serve
as a fin; or a webbed hand might have all its bones, or certain bones,
lengthened to any extent, with the membrane connecting them increased,
so as to serve as a wing; yet all these modifications would not tend to alter
the framework of the bones or the relative connection of the parts. If we
suppose that an early progenitor — the archetype, as it may be called —
of all mammals, birds, and reptiles had its limbs constructed on the exist-
ing general pattern, for whatever purpose they served, we can at once
perceive the plain signification of the homologous construction of the
limbs throughout the class.
There is another and equally curious branch of our subject; namely,
serial homologies, or the comparison of the different parts or organs in the
same individual, and not of the same parts or organs in different mem-
bers of the same class. Most physiologists believe that the bones of the
skull are homologous — that is, correspond in number and in relative con-
nection— with the elemental parts of a certain number of vertebrae. The
anterior and posterior limbs in all the higher vertebrate classes are plainly
homologous. So it is with the wonderfully complex jaws and legs of
crustaceans.
How inexplicable are the cases of serial homologies on the ordinary
view of creation! Why should the brain be enclosed in a box composed of
such numerous and such extraordinarily shaped pieces of bone, apparently
representing vertebrae? As Owen has remarked, the benefit derived from
the yielding of the separate pieces in the act of parturition by mammals
will by no means explain the same construction in the skulls of birds and
reptiles. Why should similar bones have been created to form the wing
and the leg of a bat, used as they are for such totally different purposes,
namely flying and walking?
On the theory of natural selection, we can, to a certain extent, answer
these questions. We need not here consider how the bodies of some ani-
mals first became divided into a series of segments, or how they became
divided into right and left sides, with corresponding organs, for such
questions are almost beyond investigation. It is, however, probable that
some serial structures are the result of cells multiplying by division, entail-
ing the multiplication of the parts developed from such cells. It must
suffice for our purpose to bear in mind that an indefinite repetition of the
same part or organ is the common characteristic, as Owen has remarked,
of all low or little specialised forms; therefore the unknown progenitor of
the Vertebrata probably possessed many vertebrae; the unknown progeni-
tor of the Articulata, many segments; and the unknown progenitor of
flowering plants, many leaves arranged in one or more spires. We have
also formerly seen that parts many times repeated are eminently liable to
vary, not only in number, but in form. Consequently such parts, being
already present in considerable numbers, and being highly variable, would
DARWIN — ORIGIN OF SPECIES 437
naturally afford the materials for adaptation to the most different pur-
poses; yet they would generally retain, through the force of inheritance,
plain traces of their original or fundamental resemblance. They would
retain this resemblance all the more, as the variations which afforded the
basis for their subsequent modification through natural selection would
tend from the first to be similar; the parts being at an early stage of
growth alike, and being subjected to nearly the same conditions. Such
parts, whether more or less modified , unless their common origin became
wholly obscured, would be serially homologous.
Development and Embryology
This is one of the most important subjects in the whole round of
history. The metamorphoses of insects, with which everyone is familiar,
are generally effected abruptly by a few stages; but the transformations are
in reality numerous and gradual, though concealed. A certain ephemerous
insect (Chloeon) during its development moults, as shown by Sir J. Lub-
bock, above twenty times, and each time undergoes a certain amount of
change; and in this case we see the act of metamorphosis performed in
a primary and gradual manner. Many insects, and especially certain crusta-
ceans, show us what wonderful changes of structure can be effected
during development. Such changes, however, reach their acme in the so-
called alternate generations of some of the lower animals. It is, for in-
stance, an astonishing fact that a delicate branching coralline, studded
with polypi and attached to a submarine rock, should produce, first by
budding and then by transverse division, a host of huge floating jelly-
fishes; and that these should produce eggs, from which are hatched- swim-
ming animalcules, which attach themselves to rocks and become developed
into branching corallines; and so on in an endless cycle.
It has already been stated that various parts in the same individual
which are exactly alike during an early embryonic period become widely
different and serve for widely different purposes in the adult state. So
again it has been shown that generally the embryos of the most distinct
species belonging to the same class are closely similar, but become, when
fully developed, widely dissimilar. The larvae of most crustaceans, at cor-
responding stages of development, closely resemble each other, however
different the adult may become; and so it is with very many other animals.
A trace of the law of embryonic resemblance occasionally lasts till a rather
late age: thus birds of the same genus, and of allied genera, often resemble
each other in their immature plumage; as we see in the spotted feathers
in the young of the thrush group. In the cat tribe, most of the species
when adult are striped or spotted in lines; and stripes or spots can be
plainly distinguished in the whelp of the lion and the puma.
It is commonly assumed, perhaps from monstrosities affecting the
embryo at a very early period, that slight variations or individual differ-
ences necessarily appear at an equally early period. We have little evidence
438 MASTERWORKS OF SCIENCE
on this head, but what we have certainly points the other way; for it is
notorious that breeders of cattle, horses, and various fancy animals cannot
positively tell, until some time after birth, what will be the merits or de-
merits of their young animals. We see this plainly in our own children;
we cannot tell whether a child will be tall or short, or what its precise
features will be. The question is not at what period of life each variation
may have been caused, but at what period the effects are displayed. The
cause may have acted, and I believe often has acted, on one or both parents
before the act of generation. It deserves notice that it is of no importance
to a very young animal, as long as it remains in its mother's womb or in
the egg, or as long as it is nourished and protected by its parent, whether
most of its characters are acquired a little earlier or later in life. It would
not signify, for instance, to a bird which obtained its food by having a
much-curved beak whether or not whilst young it possessed a beak of
this shape, as long as it was fed by its parents.
I have stated in the first chapter that at whatever age a variation first
appears in the parent, it tends to reappear at a corresponding age in the
offspring. Certain variations can only appear at corresponding ages; for
instance, peculiarities in the caterpillar, cocoon, or imago states of the
silk moth; or, again, in the full-grown horns of cattle. But variations,
which, for all that we can see might have first appeared either earlier or
later in life, likewise tend to reappear at a corresponding age in the off-
spring and parent. I am far from meaning that this is invariably the case,
and I could give several exceptional cases of variations (taking the word
in the largest sense) which have supervened at an earlier age in the child
than in the parent.
These two principles, namely, that slight variations generally Appear
at a not very early period of life and are inherited at a corresponding not
early period, explain, as I believe, all the above-specified leading facts in
embryology. But first let us look to an analogous case in our domestic
varieties. Some authors who have written on Dogs maintain that the
greyhound and bulldog, though so different, are really closely allied varie-
ties, descended from the same wild stock; hence I was curious to see how
far their puppies differed from each other: I was told by breeders that
they differed just as much as their parents, and this, judging by the eye,
seemed almost to be the case; but on actually measuring the old dogs and
their six-days-old puppies, I found that the puppies had not acquired
nearly their full amount of proportional difference.
If, on the other hand, it profited the young of an animal to follow
habits of life slightly different from those of the parent form, and conse-
quently to be constructed on a slightly different plan, or if it profited a
larva already different from its parent to change still further, then, on the
principle of inheritance at corresponding ages, the young or the larvae
might be rendered by natural selection more and more different from
their parents to any conceivable extent. Differences in the larva might,
also, become correlated with successive stages of its development; so that
the larva in the first stage might come to differ greatly from the larva in
DARWIN — ORIGIN OF SPECIES 439
the second stage, as is die case with many animals. The adult might also
become fitted for sites or habits, in which organs of locomotion or of the
senses, &c., would be useless; and in this case the metamorphosis would
be retrograde.
From the remarks just made we can see how by changes of structure
in the young, in conformity with changed habits of life, together with
inheritance at corresponding ages, animals might come to pass through,
stages of development, perfectly distinct from the primordial condition
of their adult progenitors. Most of our best authorities are now convinced
that the various larval and pupal stages of insects have thus been acquired
through adaptation, and not through inheritance from some ancient form.
Now let us apply these two principles to species in a state of nature.
Let us take a group of birds, descended from some ancient form and
modified through natural selection for different habits. Then, from the
many slight successive variations having supervened in the several species
at a not early age, and having been inherited at a corresponding age, the
young will have been but little modified, and they will still resemble each
other much more closely than do the adults. We may extend^ this view to
widely distinct structures and to whole classes. The forelimbs, for in-
stance, which once served as legs to a remote progenitor, may have
become, through a long course of modification, adapted in one descendant
to act as hands, in another as paddles, in another as wings; but on the
above two principles the forelimbs will not have been much modified in
the embryos of these several forms; although in each form the forelimb
will differ greatly in the adult state. Whatever influence long-continued
use or disuse may have had in modifying the limbs or other parts of any
species, this will chiefly or solely have affected it when nearly mature,
when it was compelled to use its full powers to gain its own living; and
the effects thus produced will have been transmitted to the offspring at a
corresponding nearly mature age. Thus the young will not be modified,,
or will be modified only in a slight degree, through the effects of the
increased use or disuse of parts.
As all the organic beings, extinct and recent, which have ever lived
can be arranged within a few great classes; and as all within each class
have, according to our theory, been connected together by fine gradations,
the best, and, if our collections were nearly perfect, the only possible
arrangement would be genealogical; descent being the hidden bond of con-
nection which naturalists have been seeking under the term of the
Natural System. On this view we can understand how it is that in the
eyes of most naturalists the structure of the embryo is even more impor-
tant for classification than that of the adult. In two or more groups of
animals, however much they may differ from each other in structure and
habits in their adult condition, if they pass through closely similar em-
bryonic stages, we may feel assured that they all are descended from one
parent form and are therefore closely related. Thus community in embry-
onic structure reveals community of descent; but dissimilarity in embryonic
development does" not prove discommunity of descent, for in one of two
440 MASTERWORKS OF SCIENCE
groups the developmental stages may have been suppressed, or may have
been so greatly modified through adaptation to new habits of life as to be
no longer recognisable. Even in groups, in which^ the adults have been
modified to an extreme degree, community of origin is often revealed by
the structure of the larvae; cirripedes, though externally so like shellfish,
are at once known by their larvae to belong to the great class of crusta-
ceans. As the embryo often shows us more or less plainly the structure
of the less modified and ancient progenitor of the group, we can see why
ancient and extinct forms so often resemble in their adult state the em-
bryos of existing species of the same class. Agassiz believes this to be a
universal law of nature; and we may hope hereafter to see the law proved
true. It can, however, be proved true only in those cases in which the
ancient state of the progenitor of the group has not been wholly oblit-
erated, either by successive variations having supervened at a very early
period of growth or by such variations having been inherited at an earlier
age than that at which they first appeared. It should also be borne in
mind that the law may be true, but yet, owing to the geological record
not extending far enough back in time, may remain for a long period^
or forever, incapable of demonstration. The law will not strictly hold
good in those cases in which an ancient form became adapted in its larvae
state to some special line of life and transmitted the same larval state to
a whole group of descendants; for such larvae will not resemble any still
more ancient form in its adult state.
Thus, as it seems to me, the leading facts in embryology, which are
second to none in importance, are explained on the principle of variations
in the many descendants from some one ancient progenitor, having ap-
peared at a not very early period of life, and having been inherited at a
corresponding period* Embryology rises greatly in interest when we look
at the embryo as a picture, more or less obscured, of the progenitor, either
in its adult or larval state, of all the members of the same great class.
XIV. CONCLUSION
THAT many and serious objections may be advanced against the theory
of descent with modification through variation and natural selection, I
do not deny. I have endeavoured to give to them their full force. Nothing
at first can appear more difficult to believe than that the more complex
organs and instincts have been perfected, not by means superior to, though
analogous with, human reason, but by the accumulation of innumerable
slight variations, each good for the individual possessor. Nevertheless,
this difficulty, though appearing to our imagination insuperably great,
cannot be considered real if we admit the following propositions, namely,
that all parts of the organisation and instincts offer, at least, individual
differences — that there is a struggle for existence leading to the preser-
vation of profitable deviations of structure or instinct — and, lastly, that
gradations in the state of perfection of each organ may have existed, each
DARWIN — ORIGIN OF SPECIES 441
good of Its kind. The truth o£ these propositions cannot, I think, be dis-
puted.
It may be asked how far I extend the doctrine of the niodification of
bpe'cies. The question is difficult to answer, because the more distinct the
forms are which we consider, by so much the arguments in favour of com-
munity of descent become fewer in number and less in force. But some
arguments of the greatest weight extend very far. All the members of
whole classes are connected together by a chain of affinities, and all can
be classed on the same principle, in groups subordinate to groups. Fossil
remains sometimes tend to fill up very wide intervals between existing
orders.
Organs in a rudimentary condition plainly show that an early progen-
itor had the organ in a fully developed condition; and this In some cases
Implies an enormous amount of modification in the descendants. Through-
out whole classes various structures are formed on the same pattern, and
at a very early age the embryos closely resemble each other. Therefore
I cannot doubt that the theory of descent with modification embraces all
the members of the same great class or kingdom. I believe that animals
are descended from at most only four or five progenitors, and plants from
an equal or lesser number.
Analogy would lead me one step farther, namely, to the belief that all
animals and plants are descended from some one prototype. But analogy
may be a deceitful guide. Nevertheless all living things have much in
common, in their chemical composition, their cellular structure, their laws
of growth, and their liability to injurious influences. We see this even in
so trifling a fact as that the same poison often similarly affects plants and
animals; or that the poison secreted by the gallfly produces monstrous
growths on the wild rose or oak tree. With all organic beings, excepting
perhaps some of the very lowest, sexual production seems to be essen-
tially similar. With all, as far as is at present known, the germinal vesicle
is the same; so that all organisms start from a common origin. If we look
even to the two main divisions — namely, to the animal and vegetable
kingdoms — certain low forms are so far Intermediate In character that
naturalists have disputed to which kingdom they should be referred. As
Professor Asa Gray has remarked, "the spores and other reproductive
bodies of many of the lower algae may claim to have first a characteris-
tically animal and then an unequivocally vegetable existence." Therefore,
on the principle of natural selection with divergence of character, It does
not seem incredible that, from such low and intermediate form, both ani-
mals and plants may have been developed; and, if we admit this, we must
likewise admit that all the organic beings which have ever lived on this
earth may be descended from some one primordial form. But this infer-
ence is chiefly grounded on analogy and It Is immaterial whether or not
it be accepted.
When the views advanced by me in this volume, and by Mr. Wallace,
or when analogous views on the origin o£ species are generally admitted,
we can dimly foresee that there will be a considerable revolution in natural
442 MASTERWORKS OF SCIENCE
history. The other and more general departments of natural history will
rise greatly in interest. The terms used by naturalists, of affinity, relation-
ship, community of type, paternity, morphology, adaptive characters, rudi-
mentary and aborted organs, &c,, will cease to be metaphorical, and will
have a plain signification. When we no longer look at an organic being as
a savage looks at a ship, as something wholly beyond his comprehension;
when we regard every production of nature as one which has had a long
history; when we contemplate every complex structure and instinct as
the summing up of many contrivances, each useful to the possessor, in
the same way as any great mechanical invention is the summing up of the
labour, the experience, the reason, and even the blunders of numerous
workmen; when we thus view each organic being, how far more interest-
ing— I speak from experience — does the study of natural history become!
A grand and almost untrodden field o£ inquiry will be opened, on the
causes and laws of variation, on correlation, on the effects of use and dis-
use, on the direct action of external conditions, and so forth. The study of
domestic productions will rise immensely in value. A new variety raised
by man will be a more important and interesting subject for study than
one more species added to the infinitude of already recorded species. Our
classifications will come to be, as far as they can be so made, genealogies;
and will then truly give what may be called the plan of creation. The
rules for classifying will no doubt become simpler when we have a definite
object in view. We possess no pedigrees or armorial bearings; and we have
to discover and trace the many diverging lines of descent in our natural
genealogies, by characters of any kind which have long been inherited.
Rudimentary organs will speak infallibly with respect to the nature of
long-lost structures. Species and groups of species which are called aber-
rant, and which may fancifully be called living fossils, will aid us in form-
ing a picture of the ancient forms of life. Embryology will often reveal to
us the structure, in some degree obscured, of the prototype of each great
class.
Authors of the highest eminence seem to be fully satisfied with the
view that each species has been independendy created. To my mind it
accords better with what we know of the laws impressed on matter by the
Creator that the production and extinction of the past and present inhabit-
ants of the world should have been due to secondary causes, like those
determining the birth and death of the individual. When I view all beings
not as special creations, but as the lineal descendants of some few beings
which lived long before the first bed of the Cambrian system was de-
posited, they seem to me to become ennobled. Judging from the past, we
may safely infer that not one living species will transmit its unaltered
likeness to a distant futurity. And of the species now living very few will
transmit progeny of any kind to a far-distant futurity; for the manner in
which all organic beings are grouped shows that the greater number of
species in each genus, and all the species in many genera, have left no
descendants, but have become utterly ^extinct. We can so far take a pro-
phetic glance into futurity as to foretell that it will be the common and
DARWIN — ORIGIN OF SPECIES 443
widely spread species, belonging to the laiger and dominant groups
within each class, which will ultimately prevail and procreate new and
dominant species. As all the living forms of life are the lineal descendants
of those which lived long before the Cambrian epoch, we may feel certain
that the ordinary succession by generation has never once been broken,
and that no cataclysm has desolated the whole world. Hence we may look
with some confidence to a secure future of great length. And as natural
selection works solely by and for the good of each being, all corporeal and
mental endowments will tend to progress towards perfection.
It is interesting to contemplate a tangled bank, clothed with many
plants of many kinds, with birds singing on the bushes, with various in-
sects flitting about, and with worms crawling through the damp earth,
and to reflect that these elaborately constructed forms, so different from
each other, and dependent upon each other in so complex a manner, have
all been produced by laws acting around us. These laws, taken in the
largest sense, being Growth with Reproduction; Inheritance which is al-
most implied by reproduction; Variability from the indirect and direct
action of the conditions of life, and from use and disuse: a Ratio Q£
Increase so high as to lead to a Struggle for Life, and as a consequence
to Natural Selection, entailing Divergence of Character and the Extinction
of less-improved forms. Thus, from the war of nature, from famine and
death, the most exalted object which we are capable of conceiving,
namely, the production of the higher animals, directly follows. There is
grandeur in this view of life, with its several powers, having been origi-
nally breathed by the Creator into a few forms or into one; and that,
whilst this planet has gone cycling on according to the fixed law of gravity,
from so simple a beginning endless forms most beautiful and most won-
derful have been, and are being, evolved.
EXPERIMENTAL RESEARCHES
IN ELECTRICITY
MICHAEL FARADAY
CONTENTS
Experimental Researches in Electricity
I. Identity of Electricities Derived from Different Sources
1. Voltaic Electricity
2. Ordinary Electricity
3. Magneto-Electricity
4. Thermo-Electricity
5. Animal Electricity
II. New Conditions of Electro-chemical Decomposition
III. Electro-chemical Decomposition — Continued
On a new Measurer of Volta-electricity
On the primary or secondary character of the bodies evolved at the
Electrodes
On the definite nature and extent of Electro-chemical Decomposition
On the absolute quantity of Electricity associated with the particles
or atoms of Matter.
IV, Electricity of the Voltaic Pile
MICHAEL FARADAY
THE FARADAYS cherished a tradition that a progenitor had
come from Ireland into northern England, There, in West-
morland, the family first appears in eighteenth-century rec-
ords as members of a Sandemanian (or Glassite) congrega-
tion. James Faraday, born in 1761, became a blacksmith,
married Margaret Hastwell, and removed to London. His four
children were born in London or in Surrey, near by. Michael,
the third child, was born in Newington, Surrey, in 1791. Be-
cause James never earned much, and was besides afflicted in
health, the children grew up in poverty. Michael later re-
ported that his formal education was confined to instruction
in the three Rs at a common day school, and that he spent his
free hours at home or in the street. When he was twelve he
entered the service of a bookbinder and bookseller as errand
boy, having practically the duties of a newspaper boy. The
following year he was apprenticed to the same bookbinder for
a seven-year period.
Faraday's true education began during these years of ap-
prenticeship. He read the books he was binding, he attended
the evening lectures of Mr. Tatam, founder of a mutual im-
provement group called the City Philosophical Society, and he
cultivated the acquaintance of several young men who shared
his ardency for education and self-improvement. Of his read-
ing, Faraday wrote that he "delighted m Marcet's Converse
tions in Chemistry, and the electrical treatises in the TLncyclo~
paedia J$ritannica" In his lodgings with his master, he per*
formed such simple experiments in chemistry as he could
finance for a few pennies, and he actually built an electrical
machine and other bits of electrical apparatus.
About the time Faraday *s apprenticeship was ending, in
i8ia, a customer of his master's took him to hear Sir
Humphry Davy lecture at the Royal Institution, The young
448 MASTERWORKS OF SCIENCE
man's interest was so fired that he attended more of Davy's
lectures, took notes on them, elaborated and illustrated his
notes with drawings, and resolved to become a scientist rather
than a bookbinder. He had the audacity to write to Sir
Humphry, asking for an opportunity to work in science, and
he enclosed his illustrated lecture notes. Sir Humphry was
impressed. He talked to the young man, liked him, advised
him not to devote his life to science — which he described as a
hard mistress — laughed at his notion that men of .science had
the highest and purest moral motives, and offered him an as-
sistantship at the Royal Institution. An assistant was granted
a salary of twenty-five shillings a week and two rooms at the
top of the house. Faraday accepted the offer.
Davy used Faraday's services in his experiments with the
explosive nitrogen trichloride, and thought so well of him
that when, in the fall of 1813, he decided to go to the Conti-
nent for an extended tour, he took him along as his amanuen-
sis. Unfortunately, Davy's valet withdrew at the last moment,
and his duties fell upon Faraday. He squirmed; but he per-
sisted in completing the trip with Sir Humphry and Lady
Davy, for he was aware that association with the great man
was in itself an education. So for two years he traveled
through France and Switzerland and the Tyrol and Italy,
studying French and Italian diligently, assisting Sir Humphry
in the performance of experiments and demonstrations — one
of the most fascinating was the burning, at Florence, of a
diamond in an atmosphere of oxygen, using the great lenses
belonging to the Duke of Florence as a burning glass — making
the acquaintance of such scientists as Volta and the elder
de la Rive, and writing voluminous letters home to England
promising that once back there he would never leave again.
In 1815, Sir Humphry and his party returned to England.
Very soon Faraday was ba'ck at the Royal Institution as a
laboratory assistant and superintendent of apparatus. He had
now thirty shillings a week and decent living quarters. At
once he called in his old friends of the apprentice days to con-
tinue with him their activities for mutual educational im-
provement. Now a member of the City Philosophical Society,
he lectured before it for the first time in 1816, his subject
being "The General Properties of Matter." Thereafter he
studied elocution with a teacher and devoted some part of his
attention to means of making himself a good lecturer. As one
of his duties at the Institution, he attended all lectures given
there. How much he profited by observing the methods of
successful speakers appears from his own success when he first
lectured at the Institution in 1827. His series begun then con-
tinued for more than thirty years. Europe has never had in
RESEARCHES IN ELECTRICITY 449
science a more practiced, brilliant, and successful popular
instructor.
In 1816, Faraday made his first positive contribution to
scientific literature, an analysis of native caustic lime from
Tuscany. He printed the paper in the Quarterly Journal of
Science; in the same Journal, during the next four years, he
printed thirty-seven articles and notes. These were on various
subjects in physics and chemistry, for he had not yet settled
upon electricity as his special interest. In 1823 he succeeded in
liquefying chlorine. The experiment had grown out of a sug-
gestion of Davy's; and Davy claimed that credit for the ac-
complishment belonged to him. Only Faraday's modesty and
disinterestedness prevented a break between the two men. In
the following year, when Faraday was nominated to a fellow-
ship In the Royal Society, Davy displayed ill will often inter-
preted as jealousy. Despite his opposition, Faraday was
elected, and the friction between the two lessened quickly. In
1825 it was Davy who nominated Faraday to become the
director of the laboratory at the Royal Institution.
While investigating the condensed oil gas manufactured
by the Portable Gas Company, Faraday discovered benzol
(which he called bicarburet of hydrogen). Some of his biogra-
phers have made the rather extravagant claim that he is there-
fore responsible for the whole enormous aniline trade in-
dustry. About the same time, In 1829, he became a lecturer at
the Royal Military Academy at Woolwich and a member of
the Scientific Advising Committee of the Admiralty. A few
years later he became Scientific Adviser to Trinity House.
Almost until his death he retained these connections with the
government, generally receiving no stipend for the advice and
decisions he gave on the ventilation of lighthouses, the pur-
chase and manufacture of optical equipment, the selection of
paints, cottons, oils, lightning conductors for lighthouses, and
so on. He thought that a good subject owed such services to
his government.
Though he had begun some experiments on magnetism and
electricity as early as 1823, not until some years later did Fara-
day devote himself to the great experiments in electricity for
which he Is principally famous. In 1831 he discovered electro-
magnetic induction. His results he gave to the Royal Society
in his First Series of Experimental Researches in Electricity.
In the years following he contributed further series of papers
regularly. From these the following selections are taken.
The publication of the Experimental Researches in Elec-
tricity established Faraday's reputation with the non-scientific
world. Immediately commerce and industry began to bid for
his services. In the next year, by his advisory work, he added
450 MASTERWQRKS OF SCIENCE
a full thousand pounds to his two-hundred-pound stipend
from the Institution. The following year he earned more.
Then he made up his mind that he could serve only one mas-
ter, and that he preferred science to wealth. In subsequent
years he accepted employment apart from the pure research
and lecturing of the Institution at a sharply declining rate;
after 1845 he never accepted a penny for any industrial work.
Faraday had married in 1821 the daughter of an elder in
the Sandemanian Congregation of which he was a member.
With her he lived a life compounded of the sweetest sympa-
thy and understanding. Both were extremely devout, for Fara-
day kept his religious convictions — the Sandemanians held to
doctrines which would now be labeled fundamentalist — and
his scientific views stricdy apart. In 1840 he was elected an
elder in his church, and thus had pressed upon him the duty
of preaching a sermon on alternate Sundays. Possibly it was
this addition to his already great intellectual load which
caused him to suffer a partial breakdown in 1841. He suf-
fered particularly from loss of memory; he had to take a long
holiday, and for three years he abandoned his studies.
The long vacation obviously did not impair his powers.
In 1845 he discovered the influence of a magnetic field of force
on polarized light, and in the same year he established the dis-
tinction between magnetic and diamagnetic substances. The
two great accomplishments won for him, in 1846, from the
Royal Society, both the Royal and the Rumford medals. Such
honors were by this time no novelties to him. Perhaps, indeed,
no other scientist has ever been equally recognized, feted, and
decorated in his own lifetime. He received no fewer than
ninety-five honorary titles and marks of distinction from the
learned societies of Europe and America. He deserved them.
For among the incredibly numerous discoveries credited to
him, four must be characterized as massive: magneto-electric
induction, the chemical phenomena of the electric current, the
magnetization of light, and diamagnetism. And only com-
pared with these are his studies in the liquefaction of gases,
in factional electricity, in regelation, of small importance.
Twice Faraday did refuse honors. In 1835 he refused a
government pension — which he was subsequently persuaded
to accept. And twice he declined to become president of the
Royal Society. He did not refuse the house on Hampton
Court Green which Queen Victoria, through the good offices
of the Prince Consort, offered him in 1858. There he spent
his declining years. In 1865 he made his last report to Trinity
House and relinquished his duties at the .Royal Institution.
In 1867 he died.
Faraday's skill as an experimenter and his success as a
RESEARCHES IN ELECTRICITY 451
lecturer depended In no small degree on his remarkable sense
of order, his pertinacity, and his control over a kind o£ Celtic
impulsiveness. His biographer Tyndall, who was his successor
at the Royal Institution and his great personal friend, remarks
that the man was never swallowed up in the scientist. He
speaks eloquently of Faraday's long friendships with Davy,
Biot, the two de la Rives, Arago, Humboldt, and a host of
students and assistants. To sum up the man, Tyndall quotes
from St. Paul: "blameless, vigilant, sober, of good behaviour,
apt to teach, not given to filthy lucre."
EXPERIMENTAL RESEARCHES
IN ELECTRICITY
7. IDENTITY OF ELECTRICITIES DERIVED
FROM DIFFERENT SOURCES
THE PROGRESS of the electrical researches which I have had the honour
to present to the Royal Society brought me to a point at which it was
essential for the further prosecution of my inquiries that no doubt should
remain of the identity or distinction of electricities excited by different
means. I have satisfied myself that they are identical, and I hope the ex-
periments which I have to offer, and the proofs flowing from them, will be
found worthy the attention of the Royal Society.
The various phenomena exhibited by electricity may, for the purposes
of comparison, be arranged under two heads; namely, those connected
with electricity of tension, and those belonging to electricity in motion.
This distinction is taken at present not as philosophical, but merely as
convenient. The effect of electricity of tension, at rest, is either attraction
or repulsion at sensible distances. The effects of electricity in motion or
electrical currents may be considered as ist, Evolution of heat; 2nd, Mag-
netism; 3rd, Chemical decomposition; 4th, Physiological phenomena; 5th,
Spark. It will be my object to compare electricities from different sources,
and especially common and voltaic electricities, by their power of produc-
ing these effects.
j. Voltaic Electricity
Tension. — When a voltaic battery of 100 pairs of plates has its extremi-
ties examined by the ordinary electrometer, it is well known that they
are found positive and negative, the gold leaves at the same extremity
repelling each other, the gold leaves at different extremities attracting
each other, even when half an inch or more of air intervenes.
That ordinary electricity is discharged by points with facility through
air, that it is readily transmitted through highly rarefied air, and also
through heated air, as for instance a flame, is due to its high tension. I
sought, therefore, for similar effects in the discharge of voltaic electricity,
using as a test of the passage of the electricity either the galvanometer
or chemical action produced by the arrangement hereafter to be described.
The voltaic battery I had at my disposal consisted of 140 pairs of
RESEARCHES IN ELECTRICITY 453
plates four inches square, with double coppers. It was insulated through-
out, and diverged a gold-leaf electrometer about one third of an inch. On
endeavouring to discharge this battery by delicate points very nicely ar-
ranged and approximated, either in the air or in an exhausted receiver,
I could obtain no indications of a current, either by magnetic or chemi-
cal action. In this, however, was found no point of discordance between
voltaic and common electricity; for when a Leyden battery was charged
so as to deflect the gold-leaf electrometer to the same degree, the points.
were found equally unable to discharge it with such effect as to produce
either magnetic or chemical action. This was not because common elec-
tricity could not produce both these effects, but because when of such
low intensity the quantity required to make the effects visible (being
enormously great) could not be transmitted in any reasonable time. In
conjunction with the other proofs of identity hereafter to be given, these
effects of points also prove identity instead of difference between voltaic
and common electricity.
e
, U I. T U "feAI^Sl
FIG. i.
As heated air discharges common electricity with far greater facility
than points, I hoped that voltaic electricity might in this way also ^be
discharged. An apparatus was therefore constructed (Fig. i), in which
A B is an insulated glass rod upon which two copper wires, C, D, are
fixed firmly; to these wires are soldered two pieces of fine plating wire,
the ends of which are brought very close to each other at e, but without
touching; the copper wire C was connected with the positive pole of a
voltaic battery, and the wire D with a decomposing apparatus, from
which the communication was completed to the negative pole of the bat-
tery. In these experiments only two troughs, or twenty pairs of plates^
were used.
Whilst in the state described, no decomposition took place at the
point a, but when the side of a spirit-lamp flame was applied to the^two
platina extremities at e, so as to make them bright red-hot, decomposition
occurred; iodine soon appeared at the point a, and the transference of
electricity through the heated air was established. On raising the tempera-
ture of the points e by a blowpipe, the discharge was rendered still more
free, and decomposition took place instantly. On removing the source of
heat, the current immediately ceased. On putting the ends of the wires
very close by the side of and parallel to each other, but not touching, the
454 MASTERWORKS OF SCIENCE
effects were perhaps more readily obtained than before. On using a larger
voltaic battery, they were also more freely obtained.
These effects, not hitherto known or expected under this form, are
only cases of the discharge which takes place through air between the
charcoal terminations of the poles of a powerful battery, when they are
gradually separated after contact. Then the passage is through heated air
exactly as with common electricity, and Sir H. Davy has recorded that
with the original battery of the Royal Institution this discharge passed
through a space of at least four inches. In the exhausted receiver the elec-
tricity would stride through nearly half an inch of space, and the com-
bined effect of rarefaction and heat was such upon the inclosed air as to
enable it to conduct the electricity through a space of six or seven inches.
The instantaneous charge of a Leyden battery by the poles of a voltaic
apparatus is another proof of the tension, and also the quantity, of elec-
tricity evolved by the latter. Sir H. Davy says, "When the two conductors
from the ends of the combination were connected with a Leyden battery,
one with the internal, the other with the external coating, the battery
instantly became charged; and on removing the wires and making- the
proper connections, either a shock or a spar\ could be perceived: and the
least possible time of contact was sufficient to renew the charge to its full
intensity."
In motion: i. Evolution of heat. — The evolution of heat in wires and
fluids by the voltaic current is matter of general notoriety.
ii. Magnetism. — No fact is better known to philosophers than the
power of the voltaic current to deflect the magnetic needle, and to make
magnets according to certain laws; and no effect can be more distinctive
of an electrical current.
. in. Chemical decomposition. — The chemical powers of the voltaic
current, and their subjection to certain laws, are also perfectly well known.
iv. Physiological effects. — The power of the voltaic current, when
strong, to shock and convulse the whole animal system, and when weak
to affect the tongue and the eyes, is very characteristic.
v. Sfar^ — The brilliant star of light produced by the discharge of a
voltaic battery is known to all as the most beautiful light that man can
produce by art.
That these effects may be almost infinitely varied, some being exalted
whilst others are diminished, is universally acknowledged; and yet with-
out any doubt of the identity of character of the voltaic currents thus
made to differ in their effect. The beautiful explication of these variations
afforded by Cavendish's theory of quantity and intensity requires no sup-
port at present, as it is not supposed to be doubted.
In consequence of the comparisons that will hereafter arise between
wires carrying voltaic and ordinary electricities, and also because of cer-
tain views of the condition of a wire or any other conducting substance
connecting the poles of a voltaic apparatus, it will be necessary to give
some definite expression of what is called the8 voltaic current, in contra-
distinction to any supposed peculiar state of arrangement, not progressive,
RESEARCHES IN ELECTRICITY 455
which the wire or the electricity within it may be supposed to assume.
If two voltaic troughs P N, P' N', Fig. 2, be symmetrically arranged and
insulated, and the ends N P' connected by a wire, over which a magnetic
needle is suspended, the wire will exert no effect over the needle; but
immediately that the ends P N7 are connected by another wire, the needle
will be deflected, and will remain so as long as the circuit is complete.
Now if the troughs merely act by causing a peculiar arrangement in the
wire either of its particles or its electricity, that arrangement constituting
its electrical and magnetic state, then the wire N P7 should be in a similar
state of arrangement before P and N7 were connected to what it is after-
wards, and should have deflected the needle, although less powerfully,
perhaps to one half the extent which would result when the communica-
tion is complete throughout. But if the magnetic efiects depend upon a
current, then it is evident why they could not be produced in any degree
r
N P'l
FIG. 2.
before the circuit was complete; because prior to that no current could
exist.
By current, I mean anything progressive, whether it be a fluid of
electricity, or two fluids moving in opposite directions, or merely vibra-
tions, or, speaking still more generally, progressive forces. By arrange-
ment, I understand a local adjustment of particles, or fluids, or forces,
not progressive, Many other reasons might be urged in support of the
view of a current rather than an arrangement, but I am anxious to avoid
stating unnecessarily what will occur to others at the moment.
2. Ordinary Electricity
By ordinary electricity I understand that which can be obtained from
the common machine, or from the atmosphere, or by pressure, or cleavage
of crystals, or by a multitude of other operations; its distinctive character
being that of great intensity, and the exertion of attractive and repulsive
powers, not merely at sensible but at considerable distances.
Tension. — The attractions and repulsions at sensible distances, caused
by ordinary electricity, are well known to be so powerful in certain cases
as to surpass, almost infinitely, the similar phenomena produced by elec-
tricity, otherwise excited. But still those attractions and repulsions are
exactly of the same nature as those already referred to under the head
Tension, Voltaic electricity; and the difference in degree between them
is not greater than often occurs between cases of ordinary electricity only.
456 MASTERWORKS OF SCIENCE
The discharge of common electricity through heated air is a well-
known fact. The parallel case of voltaic electricity has already been de-
scribed.
In motion: i. Evolution of heat. — The heating power of common
electricity, when passed through wires or other substances, is perfectly
well known. The accordance between it and voltaic electricity is in this
respect complete.
ii. Magnetism. — Voltaic electricity has most extraordinary and ex-
alted magnetic powers. If common electricity be identical with it, it ought
to have the same powers. In rendering needles or bars magnetic, it is
found to agree with voltaic electricity, and the direction of the magne-
tism, in both cases, is the same; but in deflecting the magnetic needle,
common electricity l\as been found deficient, so that sometimes its power
has been denied altogether, and at other times distinctions have been
hypothetically assumed for the purpose of avoiding the difficulty.
M. Colladon, of Geneva, considered that the difference might be
due to the use of insufficient quantities of common electricity in all the
experiments before made on this head; and in a memoir read to the
Academic des Sciences in 1826, describes experiments in which, by the
use of a battery, points, and a delicate galvanometer, he succeeded in ob-
taining deflections, and thus establishing identity in that respect. I -am
happy to say that my results fully confirm those by M. Colladon, and I
should have had no occasion to describe them, but that they are essential
as proofs of the accuracy of the final and general conclusions I am enabled
to draw respecting the magnetic and chemical action of electricity.
The plate electrical machine I have used is fifty inches in diameter;
it has two sets of rubbers; its prime conductor consists of two brass cylin-
ders connected by a third, the whole length being twelve feet, and the
surface in contact with air about 1422 square inches. When in good exci-
tation, one revolution of the plate will give ten or twelve sparks from
the conductors, each an inch in length. Sparks or flashes from ten to four-
teen inches in length may easily be drawn from the conductors. Each turn
of the machine, when worked moderately, occupies about four fifths of
a second.
The electric battery consisted of fifteen equal jars. They are coated
eight inches upwards from the bottom, and are twenty-three inches in
circumference, so that each contains 184 square inches of glass, coated on
both sides; this is independent of the bottoms, which are of thicker glass,
and contain each about fifty square inches.
A good discharging train was arranged by connecting metallically a
sufficiently thick wire with the metallic gas pipes of the house, with the
metallic gas pipes belonging to the public gasworks of London, and also
with the metallic water pipes of London. It was so effectual in its office
as to carry off instantaneously electricity of the feeblest tension, even that
of a single voltaic trough, and was essential to many of the experiments.
It was to the retarding power of bad conductors, with the intention
of diminishing its intensity without altering its quantity f that I first
RESEARCHES IN ELECTRICITY 457
looked with the hope of being able to make common electricity assume
more of the characters and power of voltaic electricity than it Is usually
supposed to have.
The coating and armour of the galvanometer were first connected
with the discharging train; the end B (Fig. 3) of the galvanometer wire
was connected with the outside coating of the battery, and then both
these with the discharging train; the end A of the galvanometer wire was
connected with a discharging rod by a wet thread four feet long; and
finally, wrhen the battery had been positively charged by about forty turns
of the machine, it was discharged by the rod and the thread through the
galvanometer. The needle immediately moved.
FIG. 3.
During the time that the needle completed its vibration in the first
direction and returned, the, machine was worked, and the battery re-
charged; and when the needle in vibrating resumed its first direction, the
discharge was again made through the galvanometer. By repeating this
action a few times, the vibrations soon extended to above 40° on each side
of the line of .rest.
This effect could be obtained at pleasure. Nor was it varied, appar-
ently, either in direction or degree, by using a short thick string, or even
four short thick strings in place of the long fine thread. With a more
delicate galvanometer, an excellent swing of the needle could be obtained
by one discharge of the battery.
On reversing the galvanometer communications so as to pass the dis-
charge through from B to A, the needle was equally well deflected, but
in the opposite direction.
The deflections were in the same direction as if a voltaic current had
been passed through the galvanometer, Le. the positively charged surface
of the electric battery coincided with the positive end of the voltaic appa-
ratus, and the negative surface of the former with the negative end of
the latter.
The battery was then thrown out of use, and the communications so
arranged that the current could be passed from the prime conductor, by
the discharging rod held against it, through the wet string, through the
galvanometer coil, and into the discharging train, by which it was finally
dispersed. This current could be stopped at any moment, by removing the
discharging rod, and either stopping the machine or connecting the prime
conductor by another rod with the discharging train; and could be as in-
stantly renewed. The needle was so adjusted that, whilst vibrating in
moderate and small arcs, it required time equal to twenty-five beats of a
watch to pass in one direction through the arc, and of course an equal
time to pass in the other direction.
458 MASTERWQRKS OF SCIENCE ^
Thus arranged, and the needle being stationary, the current, direct
from the machine, was sent through the galvanometer for twenty-five
beats, then interrupted for other twenty-five beats, renewed for twenty-
five beats more, again interrupted for an equal time, and so on contin-
ually. The needle soon began to vibrate visibly, and after several alterna-
tions of this kind, the vibration increased to 40° or more.
On changing the direction of the current through the galvanometer,
the direction of the deflection of the needle was also changed. In all cases
the motion of the needle was in direction the same as that caused either
by the use of the electric battery or a voltaic trough.
I now rejected the wet string, and substituted a copper wire, so that
the electricity of the machine passed at once into wires communicating
directly with the discharging train, the galvanometer coil being one of the
wires used for the discharge. The effects were exactly those obtained
above.
Instead of passing the electricity through the system, by bringing the
discharging rod at the end of it into contact with the conductor, four
points were fixed on to the rod; when the current was to pass, they were
held about twelve inches from the conductor, and when it was not to pass,
they were turned away. Then operating as before, except with this varia-
tion, the needle was soon powerfully deflected, and in perfect consistency
with the former results. Points afforded the means by which Colladon, in
all cases; made his discharges.
Finally, I passed the electricity first through an exhausted receiver,
so as to make it there resemble the aurora borealis, and then through the
galvanometer to the earth; and it was found still effective in deflecting
the needle, and- apparently with the same force as before.
From all these experiments, it appears that a current of common elec-
tricity, whether transmitted through water or metal, or rarefied air, or by
means of points in common air, is still able to deflect the needle; the only
requisite being, apparently, to allow time for its action: that it is, in fact,
just as magnetic in every respect as a voltaic current, and that in this
character therefore no distinction exists.
iii. Chemical decomposition. — The chemical action of voltaic elec-
tricity is characteristic of that agent, but not more characteristic than are
the laws under which the bodies evolved by decomposition arrange them-
selves at the poles. Dr. Wollaston showed that common electricity resem-
bled it in these effects, and "that they are both essentially the same."
I first repeated Wollaston's fourth experiment, in which the ends of
coated silver wires are immersed in a drop of sulphate of copper. By pass-
ing the electricity of the machine through such an arrangement, that end
in the drop which received the electricity became coated with metallic
copper. One hundred turns of the machine produced an evident effect;
two hundred turns a very sensible one. The decomposing action was, how-
ever, very feeble. Very little copper was precipitated, and no sensible
trace of silver from the other pole appeared in the solution.
A much more convenient and effectual arrangement for chemical de-
RESEARCHES IN ELECTRICITY
459
compositions by common electricity is the following. Upon a glass plate,
Fig. 4, placed over but raised above a piece o£ white paper, so that shadows
may not interfere, put two pieces of tinfoil a, b; connect one of these by
an insulated wire c, or wire and string, with the machine, and the other,
g, with the discharging train or the negative conductor; provide two
pieces of fine platina wire, bent as in Fig. 5, so that the part d, f shall be
FIG. 4.
nearly upright, whilst the whole is resting on the three bearing points
p, c, /; place these as in Fig. 4; the points p, n then become the decom-
posing poles. In this way surfaces of contact, as minute as possible, can
be obtained at pleasure, and the connection can be broken or renewed
in a moment, and the substances acted upon examined with the utmost
facility.
A coarse line was made on the glass with solution of sulphate of
copper, and the terminations p and n put into it; the foil a was connected
FIG. 5.
with the positive conductor of the machine by wire and wet string, so
that no sparks passed: twenty turns of the machine caused the precipita-
tion of so much copper on the end n that it looked like copper wire;
no apparent change took place at p.
On combining a piece of litmus with a piece of turmeric paper, wet-
ting both with solution of sulphate of soda, and putting the paper on the
glass, so that p was on the litmus and n on the turmeric, a very few turns
of the machine sufficed to show the evolution of acid at the former and
alkali at the latter, exactly in the manner effected by a volta-electric cur-
rent.
Decompositions took place equally well, whether the electricity
passed from the machine to the foil a, through water, or through wire
46Q MASTERWORKS OP SCIENCE
only; by contact with the conductor, or by spares there; provided the
sparks were not so large as to cause the electricity to pass in sparks from
p to n, or towards n; and I have seen no reason to believe that in cases
of true electro-chemical decomposition by the machine, the electricity
passed in sparks from the conductor, or at any part of the current, is able
to do more, because of its tension, than that which is made to pass merely
as a regular current.
Finally, the experiment was extended into the following form, sup-
plying in this case the fullest analogy between common and voltaic elec-
tricity. Three compound pieces of litmus and turmeric paper were mois-
tened in solution of sulphate of soda, and arranged on a plate of glass
with platina wires, as in Fig. 6. The wire m was connected with the
prime conductor of the machine, the wire t with the discharging train,
771
FIG. 6.
and the wires r and s entered into the course of the electrical current by
means of the pieces of moistened paper; they were so bent as to rest each
on three points, n, r, p; n} s, p, the points r and s being supported by the
glass, and the others by the papers: the three terminations p, p, p rested
on the litmus, and the other three n, n, n on the turmeric paper. On work-
ing the machine for a short time only, acid was evolved at all the poles
or terminations pf p, p, by which the electricity entered the solution, and
alkali at the other poles n, n, n, by which the electricity left the solution,
I have been the more anxious to assign the true value of this experi-
ment as a test of electro-chemical action, because I shall have occasion to
refer to it in cases of supposed chemical action by magneto-electric and
other electric currents and elsewhere. But, independent of it, there can-
not be now a doubt that Dr. Wollaston was right in his general conclusion;
and that voltaic and common electricity have powers of chemical decom-
position, alike in their nature, and governed by the same law of arrange-
ment.
iv. Physiological effects. — The power of the common electric current
to shock and convulse the animal system, and when weak to affect the
tongue and the eyes, may be considered as the same with the similar power
of voltaic electricity, account being taken of the intensity of the one elec-
tricity and duration of the other. When a wet thread was interposed in
the course of the current of common electricity from the battery charged
by eight or ten revolutions of the machine in good action, and the dis-
RESEARCHES IN ELECTRICITY 461
charge made by platina spatulas through the tongue or the gums, the effect
upon the tongue and eyes was exactly that of a momentary feeble voltaic
circuit.
v. Spar\. — The beautiful flash of light attending the discharge of
common electricity is well known. It rivals in brilliancy, if it does not
•even very much surpass, the light from the discharge of voltaic electricity;
but it endures for an instant only, and is attended by a sharp noise like
that of a small explosion. Still no difficulty can arise in recognising it to
be the same spark as that from the voltaic battery, especially under cer-
tain circumstances. The eye cannot distinguish the difference between a
voltaic and a common electricity spark, if they be taken between amal-
gamated surfaces of metal, at intervals only, and through the same dis-
tance of air.
5. Magneto-Electricity
Tension. — The attractions and repulsions due to the tension of ordi-
nary electricity have been well observed with that evolved by magneto-
electric induction. M. Pixii, by using an apparatus, clever in its construc-
• tion and powerful in its action, was able to obtain great divergence of the
gold leaves of an electrometer.
In motion: i. Evolution of heat. — The current produced by magneto-
electric induction can heat a wire in the manner of ordinary electricity.
At the British Association of Science at Oxford, in June of the present year,
I had the pleasure, in conjunction with Mr. Harris, Professor Daniell, Mr.
Duncan, and others, of making an experiment, for which the great magnet
in the museum, Mr. Harris's new electrometer and the magneto-electric
coil were put in requisition. The latter had been modified in the manner
I have elsewhere described, so as to produce an electric spark when its
contact with the magnet was made or broken. The terminations of the
spiral, adjusted so as to have their contact with each other broken when
the spark was to pass, were connected with the wire in the electrometer,
and it was found that each time the magnetic contact was made and
broken, expansion of the air within the instrument occurred, indicating
an increase, at the moment, of the temperature of the wire.
ii. Magnetism. — These currents were discovered by their magnetic
power.
iii. Chemical decomposition. — I have made many endeavours to effect
chemical decomposition by magneto-electricity, but unavailingly. The ap-
paratus of M. Pixii already referred to has, however, in the hands of him-
self and M. Hachette, given decisive chemical results, so as to complete
this link in the chain of evidence. Water was decomposed by it, and the
oxygen and hydrogen obtained in separate tubes according to the law gov-
erning volta-electric and machine-electric decomposition.
iv. Physiological effects. — A frog was convulsed in the earliest experi-
ments on these currents. The sensation upon the tongue, and the flash
before the eyes, which I at first obtained only in a feeble degree, have
462 MASTERWORKS OF SCIENCE
been since exalted by more powerful apparatus, so as to become even dis-
agreeable.
v. SparJ^. — The feeble spark which I first obtained with these cur-
rents has been varied and strengthened by Signori Nobili and Antinori,.
and others, so as to leave no doubt as to its identity with the commoa
electric spark.
4. Thermo-Electricity
With regard to thermo-electricity (that beautiful form of electricity
discovered by Seebeck), the very conditions under which it is excited
are such as to give no ground for expecting that it can be raised like com-
mon electricity to any high degree of tension; the effects, therefore, due
to that state are not to be expected. The sum of evidence respecting its
analogy to the electricities already described is, I believe, as follows: —
Tension. The attractions and repulsions due to a certain degree of tension
have not been observed. In currents: i. Evolution of heat. I am not aware
that its power of raising temperature has been observed, ii. Magnetism*
It was discovered, and is best recognised, by its magnetic powers, iii.
Chemical decomposition has not been effected by it. iv. Physiological*
effects. Nobili has shown that these currents are able to cause contrac-
tions in the limbs of a frog. v. Spar^. The spark has not yet been seen.
Only those effects are weak or deficient which depend upon a certain
high degree of intensity; and if common electricity be reduced in that
quality to a similar degree with the thermo-electricity, it can produce no-
effects beyond the latter.
5. Animal Electricity
After an examination of the experiments of Walsh, Ingenhousz,,
Cavendish, Sir H. Davy, and Dr. Davy, no doubt remains on my mind
as to the identity of the electricity of the torpedo with common and
voltaic electricity; and I presume that so little will remain on the minds
of others as to justify my refraining from entering at length into the
philosophical proofs of that identity. At present the sum of evidence is as
follows: —
Tension. — No sensible attractions or repulsions due to tension have
been observed.
In motion: i. Evolution of heat; not yet observed; I have little or no
doubt that Harris's electrometer would show it.
ii. Magnetism. — Perfectly distinct. According to Dr. Davy, the cur-
rent deflected the needle and made magnets under the same law, as to-
direction, which governs currents of ordinary and voltaic electricity.
iii. Chemical decomposition. — Also distinct; and though Dr. Davy
used an apparatus of similar construction with that of Dr. Wollaston, still
no error in the present case is involved, for the decompositions were
RESEARCHES IN ELECTRICITY
463
polar, and in their nature truly electro-chemical. By the direction of the
magnet, it was found that the under surface of the fish was negative, and
the upper positive; and in the chemical decompositions, silver and lead
were precipitated on the wire connected with the under surface, and not
on the other; and when these wires were either steel or silver, in solution
of common salt, gas (hydrogen?) rose from the negative wire, but none
from the positive.
iv. Physiological effects. — These are so characteristic that by them
the peculiar powers of the torpedo and gymnotus are principally rec-
ognised.
v. Spar\. — The electric spark has not yet been obtained.
In concluding this summary of the powers of torpedinal electricity, I
cannot refrain from pointing out the enormous absolute quantity of elec-
tricity which the animal must put in circulation at each effort. It is doubt-
ful whether any common electrical machine has as yet been able to supply
electricity sufficient in a reasonable time to cause true electro-chemical
decomposition of water, yet the current from the torpedo has done it. The
same high proportion is shown by the magnetic effects. These circum-
stances indicate that the torpedo has power (in the way probably that
Cavendish describes) to continue the evolution for a sensible time, so that
its successive discharges rather resemble those of a voltaic arrangement,
intermitting in its action, than those of a Leyden apparatus, charged and
discharged many, times in succession. In reality, however, there is no phil-
osophical difference between these two cases.
The general conclusion which must, I think, be drawn from this col-
lection of facts is that electricity, whatever may be its source, is identical
in its nature. The phenomena in the five "kinds of species quoted differ,
not in their character but only in degree; and in that respect vary in pro-
portion to the variable circumstances of quantity and intensity which can
at pleasure be made to change in almost any one of the kinds of electricity
as much as it does between one kind and another.
Table of the experimental Effects common to the Electricities derived from
different Sources.
Physiologi-
cal Effects.
Magnetic
Deflection.
Cfl
qj aj
d. -0
a
CO
Heating •
Power.
True
Chemical
Action,
Attraction
and
Repulsion.
Discharge
by
Hot Air.
i. Voltaic electricity
X
X
X
X
X
X
X
X
2. Common electricity
X
X
X
X
X
X
X
X
3. Magneto-electricity
X
X
X
X
X
X
X
4. Thermo-electricity
X
X
+
+
+
+
5. Animal electricity
X
X
X
+
+
X
464 MASTERWORKS OF SCIENCE
77. NEW CONDITIONS .OF ELECTRO-CHEMICAL
DECOMPOSITION
THE TENSION of machine electricity causes it, however small in quantity,
to pass through any length of water, solutions, or other substances class-
ing with these as conductors, as fast as it can be produced, and therefore,
in relation to quantity, as fast as it could have passed through much
shorter portions of the same conducting substance. With the voltaic bat-
tery the case is very different, and the passing current of electricity sup-
plied by it suffers serious diminution in any substance, by considerable
extension of its length, but especially in such bodies as those mentioned
above.
I endeavoured to apply this facility of transmitting the current of
electricity through any length of a conductor to an investigation of the
transfer of the elements in a decomposing body, in contrary directions,
towards the poles. The general form of apparatus used in these experi-
ments has been already described; and also a particular experiment, in
which, when a piece of litmus paper and a piece of turmeric paper were
combined and moistened in solution of sulphate of soda, the point of the
wire from the machine (representing the positive pole) put upon the
litmus paper, and the receiving point from the discharging train, repre-
senting the negative pole, upon the turmeric paper, a very few turns of
the machine sufficed to show the evolution of acid at the former, and
alkali at the latter, exactly in the manner effected by a volta-electric
current.
The pieces of litmus and turmeric paper were now placed each upon
a separate plate of glass, and connected by an insulated string four feet
long, moistened in the same solution of sulphate of soda: the terminal
decomposing wire points were placed upon the papers as before. On
working the machine, the same evolution of acid and alkali appeared as
in the former instance, and with equal readiness, notwithstanding that
the places of their appearance were four feet apart from each other.
Finally, a piece of string, seventy feet long, was used. It was insulated in
the air by suspenders of silk, so that the electricity passed through its
entire length: decomposition took place exactly as in former cases, alkali
and acid appearing at the two extremities in their proper places.
The negative point of the discharging train, the turmeric paper, and
the string were then removed; the positive point was left resting upon the
litmus paper, and the latter touched by a piece of moistened string held
in the hand. A few turns of the machine evolved acid at the positive
point as freely as before.
These experiments were varied so as to include the action of only one
metallic pole, but that not the pole connected with the machine. Tur-
meric paper was moistened in solution of sulphate of soda, placed upon
glass, and connected with the discharging train by a decomposing wire; a
RESEARCHES IN ELECTRICITY
465
piece of wet string was hung from it, the lower extremity of which was
brought opposite a point connected with the positive prime conductor of
the machine. The machine was then worked for a few turns, and alkali
immediately appeared at the point of the discharging train which rested
on the turmeric paper. Corresponding effects took place at the negative
conductor of a machine.
These cases are abundantly sufficient to show that electro-chemical
decomposition does not depend upon the simultaneous action of two
metallic poles, since a single pole might be used, decomposition ensue,
and one or other of the elements liberated, pass to the pole, according as
it was positive or negative. In considering the course taken by, and the
final arrangement of, the other element, I had little doubt that I should
find it had receded towards the other extremity, and that the air itself
had acted as a pole, an expectation which was fully confirmed in the
following manner.
FIG. 7.
A piece of turmeric paper, not more than 0.4 of an inch in length
and 0.5 of an inch in width, was moistened with sulphate of soda and
placed upon the edge of a glass plate opposite to, and about two inches
from, a point connected with the discharging train (Fig. 7); a piece of
tinfoil, resting upon the same glass plate, was connected with the ma-
chine, and also with the turmeric paper, by a decomposing wire a. The
machine was then worked, the positive electricity passing into the tur-
meric paper at the point p, and out at the extremity n. After forty or fifty
turns of the machine, the extremity n was examined, and the two points
or angles found deeply coloured by the presence of free alkali.
Arrangements were then made in which no metallic communication
with the decomposing matter was allowed, but both poles (if they might
FIG. 8.
466 MASTERWORKS OF SCIENCE
now be called by that name) formed of air only. A piece of turmeric paper
a, Fig. 8, and a piece of litmus paper b were dipped in solution of sulphate
of soda, put together so as to form one moist pointed conductor, and sup-
ported on wax between two needle points, one p connected by a wire
with the conductor of the machine,'and the other, n, with the discharging
train. The interval in each case between the points was about half an
inch: the positive point p was opposite the litmus paper; the negative
point n opposite the turmeric. The machine was then worked for a time,
upon which evidence of decomposition quickly appeared, for the point of
the litmus b became reddened from acid evolved there, and the point of
the turmeric a red from a similar and simultaneous evolution of alkali.
Upon turning the paper conductor round, so that the litmus point
should now give off the positive electricity, and the turmeric point receive
it, and working the machine for a short time, both the red spots disap-
peared, and as on continuing the action of the machine no red spot was
re-formed at the litmus extremity, it proved that in the first instance the
effect was not due to the action of brushes or mere electric discharges
causing the formation of nitric acid from the air.
If the combined litmus and turmeric paper in this experiment be
considered as constituting a conductor independent of the machine or the
discharging train, and the final places of the elements evolved be consid-
ered in relation to this conductor, then it will be found that the acid col-
lects at the negative or receiving end or pole of the arrangement, and the
alkali at the positive or delivering extremity.
Finally, a series of four small compound conductors, consisting of
litmus and turmeric paper (Fig. 9) moistened in solution of sulphate of
n a'ba'ba'ba'b p
v!±£=r=' — <z> <^> <o <n> — -s±y
FIG. 9.
soda, were supported on glass rods, in a line at a little distance from each
other, between the points p and n of the machine and discharging train,
so that the electricity might pass in succession through them, entering in
at the litmus points b, b and passing out at the turmeric points a, a. On
working the machine carefully, so as to avoid sparks and brushes, I soon
obtained evidence of decomposition in each of the moist conductors, for
all the litmus points exhibited free acid, and the turmeric points equally
showed free alkali.
These cases of electro-chemical decomposition are in their nature
exactly of the same kind as those affected under ordinary circumstances
by the voltaic battery, notwithstanding the great differences as to the
presence or absence, or at least as to the nature, of the parts usually called
poles; and also of the final situation of the elements eliminated at the
electrified boundary surfaces. They indicate at once an internal action of
the parts suffering decomposition, and appear to show that the power
RESEARCHES IN ELECTRICITY 467
which is effectual m separating the elements is exerted there, and not at
the poles.
Theory of Electro-chemical Decomposition
The extreme beauty and value of electro-chemical decompositions
have given to that power which the voltaic pile possesses of causing their
occurrence an interest surpassing that of any other of its properties; for
the power is not only intimately connected with the continuance, if not
with the production, of the electrical phenomena,, but it has furnished us
with the most beautiful demonstrations of the nature of many compound
bodies; has in the hands of Becquerel been employed in compounding
substances; has given us several new combinations, and sustains us with
the hope that when thoroughly understood it will produce many more.
What may be considered as the general facts of electro-chemical de-
composition are agreed to by nearly all who have written on the subject.
They consist in the separation of the decomposable substance acted upon
into its proximate or sometimes ultimate principles, whenever both poles
of the pile are in contact with that substance in a proper condition; in
the evolution of these principles at distant points, i.e. at the poles of the
pile, where they are either finally set free or enter into union with the
substance of the poles; and in the constant determination of the evolved
elements or principles to particular poles according to certain well-ascer-
tained laws.
But the views of men of science vary much as to the nature of the
action by which these effects are produced; and as it is certain that we
shall be better able to apply the power when we really understand the
manner in which it operates, this difference of opinion is a strong induce-
ment to further inquiry. I have been led to hope that the following inves-
tigations might be considered, not as an increase of that which is doubt-
ful, but a real addition to this branch of knowledge.
That electro-chemical decomposition does not depend upon any di-
rect attraction and repulsion of the poles (meaning thereby the metallic
terminations either of the voltaic battery or ordinary electrical machine
arrangements) upon the elements in contact with or near to them ap-
peared very evident from the experiments made in air, when the sub-
stances evolved did not collect about any poles, but, in obedience to the
direction of the current, were evolved, and I would say ejected, at the ex-
tremities of the decomposing substance. But notwithstanding the extreme
dissimilarity in the character of air and metals, and the almost total dif-
ference existing between them as to their mode of conducting electricity
and becoming charged with it, it might perhaps still be contended, al-
though quite hypothetical^, that the bounding portions of air were now
the surfaces or places of attraction, as the metals had been supposed to be
before. In illustration of this and other points, I endeavoured to devise an
arrangement by which I could decompose a body against a surface of
water, as well as against air or metal, and succeeded in doing so unexcep-
468
MASTERWORKS OF SCIENCE
tionably in the following manner. As the experiment for very natural
reasons requires many precautions to be successful, and will be referred
to hereafter in illustration of the views I shall venture to give, I must
describe it minutely.
A glass basin (Fig. 10), four inches in diameter and four inches deep,,
had a division of mica a fixed across the upper part so as to descend one
inch and a half below the edge, and be perfectly watertight^ the sides: a
plate of platina b, three inches wide, was put into the basin on one side
of the division a, and retained there by a glass block below, so that any
gas produced by it in a future stage of the experiment should not ascend
beyond the mica and cause currents in the liquid on that side. A strong
solution of sulphate of magnesia was carefully poured without splashing
into the basin, until it rose a little above the lower edge of the mica divi-
sion a, great care being taken that the glass or mica on the unoccupied or
FIG. 10.
c side of the division in the figure should not be moistened by agitation
of the solution above the level to which it rose. A thin piece of clean cork,
well wetted in distilled water, was then carefully and lightly placed on the
solution at the c side, and distilled water poured gently onto it until a
stratum the eighth of an inch in thickness appeared over the sulphate of
magnesia; all was then left for a few minutes, that any solution adhering
to the cork might sink away from it, or be removed by the water on
which it now floated; and then more distilled water was added in a simi-
lar manner, until it reached nearly to the top of the glass. In this way
solution of the sulphate occupied the lower part of the glass, and also the
upper on the right-hand side of the mica; but on the left-hand side of the
division a stratum of water from c to d, one inch and a half in depth,
reposed upon it, the two presenting, when looked through horizontally, a
comparatively definite plane of contact. A second platina pole e was ar-
ranged so as to be just under the surface of the water, in a position nearly
horizontal, a little inclination being given to it, that gas evolved during
RESEARCHES IN ELECTRICITY - 469
decomposition might escape: the part immersed was three inches and a
half long by one inch wide, and about seven eighths of an inch of water
intervened between it and the solution of sulphate of magnesia.
The latter pole e was now connected with" the negative end of a
voltaic battery, of forty pairs of plates four inches square, whilst the for-
mer pole b was connected with the positive end. There was action and
gas evolved at both poles; but from the intervention of the pure water,
the decomposition was very feeble compared to what the battery would
have effected in a uniform solution. After a little while (less than a min-
ute), magnesia also appeared at the negative side: it did not ma\e its
appearance at the negative metallic pole, but in the water, at the plane
where the solution and the water met; and on looking at it horizontally,
it could be there perceived lying in the water upon the solution, not rising
more than the fourth of an inch above the latter, whilst the water between
it and the negative pole was perfectly clear. On continuing the action, the
bubbles of hydrogen rising upwards from the negative pole impressed a
circulatory movement on the stratum of water, upwards in the middle,
and downwards at the side, which gradually gave an ascending form to
the cloud of magnesia in the part just under the pole, having an appear-
ance as if it were there attracted to it; but this was altogether an effect of
the currents, and did not occur until long after the phenomena looked for
were satisfactorily ascertained.
After a little while the voltaic communication was broken, and the
platina poles removed with as little agitation as possible from the water
and solution, for the purpose of examining the liquid adhering to them.
The pole e, when touched by turmeric paper, gave no traces of alkali, nor
could anything but pure water be found upon it. The pole b, though
drawn through a much greater depth and quantity of fluid, was found so
acid as to give abundant evidence to litmus paper, the tongue, and other
tests. Hence there had been no interference of alkaline salts in any way,
undergoing first decomposition, and then causing the separation of the
magnesia at a distance from the pole by mere chemical agencies. This ex-
periment was repeated again and again, and always successfully.
As, therefore, the substances evolved in cases of electro-chemical de-
composition may be made to appear against air — which, according to
common language, is not a conductor, nor is decomposed — or against
water, which is a conductor, and can be decomposed — as well as against
the metal poles, which are excellent conductors, but undecomposable —
there appears but little reason to consider the phenomena generally, as
due to the attraction or attractive powers of the latter, when used in the
ordinary way, since similar attractions can hardly be imagined in the
former instances.
If the wires of a galvanometer be terminated by plates, and these be
immersed in dilute acid, contained in a regularly formed rectangular glass
trough, connected at each end with a voltaic battery by poles*equal to the
section of the fluid, a part of the electricity will pass through the instru-
ment and cause a certain deflection. And if the plates are always retained
470 MASTERWORKS OF SCIENCE
at the same distance from each other and from the sides of the trough,
are always parallel to each other, and uniformly placed relative to the
fluid, then, whether they are immersed near the middle of the decom-
posing solution or at one end, still the instrument will indicate the same
deflection, and consequently the same electric influence.
It is very evident that when the width of the decomposing conductor
varies, as is always the case when mere wires or plates, as poles, are
dipped into or are surrounded by solution, no constant expression can be
given as to the action upon a single particle placed in the course of the
current, nor any conclusion of use, relative to the supposed attractive or
repulsive force of the poles, be drawn. The force will vary as the distance
from the pole varies; as the particle is directly between the poles or more
or less on one side; and even as it is nearer to or further from the sides of
the containing vessels, or as the shape of the vessel itself varies; and, in
fact, by making variations in the form of the arrangement, the force upon
any single particle may be made to increase, or diminish, or remain con-
stant, whilst the distance between the particle and the pole shall remain
the same; or the force may be made to increase, or diminish, or remain
constant, either as the distance increases or as it diminishes.
From numerous experiments, I am led to believe the following gen-
eral expression to be correct; but I purpose examining it much further,
and would therefore wish not to be considered at present as pledged to
its accuracy. The sum of chemical decomposition is constant for any sec-
tion taken across a decomposing conductor, uniform in its nature, at
whatever distance the poles may be from each other or from the section;
or however that section may intersect the currents, whether directly
across them or so oblique as to reach almost from pole to pole, or whether
it be plane, or curved, or irregular in the utmost degree; provided the
current of electricity be retained constant in quantity, and that the section
passes through every part of the current through the decomposing con-
ductor.
I have reason to believe that the statement might be made still more
general, and expressed thus: That for a constant quantity of electricity,
whatever the decomposing conductor may be, whether water, saline solu-
tions, acids, fused bodies, etc.f the amount of electro-chemical action is
also a constant quantity, i.e. would always be equivalent to a standard
chemical effect founded upon ordinary chemical affinity. I have this in-
vestigation in hand, with several others, and shall be prepared to give it
in the next part of these Researches.
Electro-chemical decomposition is well known to depend essentially
upon the current of electricity. I have shown that in certain cases the de-
composition is proportionate to the quantity of electricity passing, what-
ever may be its intensity or its source, and that the same is probably true
for all cases, even when the utmost generality is taken on the one hand
and great precision of expression on the other.
Passing to the consideration of electro-chemical decomposition, it ap-
pears to me that the effect is produced by an internal corpuscular action,
RESEARCHES IN ELECTRICITY 471
exerted according to the direction of the electric current, and that it is
due to a force either super added to or giving direction to the ordinary
chemical affinity of the bodies present. The body under decomposition
may be considered as a mass of acting particles, all those which are in-
cluded in the course of the electric current contributing to the final effect;
and it is because the ordinary chemical affinity is relieved, weakened, or
partly neutralised by the influence of the electric current in one direction
parallel to the course of the latter, and strengthened or added to in the
opposite direction, that the combining particles have a tendency to pass
in opposite courses..
In this view the effect is considered as essentially dependent upon the
mutual chemical affinity of the particles of opposite kinds. Particles a a,
Fig. ii, could not be transferred or travel from one pole N towards the
other P unless they found particles of the opposite kind b b, ready to pass
in the contrary direction: for it is by virtue of their increased affinity for
those particles, combined with their diminished affinity for such as are
behind them in their course, that they are urged forward: and when any
one particle a} Fig. 12, arrives at the pole, it is excluded or set free, be-
B <z
© o
FIG. n. FIG. 12. '
cause the particle b of the opposite kind, with which it was the moment
before in combination, has, under the .superinducing influence of the cur-
rent, a greater attraction for the particle a, which is before it in its course,
than for the particle a, towards which its affinity has been weakened.
As far as regards any single compound particle, the case may be con-
sidered as analogous to one of ordinary decomposition, for in Fig. 12, a
may be conceived to be expelled from the compound a b by the superior
attraction of a for b, that superior attraction belonging to it in conse-
quence of the relative position of a b and a to the direction of the axis of
electric power superinduced by the current. But as all the compound par-
ticles in the course of the current, except those actually in contact with
the poles, act conjointly, and consist of elementary particles, which whilst
they are in one direction expelling are in the other being expelled, the
case becomes more complicated but not more difficult of comprehension.
It is not here assumed that the acting particles must be in a right line
between the poles. The lines of action which may be supposed to repre-
sent the electric currents passing through a decomposing liquid have in
many experiments very irregular forms; and even in the simplest case of
two wires or points immersed as poles in a drop or larger single portion
of fluid, these lines must diverge rapidly from the poles; and the direction
in which the chemical affinity between particles is most powerfully modi-
fied will vary with the direction of these lines, according constantly with
them. But even in reference to these lines or currents, it is not supposed
that the particles which mutually affect each other must of necessity be
472 MASTERWORKS OF SCIENCE
parallel to them, but only that they shall accord generally with their direc-
tion. Two particles, placed in a line perpendicular to the electric current
passing in any particular place, are not supposed to have their ordinary
chemical relations towards each other affected; but as the line joining
them is inclined one way to the current their mutual affinity is increased;
as it is inclined in the other direction it is diminished; and the effect is
a maximum, when that line is parallel to the current.
That the actions, o£ whatever kind they may be, take place frequently
in oblique directions is evident from the circumstance of those particles
being included which in numerous cases are not in a line between the
poles. Thus, when wires are used as poles in a glass of solution, the de-
compositions and recompositions occur to the right or left of the direct
line between the poles, and indeed in every part to which the currents
extend, as is proved by many experiments, and must therefore often occur
between particles obliquely placed as respects the current itself; and when
a metallic vessel containing the solution is made one pole, whilst a mere
point or wire is used for the other, the decompositions and recomposi-
tions must frequently be still more oblique to the course of the currents.
I hope I have now distinctly stated, although in general terms, the
view I entertain of the cause of electro-chemical decomposition, as jar as
that cause can at present be traced and understood. 1 conceive the effects
to arise from forces which are internal, relative to the matter under de-
composition:— and not external, as they might be considered, if directly
dependent upon the poles. I suppose that the effects are due to a modi-
fication, by the electric current, of the chemical affinity of -the particles
through or by which that current is passing, giving them the power of
acting more forcibly in one direction than in another, and consequently
making them travel by a series of successive decompositions and recom-
positions in opposite directions, and finally causing their expulsion or ex-
clusion at the boundaries of the body under decomposition, in the direc-
tion of the current, and that in larger or smaller quantities, according as
the current is more or less powerful. I think, therefore, it would be more
philosophical, and more directly expressive of the facts, to speak of such
a body in relation to the current passing through it, rather than to the
poles, as they are usually called, in contact with it; and say that whilst
under decomposition, oxygen, chlorine, iodine, acids, etc., are rendered
at its negative extremity, and combustibles, metals, alkalies, bases, etc., at
its positive extremity. I do not believe that a substance can be transferred
in the electric current beyond the point where it ceases to find particles
with which it can combine; and I may refer to the experiments made in
air, and in water, already quoted, for facts illustrating these views in the
first instance.
The theory I have ventured to put forth appears to me to explain all
the prominent features of electro-chemical decomposition in a -satisfactory
manner.
In the first place, it explains why, in all ordinary cases, the evolved
substances appear only at the poles; for the poles are the limiting surfaces
RESEARCHES IN ELECTRICITY 473
of the decomposing substance, and except at them, every particle finds
other particles having a contrary tendency with which it can combine.
Then it explains why, in numerous cases, the elements or evolved
substances are not retained by the poles; and this is no small difficulty in
those theories -which refer the decomposing effect directly to the attrac-
tive power of the poles. If, in accordance with the usual theory, a piece of
platina be supposed to have sufficient power to attract a particle of hydro-
gen from the particle of oxygen with which it was the instant before
combined, there seems no sufficient reason, nor any fact, except those to
be explained, which shows why it should not, according to analogy with
all ordinary attractive forces, as those of gravitation, magnetism, cohesion,
chemical affinity, etc., retain that particle which it had just before taken
from a distance and from previous combination. Yet it does not do so,
but allows it to escape freely. Nor does this depend upon its assuming the
gaseous state, for acids and alkalies, etc., are left equally at liberty to
diffuse themselves through the fluid surrounding the pole, and show no
particular tendency to combine with or adhere to the latter.
But in the theory that I have just given, the effect appears to be a
natural consequence of the action: the evolved substances are expelled
from the decomposing mass, not drawn out by an attraction which ceases
to act on one particle without any assignable reason, while it continues to
act on another of the same kind: and whether the poles be metal, water,
or air, still the substances are evolved, and are sometimes set free, whilst
at others they unite to the matter of the poles, according to the chemical
nature of the latter, i.e. their chemical relation to those particles which
are leaving the substance under operation.
The theory accounts for the transfer of elements in a manner which
seems to me at present to leave nothing unexplained; and it was, indeed,
the phenomena of transfer in the numerous cases of decomposition of
bodies rendered fluid by heat, which, in conjunction with the experiments
in air, led to its construction.
Chloride of silver furnishes a beautiful instance, especially when de-
composed by silver-wire poles. Upon fusing a portion of it on a piece of
glass, and bringing the poles into contact with it, there is abundance of
silver evolved at the negative pole, and an equal abundance absorbed at
the positive pole, for no chlorine is set free: and by careful management,
the negative wire may be withdrawn from the fused globule as the silver
is reduced there, the latter serving as the continuation of the pole, until a
wire or thread of revived silver, five or six inches in length, is produced;
at the same time the silver at the positive pole is as rapidly dissolved by
the chlorine, which seizes upon it, so that the wire has to be continually
advanced as it is melted away. The whole experiment includes the action
of only two elements, silver and chlorine, and illustrates in a beautiful
manner their progress in opposite directions, parallel to the electric cur-
rent, which is for the time giving a uniform general direction to their
mutual affinities.
According to my theory, an element or a substance not decomposable
474 MASTERWORKS OF SCIENCE
under the circumstances of the experiment (as, for instance, a dilute acid
or alkali) should not be transferred, or pass from pole to pole, unless it
be in chemical relation to some other element or substance tending to
pass in the opposite direction, for the effect is considered as essentially
due to the mutual relation of such particles.
In support of these arguments, it may be observed that as yet no de-
termination of a substance to a pole, or tendency to obey the electric cur-
rent, has been observed (that I am aware of) in cases of mere mixture; i.e.
a substance diffused through a fluid, but having no sensible chemical
affinity with it or with substances that may be evolved from it during the
action, does not in any case seem to be affected by the electric current.
Pulverised charcoal was diffused through dilute sulphuric acid, and sub-
jected with the solution to the action of a voltaic battery, terminated by
platina poles; but not the slightest tendency of the charcoal to the nega-
tive pole could be observed. Sublimed sulphur was diffused through simi-
lar acid, and submitted to the same action, a silver plate being used as
the negative pole; but the sulphur had no tendency to pass to that pole,
the silver was not tarnished, nor did any sulphuretted hydrogen appear.
The case of magnesia and water, with those * of comminuted metals in
certain solutions, is also of this kind; and, in fact, substances which have
the instant before been powerfully determined! towards the pole, as mag-
nesia from sulphate of magnesia, become entirely indifferent to it the
moment they assume their independent state, and pass away, diffusing
themselves through the surrounding fluid.
It may be expressed as a general consequence that the more directly
bodies are opposed to each other in chemical affinity, the more ready is
their separation from each other in cases of electro-chemical decomposi-
tion, i.e. provided other circumstances, as insolubility, deficient conduct-
ing power, proportions, etc., do not interfere. This is well known to be
the case with water and saline solutions; and I have found it to be equally
true with dry chlorides, iodides, salts, etc., rendered subject to electro-
chemical decomposition by fusion. So that in applying the voltaic battery
for the purpose of decomposing bodies not yet resolved into forms of
matter simpler than their own, it must be remembered that success may
depend not upon the weakness, or failure upon the strength, of the
affinity by which the elements sought for are held together, but contrari-
wise; and then modes of application may be devised by which, in associa-
tion with ordinary chemical powers, and the assistance of fusion, we may
be able to penetrate much further than at present into the constitution of
our chemical elements.
Some of the most beautiful and surprising cases of electro-chemical
decomposition and transfer which Sir Humphry Davy described in his
celebrated paper were those in which acids were passed through alkalies,
and alkalies or earths through acids; and the way in which substances
having the most powerful attractions for each other were thus prevented
from combining, or, as it is said, had their natural affinity destroyed or
suspended throughout the whole of the circuit, excited the utmost aston-
RESEARCHES IN ELECTRICITY 475
ishment. But if I be right in the view I have taken of the effects, it will
appear that that which made the wonder is in fact the essential condition
of transfer and decomposition, and that the more alkali there is in the
course of an acid, the more will the transfer of that acid be facilitated
from pole to pole; and perhaps a better illustration of the difference be-
tween the theory I have ventured and those previously existing cannot be
offered than the views they respectively give of such facts as these.
///. ELECTRO-CHEMICAL DECOMPOSITION— Continued
THE THEORY which I believe to be a true expression of the facts of electro-
chemical decomposition, and which I have therefore detailed in a former
part of these Researches, is so much at variance with those previously ad-
vanced that I find the greatest difficulty in stating results, as I think, cor-
rectly, whilst limited to the use of terms which are current with a certain
accepted meaning. Of this kind is the term pole, with its prefixes of posi-
tive and negative, and the attached ideas of attraction and repulsion. The
general phraseology is that the positive pole attracts oxygen, acids, etc., or,
more cautiously, that it determines their evolution upon its surface; and
that the negative pole acts in an equal manner upon hydrogen, combusti-
bles, metals, and bases. According to my view, the determining force is
not at the poles, but within the body under decomposition; and the
oxygen and acids are rendered at the negative extremity of that body>
whilst hydrogen, metals, etc., are evolved at the positive extremity.
To avoid, therefore, confusion and circumlocution, and for the sake
of greater precision of expression than I can otherwise obtain, I have de-
liberately considered the subject with two friends, and with their assist-
ance and concurrence in framing them, I purpose henceforward using cer-
tain other terms, which I will now define. The poles, as they are usually
called, are only the doors or ways by which the electric current passes into
and out of the decomposing body; and they, of course, when in contact
with that body, are the limits of its extent in the direction of the current.
The term has been generally applied to the metal surfaces in contact with"
the decomposing substance; but whether philosophers generally would
also apply it to the surfaces of air and water, against which I have effected
electro-chemical decomposition, is subject to doubt. In place of the term
pole, I propose using that of 'Electrode, and I mean thereby that substance,
or rather surface, whether of air, water, metal, or any other body, which
bounds the extent of the decomposing matter in the direction of the
electric current.
The surfaces at which, according to common phraseology, the electric
current enters and leaves a decomposing body are most important places
of action, and require to be distinguished apart from the poles, with
which they are mostly, and the electrodes, with which they are always, in
contact. Wishing for a natural standard of electric direction to which I
might refer these, expressive of their difference and at the same time free
476 MASTERWORKS OF SCIENCE
from all theory, I have thought it might be found in the earth. If the
magnetism of the earth be due to electric currents passing round it, the
latter must be in a constant direction, which, according to present usage
of speech, would be from- east to west, or, which will strengthen this help
to the memory, that in which the sun appears to move. If in any case of
electro-decomposition we consider the decomposing body as placed so
that the current passing through it shall be in the same direction, and
parallel to that supposed to exist in the earth, then the surfaces at which
the electricity is passing into and out of the substance would have an in-
variable reference, and exhibit constantly the same relations of powers.
Upon this notion we purpose calling that towards the east the anode, and
that towards the west the cathode; and whatever changes may take place
in our views of the nature of electricity and electrical action, as they must
affect the natural standard referred to, in the same direction, and to an
equal amount with any decomposing substances to which these terms
may at any time be applied, there seems no reason to expect that they
will lead to confusion or tend in any way to support false views. The
anode is therefore that surface at which the electric current, according to
our present expression, enters: it is the negative extremity of the decom-
posing body; is where oxygen, chlorine, acids, etc., are evolved; and is
against or opposite the positive electrode. The cathode is that surface at
which the current leaves the decomposing body, and is its positive ex-
tremity; the combustible bodies, metals, alkalies, and bases, are evolved
there, and it is in contact with the negative electrode.
I shall have occasion in these Researches, also, to class bodies together
according to certain relations derived from their electrical actions; and
wishing to express those relations without at the same time involving the
expression of any hypothetical views, I intend using the following names
and terms. Many bodies are decomposed directly- by the electric current,
their elements being set free; these I propose to call electrolytes. Water,
therefore, is an electrolyte. The bodies which, like nitric or sulphuric
acids, are decomposed in a secondary manner are not included under this
term. Then, for electro-chemically decomposed, I shall often use the term
electrolysed, derived in the same way, and implying that the body spoken
of is separated into its components under the influence of electricity: it is
analogous in its sense and sound to analyse, which is derived in a similar
manner. The term electrolytical will be understood at once: muriatic acid
is electrolytical, boracic acid is not.
Finally, I require a term to express those bodies which can pass to
the electrodes, or, as they are usually called, the poles. Substances are fre-
quently spoken of as being electro-negative or electro-positive, according
as they go under the supposed influence of a direct attraction to the posi-
tive or negative pole. But these terms are much too significant for the use
to which I should have to put them; for though the meanings are perhaps
right, they are only hypothetical, and may be wrong; and then, through a
very imperceptible, but still very dangerous, because continual, influence,
they do great injury to science, by contracting and limiting the habitual
RESEARCHES IN ELECTRICITY 477
views of those engaged in pursuing it. I propose to distinguish such
bodies by calling those anions which go to the anode of the decomposing
body; and those passing to the cathode, cations; and when I have occasion
to speak of these together, I shall call them ions. Thus the chloride of
lead is an electrolyte -, and when electrolysed evolves the two ionst chlorine
and lead, the former being an anion and the latter a cation.
On a new Measurer of Volta-electricity
I have already said, when introducing my theory of electro-chemical
decomposition, that the chemical decomposing action of a current is con-
stant for a constant quantity of electricity, notwithstanding the greatest
variations in its sources, in its intensity, in the size of the electrodes used,
in the nature of the conductors (or non-conductors) through which it is
passed, or in other circumstances. The conclusive proofs of the truth of
these statements shall be given almost immediately.
I endeavoured upon this law to construct an instrument which should
measure out the electricity passing through it, and which, being inter-
posed in the course of the current used in any particular experiment,
should serve at pleasure, either as a comparative standard of effect or as a
positive measurer of this subtile agent.
There is no substance better fitted, under ordinary circumstances, to
be the indicating body in such an instrument than water; for it is de-
composed with facility when rendered a better conductor by the addition
of acids or salts; its elements may in numerous cases be obtained and col-
lected without any embarrassment from secondary action, and, being gas-
eous, they are in the best physical condition for separation and measure-
ment.
The first precaution needful in the construc-
tion of the instrument was to avoid the recombi-
nation of the evolved gases, an effect which the
positive electrode has been found so capable of
producing. For this purpose various forms of de-
composing apparatus were used. The first con-
sisted of straight tubes, each containing a plate
and wire of platina soldered together by gold, and
fixed hermetically in the glass at the closed ex-
tremity of the tube (Fig. 13). The tubes were
about eight inches long, 0.7 of an inch in diameter,
and graduated. The platina plates were about an
_ inch long, as wide as the tubes would permit, and
P adjusted as near to the mouths of the tubes as was p
consistent with the safe collection of the gases
evolved. In certain cases, where it was required to evolve the elements
upon as small a surface as possible, the metallic extremity, instead of
being a plate, consisted of the wire bent into the form of a ring (Fig.
478 MASTERWORKS OF SCIENCE
14). When these tubes were used as measurers, they were filled with the
dilute sulphuric acid, inverted in a basin of the same liquid (Fig. 15), and
placed in an inclined position, with their mouths near to each other, that
as little decomposing matter should intervene as possible; and also in such
a direction that the platina plates should be in vertical planes.
FIG. 15.
Another form of apparatus is that delineated (Fig. 16). The tube is
bent in the middle; one end is closed; in that end is fixed a wire and
plate, a, proceeding so far downwards that, when in the position figured,
it shall be as near to the angle as possible, consistently with the collection,
at the closed extremity of the tube, of all the gas evolved against it. The
plane of this plate is also perpendicular. The other metallic termination,
b, is introduced at the time decomposition is to be effected, being
FIG. 16.
brought as near the angle as possible, without causing any gas to pass
from it towards the closed end of the instrument. The gas evolved against
it is allowed to escape.
The third form of apparatus contains both electrodes in the same
tube; the transmission, therefore, of the electricity and the consequent
decomposition is far more rapid than in the separate tubes. The resulting
gas is the sum of the portions evolved at the two electrodes, and the in-
strument is better adapted than either of the former as a measurer of the
quantity of voltaic electricity transmitted in ordinary cases. It consists of
a straight tube (Fig. 17) closed at the upper extremity, and graduated,
through the sides of which pass platina wires (being fused into the glass),
which are connected with two plates within. The tube is fitted by grind-
ing into one mouth of a double-necked bottle. If the latter be one half or
two thirds full of the dilute sulphuric acid, it will, upon inclination of
the whole, flow into the tube and fill it. When an electric current is passed
through the instrument, the gases evolved against the plates collect in the
RESEARCHES IN ELECTRICITY
479
uPPer portion of the tube and are not subject to the recombining power
of the platina.
FIG. 17.
Another form of the instrument is given in Fig. 18.
A fifth form is delineated (Fig. 19). This I have found exceedingly
useful in experiments continued in succession for days together, and
where large quantities of indicating gas were to be collected. It is fixed on
a weighted foot, and has the form of a small retort containing the two
electrodes: the neck is narrow and sufficiently long to deliver gas issuing
from it into a jar placed in a small pneumatic trough. The electrode
chamber, sealed hermetically at the part held in the stand, is five inches
in length and 0.6 of an inch in diameter; the neck about nine inches in
length and 0.4 of an inch in diameter internally. The figure will fully
indicate the construction.
FIG. 1 8.
FIG. 19.
Next to the precaution of collecting the gases, if mingled, out of
contact with the platina was the necessity of testing the law of a defi-
nite electrolytic action, upon water at least, under all varieties of condi-
tion; that, with a conviction of its certainty, might also be obtained a
knowledge of those interfering circumstances which would require to be
practically guarded against.
The first point investigated was the influence or indifference of ex-
480 MASTERWORKS OF SCIENCE
tensive variations in the size of the electrodes, for which purpose instru-
ments like those last described were used. One of these had plates 0.7 of
an inch wide and nearly four inches long; another had plates only 0.5 of
an inch wide and 0.8 of an inch long; a third had wires 0.02 of an inch
in diameter and three inches long; and a fourth, similar wires only half
an inch in length. Yet when these were filled with dilute sulphuric acid,
and, being placed in succession, had one common current of electricity
passed through them, very nearly the same quantity of gas was evolved in
all. The difference was sometimes in favour of one and sometimes on the
side of another; but the general result was that the largest quantity of
gases was evolved at the smallest electrodes, namely, those consisting
merely of platina wires.
Experiments of a similar kind were made with the single-plate
straight tubes, and also with the curved tubes, with similar consequences;
and when these, with the former tubes, were arranged together in various
ways, the result, as to the equality of action of large and small metallic
surfaces when delivering and receiving the same current of electricity,
was constantly the same. As an illustration, the following numbers are
given. An instrument with two wires evolved 74.3 volumes of mixed
gases; another with plates, 73.25 volumes; whilst the sum of the oxygen
and hydrogen in two separate tubes amounted to 73.65 volumes. In an-
other experiment the volumes were 55.3, 55.3, and 54.4.
But it was observed in these experiments that in single-plate tubes
more hydrogen was evolved at the negative electrode than was propor-
tionate to the oxygen at the positive electrode; and generally, also, more
than was proportionate to the oxygen and hydrogen in a double-plate
tube. Upon more minutely examining these effects, I was led to refer
them, and also the differences between wires and plates, to the solubility
' of the gases evolved, especially at the positive electrode.
With the intention of avoiding this solubility of the gases as much
as possible, I arranged the decomposing plates in a vertical position, that
the bubbles might quickly escape upwards and that the downward cur-
rents in the fluid should not meet ascending currents of gas. This pre-
caution I found to assist greatly in producing constant results, and espe-
cially in experiments to be hereafter referred to, in which other liquids
than dilute sulphuric acid, as for instance solution of potash, were used.
The irregularities in the indications of the measurer proposed, aris-
ing from the, solubility just referred to, are but small, and may be very
nearly corrected by comparing the results of two or three experiments.
They may also be almost entirely avoided by selecting that solution which
is found to favour them in the least degree; and still further by collecting
the hydrogen only, and using that as the indicating gas; for, being much
less soluble than oxygen, being evolved with twice the rapidity and in
larger bubbles, it can be collected more perfectly and in greater purity.
From the foregoing and many other experiments, it results that vari-
ation in the size of the electrodes causes no variation in the chemical
action of a given quantity of electricity upon water*
RESEARCHES IN ELECTRICITY 481
The next point in regard to which the principle of constant electro-
chemical action was tested was variation of intensity. In the first place,,
the preceding experiments were repeated, using batteries of an equal
number of plates, strongly and weakly charged; but the results were alike.
They were then repeated, using batteries sometimes containing forty and
at other times only five pairs of plates; but the results were still the same.
Variations therefore in the intensity, caused by difference in the strength
of charge or in the number of alternations used, produced no difference as
to the equal action of large and small electrodes.
The third point, in respect to which the principle of equal electro-
chemical action on water was tested, was variation of the strength of the'
solution used. In order to render the water a conductor, sulphuric acid
had been added to it; and it did not seem unlikely that this substance,
with many others, might render the water more subject to decomposi-
tion, the electricity remaining the same in quantity. But such did not
prove to be the case. Diluted sulphuric acid, of different strengths, was
introduced into different decomposing apparatus and submitted simulta-
neously to the action of the same electric current. Slight differences oc-
curred, as before, sometimes in one direction, sometimes in another; but
the final result was that exactly the same quantity of water was decom-
posed in all the solutions by the same quantity of electricity, though the
sulphuric acid in some was seventyfold what it was in others. The
strengths used were of specific gravity 1.495, and downwards.
Although not necessary for the practical use of the instrument I am
describing, yet as connected with the important point of constant electro-
chemical action upon water, I now investigated the effects produced by
an electric current passing through aqueous solutions of acids, salts, and
compounds, exceedingly different from each other in their nature, and
found them to yield astonishingly uniform results. But many of them
which are connected with a secondary action will be more usefully de-
scribed hereafter.
When solutions of caustic potassa or soda, or sulphate of magnesia,,
or sulphate of soda were acted upon by the electric current, just as much
oxygen and hydrogen was evolved from them as from the diluted sul-
phuric acid, with which they were compared. When a solution of am-
monia, rendered a better conductor by sulphate of ammonia, or a solution
of subcarbonate of potassa was experimented with, the hydrogen evolved
was in the same quantity as that set free from the diluted sulphuric acid
with which they were compared. Hence changes in the nature of the
solution do not alter the constancy of electrolytic action upon water,
I consider the foregoing investigation as sufficient to prove the very
extraordinary and important principle with respect to WATER, that when
subjected to the influence of the electric current, a quantity of it is de-
composed exactly proportionate to the quantity of electricity which has
passed, notwithstanding the thousand variations in the conditions and
circumstances under which it may at the time be placed; and further, that
when the interference of certain secondary effects, together with the solu-
482 MASTERWORKS OF SCIENCE
tion or recombination of the gas and the evolution of air, is guarded
against, the products of the decomposition may be collected with such
accuracy as to afford a very excellent and valuable measurer of the elec-
tricity concerned in their evolution.
The forms of instrument which I have given, Figs. 17, 18, 19, are
probably those which will be found most useful, as they indicate the
quantity of electricity by the largest volume of gases, and cause the least
obstruction to the passage of the current. The fluid which my present
experience leads me to prefer is a solution of sulphuric acid of specific
gravity about 1.336, or from that to 1.25; but it is very essential that there
should be no organic substance, nor any vegetable acid, nor other body,
which, by being liable to the action of the oxygen or hydrogen evolved at
the electrodes, shall diminish their quantity or add other gases to them.
In many cases when the instrument is used as a comparative standard,
or even as a measurer, it may be desirable to collect the hydrogen only,
as being less liable to absorption or disappearance in other ways than the
oxygen; whilst at the same time its volume is so large as to render it a
good and sensible indicator. In such cases the first and second form oi
apparatus have been used, Figs. 15, 16. The indications obtained were
very constant, the variations being much smaller than in those forms of
apparatus collecting both gases; and they can also be procured when solu-
tions are used in comparative experiments, which, yielding no oxygen or
only secondary results of its action, can give no indications if the educts
at both electrodes be collected. Such is the case when solutions of am-
monia, muriatic acid, chlorides, iodides, acetates or other vegetable salts,
etc., are employed.
In a few cases, as where solutions of metallic salts liable to reduction
at the negative electrode are acted upon, the oxygen may be advanta-
geously used as the measuring substance. This is the case, for instance,
with sulphate of copper.
There are therefore two general forms of the instrument which I
submit as a measurer of electricity; one in which both the gases of the
water decomposed are collected, and the other in which a single gas, as
the hydrogen only, is used. When referred to as a comparative instrument
(a use I shall now make of it very extensively), it will not often require
particular precaution in the observation; but when used as an absolute
measurer, it will be needful that the barometric pressure and the tempera-
ture be taken into account, and that the graduation of the instruments
should be to one scale; the hundredths and smaller divisions, of a cubical
inch are quite fit for this purpose, and the hundredth may be very con-
veniently taken as Indicating a DEGREE of electricity.
It can scarcely be needful to point out further than has been done
how this instrument is to be used. It is to be introduced into the course
of the electric current, the action of which is to be exerted anywhere else,
and if 60° or 70° of electricity are to be measured out, either in one or
several portions, the current, whether strong or weak, is to be continued
until the gas in the tube occupies that number of divisions or hundredths
RESEARCHES IN ELECTRICITY 483.
of a cubical inch. Or if a quantity competent to produce a certain effect
is to be measured, the effect is to be obtained, and then the indication
read off. In exact experiments it is necessary to correct the volume of gas
for changes in temperattfre and pressure, and especially for moisture. For
the latter object the volta-electrometer (Fig. 19) is most accurate, as its
gas can be measured over water, whilst the others retain it over acid or
saline solutions.
I have not hesitated to apply the term degree in analogy with the use
made of it with respect to another most important imponderable agent,
namely, heat; and as the definite expansion of air, water, mercury, etc., is
there made use of to measure heat, so the equally definite evolution of
gases is here turned to a similar use for electricity.
" The instrument offers the only actual measurer of voltaic electricity
which we at present possess. For without being at all affected by varia-
tions in time or intensity, or alterations in the current itself, of any kind,
or from any cause, or even of intermissions of action, it takes note with
accuracy of the quantity of electricity which has passed through it, and
reveals that quantity by inspection; I have therefore named it a VOLTA-
ELECTROMETER.
On the primary or secondary character of the bodies evolved
at the Electrodes
Before the volta-electrometer could be employed in determining, as a
general law, the constancy of electro-decomposition, it became necessary
to examine a distinction, already recognised among scientific men, rela-
tive to the products of that action, namely, their primary or secondary
character; and, if possible, by some general rule or principle, to decide
when they were of the one or the other kind. It will appear hereafter that
great mistakes respecting electro-chemical action and its consequences
have arisen from confounding these two classes of results together.
When a substance under decomposition yields at the electrodes those
bodies uncombined and unaltered which the electric current has sepa-
rated, then they may be considered as primary results, even though them-
selves compounds. Thus the oxygen and hydrogen from water are primary
results; and so also are the acid and alkali (themselves compound bodies)
evolved from sulphate of soda. But when the substances separated by the
current are changed at the electrodes before their appearance, then they
give rise to secondary results, although in many cases the bodies evolved
are elementary.
These secondary results occur in two ways, being sometimes due to
the mutual action of the evolved substance and the matter of the elec-
trode, and sometimes to its action upon the substances contained in the
body itself under decomposition. Thus, when carbon is made the positive
electrode in dilute sulphuric acid, carbonic oxide and carbonic acid occa-
sionally appear there instead of oxygen; for the latter, acting upon the
matter of the electrode, produces these secondary results. Or if the posi-
484 MASTERWORKS OF SCIENCE
tive electrode, in a solution of nitrate or acetate of lead, be platina, then
peroxide of lead appears there, equally a secondary result with the former,
but now depending upon an action of the oxygen on a substance in the
solution. Again, when ammonia is decomposed by platina electrodes, ni-
trogen appears at the anode; but though an elementary body, it is a sec-
ondary result in this case, being derived from the chemical action of the
oxygen electrically evolved there upon the ammonia in the surrounding
solution. In the same manner, when aqueous solutions of metallic salts
are decomposed by the current, the metals evolved at the cathode, though
elements, are always secondary results, and not immediate consequences
of the decomposing power of the electric current.
But when we take to our assistance the law of constant electro-chemi-
cal action already proved with regard to water, and which I hope to ex-
tend satisfactorily to all bodies, and consider the quantities as well as the
nature of the substances set free, a generally accurate judgment of the
primary or secondary character of the results may be formed: and this
important point, so essential to the theory of electrolysation, since it
decides what are the particles directly under the influence of the current
(distinguishing them from such as are not affected) and what are the
results to be expected, may be established with such degree of certainty as
to remove innumerable ambiguities and doubtful considerations from this
branch of the science.
Let us apply these principles to the case of ammonia, and the sup-
posed determination of nitrogen to one or the other electrode. A pure
strong solution of ammonia is as bad a conductor, and therefore as little
liable to electrolysation, as pure water; but when sulphate of ammonia
is dissolved in it, the whole becomes a conductor; nitrogen almost and
occasionally quite pure is evolved at the anode, and hydrogen at the
cathode; the ratio of the volume of the former to that of the latter varying,
but being as i to about 3 or 4. This result would seem at first to imply
that the electric current had decomposed ammonia, and that the nitrogen
had been determined towards the positive electrode. But when the elec-
tricity used was measured out by the volta-electrometer, it was found that
the hydrogen obtained was exactly in the proportion which would have
been supplied by decomposed water, whilst the nitrogen had no certain
or constant relation whatever. When, upon multiplying experiments, it
was found that, by using a stronger or weaker solution, or a more or less
powerful battery, the gas evolved at the anode was a mixture of oxygen
and nitrogen, varying both in proportion and absolute quantity, whilst
the hydrogen at the cathode remained constant, no doubt could be enter-
tained that the nitrogen at the anode was a secondary r.esult, depending
upon the chemical action of the nascent oxygen, determined to that surface
by the electric current, upon the ammonia in solution. It was the water,
therefore, which was electrolysed, not the ammonia.
I have experimented upon many bodies, with a view to determine
whether the results were primary or secondary. I have been surprised to
find how many of them, in ordinary cases, are of the latter class, and how
RESEARCHES IN ELECTRICITY 485
frequently water is the only body electrolysed in instances where other
substances have been supposed to give way. Some of these results I will
give in as few words as possible.
Nitric acid. — When very strong, it conducted well, and yielded oxy-
gen at the positive electrode. No gas appeared at the negative electrode;
but nitrous acid, and apparently nitric oxide, was formed there, which,
dissolving, rendered the acid yellow or red, and at last even effervescent,
from the spontaneous separation of nitric oxide. Upon diluting the acid
with its bulk or more of water, gas appeared at the negative electrode. Its
quantity could be varied by variations, either in the strength of the acid
or of the voltaic current: for that acid from which no gas separated at the
cathode, with a weak voltaic battery, did evolve gas there with a stronger;
and that battery which evolved no gas there with a strong acid, did cause
its evolution with an acid more dilute. The gas at the anode was always
oxygen; that at the cathode hydrogen. When the quantity of products was
examined by the volta-electrometer, the oxygen, whether from strong or
weak acid, proved to be in the same proportion as from water. When the
acid was diluted to specific gravity 1.24, or less, the hydrogen also proved
to be the same in quantity as from water. Hence I conclude that the nitric
acid does not undergo electrolysation, but the water only; that the oxygen
at the anode is always a primary result, but that the products at the
cathode are often secondary, and due to the reaction of the hydrogen upon
the nitric acid.
Nitre. — A solution of this salt yields very variable results, according
as one or other form of tube is used, or as the electrodes are large or small.
Sometimes the whole of the hydrogen of the water decomposed may be
obtained at the negative electrode; at other times, only a part of it, because
of the ready formation of secondary results. The solution is a very excel-
lent conductor of electricity.
Muriatic acid. — A strong solution gave hydrogen at the negative elec-
trode and chlorine only at the positive electrode; of the latter, a part acted
on the platina and a part was dissolved. A minute bubble of gas remained;
it was not oxygen, but probably air previously held in solution.
It was an important matter to determine whether the chlorine was a
primary result or only a secondary product, due to the action of the oxygen
evolved from water at the anode upon the muriatic acid; i.e. whether the
muriatic acid was electrolysable, and, if so, whether the decomposition
was definite.
"The muriatic acid was gradually diluted. One part with six of water
gave only chlorine at the anode. One part with eight of water gave only
chlorine; with nine of water, a little oxygen appeared with the chlorine:
but the occurrence or non-occurrence of oxygen at these strengths de-
pended, in part, on the strength of the voltaic battery used. With fifteen
parts of water, a little oxygen, with much chlorine, was evolved at the
anode. As the solution was now becoming a bad conductor of electricity,
sulphuric acid was added to it: this caused more ready decomposition, but
did not sensibly alter the proportion of chlorine and oxygen.
486 MASTERWORKS OF SCIENCE
The muriatic acid was now diluted with 100 times its volume of
dilute sulphuric acid. It still gave a large proportion of chlorine at the
anode, mingled with oxygen; and the result was the same, whether a
voltaic battery of forty pairs of plates or one containing only five pairs
were used. With acid of this strength, the oxygen evolved at the anode
was to the hydrogen at the cathode, in volume, as 17 is to 64; and there-
fore the chlorine would have been thirty volumes had it not been dissolved
by the fluid.
Next with respect to the quantity of elements evolved. On using
the volta-electrometer, it was found that, whether the strongest or the
weakest nfuriatic acid were used, whether chlorine alone or chlorine
mingled with oxygen appeared at the anode, still the hydrogen evolved
at the cathode was a constant quantity, i.e. exactly the same as the hydro-
gen which the same quantity of electricity could evolve from water.
This constancy does not decide whether the muriatic acid is elec-
trolysed or not, although it proves that if so, it must be in definite pro-
portions to the quantity of electricity used. Other considerations may,
however, be allowed to decide the point. The analogy between chlorine
and oxygen, in their relations to hydrogen, is so strong as to lead almost
to the certainty that, when combined with that element, they would per-
form similar parts in the process of electro-decomposition. They both
unite with it in single proportional or equivalent quantities. In other
binary compounds of chlorine also, where nothing equivocal depending
on the simultaneous presence of it and oxygen is involved, the chlorine
is directly eliminated at the anode by the electric current. Such is the
case with the chloride of lead, which may be justly compared with pro-
toxide of lead, and stands in the same relation to it as muriatic acid to
water. The chlorides of potassium, sodium, barium, etc., are in the same
relation to the protoxides of the same metals and present the same results
under the influence of the electric current.
From all the experiments, combined with these considerations, I con-
clude that muriatic acid is decomposed by the direct influence of the
electric current, and that the quantities evolved are, and therefore the
chemical action is, definite for a definite quantity of electricity. For though
I have not collected and measured the chlorine, in its separate state, at
the anode, there can exist no doubt as to its being proportional to the
hydrogen at the cathode; and the results are therefore sufficient to establish
the general law of constant electro-chemical action in the case of muriatic
acid.
In the dilute acid, I conclude that a part of the water is electro-
chemically decomposed, giving origin to the oxygen, which appears min-
gled with the chlorine at the anode. The oxygen may be viewed as a
secondary result; but I incline to believe that it is not so: for, if it were,
it might be expected in largest proportion from the stronger acid, whereas
the reverse is the fact. This consideration, with others, also leads me to
conclude that muriatic acid is more easily decomposed by the electric
current than water; since, even when diluted with eight or nine times its
RESEARCHES IN ELECTRICITY 487
quantity of the latter fluid, it alone gives way, the water remaining un-
affected.
Chlorides. — On using solutions of chlorides in water — for instance,
the chlorides of sodium or calcium — there was evolution of chlorine only
at the positive electrode, and of hydrogen, with the oxide of the base, as
soda or lime, at the negative electrode. The process of decomposition may
be viewed as proceeding in two or three ways, all terminating in the same
results. Perhaps the simplest is to consider the chloride as the substance
electrolysed, its chlorine being determined to and evolved at the anode,
and its metal passing to the cathode, where, finding no more chlorine, it
acts upon the water, producing hydrogen and an oxide as secondary
results. As the discussion would detain me from more important matter,
and is not of immediate consequence, I shall defer it for the present. It is,
however, of great consequence to state that, on using the volta-electrome-
ter, the hydrogen in both cases was definite; and if the results do not
prove the definite decomposition of chlorides (which shall be proved else-
where), they are not in the slightest degree opposed to such a conclusion
and do support the general law.
Tartanc acid. — Pure solution of tartaric acid is almost as bad a con-
ductor as pure water. On adding sulphuric acid, it conducted well, the
results at the positive electrode being primary or secondary in different
proportions, according to variations in the strength of the acid and the
power of the electric current. Alkaline tartrates gave a large proportion
of secondary results at the positive electrode. The hydrogen at the nega-
tive electrode remained constant unless certain triple metallic salts were
used.
Solutions, of salts containing other vegetable acids, as the benzoates;
of sugar, gum, etc., dissolved in dilute sulphuric acid; of resin, albumen,
etc., dissolved in alkalies, were in turn submitted to the electrolytic power
of the voltaic current. In all these cases, secondary results to a greater or
smaller extent were produced at the positive electrode.
In concluding this division of these Researches, it cannot but occur
to the mind that the final result of the action of the electric current upon
substances placed between the electrodes, instead of being simple, may
be very complicated. There are two modes by which these substances may
be decomposed, either by the direct force of the electric current or by
the action of bodies which that current may evolve. There are also two
modes by which new compounds may be formed, i.e. by combination of
the evolving substances, whilst in their nascent state, directly with the
matter of the electrode; or else their combination with those bodies which,
being contained in, or associated with, the body suffering decomposition,
are necessarily present at the anode and cathode. The complexity is ren-
dered still greater by the circumstance that two or more of these actions
may occur simultaneously, and also in variable proportions to each other.
But it may in a great measure be resolved by attention to the principles
already laid down.
488 MASTERWORKS OF SCIENCE
On the definite nature and extent of Electro-chemical
Decomposition
In the first part of these Researches, after proving the identity of
electricities derived from different sources, I announced a law, derived
from experiment, which seemed to me of the utmost irn-portance to the
science of electricity in general, and that branch of it denominated electro-
chemistry in particular. The law was expressed thus: The chemical power
of a current of electricity is in direct proportion to the absolute quantity
of electricity' which passes.
It is now my object to consider this great principle more closely, and-
to develop some of the consequences to which it leads. .That the evidence
for it may be the more distinct and applicable, I shall quote cases of
decomposition subject to as few interferences from secondary results as
possible, effected upon bodies very simple yet very definite in their nature.
In the first place, I consider the law as so fully established with
respect to the decomposition of water, and under so many circumstances
which might be supposed, if anything could, to exert an influence over it,
that I may be excused entering into further detail respecting that sub-
stance, or even summing up the results here.
In the next place, I also consider the law as established with respect
to muriatic acid by the experiments and reasoning already advanced, when
speaking of that substance, in the subdivision respecting primary and
secondary results.
Without speaking with the same confidence, yet from the experi-
ments described, and many others not described, relating to hydro-fluoric,
hydro-cyanic, ferro-cyanic, and sulpho-cyanic acids, and from
the close analogy which holds between these bodies and the
hydracids of chlorine, iodine, bromine, etc., I consider these
also as coming under subjection to the law and assisting to
prove its truth.
In the preceding cases, except the first, the water is be-
lieved to be inactive; but to avoid any ambiguity arising from
its presence, I sought for substances from which it should be
absent altogether; and I soon found abundance, amongst which
protochloride of tin was first subjected to decomposition in
the following manner. A piece of platina wire had one ex-
tremity coiled up into a small knob, and, having been care-
fully weighed, was sealed hermetically into a piece of bottle-
glass tube, so that the knob should be at the bottom of the FIG. 20.
tube within (Fig. 20). The tube was suspended by a piece of
platina wire, so that the heat of a spirit lamp could be applied to it.
Recently fused protochloride of tin was introduced in sufficient quantity
to occupy, when melted, about one half of the tube; the wire of the tube
was connected with a volta-electrometer, which was itself connected with
RESEARCHES IN ELECTRICITY
489
the negative end of a voltaic battery; and a platina wire connected with
the positive end of the same battery was dipped into the fused chloride in
the tube; being, however, so bent that it could not by any shake of the
hand or apparatus touch the negative electrode at the bottom of the vessel.
The whole arrangement is delineated in Fig. 21.
Under these circumstances the chloride of tin was decomposed: the
chlorine evolved at the positive electrode formed bichloride of tin, which
passed away in fumes, and the tin evolved at the negative electrode com-
bined with the platina, forming an alloy, fusible at the temperature to
which the tube was subjected, and therefore never occasioning metallic
communication through the decomposing chloride. When the experiment
had been continued so long as to yield a reasonable quantity of gas in the
volta-electrometer, the battery connection was broken, the positive elec-
trode removed, and the tube and remaining chloride allowed to cool.
When cold, the tube was broken open, the rest of the chloride and the
glass being easily separable from the platina wire and its button of alloy.
The latter when washed was then reweighed, and the increase gave the
weight of the tin reduced.
FIG. 21.
I will give the particular results of one experiment, in illustration of
the mode adopted in this and others, the results of which I shall have
occasion to quote. The negative electrode weighed at first 20 grains; after
the experiment, it, with its button of alloy, weighed 23.2 grains. The tin
evolved by the electric current at the cathode weighed therefore 3.2 grains.
The quantity of oxygen and hydrogen collected in the volta-electrometer
= 3.85 cubic inches. As TOO cubic inches of oxygen and hydrogen, in the
proportions to form water, may be considered as weighing 12.92 grains,
the 3.85 cubic inches would weigh 0.49742 of a grain; that being, there-
fore, the weight of water decomposed by the same electric current as was
able to decompose such weight of protochloride of tin as could yield 3.2
grains of metal. Now 0.49742 : 3.2 : : 9 the equivalent of water is to 57.9,
which should therefore be the equivalent of tin, if the experiment had
"been made without error, and if the electro-chemical decomposition is in
this case also definite. In some chemical works 58 is given as the chemical
equivalent of tin, in others 57.9. Both are so near to the result of the
490 MASTERWORKS OF SCIENCE
experiment, and the experiment itself is so subject to slight causes of
variation (as from the absorption of gas in the volta-electrometer), that
the numbers leave little doubt of the applicability of the law of definite:
action in this and all similar cases of electro-decomposition.
It is not often I have obtained an accordance in numbers so near as
that I have just quoted. Four experiments were made on the protochloride
of tin, the quantities of gas evolved in the volta-electrometer being from
2.05 to 10.29 cubic inches. The average of the four experiments gave 58.53
as the electro-chemical equivalent for tin.
The chloride remaining after the experiment was pure protochloride
of tin; and no one can doubt for a moment that the equivalent -of chlorine
had been evolved at the anode, and, having formed bichloride of tin as a
secondary result, had passed away.
Chloride of lead was experimented upon in a manner exactly similar,,
except that a change was made in the nature of the positive electrode;
for as the chlorine evolved at the anode forms no perchloride of lead, but
acts directly upon the platina, it produces, if that metal be used, a solution
of chloride of platina in the chloride of lead; in consequence of which a
portion of platina can pass to the cathode, and would then produce a
vitiated result. I therefore sought for, and found in plumbago, another
substance, which could be used safely as the positive electrode in such
bodies as chlorides, iodides, etc. The chlorine or iodine does not act upon
it, but is evolved in the free state; and the plumbago has no reaction,,
under the circumstances, upon the fused chloride or iodide in which it is
plunged. Even if a few particles of plumbago should separate by the heat
or the mechanical action of the evolved gas, they can do no harm in the
chloride.
The mean of three experiments gave the number of 100.85 as the
equivalent for lead. The chemical equivalent is 103.5. The deficiency in
my experiments I attribute to the solution of part of the gas in the volta-
electrometer; but the results leave no doubt on my mind that both the
lead and the chlorine are, in this case, evolved in definite quantities by
the action of a given quantity of electricity.
I endeavoured to experiment upon the oxide of lead obtained by
fusion and ignition of the nitrate in a platina crucible, but found great
difficulty, from the high temperature required for perfect fusion, and the
powerful fluxing qualities of the substance. Green-glass tubes repeatedly
failed. I at last fused the oxide in a small porcelain crucible, heated fully
in a charcoal fire; and, as it was essential that the evolution of the lead
at the cathode should take place beneath the surface, the negative elec-
trode was guarded by a green-glass tube, fused around it in such a manner
as to expose only the knob of platina at the lower end (Fig. 22), so that
it could be plunged beneath the surface, and thus exclude contact of air
or oxygen with the lead reduced there. A platina wire was employed for
the positive electrode, that metal not being subject to any action from the
oxygen evolved against it. The arrangement is given in Fig. 23.
In an experiment of this kind the equivalent for the lead came out
RESEARCHES IN ELECTRICITY
491
93.17, which is very much too small. This, I believe, was because of the
small interval between the positive and negative electrodes in the oxide
of lead; so that it was not unlikely that some of the froth and bubbles
formed by the oxygen at the anode should occasionally even touch the
lead reduced at the cathode, and re-oxidise it. When I endeavoured to
correct this by having more litharge, the greater heat required to keep it
all fluid caused a quicker action on the crucible, which was soon eaten
through, and the experiment stopped.
In one experiment of this kind I used borate of lead. It evolves lead,
under the influence of the electric current, at the anode, and oxygen at the
cathode; and as the boracic acid is not either directly or incidentally
decomposed during the operation, I expected a result dependent on the
oxide of lead. The borate is not so violent a flux as the oxide, but it
3
FIG. 22.
FIG. 23.
requires a higher temperature to make it quite liquid; and if not very
hot, the bubbles of oxygen cling to the positive electrode and retard the
transfer of electricity. The number for lead came out 101.29, which is so
near to 103.5 as to s^ow tnat tne action of the current had been definite.
Iodide of potassium was subjected to electrolytic action in a tube. The
negative electrode was a globule of lead, and I hoped in this way to retain
the potassium, and obtain results that could be weighed and compared
with the volta-electrometer indication; but the difficulties dependent upon
the high temperature required, the action upon the glass, the fusibility of
the platina induced by the presence of the lead, and other circumstances,
prevented me from procuring such results. The iodide was decomposed
with the evolution of iodine at the anode, and of potassium at the cathode,
as in former cases.
In some of these experiments several substances were placed in suc-
cession, and decomposed simultaneously by the same electric current:
thus, protochloride of tin, chloride of lead, and water were thus acted on
at once. It is needless to say that the results were comparable, the tin,
lead-, chlorine, oxygen, and hydrogen evolved being definite in quantity
and electro-chemical equivalents to each other.
Let us turn to another kind of proof of the definite chemical action
of electricity. If any circumstances could be supposed to exert an influence
492 MASTERWQRKS OF SCIENCE
over the quantity of the matters evolved during electrolytic action, one
would expect them to be present when electrodes of different substances,
and possessing very different chemical affinities for such matters, were
used. Platina has no power in dilute sulphuric acid of combining with the
oxygen at the anode, though the latter be evolved in the nascent state
against it. Copper, on the other hand, immediately unites with the oxygen,
as the electric current sets it free from the hydrogen; and zinc is not only
able to combine with it, but can, without any help from the electricity,
abstract it directly from the water, at the same time setting torrents of
hydrogen free. Yet in cases where these three substances were used as the
positive electrodes in three similar portions of the same dilute sulphuric
acid, specific gravity 1.336, precisely the same quantity of water was de-
composed by the electric current, and precisely the same quantity of hydro-
gen set free at the cathodes of the three solutions.
The experiment was made thus. Portions of the dilute sulphuric acid
were put into three basins. Three volta-electrometer tubes, of the form
Figs. 13, 15, were filled with the same acid, and one inverted in each basin.
A zinc plate, connected with the positive end of a voltaic battery, was
dipped into the first basin, forming the positive electrode there, the hydro-
gen, which was abundantly evolved from it by the direct action of the
acid, being allowed to escape. A copper plate, which dipped into the acid
of the second basin, was connected with the negative electrode of the first
basin; and a platina plate, which dipped into the acid of the third basin,
was connected with the negative electrode of the second basin. The nega-
tive electrode of the third basin was connected with a volta-electrometer,
and that with the negative end of the voltaic battery.
Immediately that the circuit was complete, the electro-chemical action
commenced in all the vessels. The hydrogen still rose in, apparently,
undiminished quantities from the positive zinc electrode in the first basin.
No oxygen was evolved at the positive copper electrode in the second
basin, but a sulphate of copper was formed there; whilst in the third
basin the positive platina electrode evolved pure oxygen gas and was itself
unaffected. But in all the basins the hydrogen liberated at the negative
platina electrodes was the same in quantity, and the same with the volume
of hydrogen evolved in the volta-electrometer, showing that in all the
vessels the current had decomposed an equal quantity of water. In this
trying case, therefore, the chemical action of electricity proved to be per-
fectly definite.
A similar experiment was made with muriatic acid diluted with its
bulk of water. The three positive electrodes were zinc, silver, and platina;
the first being able to separate and combine with the chlorine without
the aid of the current; the second combining with the chlorine only after
the current had set it free; and the third rejecting almost the whole of it.
The three negative electrodes were, as before, platina plates fixed within
glass tubes. In this experiment, as in the former, the quantity of hydrogen
evolved at the cathodes was the same for all, and the same as the hydrogen
evolved in the volta-electrometer. I have already given my reasons for
RESEARCHES IN ELECTRICITY 493
believing that in these experiments it is the muriatic acid which is directly
decomposed by the electricity; and the results prove that the quantities
so decomposed are perfectly definite and proportionate to the quantity of
electricity which has passed.
Experiments of a similar kind were then made with bodies altogether
in a different state, i.e. with fused chlorides, iodides, etc. I have already
described an experiment with fused chloride of silver, in which the elec-
trodes were of metallic silver, the one rendered negative becoming in-
creased and lengthened by the addition of metal, whilst the other was
dissolved and eaten away by its abstraction. This experiment was repeated,
two weighed pieces of silver wire being used as the electrodes, and a volta-
electrometer included in the circuit. Great care was taken to withdraw
the negative electrode so regularly and steadily that the crystals of reduced
silver should not form a metallic communication beneath the surface of
the fused chloride. On concluding the experiment the positive electrode
was reweighed, and its loss ascertained. The mixture of chloride of silver
and metal, withdrawn in successive portions at the negative electrode, was
digested in solution of ammonia, to remove the chloride, and the metallic
silver remaining also weighed: it was the reduction at the cathode, and
exactly equalled the solution at the anode; and each portion was as nearly
as possible the equivalent to the water decomposed in the volta-elec-
trometer.
The infusible condition of the silver at the temperature used and the
length and ramifying character of its crystals render the above experiment
difficult to perform and uncertain in its results. I therefore wrought with
chloride of lead, using a green-glass tube formed as in Fig. 24. A weighed
platina wire was fused into the bottom of a small tube, as before described.
The tube was then bent to an angle, at about half an inch distance from
the closed end; and the part between the angle and the extremity, being
softened, was forced upward, as in the figure, so as to form a bridge, or
rather separation, producing two little depressions or basins, a, b, within
the tube. This arrangement was suspended by a platina wire, as before,
so that the heat of a spirit lamp could be applied to it, such inclination
being given to it as would allow all air to escape during the fusion of the
chloride of lead. A positive electrode was then provided, by bending up
the end of a platina wire into a knot, and fusing about twenty grains of
metallic lead onto it, in a small closed tube of glass, which was afterwards
broken away. Being so furnished, the wire with its lead was weighed, and
the weight recorded.
494 MASTERWORKS OF SCIENCE
Chloride of lead was now introduced into the tube and carefully
fused. The leaded electrode was also introduced; after which the metal,
at its extremity, soon melted. In this state of things the tube was filled
up to c with melted chloride of lead; the end of the electrode to be
rendered negative was in the basin b, and the electrode of melted lead
was retained in the basin a, and, by connection with the proper conduct-
ing wire of a voltaic battery, was rendered positive. A volta-electrometer
was included in the circuit.
Immediately upon the completion of the communication with the
voltaic battery, the current passed, and decomposition proceeded. No
chlorine was evolved at the positive electrode; but as the fused chloride
was transparent, a button of alloy could be observed gradually forming
and increasing in size at b, whilst the lead at a could also be seen gradu-
ally to diminish. After a time, the experiment was stopped; the tube
allowed to cool, and broken open; the wires, with their buttons, cleaned
and weighed; and their change in weight compared with the indication
of the volta-electrometer.
In this experiment the positive electrode had lost just as much lead
as the negative one had gained, and the loss and gain were very nearly
the equivalents of the water decomposed in the volta-electrometer, giving
for lead the number 101.5. I* *s therefore evident, in this instance, that
causing strong affinity, or no affinity, for the substance evolved at the
anode, to be active during the experiment, produces no variation in the
definite action of the electric current.
Then protochloride of tin was subjected to the electric current in the
same manner, using, of course, a tin positive electrode. No bichloride of
tin was now formed. On examining the two electrodes, the positive had
lost precisely as mucH as the negative had gained; and by comparison
with the volta-clectrometer, the number for tin carne out 59.
All these facts combine into, I think, an irresistible mass of evidence,
proving the truth of the important proposition which I at first laid down,
namely, that the chemical power of a current of electricity is in direct
proportion to the absolute quantity of electricity which passes. They
prove, too, that this is not merely true with one substance, as water, but
generally with all electrolytic bodies; and, further, that the results obtained
with any one substance do not merely agree amongst themselves, but also
with those obtained from other substances, the whole combining together
into one series of definite electro-chemical actions.
The doctrine of definite electro-chemical action just laid down, and,
I believe, established, leads to some new views of the relations and classifi-
cations of bodies associated with or subject to this action. Some of these
I shall proceed to consider.
In the first place, compound bodies may be separated into two great
classes, namely, those which are decomposable by the electric current and
those which are act: of the latter, some arc conductors, others non-
conductors,, of voltaic electricity. The former do net depend for their
decomposability upon the nature of their elements only; for, of the same
RESEARCHES IN ELECTRICITY 495
two elements, bodies may be formed of which one shall belong to one
class and another to the other class; but probably on the proportions also.
I propose to call bodies of this, the decomposable class, Electrolytes.
Then, again, the substances into which these divide, under the in-
fluence of the electric current, form an exceedingly important general
class. They are combining bodies; are directly associated with the funda-
mental parts of the doctrine of chemical affinity; and have each a definite
proportion, in which they are always evolved during electrolytic action.
I have proposed to call these bodies generally ions, or particularly anions
and cations, according as they appear at the anode or cathode; and the
numbers representing the proportions in which they are evolved, electro-
chemical equivalents. Thus hydrogen, oxygen, chlorine, iodine, lead, tin
are ions; the three former are anions, the two metals are cations, and i, 8,
36, 125, 104, 58 are their electro-chemical equivalents nearly.
A summary of certain points already ascertained respecting electro-
lytes, ions, and electro-chemical equivalents may be given in the following
general form of propositions, without, I hope, including any serious error.
i. A single ion, i.e. one not in combination with another, will have
no tendency to pass to either of the electrodes, and will be perfectly in-
different to the passing current, unless it be itself a compound of more
elementary ions, and so subject to actual decomposition. Upon this fact
is founded much of the proof adduced in favour of the new theory of
electro-chemical decomposition, which I put forth in a former part of
these Researches.
ii. If one ion be combined in right proportions with another strongly
opposed to it in its ordinary chemical relations, i.e. if an anion be com-
bined with a cation, then both will travel, the one to the anode, the other
to the cathode, of the decomposing body.
iii. If, therefore, an ion pass towards one of the electrodes, another
ion must also be passing simultaneously to the other electrode, although,
from secondary action, it may not make its appearance.
iv. A body decomposable directly by the electric current, i.e. an
electrolyte, must consist of two ions, and must also render them up during
the act of decomposition.
v. There is but one electrolyte composed of the same two elementary
ions; at least such appears to be the fact, dependent upon a law, that only
single electro-chemical equivalents of elementary ions can go to the elec-
trodes, and not multiples.
vi. A body not decomposable when alone, as boracic acid, is not
directly decomposable by the electric current when in combination. It
may act as an ion going wholly to the anode or cathode, but does not
yield up its elements, except occasionally by a secondary action. Perhaps
it is superfluous for me to point out that this proposition has no relation
to such cases as that of water, which, by the presence of other bodies, is
rendered a better conductor of electricity, and therefore is more freely
decomposed.
vii. The nature of the substance of which the electrode is formed,
4% MASTERWORKS OF SCIENCE
provided it be a conductor, causes no difference in the electro-decompo-
sition, either in kind or degree: but it seriously influences, by secondary
action, the state in which the ions finally appear. Advantage may be taken
of this principle in combining and collecting such ions as, if evolved in
their free state, would be unmanageable.
viii. A substance which, being used as the electrode, can combine
with the ion evolved against it is also, I believe, an ion, and combines,
in such cases, in the quantity represented by its electro-chemical equiva-
lent. All the experiments I have made agree with this view; and it seems
to me, at present, to result as a necessary consequence. Whether, in the
secondary actions that take place, where the ion acts not upon the matter
of the electrode but on that which is around it in the liquid, the same
consequence follows, will require more extended investigation to deter-
mine.
ix. Compound ions are not necessarily composed of electro-chemical
equivalents of simple ions. For instance, sulphuric acid, boracic acid,
phosphoric acid are ions, but not electrolytes, i.e. not composed of electro-
chemical equivalents of simple ions.
x. Electro-chemical equivalents are always consistent; i.e. the same
number which represents the equivalent of a substance A when it is
separating from a substance B will also represent A when separating from
a third substance C. Thus, 8 is the electro-chemical equivalent of oxygen,
whether separating from hydrogen, or tin, or lead; and 103.5 is the electro-
chemical equivalent of lead, whether separating from oxygen, or chlorine,
- or iodine.
xi. Electro-chemical equivalents coincide, and are the same, with
ordinary chemical equivalents.
By means of experiment and the preceding propositions, a knowledge
of ions and their electro-chemical equivalents may be obtained in various
ways.
In the first place, they may be determined directly, as has been done
with hydrogen, oxygen, lead, and tin in the numerous experiments al-
ready quoted.
In the next place, from propositions ii and iii may be deduced the
knowledge of many other ions, and also their equivalents. When chloride
of lead was decomposed, platina being used for both electrodes, there
could remain no more doubt that chlorine was passing to the anode, al-
though it combined with the platina there, than when the positive elec-
trode, being of plumbago, allowed its evolution in the free state; neither
could there, in either case, remain any doubt that for every 103.5 parts
of lead evolved at the cathode, 36 parts of chlorine were evolved at the
anode, for the remaining chloride of lead was unchanged. So also, when
in a metallic solution one volume of oxygen, or a secondary compound
containing that proportion, appeared at the anode, no doubt could arise
that hydrogen, equivalent to two volumes, had been determined to the
cathode, although, by a secondary action, it had been employed in reduc-
ing oxides of lead, copper, or other metals to the metallic state. In this
RESEARCHES IN ELECTRICITY 497
manner, then, we learn from the experiments already described in these
Researches that chlorine, iodine, bromine, fluorine, calcium, potassium,
strontium, magnesium, manganese, etc., are ions, and that their electro*
chemical equivalents are the same as their ordinary chemical equivalents.
Propositions iv and v extend our means o£ gaming information. For
if a body of known chemical composition is found to be decomposable,
and the nature of the substance evolved as a primary or even a secondary
result at one of the electrodes be ascertained, the electro-chemical equiva-
lent of that body may be deduced from the known constant composition
of the substance evolved. Thus, when fused protiodide of tin is decom-
posed by the voltaic current the conclusion may be drawn that both the
iodine and tin are ions, and that the proportions in which they combine
in the fused compound express their electro-chemical equivalents. Again,
with respect to the fused iodide of potassium, it is an electrolyte; and the
chemical equivalents will also be the electro-chemical equivalents.
I think I cannot deceive myself in considering the doctrine of definite
electro-chemical action as of the utmost importance. It touches by its facts,
more directly and closely than any former fact, or set of facts, has done,
upon the beautiful idea that ordinary chemical affinity is a mere conse-
quence of the electrical attractions of the particles of different kinds of
matter; and it will probably lead us to the means by which we may en-
lighten that which is at present so obscure, and either fully demonstrate
the truth of the idea or develop that which ought to replace it.
On the absolute quantity of Electricity associated with
the panicles or atoms of Matter
The theory of definite electrolytical or electro-chemical action appears
to me to touch immediately upon the absolute quantity of electricity or
electric power belonging to different bodies. It is impossible, perhaps,
to speak on this point without committing oneself beyond what present
facts will sustain; and yet it is equally impossible, and perhaps would be
impolitic, not to reason upon the subject. Although we know nothing of
what an atom is, yet we cannot resist forming some idea of a small par-
ticle, which represents it to the mind; and though we are in equal, if not
greater, ignorance of electricity, so as to be unable to say whether it is
a particular matter or matters, or mere motion of ordinary matter, or some
third kind of power or agent, yet there is an immensity of facts which
justify us in believing that the atoms of matter are in some way endowed
or associated with electrical powers, to which they owe their most striking
qualities, and amongst them their mutual chemical affinity. As soon as we
perceive, through the teaching of Dalton, that chemical powers are, how-
ever varied the circumstances in which they are exerted, definite for each
body, we learn to estimate the relative degree of force which resides in
such bodies; and when upon that knowledge comes the fact that the elec-
tricity, which we appear to be capable of loosening from its habitation
498 MASTERWORKS OF SCIENCE
for a while and conveying from place to place, whilst it retains its chemi-
cal force, can be measured out, and being so measured is found to be
as definite in its action as any of those portions which, remaining associ-
ated with the particles of matter, give them their chemical relation; we
seem to have found the link which connects the proportion of that we
have evolved to the proportion of that belonging to the particles in their
natural state.
Now it is wonderful to observe how small a quantity of a compound
body is decomposed by a certain portion of electricity. Let us, for in-
stance, consider this and a few other points in relation to water. One grain
of water, acidulated to facilitate conduction, will require an electric cur-
rent to be continued for three minutes and three quarters of time to effect
its decomposition, which current must be powerful enough to retain a
platina wire %Q4th of an inch in thickness, red hot, in the air during the
whole time; and if interrupted anywhere by charcoal points, will produce
a very brilliant and constant star of light. If attention be paid to the
instantaneous discharge of electricity of tension, as illustrated in the
beautiful experiments of Mr. Wheatstone, and to what I have said else-
where on the relation of common and voltaic electricity, it will not be
too much to say that this necessary quantity of electricity is equal to a
very powerful flash of lightning. Yet we have it under perfect command;
can evolve, direct, and employ it at pleasure; and when it has performed
its full work of electrolysation, it has only separated the elements of a
single grain of water.
On the other hand, the relation between the conduction of the elec-
tricity and the decomposition of the water is so close that one cannot take
place without the other. If the water is altered only in that small degree
which consists in its having the solid instead of the fluid state, the con-
duction is stopped, and the decomposition is stopped with it. Whether
the conduction be considered as depending upon the decomposition or
not, still the relation of the two functions is equally intimate and in-
separable.
Considering this close and twofold relation, namely, that without
decomposition transmission of electricity does not occur; and, that for a
given definite quantity of electricity passed, an equally definite and con-
stant quantity of water or other matter is decomposed; considering also
that the agent, which is electricity, is simply employed in overcoming
electrical powers in the body subjected to its action; it seems a probable
and almost a natural consequence that the quantity which passes is the
equivalent of, and therefore equal to, that of the particles separated; i.e.
that if the electrical power which holds the elements of a grain of water
in combination, or which makes a grain of oxygen and hydrogen in the
right proportions unite into water when they are made to combine, could
be thrown into the condition of a current, it would exactly equal the
current required for the separation of that grain of water into its elements
again.
This view of the subject gives an almost overwhelming idea of the
RESEARCHES IN ELECTRICITY 499
extraordinary quantity or degree of electric power which naturally belongs
to the particles of matter; but it is not inconsistent in the slightest degree
with the facts which can be brought to bear on this point. To illustrate
this I must say a few words on the voltaic pile.
IV. ELECTRICITY OF THE VOLTAIC PILE
THOSE BODIES which, being interposed between the metals of the voltaic
pile, render it active are all of them electrolytes; and it cannot but press
upon the attention of everyone engaged in considering this subject that
in those bodies (so essential to the pile) decomposition and the trans-
mission of a current are so intimately connected that one cannot happen,
without the other. This I have shown abundantly in water, and numerous
other cases. If, then, a voltaic trough have its extremities connected by a
body capable of being decomposed, as water, we shall have a continuous
current through the apparatus; and whilst it remains in this state we may
look at the part where the acid is acting upon the plates and that where
the current is acting upon the water as the reciprocals of each other. In
both parts we have the two conditions inseparable in such bodies as these,
namely, the passing of a current, and decomposition; and this is as true
of the cells in the battery as of the water cell; for no voltaic battery has
as yet been constructed in which the chemical action is only that of com-
bination: decomposition is always included, and is, I believe, an essential
chemical part.
But the difference in the two parts of the connected battery, that is,
the decomposition or experimental cell and the acting cells, is simply this.
In the former we urge the current through, but it, apparently of necessity,
is accompanied by decomposition: in the latter we cause decompositions
by ordinary chemical actions (which are, however, themselves electrical),
and, as a consequence, have the electrical current; and as the decomposi-
tion dependent upon the current is definite in the former case, so is the
current associated with the decomposition also definite in the latter.
Let us apply this in support of what I have surmised respecting the
enormous electric power of each particle or atom of matter. I showed in
a former part of these Researches on the relation by measure of common
and voltaic electricity that two wires, one of platina and one of zinc, each
one eighteenth of an inch in diameter, placed five sixteenths of an inch
apart and immersed to the depth of five eighths of an inch in acid, con-
sisting of one drop of oil of vitriol and four ounces of distilled water at
a temperature of about 60° Fahr., and connected at the other extremities
by a copper wire eighteen feet long and one eighteenth of an inch in thick-
ness, yielded as much electricity in little more than three seconds of time
as a Leyden battery charged by thirty turns of a very large and powerful
plate electric machine in full action. This quantity, though sufficient if
passed at once through the head of a rat or cat to have killed it, as by a
flash of lightning, was evolved by the mutual action of so small a portion
500 MASTERWORKS OF SCIENCE
of the zinc wire and water in contact with it that the loss of weight sus-
tained by either would be inappreciable by our most delicate instruments;
and as to the water which could be decomposed by that current, it must
have been insensible in quantity, for no trace of hydrogen appeared upon
the surface of the platina during those three seconds.
What an enormous quantity of electricity, therefore, is required for
the decomposition of a single grain of water! We have already seen that
it must be in quantity sufficient to sustain a' platina wire %o4tn °f an incn
in thickness, red hot, in contact with the air, for three minutes and three
quarters, a quantity which is almost infinitely greater than that which
could be evolved by the little standard voltaic arrangement to which I
have just referred. I have endeavoured to make a comparison by the loss
of weight of such a wire in a given time in such an acid, according to a
principle and experiment to be almost immediately described; but the
proportion is so high that I am almost afraid to mention it. It would
appear that 800,000 such charges of the Leyden battery as I have referred
to above would be necessary to supply electricity sufficient to decompose
a single grain of water; or, if I am right, to equal the quantity of elec-
tricity which is naturally associated with the elements of that grain of
water, endowing them with their mutual chemical affinity.
In further proof of this high electric condition of the particles of
matter, and the identity as to quantity of that belonging to them with
that necessary for their separation, I will describe an experiment of great
simplicity but extreme beauty, when viewed in relation to the evolution
of an electric current and its decomposing powers.
A dilute sulphuric acid, made by adding about one part by measure
of oil of vitriol to thirty parts of water, will act energetically upon a piece
of zinc plate in its ordinary and simple state; but, as Mr. Sturgeon has
shown, not at all, or scarcely so, if the surface of the metal has in the first
instance been amalgamated; yet the amalgamated zinc will act powerfully
with platina as an electromotor, hydrogen being evolved on the surface
of the latter metal, as the zinc is oxidised and dissolved. The amalgama-
tion is best effected by sprinkling a few drops of mercury upon the surface
of the zinc, the latter being moistened with the dilute acid, and rubbing
with the fingers or tow so as to extend the liquid metal over the whole
of the surface. Any mercury in excess, forming liquid drops upon the
zinc, should be wiped off.
Two plates of zinc thus amalgamated were dried and accurately
weighed; one, which we will call A, weighed 163.1 grains; the other, to
be called B, weighed 148.3 grains. They were about five inches long and
0.4 of an inch wide. An earthenware pneumatic trough was filled with
dilute sulphuric acid, of the strength just described, and a gas jar, also
filled with the acid, inverted in it. A plate of platina of nearly tie same
length, but about three times as wide as the zinc plates, was put up into
this jar. The zinc plate A was also introduced into the jar and brought
in contact with the platina, and at the same moment the plate B was put
into the acid of the trough, but out of contact with other metallic matter.
RESEARCHES IN ELECTRICITY 501
Strong action immediately occurred in the jar upon the contact of the
zinc and platina plates. Hydrogen gas rose from the platina and was col-
lected m the jar, but no hydrogen or other gas rose from either zinc
plate. In about ten or twelve minutes, sufficient hydrogen having been
collected, the experiment was stopped; during its progress a few small
bubbles had appeared upon plate B, but none upon plate A. The plates
were washed in distilled water, dried, and reweighed. Plate B weighed
148.3 grains, as before, having lost nothing by the direct chemical action
of the acid. Plate A weighed 154.65 grains, 8.45 grains of it having been
oxidised and dissolved during the experiment.
The hydrogen gas was next transferred to a water trough and meas-
ured; it amounted to 12.5 cubic inches, the temperature being 52° and
the barometer 29.2 inches. This quantity, corrected for temperature, pres-
sure, and moisture, becomes 12.15453 cubic inches of dry hydrogen at
mean temperature and pressure; which, increased by one half for the oxy-
gen that must have gone to the anode, i.e. to the zinc, gives 18.232 cubic
inches as the quantity of oxygen and hydrogen evolved from the water
decomposed by the electric current. According to the estimate of the
weight of the mixed gas before adopted, this volume is equal to 2.3535544
grains, which therefore is the weight of water decomposed; and this
quantity is to 8.45, the quantity of zinc oxidised, as 9 is to 32.31. Now
taking 9 as the equivalent number of water, the number 32.5 is given as
the equivalent number of zinc; a coincidence sufficiently near to show,
what indeed could not but happen, that for an equivalent of zinc oxidised
an equivalent of water must be decomposed.
But let us observe how the water is decomposed. It is electrolysed,
i.e. is decomposed voltaically, and not in the ordinary manner (as to
appearance) of chemical decompositions; for the oxygen appears at the
anode and the hydrogen at the cathode of the body under decomposition,
and these were in many parts of the experiment above an inch asunder.
Again, the ordinary chemical affinity was not enough under the circum-
stances to effect the decomposition of the water, as was abundantly proved
by the inaction on plate B; the voltaic current was essential. And to pre-
sent any idea that the chemical affinity was almost sufficient to decom-
pose the water, and that a smaller current of electricity might, under the
circumstances, cause the hydrogen to pass to the cathode, I need only refer
to the results which I have given to show that the chemical action at the
electrodes has not the slightest influence over the quantities of water or
•other substances decomposed between them, but that they are entirely
dependent upon the quantity of electricity which passes.
What, then, follows as a necessary consequence of the whole experi-
ment? Why, this: that the chemical action upon 32.31 parts, or one equiva-
lent of zinc, in this simple voltaic circle was able to evolve such quantity
of electricity in the form of a current as, passing through water, should
•decompose 9 parts, or one equivalent of that substance: and considering
the definite relations of electricity as developed in the preceding parts
of the present paper, the results prove that the quantity of electricity
502 MASTERWORKS OF SCIENCE
which, being naturally associated with the particles of matter, gives them
their combining power is able, when thrown into a current, to separate
those particles from their state of combination; or, in other words, that
the electricity which decomposes and that which is evolved by the decom-
position of a certain quantity of matter are ali\e.
The harmony which this theory of the definite evolution and the
equivalent definite action of electricity introduces into the associated
theories of definite proportions and electro-chemical affinity is very great.
According to it, the equivalent weights of bodies are simply those quanti-
ties of them which contain equal quantities of electricity, or have naturally
equal electric powers; it being the ELECTRICITY which determines the
equivalent number, because it determines the combining force. Or, if
we adopt the atomic theory or phraseology, then the atoms of bodies
which are equivalents to each other in their ordinary chemical action
have equal quantities of electricity naturally associated with them. But I
must confess I am jealous of the term atom; for though it is very easy to
talk of atoms, it is very difficult to form a clear idea of their nature, espe-
cially when compound bodies are under consideration.
But admitting that chemical action is the source of electricity, what
an infinitely small fraction of that which is active do we obtain and
employ in our voltaic batteries! Zinc and platina wires, one eighteenth
of an inch in diameter and about half an inch long, dipped into dilute
sulphuric acid so weak that it is not sensibly sour to the tongue, or
scarcely to our most delicate test papers, will evolve more electricity in
one twentieth of a minute than any man would willingly allow to pass
through his body at once. The chemical action of a grain of water upon
four grains of zinc can evolve electricity equal in quantity to that of a
powerful thunderstorm. Nor is it merely true that the quantity is active;
it can be directed and made to perform its full equivalent duty. Is there
not, then, great reason to hope and believe that, by a closer experimental
investigation of the principles which govern the development and action
of this subtile agent, we shall be able to increase the power of our bat-
teries or invent new instruments which shall a thousandfold surpass in
energy those which we at present possess?
EXPERIMENTS IN PLANT-
HYBRIDIZATION
ty
GREGOR JOHANN MENDEL
CONTENTS
Experiments in Plant-Hybridization
Introductory Remarks
Selection of the Experimental Plants
Division and Arrangement of the Experiments
The Forms of the Hybrids
The First Generation [Bred] from the Hybrids
The Second Generation [Bred] from the Hybrids
The Subsequent Generations [Bred] from the Hybrids
The Offspring of Hybrids in which Several Differentiating Characters Are
Associated
The Reproductive Cells of the Hybrids
Concluding Remarks
GREGOR JOHANN MENDEL
1822-1884
GREGOR JOHANN MENDEL channeled his energies into work in
natural science and work in the church. His local contem-
poraries considered him a churchman who dabbled in scien-
tific inquiry. Posterity has remembered him as a scientist who
was, almost incidentally, a churchman. To Mendel, neither his
scientific nor his church labors were interesting- and important
to the exclusion of the other., and he did not find his science
and his religion incompatible. Indeed, the capabilities which
made possible his scientific work were precisely those which
brought him success as a churchman.
tie was born on July 22, 1822, at Heinzendorf bei Odrau,
in Austrian Silesia. His father, a small independent farmer,
taught his son something of the art of grafting fruit trees, and
later provided some means for the boy's formal education. His
maternal uncle, Anton Schwirtlich, a man of intellectual tastes,
had founded the first village school in Heinzendorf, and may
well have encouraged his nephew's ambitions for schooling.
His younger sister contributed to the cost of his education a
portion of her dowry — a loan he subsequently more than re-
paid by providing for the education of her three sons. Con-
cerning other members of the family, there is practically no
pertinent information.
Young Mendel attended the local school founded by his
uncle, then the government school which succeeded it, then
the better school at neighboring Leipnik. There he so distin-
guished himself as a student that his family strained its finan-
cial means to afford him the gymnasium at Troppau and a
subsequent year at Olmiitz, During his residence at Troppau
an Augustinian monk, one of his teachers, apparently showed
the young man a way to a career in education — membership
in a religious order. In consequence, Mendel applied for mem-
bership in the Augustinian House of St. Thomas in Briinn
506 MASTERWORKS OF SCIENCE
(the Konigskloster), was accepted, took the name Gregor "in
religion" — he had been baptized Johann — and devoted him-
self to the institution's program in education. In 1847 he was
ordained a priest; in 1851, at the expense of the cloister, he
went to Vienna for two years of study in the natural sciences;
from 1853 to 1868 he taught scientific subjects, especially phys-
ics, in the Realschule at Briinn. In the latter year he was
elected Abbot of the Konigskloster.
As the Abbot of the Cloister, Mendel became involved in
a dispute with the government which lasted during his whole
tenure of office, until his death in 1884. There had been en-
acted in 1872 a measure imposing special taxes on the prop-
erty of religious houses. Mendel held the exaction to be
unjust, to be special legislation which distinguished inequi-
tably among various property holders; he refused payment
of the sum levied against the Konigskloster. Several other
monasteries similarly refused payment, for the same reason.
These others gradually retreated from their position, cajoled
and threatened and persuaded by government agents who
offered compromises and concessions. Finally, only the Konigs-
kloster stood by its abbot's original declaration of principles.
Mendel lost friends; the property of the Cloister was dis-
trained upon; lawsuits multiplied. Still the abbot stood firm.
Even at the time of his death the question remained unsolved.
But a few years later the tax was quietly removed.
The same stiff-necked adherence to position, the same
pertinacity, the same thorough attention to detail, which en-
abled Mendel for so many years to oppose the government,
distinguish his scientific work. This work began about the
time he entered the Augustinian Order and continued for a
full twenty-two years — until his election as Abbot. Thereafter -
the administrative responsibility he had to carry prevented
further experimentation, and his later years are, for the his-
torian of science, wholly barren.
During the twenty-two years of his active experimenting,
Mendel interested himself in a variety of subjects. He studied
sunspots, kept a close record of meteorological phenomena and
published his observations annually in the Briinn Abhand-
lungen, established fifty beehives in the Cloister gardens in
order to study heredity, and so on. What he learned from his
bees is now not known, for his notes have been lost — possibly
destroyed by Mendel himself. His interest in heredity led him,
however, also to the study of peas, and out of that study he
developed the theory which under the name Mendelism has
won more adherents than any other in the last fifty years.
At least as early as 1855 the problems of heredity inter-
ested Mendel. At that time half a dozen naturalists and
MENDEL — PLANT-HYBRIDIZATION 507
hybridizers were attempting to solve the problem of the origin
of species; Darwin's ideas, widely circulated in his magnifi-
cent books, had not yet persuaded the whole scientific world.
Mendel stated the problem to himself with great clarity, chose
as his material the edible pea because the varieties in cultiva-
tion are distinguished from one another by striking charac-
teristics easy to recognize, and then settled down to eight
years of planting, cross-fertilizing, reaping, and replanting.
Above all, he undertook the wearisome, endless labor of con-
stantly recording results. From these results he proceeded to
the penetrating analysis which permitted him, in 1865, to read
a report of his findings to the Academy of Briinn. The fol-
lowing year the Academy published his report.
Familiar with the work of earlier hybridizers, Mendel
saw that for success he would need, unlike his predecessors,
to consider separately each characteristic of the strain he was
breeding; that he would need to keep each generation quite
distinct from each other generation; that he would need to
record separately the progeny from different individuals.
When he had decided to use edible peas as his subject, he
chose a pair of varieties of which one was tall — six to seven
feet — and one dwarf — nine to eighteen inches. He then cross-
bred these varieties to discover to what height the progeny
would grow. He called tallness one characteristic and named
it dominant; he called dwarfness an opposite characteristic
and named it recessive.
In the wide Cloister gardens Mendel raised generation
after generation of his peas, always planting all the seed ob-
tained from the last preceding experiment. He studied the
contrasting characteristics of smoothness and rugosity, of
green and yellow coloration in the cotyledons, and so on,
Eventually his plantings occupied a great part of the garden
space. Similarly, his results occupy a great space in the theories
of genetics.
When he had completed his work with peas, Mendel did
a series of similar experiments with Hieraciurn, and gave the
results, which corroborated those of the experiments with,
peas, to the Briinn Academy in 1869. Then his work as abbot
began, and he did no further experimenting.
The publication of Mendel's two papers in the Proceed-
ings of the Briinn Academy attracted literally no attention.
Darwin had printed the Origin in 1859, so startling the scien-
tific and lay worlds, so amazing and almost stupefying them,
that no one paid heed to the records of the quiet, unknown
Augustinian. He did not himself, apparently, send copies of
his papers to the great naturalists whose work he knew and
revered. Though the Academy of Briinn exchanged publica-
508 MASTER.WQRKS OF SCIENCE
tions with other European academies, including the Royal and
Linnaean societies of London, no one read Mendel's papers
with any appreciation of the work he had done or of the
importance attaching to his conclusions.
Meantime the pertinacity, the devotion, the tireless skill
which Mendel had given to his biological experiments he
was now dedicating to the administrative labors of the Konigs-
kloster. The quarrel with the government heightened. His
health began to fail. In 1884 he died — still unknown among
the scientists.
Sixteen years later, in 1900, within a few months, three
naturalists — de Vries, Correns, and Tschermak — published
independent papers each giving the substance of Mendel's
treatise and each confirming it. A year later the original paper
appeared in an English translation in the Journal of the Royal
Horticultural Society, In 1902, W. Bateson published a revised
translation, the major part of which follows. Mendel's time
of fame had come, and it endures.
EXPERIMENTS IN PLANT-
HYBRIDIZATION
INTRODUCTORY REMARKS
EXPERIENCE of artificial fertilization, such as is effected with ornamental
plants in order to obtain new variations in colour, has led to the experi-
ments which will here be discussed. The striking regularity with which
the same hybrid forms always reappeared whenever fertilization took
place between the same species induced further experiments to be under-
taken, the object of which was to follow up the developments of the
hybrids in their progeny.
Those who survey the work done in this department will arrive at
the conviction that among all the numerous experiments made, not one
has been carried out to such an extent and in such a way as to make it
possible to determine the number of different forms under which the
offspring of hybrids appear, or to arrange these forms with certainty
according to their separate generations, or definitely to ascertain their
statistical relations.
It requires indeed some courage to undertake a labour of such far-
reaching extent; this appears, however, to be the only right way by which
we can finally reach the solution of a question the importance of which
cannot be overestimated in connection with the history of the evolution
of organic forms.
The paper now presented records the results of such a detailed ex-
periment. This experiment was practically confined to a small plant
group, and is now, after eight years' pursuit, concluded in all essentials.
Whether the plan upon which the separate experiments were conducted
and carried out was the best suited to attain the desired end is left to the
friendly decision of the reader.
SELECTION OF THE EXPERIMENTAL PLANTS
THE VALUE and utility of any experiment are determined by the fitness of
the material to the purpose for which it is used, and thus in the case
before us it cannot be immaterial what plants are subjected to experiment
and in what manner such experiments are conducted.
The selection of the plant group which shall serve for experiments o£
510 MASTERWORKS OF SCIENCE
this kind must be made with all possible care if it be desired to avoid
from the outset every risk of questionable results.
The experimental plants must necessarily —
1. Possess constant differentiating characters.
2. The hybrids of such plants must, during the flowering period, be
protected from the influence of all foreign pollen, or be easily capable of
such protection.
The hybrids and their offspring should suffer no marked disturbance
in their fertility in the successive generations.
Accidental impregnation by foreign pollen, if it occurred during the
experiments and were not recognized, would lead to entirely erroneous
conclusions. Reduced fertility or entire sterility of certain forms, such as
occurs in the offspring of many hybrids, would render the experiments
very difficult or entirely frustrate them. In order to discover the relations
in which the hybrid forms stand towards each other and also towards
their progenitors it appears to be necessary that all members of the series
developed in each successive generation should be, without exception,,
subjected to observation.
At the very outset special attention was devoted to the Leguminosae
on account of their peculiar floral structure. Experiments which were
made with several members of this family led to the result that the genus
Pisum was found to possess the necessary qualifications.
Some thoroughly distinct forms of this genus possess characters
which are constant, and easily and certainly recognizable, and when their
hybrids are mutually crossed they yield perfectly fertile progeny. Further-
more, a disturbance through foreign pollen cannot easily occur, since the
fertilizing organs are closely packed inside the keel and the anther bursts
within the bud, so that the stigma becomes covered with pollen even
before the flower opens. This circumstance is of especial importance. As
additional advantages worth mentioning, there may be cited the easy cul-
ture of these plants in the open ground and in pots, and also their rela-
tively short period of growth. Artificial fertilization is certainly a some-
what elaborate process, but nearly always succeeds. For this purpose the
hud -is opened before it is perfectly developed, the keel is removed, and
each stamen carefully extracted by means of forceps, after which the
stigma can at once be dusted over with the foreign pollen.
DIVISION AND ARRANGEMENT OF THE EXPERIMENTS
IF TWO PLANTS which differ constantly in one or several characters be
crossed, numerous experiments have demonstrated that the common char-
acters are transmitted unchanged to the hybrids and their progeny; but
each pair of differentiating characters, on the other hand, unite in the
hybrid to form a new character, which in the progeny of the hybrid is
usually variable. The object of the experiment was to observe these varia-
tions in the case of each pair of differentiating characters, and to deduce
MENDEL — PLANT-HYBRIDIZATION 511
the law according to which they appear in the successive generations. The
experiment resolves itself therefore into just as many separate experiments
as there are constantly differentiating characters presented in the experi-
mental plants.
The various forms of Peas selected for crossing showed differences in
the length and colour of the stem; in the size and form of the leaves; in
the position, colour, and size of the flowers; in the length of the flower
stalk; in the colour, form, and size of the pods; in the form and size of
the seeds; and in the colour of the seed coats and of the albumen [cotyle-
dons]. Some of the characters noted do not permit of a sharp and certain
separation, since the difference is of a "more or less" nature, which is
often difficult to define. Such characters could not be utilized for the sepa-
rate experiments; these could only be applied to characters which stand
out clearly and definitely in the plants. Lastly, the result must show
whether they, in their entirety, observe a regular behaviour in their hybrid
unions, and whether from these facts any conclusion can be come to re-
garding those characters which possess a subordinate significance in the
type.
The characters which were selected for experiment relate:
1. To the difference in the form of the- ripe seeds. These are either
round or roundish, the depressions, if any, occur on the surface, being
always only shallow; or they are irregularly angular and deeply wrinkled
(P. quadratum).
2. To the difference in the colour of the seed albumen (endosperm).
The albumen of the ripe seeds is either pale yellow, bright yellow and
orange coloured, or it possesses a more or less intense green tint. This
difference of colour is easily seen in the seeds as their coats are trans-
parent.
3. To the difference in the colour of the seed coat. This is either
white, with which character white flowers are constantly correlated; or it
is grey, grey-brown, leather-brown, with or without violet spotting, in
which case the colour of the standards is violet, that of the wings purple/
and the stem in the axils of the leaves is of a reddish tint. The grey seed
coats become dark brown in boiling water.
4. To the difference in the form of the ripe pods. These are either
simply inflated, not contracted in places; or they are deeply constricted
between the seeds and more or less wrinkled (P. saccharatum).
5. To the difference in the colour of the unripe pods. They are either
light to dark green, or vividly yellow, in which colouring the stalks, leaf
veins, and calyx participate.
6. To "the difference in the position of the flowers. They are either
axial, that is, distributed along the main stem; or they are terminal, that
is, bunched at the top of the stem and arranged almost in a false umbel;
in this case the upper part of the stem is more or less widened in section
(P. umbellatum).
7. To the difference in the length of the stem. The length of the stem
is very various in some forms; it is, however, a constant character for each*
512
MASTERWORKS OF SCIENCE
In so far that healthy plants, grown in the same soil, are only subject to
unimportant variations in this character.
In experiments with this character, in order to be able to discriminate
with certainty, the long axis of 6 to 7 ft. was always crossed with the short
one of % ft. to i% ft.
Each two of the differentiating characters enumerated above were
united by cross-fertilization. There were made for the
ist trial 60 fertilizations on 15 plants.
2nd
3rd
4th
5th
6th
7th
58
35
40
23
34
37
10
10
10
5
10
10
Furthermore, in all the experiments reciprocal crossings were effected
in such a way that each of the two varieties which in one set of fertiliza-
tions served as seed bearer in the other set was used as the pollen plant.
The plants were grown in garden beds, a few also in pots, and were
maintained in their naturally upright position by means of sticks,
branches of trees, and strings stretched between. For each experiment a
number of pot plants were placed during the blooming period in a green-
house, to serve as control plants for the main experiment in the open as
regards possible disturbance by insects. Among the insects which visit
Peas the beetle Bruchus pisi might be detrimental to the experiments
should it appear in numbers. The female of this species is known to lay
the eggs in the flower, and in so doing opens the keel; upon the tarsi of
one specimen, which was caught in a flower, some pollen grains could
clearly be seen under a lens.
The risk of false impregnation by foreign pollen is, however, a very
slight one with Pisum, and is quite incapable of disturbing the general
result. Among more than 10,000 plants which were carefully examined
there were only a very few cases where an indubitable false impregnation
had occurred. Since in the greenhouse such a case was never remarked, it
may well be supposed that Bruchus pisi, and possibly also abnormalities
in the floral structure, were to blame.
[F±] THE FORMS OF THE HYBRIDS
EXPERIMENTS which in previous years were made with ornamental plants
have already afforded evidence that the hybrids, as a rule, are not exactly
intermediate between the parental species. With some of the more strik-
ing characters, those, for instance, which relate to the form and size of
the leaves, the pubescence of the several parts, &c., the intermediate, in-
deed, is nearly always to be seen; in other cases, however, one of the two
parental characters is so preponderant that it is difficult, or quite impossi-
ble, to detect the other in the hybrid.
MENDEL — PL ANT-HYBRIDIZ ATI ON 513
This is precisely the case with the Pea hybrids. In the case of each of
the seven crosses the hybrid character resembles that of one of the paren-
tal forms so closely that the other either escapes observation completely or
cannot be detected with certainty. This circumstance is of great impor-
tance in the determination and classification of the forms under which the
offspring of the hybrids appear. Henceforth in this paper those characters
which are transmitted entire, or almost unchanged in the hybridization,
and therefore in themselves constitute the characters of the hybrid, are
termed the dominant, and those which become latent in the process reces-
sive. The expression "recessive" has been chosen because the characters
thereby designated withdraw or entirely disappear in the hybrids, but
nevertheless reappear unchanged in their progeny, as will be demon-
strated later on.
It was furthermore shown by the whole of the experiments that it is
perfectly immaterial whether the dominant characters belong to the seed
bearer or to the pollen parent; the form of the hybrid remains identical in
both cases.
Of the differentiating characters which were used in the experiments
the following are dominant:
1. The round or roundish form of the seed with or without shallow
depressions.
2. The yellow colouring of the seed albumen [cotyledons].
3. The grey, grey-brown, or leather-brown colour of the seed coat, in
association with violet-red blossoms and reddish spots in the leaf axils.
4. The simply inflated form of the pod.
5. The green colouring of the unripe pod in association with the
same colour in the stems, the leaf veins, and the calyx.
6. The distribution of the flowers along the stem.
7. The greater length of stem.
With regard to this last character it must be stated that the longer
of the two parental stems is usually exceeded by the hybrid, a fact which
is possibly only attributable to the greater luxuriance which appears in all
parts of plants when stems of very different length are crossed. Thus, for
instance, in repeated experiments, stems of i ft. and 6 ft. in length yielded
without exception hybrids which varied in length between 6 ft. and 7%
ft.
[F2] THE FIRST GENERATION [BRED] FROM THE HYBRIDS
IN THIS GENERATION there reappear, together with the dominant characters,
also the recessive ones with their peculiarities fully developed, and this
occurs in the definitely expressed average proportion of three to one, so
that among each four plants of this generation three display the dominant
character and one the recessive. This relates without exception to all the
characters which were investigated in the experiments. The angular
wrinkled form of the seed, the green colour of the albumen, the white
514
MASTERWORKS OF SCIENCE
colour of the seed coats and the flowers, the constrictions of the pods, the
yellow colour of the unripe pod, of the stalk, of the calyx, and of the leaf
venation, the umbel-like form of the inflorescence, and the dwarfed stem,
all reappear in the numerical proportion given, without any essential al-
teration. Transitional forms were not observed in any experiment.
Since the hybrids resulting from reciprocal crosses are formed alike
and present no appreciable difference in their subsequent development,
consequently the results [of the reciprocal crosses] can be reckoned to-
gether in each experiment. The relative numbers which were obtained for
each pair of differentiating characters are as follows:
GREEN ROUND
YELLOW WRINKLED
X (i'i/li^-l lt;:
GW
INHERITANCE OF SEED CHARACTERS IN PEA
The seed of a green round variety fertilized by pollen" of a yellow wrinkled
variety are yellow and round (Fi). The reciprocal cross would give the same
result. Two pods of Fs seed borne by the Fi plant are shown. There were 6
yellow round, 3 green round, 3 yellow wrinkled, i green wrinkled.
Expt. i. Form of seed. — From 253 hybrids 7,324 seeds were obtained
in the second trial year. Among them were 5,474 round or roundish ones
and 1,850 angular wrinkled ones. Therefrom the ratio 2.96 to i is deduced.
Expt. 2. Colour of albumen. — 258 plants yielded 8,023 seeds, 6,022
yellow, and 2,001 green; their ratio, therefore, is as 3.01 to i.
In these two experiments each pod yielded usually both kinds of seed.
In well-developed pods which contained on the average six to nine seeds,
it often happened that all the seeds were round (.Expt. i) or all yellow
(Expt. 2); on the other hand there were never observed more than five
wrinkled or five green ones in one pod. It appears to make no difference
whether the pods are developed early or later in the hybrid or whether
they spring from the main axis or from a lateral one. In some few plants
MENDEL— -PLANT-HYBRIDIZATION 515
only a few seeds developed in the first formed pods, and these possessed
exclusively one of the two characters, but in the subsequently developed
pods the normal proportions were maintained nevertheless.
These two experiments are important for the determination of the
average ratios, because with a smaller number of experimental plants they
show that very considerable fluctuations may occur. In counting the seeds,
also, especially in Expt. 2, some care is requisite, since in some of the
seeds of many plants the green colour of the albumen is less developed,
and at first may be easily overlooked. The cause of this partial disappear-
ance of the green colouring has no connection with the hybrid character
of the plants, as it likewise occurs in the parental variety. This peculiarity
[bleaching] is also confined to the individual and is not inherited by the
offspring. In luxuriant plants this appearance was frequently noted. Seeds
which are damaged by insects during their development often vary in
colour and form, but, with 'a little practice in sorting, errors are easily
avoided. It is almost superfluous to mention that the pods must remain
on the plants until they are thoroughly ripened and have become dried,
since it is only then that the shape and colour of the seed are fully
developed.
Expt. 3. Colour of the seed coats. — Among 929 plants 705 bore violet-
red flowers and grey-brown seed coats; 224 had white flowers and white
seed coats, giving the proportion 3.15 to i.
Expt. 4. Form of pods. — Of 1,181 plants 882 had them simply in-
flated, and in 299 they were constricted. Resulting ratio, 2.95 to i.
Expt. 5. Colour of the unripe pods. — The number of trial plants was
580, of which 428 had green pods and 152 yellow ones. Consequently
these stand in the ratio 2.82 to i.
Expt. 6. Position of flowers. — Among 858 cases 651 had inflorescences
axial and 207 terminal. Ratio, 3.14 to i.
Expt. 7. Length of stem. — Out of 1,064 plants, in 787 cases the stem
was long, and in 277 short. Heiice a mutual ratio of 2.84 to i. In this ex-
periment the dwarfed plants were carefully lifted and transferred to a
special bed. This precaution was necessary, as otherwise they would have
perished through being overgrown by their tall relatives. Even in their
quite young state they can be easily picked out by their compact growth
and thick dark-green foliage.
If now the results of the whole of the experiments be brought to-
gether, there is found, as between the number of forms with the domi-
nant and recessive characters, an average ratio of 2.98 to i, or 3 to i.
The dominant character can have here a double signification — viz.
that of a parental character, or a hybrid character. In which of the two
significations it appears in each separate case can only be determined by
the following generation. As a parental character it must pass over un-
changed to the whole of the offspring; as a hybrid character, on the other
hand, it must maintain the same behaviour as in the first generation [F2]»
516 MASTERWORKS OF SCIENCE
[F3] THE SECOND GENERATION [BRED] FROM THE HYBRIDS
THOSE FORMS which in the first generation [F2] exhibit the recessive char-
acter do not further vary in the second generation [F3] as regards this
character; they remain constant in their offspring.
It is otherwise with those which possess the dominant character in
the first generation [bred from the hybrids]. Of these two thirds yield
offspring which display the dominant and recessive characters in the pro-
portion of 3 to i? and thereby show exactly the same ratio1 as the hybrid
forms, while only one third remains with the dominant character constant.
The separate experiments yielded the following results:
Expt. i. Among 565 plants which were raised from round seeds of
the first generation, 193 yielded round seeds only, and remained therefore
constant in this character; 372, however, gave both round and wrinkled
seeds, in the proportion of 3 to i. The number of the hybrids, therefore,
as compared with the constants is 1.93 to i.
Expt. 2. Of 519 plants which were raised from seeds whose albumen
was of yellow colour in the first generation, 166 yielded exclusively yellow,
while 353 yielded yellow and green seeds in the proportion of 3 to i.
There resulted, therefore, a division into hybrid and constant forms in the
proportion of 2.13 to i.
For each separate trial in the following experiments 100 plants were
selected which displayed the dominant character in the first generation,
and in order to ascertain the significance of this, ten seeds of each were
cultivated.
Expt. 3. The offspring of 36 plants yielded exclusively grey-brown
seed coats, while of the offspring of 64 plants some had grey-brown and
some had white.
Expt. 4. The offspring of 29 plants had only simply inflated pods; of
the offspring of 71, on the other hand, some had inflated and some
constricted.
Expt. 5. The offspring of 40 plants had only green pods; of the off-
spring of 60 plants some had green, some yellow ones.
Expt. 6. The offspring of 33 plants had only axial flowers; of the off-
spring of 67, on the other hand, some had axial and some terminal flowers.
Expt. 7. The offspring of 28 plants inherited the long axis, and those
of 72 plants some the long and some the short axis.
In each of these experiments a certain number of the plants came
constant with the dominant character. For the determination of the pro-
portion in which the separation of the forms with the constantly per-
sistent character results, the two first experiments are of especial impor-
tance, since in these a larger number of plants can be compared. The
MENDEL — PLAN T-HYBRIDI2 ATI ON 517
ratios 1.93 to i and 2.13 to i gave together almost exactly the average
ratio of 2 to i. The sixth experiment gave a quite concordant result; in
the others the ratio varies more or less, as was only to be expected in view
of the smaller number of 100 trial plants. Experiment 5, which shows the
greatest departure, was repeated, and then, in lieu of the ratio of 60 and
40, that of 65 and 35 resulted. The average ratio of a to i appears, there-
fore, as fixed with certainty. It is therefore demonstrated that, of those
forms which possess the dominant character in the first generation, twa
thirds have the hybrid character, while one third remains constant with
the dominant character.
The ratio of 3 to i, in accordance with which the distribution of the
dominant and recessive characters results in the first generation, resolves
itself therefore in all experiments into the ratio of 2 : i : i if the domi-
nant character be differentiated according to its significance as a hybrid
character or as a parental one. Since the members of the first generation
[F2] spring directly from the seed of the hybrids [F^], it is now clear
that the hybrids form seeds having one or other of the two differentiating
characters, and of these one half develop again the hybrid form, while the
other half yield plants which remain constant and receive the dominant
or the recessive characters [respectively} in equal numbers.
THE SUBSEQUENT GENERATIONS [BRED] FROM THE
HYBRIDS
THE PROPORTIONS in which the descendants of the hybrids develop and
split up in the first and second generations presumably hold good for all
subsequent progeny. Experiments i and 2 have already been carried
through six generations, 3 and 7 through five, and 4, 5, and 6 through
four, these experiments being continued from the third generation with
a small number of plants, and no departure from the rule has been per-
ceptible. The offspring of the hybrids separated in each generation in the
ratio of 2 : i : i into hybrids and constant forms.
If A be taken as denoting one of the two constant characters, for in-
stance the dominant, a, the recessive, and Aa the hybrid form in which
both are conjoined, the expression
shows the terms in the series for the progeny of the hybrids of two differ-
entiating characters.
The observation made by Gartner, Kolreuter, and others, that hybrids
are inclined to revert to the parental forms, is also confirmed by the ex-
periments described. It is seen that the number of the hybrids which arise
from one fertilization, as compared with the number of forms which be-
come constant, and their progeny from generation to generation, is con-
tinually diminishing, but that nevertheless they could not entirely disap-
pear. If an average equality of fertility in all plants in all generations be
518
MASTERWORKS OF SCIENCE
assumed, and if, furthermore, each hybrid forms seed of which one half
yields hybrids again, while the other half is constant to both characters in
equal proportions, the ratio of numbers for the offspring in each genera-
tion is seen by the following summary, in which A and a denote again the
two parental characters, and Aa the hybrid forms. For brevity's sake it
may be assumed that each plant in each generation furnishes only 4 seeds.
Generation
i
2
3
4
5
n
A
i
6
28
120
496
Aa
2
4
8
16
32
i
6
28
120
496
RATIOS
A
.<4#
£
i
2
I
3
2
3
7
2
7
15
2
15
31
2
31
2n~ I
2
2f
In the tenth generation, for instance, 2ra — 1=1023. There result, there-
fore, in each 2,048 plants which arise in this generation, 1,023 with the
constant dominant character, 1,023 with the recessive character, and only
two hybrids.
THE OFFSPRING OF HYBRIDS IN WHICH SEVERAL
DIFFERENTIATING CHARACTERS ARE ASSOCIATED
IN THE EXPERIMENTS above described plants were used which differed only
in one essential character. The next task consisted in ascertaining whether
the law of development discovered in these applied to each pair of differ-
entiating characters when several diverse characters are united in the
hybrid by crossing. As regards the form of the hybrids in these cases, the
experiments showed throughout that this invariably more nearly ap-
proaches to that one of the two parental plants which possesses the
greater number of dominant characters. If, for instance, the seed plant has
a short stem, terminal white flowers, and simply inflated pods; the pollen
plant, on the other hand, a long stem, violet-red flowers distributed along
the stem, and constricted pods; the hybrid resembles the seed parent only
in the form of the pod; in the other characters it agrees with the pollen
parent. Should one of the two parental types possess only dominant char-
acters, then the hybrid is scarcely or not at all distinguishable from it.
Two experiments were made with a considerable number of plants.
In the jSrst experiment the parental plants differed in the form of the
seed and in the colour of the albumen; in the second in the form of the
seed, in the colour of the albumen, and in the colour of the seed coats.
Experiments with seed characters give the result in the simplest and
most certain way.
In order to facilitate study of the data in these experiments, the dif-
ferent characters of the seed plant will be indicated by A, B, Cf those of
the pollen plant by a, b, c, and the hybrid forms of the characters by Aa,
Bb, and Cc.
MENDEL — PLANT-HYBRIDIZATION
519
Expt. i. — AB, seed parents;
A, form round;
B, albumen yellow.
ab, pollen parents;
a, form wrinkled;
bf albumen green.
The fertilized seeds appeared round and yellow like those of the seed
parents. The plants raised therefrom yielded seeds of four sorts, which
frequently presented themselves in one pod. In all, 556 seeds were yielded
by 15 plants, and of these there were:
315 round and yellow,
101 wrinkled and yellow,
1 08 round and green,
32 wrinkled and green.
All were sown the following year. Eleven of the round yellow seeds did
not yield plants3 and three plants did not form seeds. Among the rest:
38 had round yellow seeds AB
65 round yellow and green seeds " ABb
60 round yellow and wrinkled yellow seeds AaB
138 round yellow and green, wrinkled yellow and green
seeds AaBb.
From the wrinkled yellow seeds 96 resulting plants bore seed, of which:
28 had only wrinkled yellow seeds aB
68 wrinkled yellow and green seeds aBb.
From 108 round green seeds 102 resulting plants fruited, of which:
35 had only round green seeds Ab
67 round and wrinkled green seeds Aab.
The wrinkled green seeds yielded 30 plants which bore seeds all of like
character; they remained constant abs
The offspring of the hybrids appeared therefore under nine different
forms, some of them in very unequal numbers. When these are collected
and co-ordinated we find:
38 plants with the sign AB
Ab
aB
ab
35
28
30
65
68
60
6l
138
ABb
aBb
AaB
Aab
AaBb.
The whole of the forms may be classed into three essentially different
groups. The first includes those with the signs AB, Ab> aBt and ab: they
520 _ MASTERWORKS OF SCIENCE _
possess only constant characters and do not vary again in the next genera-
tion. Each of these forms is represented on the average thirty-three times.
The second group includes the signs ABb, dBb, AaB, Aab: these are con-
stant in one character and hybrid in another, and vary in the next genera-
tion only as regards the hybrid character. Each of these appears on an
average sixty-five times. The form AaBb occurs 138 times: it is hybrid in
both characters, and behaves exactly as do the hybrids from which it is
derived.
If the numbers in which the forms belonging to these classes appear
be compared, the ratios of i, 2, 4 are unmistakably evident. The numbers
32, 65, 138 present very fair approximations to the ratio numbers of 33,,
66, 132.
The developmental series consists, therefore, of nine classes, of which
four appear therein always once and are constant in both characters; the
forms AB, ab, resemble the parental forms, the two others present combi-
nations between the conjoined characters A} a, B, b, which combinations
are likewise possibly constant. Four classes appear always twice, and are
constant in one character and hybrid in the other. One class appears four
times, and is hybrid in both characters. Consequently the offspring of the
hybrids, if two kinds of differentiating characters are combined therein,
are represented by the expression
This expression is indisputably a combination series in which the
two expressions for the characters A and a, B and b are combined. We
arrive at the full number of the classes of the series by the combination of
the expressions:
Expt. 2.
ABC, seed parents; abc, pollen parents;
A, form round; a, form wrinkled;
B, albumen yellow; b, albumen green;
C, seed coat grey-brown. cf seed coat white.
This experiment was made in precisely the same way as the previous
one. Among all the experiments it demanded the most time and trouble.
From 24 hybrids* 687 seeds were obtained in all; these were all either
spotted, grey-brown or grey-green, round or wrinkled. From these in the
following year 639 plants fruited, and, as further investigation showed,
there were among them:
8 plants ABC 22 plants ABCc 45 plants ABbCc
14 " ABc 17 " AbCc 36 " dBbCc
9 " AbC 25 " aBCc 38 " AaBCc
ii " Abc 20 " abCc 40 " AaBCc
8 " aBC 15 " ABbC 49 " AaBbC
MENDEL — PLANT-HYBRIDIZATION 521
10 plants aBc 18 plants ABbc
48 plants AaBbc
10 " abC 19
dBbC
7 " abc 24
aBbc
14
AaBC
78 " AaBbCc
18
AaBc
20
AabC
16
Aabc
The whole expression contains 27 terms. Of these 8 are constant in
all characters, and each appears on the average 10 times; 12 are constant
in two characters and hybrid in the third; each appears on the average 19
times; 6 are constant in one character and hybrid in the other two; each
appears on the average 43 times. One form appears 78 times and is hybrid
in all of the characters. The ratios 10, 19, 43, 78 agree so closely with the
ratios 10, 20, 40, 80, or i, 2, 4, 8, that this last undoubtedly represents the
true value.
The development of the hybrids when the original parents differ in
three characters results therefore according to the following expression:
ABC + ABc + AbC + Abc + aBC + aBc + abC + abc + zABCc +
zAbCc + zaBCc + zabCc + 2,ABbC + zABbc + zaBbC +
2AaBC + *AaBc + *AabC + zAabc + ^ABbCc
aBbC + \AaBbc + ZAaBbCc.
Here also is involved a combination series in which the expressions
for the characters A and a, B and b, C and c, are united. The expressions
A-\-2Aa-\-a
give all the classes of the series. The constant combinations which occur
therein agree with all combinations which are possible between the char-
acters A, B, C, a, b, c; two thereof, ABC and abc, resemble the two
original parental stocks.
In addition, further experiments were made with a smaller number
of experimental plants in which the remaining characters by twos and
threes were united as hybrids: all yielded approximately the same results.
There is therefore no doubt that for the whole of the characters involved
in the experiments the principle applies that the offspring of the hybrids
in which several essentially different characters are combined exhibit the
terms of a series of combinations, in which the developmental series for
each pair of differentiating characters are united. It is demonstrated at
the same time that the relation of each fair of different characters in
hybrid union is independent of the other differences in the two original
parental stocks. •
If n represent the number of the differentiating characters in the two
original stocks, 3" gives the number of terms of the combination series, 4"
the number of individuals which belong to the series, and 2n the number
of unions which remain constant. The series therefore contains, if the
522 MASTERWORKS OF SCIENCE
original stocks differ in four characters, 34=8i classes, 4^=256 individ-
uals, and 24=i6 constant forms; or, which is the same, among each 256
offspring of the hybrids there are 81 different combinations, 16 of which
are constant.
All constant combinations which in Peas are possible by the combi-
nation of the said seven differentiating characters were actually obtained
by repeated crossing. Their number is given by 27=i28. Thereby is simul-
taneously given the practical proof that the constant characters which ap-
pear in the several varieties of a group of plants may be obtained in all
the associations which are possible according to the [mathematical} laws
of combination, by means of repeated artificial fertilization.
If we endeavour to collate in a brief form the results arrived at, we
find that those differentiating characters, which admit of easy and certain
recognition in the experimental plants, all behave exactly alike in their
hybrid associations. The offspring of the hybrids of each pair of differenti-
ating characters are, one half, hybrid again, while the other half are con-
stant in equal proportions having the characters of the seed and pollen
parents respectively. If several differentiating characters are combined by
cross-fertilization in a hybrid, the resulting offspring form the terms of
a combination series in which the combination series for each pair of
differentiating characters are united.
The uniformity of behaviour shown by the whole of the characters
submitted to experiment permits, and fully justifies, the acceptance of
the principle that a similar relation exists in the other characters which
appear less sharply defined in plants, and therefore could not be included
in the separate experiments. An experiment with peduncles of different
lengths gave on the whole a fairly satisfactory result, although the dif-
ferentiation and serial arrangement of the forms could not be effected
with that certainty which is indispensable for correct experiment.
THE REPRODUCTIVE CELLS OF THE HYBRIDS
THE RESULTS of the previously described experiments led to further experi-
ments, the results of which appear fitted to afford some conclusions as
regards the composition of the egg and pollen cells of hybrids. An im-
portant clue is afforded in Pisum by the circumstance that among the
progeny of the hybrids constant forms appear, and that this occurs, too,
in respect of all combinations of the associated characters. So far as experi-
ence goes, we find it in every case confirmed that constant progeny can
only be formed when the egg cells and the fertilizing pollen are of like
character, so that both are provided with the material for creating quite
similar individuals, as is the case with the normal fertilization of pure
species. We must therefore regard it as certain that exactly similar factors
must be at work also in the production of the constant forms in the hybrid
plants. Since the various constant forms are produced in one plant, or
even in one flower bf a plant, the conclusion appears logical that iii the
MENDEL — PLANT-HYBRIDIZATION 523
ovaries of the hybrids there are formed as many sorts of egg cells, and in
the anthers as many sorts of pollen cells, as there are possible constant
combination forms, and that these egg and pollen cells agree in their
internal composition with those of the separate forms.
In point of fact it is possible to demonstrate theoretically that this
hypothesis would fully suffice to account for the development of the
hybrids in the separate generations, if we might at the same time assume
that the various kinds of egg and pollen cells were formed in the hybrids
on the average in equal numbers.
In order to bring these assumptions to an experimental proof, the
following experiments were designed. Two forms which were constantly
different in the form of the seed and the colour of the albumen were
united by fertilization.
If the differentiating characters are again indicated as A, B, a, b* we
have:
ABt seed parent; ab, pollen parent;
A, form round; a, form wrinkled;
B, albumen yellow. b, albumen green.
The artificially fertilized seeds were sown together with several seeds
of both original stocks, and the most vigorous examples were chosen for
the reciprocal crossing. There were fertilized:
1. The hybrids with the pollen of AB.
2. The hybrids " " ab.
3. AB " " the hybrids.
4. ab " " the hybrids.
For each of these four experiments the whole of the flowers on three
plants were fertilized. If the above theory be correct, there must be de-
veloped on the hybrids egg^and pollen cells of the forms AB, Ab, aB, ab,
and there would be combined:
1. The egg cells AB, Ab, aB, ab with the pollen cells AB.
2. The egg cells AB, Ab, aB, ab with the pollen cells ab.
3. The egg cells AB with the pollen cells AB, Ab, aB, ab.
4. The egg cells ab with the pollen cells AB, Ab, aB, ab.
From each of these experiments there could then result only the fol-
lowing forms:
1. AB, ABb, AaB, AaBb.
2. AaBb, Aab, aBb, ab.
3. AB, ABb, AaB, AaBb.
4. AaBb, Aab, aBb, ab.
If, furthermore, the several forms of the egg and pollen cells of the
hybrids were produced on an average in equal numbers, then in each
experiment the said four combinations should stand in the same ratio to
524 MASTERWORKS OF SCIENCE
each other. A perfect agreement in the numerical relations was, however,
not to be expected, since in each fertilization, even in normal cases, some
egg cells remain undeveloped or subsequently die, and many even of the
well-formed seeds fail to germinate when sown. The above assumption
is also limited in so far that, while it demands the formation of an equal
number of the various sorts of egg and pollen cells, it does not require
that this should apply to each separate hybrid with mathematical exact-
ness.
The first and second experiments had primarily the object of proving
the composition of the hybrid egg cells, while the third and fourth experi-
ments were to decide that of the pollen cells. As is shown by the above
demonstration, the first and third experiments and the second and fourth
experiments should produce precisely the same combinations, and even
in the second year the result should be partially visible in the form and
colour of the artificially fertilized seed. In the first and third experiments
the dominant characters of form and colour, A and B, appear in each
union, and are also partly constant and partly in hybrid union with the
recessive characters a and b, for which reason they must impress their
peculiarity upon the whole of the seeds. All seeds should therefore appear
round and yellow, if the theory be justified. In the second and fourth
experiments, on the other hand, one union is hybrid in form and in colour,
and consequently the seeds are round and yellow; another is hybrid in
form, but constant in the recessive character of colour, whence the seeds
are round and green; the third is constant in the recessive character of
form but hybrid in colour, consequently the seeds are wrinkled and yel-
low; the fourth is constant in both recessive characters, so that the seeds
are wrinkled and green. In both these experiments there were conse-
quently four sorts of seed to be expected — viz. round and yellow, round
and green, wrinkled and yellow, wrinkled and green.
The crop fulfilled these expectations perfectly. There were obtained
in the
ist Experiment, 98 exclusively round yellow seeds;
3rd " 94
In the 2nd Experiment, 31 round and yellow, 26 round and green,
27 wrinkled and yellow, 26 wrinkled and green seeds.
In the 4th Experiment, 24 round and yellow, 25 round and green, 22
wrinkled and yellow, 27 wrinkled and green seeds:
There could scarcely be now any doubt of the success of the experi-
ment; the next generation must afford the final proof. From the seed
sown there resulted for the first experiment 90 plants, and for the third
87 plants which fruited: these yielded for the
ist Exp. 3rd Exp.
20 25 round yellow seeds ....... AB
23 19 round yellow and green seeds . ABb
25 22 round and wrinkled yellow seeds . . . AaB
22 21 round and wrinkled green and yellow seeds AaBb
MENDEL — PLANT- HYBRIDIZATION 525
In the second and fourth experiments the round and yellow seeds
yielded plants with round and wrinkled yellow and green seeds, AaBb.
From the round green seeds plants resulted with round and wrinkled
green seeds, Aab.
The wrinkled yellow seeds gave plants with wrinkled yellow and
green seeds, aBb.
From the wrinkled green seeds plants were raised which yielded
again only wrinkled and green seeds, ab.
Although in these two experiments likewise some seeds did not ger-
minate, the figures arrived at already in the previous year were not affected
thereby, since each kind of seed gave plants which, as regards their seed,
were like each other and different from the others. There resulted there-
fore from the
2nd Exp. 4th Exp.
31 24 plants of the form AaBb
26 25 " " Aab
27 22 " " aBb
26 27 " " ab
In all the experiments, therefore, there appeared all the forms which
the proposed theory demands, and they came in nearly equal numbers.
In a further experiment the characters of flower colour and length
of stem were experimented upon, and selection was so made that in the
third year of the experiment each character ought to appear in half of all
the* plants if the above theory were correct. A, B, a, b serve again as indi-
cating the various characters. p
A, violet-red flowers. a, white flowers.
B, axis long. b, axis short.
There subsequently appeared
The violet-red flower-colour « (Act) in 85 plants.
" white " " (a) in 81 "
" long stem (Bb) in 87
" short " (b) in 79 "
The theory adduced is therefore satisfactorily confirmed in this experi-
ment also.
For the characters of form of pod, colour of pod, and position of
flowers experiments were also made on a small scale, and results obtained
in perfect agreement. All combinations which were possible through the
union of the differentiating characters duly appeared, and in nearly equal
numbers.
Experimentally, therefore, the theory, is confirmed that the pea hybrids
form egg and fallen cells which, in their constitution, re-present in equal
numbers all constant forms which result from the combination of the
characters united in fertilization.
526 _ MASTERWORKS OF SCIENCE _
The difference of the forms among the progeny of the hybrids, as
well as the respective ratios of the numbers in which they are observed,,
find a sufficient explanation in the principle above deduced. The simplest
case is afforded by the developmental series of each pair of differ entiating
characters. This series is represented by the expression A~\-iAa-\-a, in
which A and a signify the forms with constant differentiating characters,.
and Aa the hybrid form of both. It includes in three different classes four
individuals. In the formation of these, pollen and egg cells of the form A
and a take part on the average equally in the fertilization; hence each
form [occurs] twice, since four individuals are formed. There participate
consequently in the fertilization
The pollen cells
The egg cells
It remains, therefore, purely a matter of chance which of the two
sorts of pollen will become united with each separate egg cell. According,.
however, to the law of probability, it will always happen, on the average
of many cases, that each pollen form A and a will unite equally often with
each egg cell form A and a, consequently one of the two pollen cells A
in the fertilization will meet with the egg cell A and the other with an
egg cell a, and so likewise one pollen cell a will unite with an egg cell A,.
and the other with egg cell a.
Pollen cells A A a a
\ X
Egg cells A A a a
The result of the fertilization may be made clear by putting the signs
for the conjoined egg and pollen cells in the form of fractions, those for
the pollen cells above and those for the egg cells below the line. We then
have
A A a a
In the first and fourth term the egg and pollen cells are of like kind, conse-
quently the product of their union must be constant, viz. A and a; in the
second and third, on the other hand, there again results a union of the
two differentiating characters of the stocks, consequently the forms result-
ing from these fertilizations are identical with those of the hybrid from
which they sprang. There occurs accordingly a repeated hybridization.
This explains the striking fact that the hybrids are able to produce, besides
A a
the two parental forms, offspring which are like themselves; — and —
ct A
both give the same union Aa, since, as already remarked above, it makes
MENDEL — PLANT-HYBRIDIZATION 527
no difference in the result of fertilization to which of the two characters
the pollen or egg cells belong. We may write then
A A a a
± 1 1 = A + aAa+a.
A a A a
This represents the average result of the self-fertilization of the
hybrids when two differentiating characters are united in them. In indi-
vidual flowers and in individual plants, however, the ratios in which the
forms of the series are produced may suffer not inconsiderable fluctua-
tions. Apart from the fact that the numbers in which both sorts of egg
cells occur in the seed vessels can only be regarded as equal on the aver-
age, it remains purely a matter of chance which of the two sorts of pollen
may fertilize each separate egg cell. For this reason the separate values
must necessarily be .subject to fluctuations, and there are even extreme
cases possible, as were described earlier in connection \^ith the experi-
ments on the form of the seed and the colour of the albumen. The true
ratios of the numbers can only be ascertained by an average deduced
from the sum of as many single values as possible; the greater the num-
ber the more are merely chance effects eliminated.
The developmental series for hybrids in which two kinds of differen-
tiating characters are united contains among sixteen individuals nine dif-
ferent forms, viz.:
AB+Ab+aB+ab^ABb+iaBb+zAaB+zAab+^AaBb.
Between the differentiating characters of the original stocks Aa and Bb
four constant combinations are possible, and consequently the hybrids
produce the corresponding four forms of egg and pollen cells AB, Ab,
dBj ab, and each of these will on the average figure four times in the
fertilization, since sixteen individuals are included in the series. There-
fore the participators in the fertilization are
Pollen cells AB+AB+AB+AB+Ab+Ab+At>+Ab+aB+aB+aB+aB+
ab -\-ab-\-ab-\-ab.
Egg cells AB+AB+AB+AB+Ab+Ab+Ab+Ab+aB+aB+aB+aB+
ab + ab-\-ab-\-ab .
In the process of fertilization each pollen form unites on an average
equally often with each egg cell form, so that each of the four pollen cells
AB unites once with one of the forms of egg cell AB, Ab, aB, ab. In pre-
cisely the same way the rest of the pollen cells of the forms Ab, aB, ab
unite with all the other egg cells. We obtain therefore
AB+ABb+AaB+AaBb+ABb+Ab+AaBb+Aab+AaB+AaBb+aB+
528 MASTERWORKS OF SCIENCE .
In precisely similar fashion is the developmental series of hybrids
exhibited when three kinds of differentiating characters are conjoined
in them. The hybrids form eight various kinds of egg and pollen cells —
ABC, ABc, AbC, Abe, aBC, aEc, abC, abc — and each pollen form unites
Itself again on the average once with each form of egg cell.
The law of combination of different characters which governs the
development of the hybrids finds therefore its foundation and explana-
tion in the principle enunciated, that the hybrids produce egg cells and
pollen cells which in equal numbers represent all constant forms which
result from the combinations of the characters brought together in ferti-
lization.
CONCLUDING REMARKS
IT CAN HARDLY FAIL to be of interest to compare the observations made
regarding Pisum with the results arrived at by the tWo authorities in this
branch of knowledge, Kolreuter and Gartner, in their investigations. Ac-
cording to the opinion of both, the hybrids in outward appearance pre-
sent either a form intermediate between the original species or they
closely resemble either the one or the other type, and sometimes can
hardly be discriminated from it. From their seeds usually arise, if the
fertilization was effected by their own pollen, various forms which differ
from the normal type. As a rule, the majority of individuals obtained by
one fertilization maintain the hybrid form, while some few others come
more like the seed parent, and one or other individual approaches the
pollen parent. This, however, is not the case with all hybrids without ex-
ception. Sometimes the offspring have more nearly approached, some the
one and some the other of the two original stocks, or they all incline
more to one or the other side; while in other cases they remain perfectly
li\e the hybrid and continue constant in their offspring. The hybrids
of varieties behave like hybrids of species, but they possess greater varia-
bility of form and a more pronounced tendency to revert to the original
types.
With regard to the form of the hybrids and their development, as a
rule an agreement with the observations made in Pisum is unmistakable.
It is otherwise with the exceptional cases cited. Gartner confesses even
that the exact determination whether a form bears a greater resemblance
to one or to the other of the two original species often involved great
difficulty, so much depending upon the subjective point of view of the
observer. Another circumstance could, however, contribute to render the
results fluctuating and uncertain, despite the most careful observation and
differentiation. For the experiments plants were mostly used which rank
as good species and are differentiated by a large number of characters.
In addition to the sharply defined characters, where it is a question of
greater or less similarity, those characters must also be taken into account
which are often difficult to define in words, but yet suffice, as every plant
specialist knows, to give the forms a peculiar appearance. If it be accepted
MENDEL — PLANT-HYBRIDIZATION 529
that the development of hybrids follows the law which is valid for Pisum,
the series in each separate experiment must contain very many forms,
since the number of the terms, as is known, increases with the number
of the differentiating characters as the powers of three. With a relatively
small number of experimental plants the result therefore could only be
approximately right, and in single cases might fluctuate considerably. If,
for instance, the two original stocks differ in seven characters, and 100
and 200 plants were raised from the seeds of their hybrids to determine
the grade of relationship of the offspring, we can easily see how uncertain
the decision must become, since for seven differentiating characters the
combination series contains 16,384 individuals under 2187 various forms;
now one and then another relationship could assert its predominance, just
according as chance presented this or that form to the observer in a major-
ity of cases.
If, furthermore, there appear among the differentiating characters at
the same time dominant characters, which are transmitted entire or nearly
unchanged to the hybrids, then in the terms of the developmental series
that one of the two original parents which possesses the majority of domi-
nant characters must always be predominant. In the experiment described
relative to Pisum, in which three kinds of differentiating characters
were concerned, all the dominant characters belonged to the seed parent.
Although the terms of the series in their internal composition approach
both original parents equally, yet in this experiment the type of the seed
parent obtained so great a preponderance that out of each sixty-four plants
of the first generation fifty-four exactly resembled it, or only differed in
one character. It is seen how rash it must be under such circumstances to
draw from the external resemblances of hybrids conclusions as to their
internal nature.
Gartner mentions that in those cases where the development was
regular, among the offspring of the hybrids the two original species were
not reproduced, but only a few individuals which approached them. With
very extended developmental series it could not in fact be otherwise* For
seven differentiating characters, for instance, among more than 16,000
individuals — offspring of the hybrids — each of the two original species
would occur only once. It is therefore hardly possible that these should
appear at all among a small number of experimental plants; with some
probability, however, we might reckon upon the appearance In the series
of a few forms which approach them.
We meet with an essential difference in those hybrids which remain
constant in their progeny and propagate themselves as truly as the pure
species. According to Gartner, to this class belong the remarkably fertile
hybrids Aquilegia atropurpurea canadensis, Lavatera pseudolbia thuringi-
aca, Geum urbano-rivale, and some Dianthus hybrids; and, according to
Wichura, the hybrids of the Willow family. For the history of the evolu-
tion of plants this circumstance is of special importance, since constant
hybrids acquire the status of new species. The correctness of the facts
is guaranteed by eminent observers, and cannot be doubted. Gartner had
530 MASTERWORKS OF SCIENCE
an opportunity of following up Dianthus Armeria dehoides to the tenth
generation, since it regularly propagated itself in the garden.
With Pi sum it was shown by experiment that the hybrids form egg
and pollen cells of different kinds, and that herein lies the reason of the
variability of their offspring. In other hybrids, likewise, whose offspring
behave similarly we may assume a like cause; for those, on the other
hand, which remain constant the assumption appears justifiable that their
reproductive cells are all alike and agree with the foundation cell [ferti-
lized ovum] of the hybrid. In the opinion of renowned physiologists, for
the purpose of propagation one pollen cell and one egg cell unite in
Phanerogams into a single cell, which is capable by assimilation and
formation of new cells to become an independent organism. This devel-
opment follows a constant law, which is founded on the material compo-
sition and arrangement of the elements which meet in the cell in a vivify-
ing union. If the reproductive cells be of the same kind and agree with
the foundation cell [fertilized ovum] of the mother plant, then the devel-
opment of the new individual will follow the same law which rules the
mother plant. If it chance that an egg cell unites with a dissimilar pollen
cell, we must then assume that between those elements of both cells,
which determine opposite characters, some sort of compromise is effected.
The resulting compound cell becomes the foundation of the hybrid
organism, the development of which necessarily follows a different scheme
from that obtaining in each of the two original species. If the compro-
mise be taken to be a complete one, in the sense, namely, that the hybrid
embryo is formed from two similar cells, in which the differences are
entirely and permanently accommodated together, the further result fol-
lows that the hybrids, like any other stable plant species, reproduce them-
selves truly in their offspring. The reproductive cells which are formed
in their seed vessels and anthers are of one kind, and agree with the
fundamental compound cell [fertilized ovum].
With regard to those hybrids whose progeny is variable we may per-
haps assume that between the differentiating elements of the egg and
pollen cells there also occurs a compromise, in so far that the formatipn
of a cell as foundation of the hybrid becomes possible; but, nevertheless,
the arrangement between the conflicting elements is only temporary and
does not endure throughout the life of the hybrid plant. Since in the
habit of the plant no changes are perceptible during the whole period
of vegetation, we must further assume that it is only possible for the
differentiating elements to liberate themselves from the enforced union
when the fertilizing cells are developed. In the formation of these cells
all existing elements participate in an entirely free and equal arrange-
ment, by which it is only the differentiating ones which mutually sepa-
rate themselves. In this way the production would be rendered possible
of as many sorts of egg and pollen cells as there are combinations possible
of the formative elements.
The attribution attempted here of the essential difference in the de-
velopment of hybrids to a permanent or temporary union of the differing
MENDEL — PLANT-HYBRIDIZATION 53_1
cell elements can, of course, only claim the value of an hypothesis for
which the lack of definite data offers a wide scope. Some justification
of the opinion expressed lies in the evidence afforded' by Pisum that the
behaviour of each pair of differentiating characters in hybrid union is
independent of the other differences between the two original plants, and,
further, that the hybrid produces just so many kinds of egg and pollen
cells as there are possible constant combination forms. The differentiating
characters of two plants can finally, however, only depend upon differ-
ences in "the composition and grouping of the elements which exist in
the foundation cells [fertilized ova] of the same in vital interaction.
In conclusion, the experiments carried out by Kolreuter, Gartner, and
others with respect to the transformation of one species into another by
artificial fertilization merit special mention. Particular importance has
been attached to these experiments, and Gartner reckons them among
"the most difficult of all in hybridization."
If a species A is to be transformed into a species B, both must be
united by fertilization and the resulting hybrids then be fertilized with
the pollen of B; then, out of the various offspring resulting, that form
would be selected which stood in nearest relation to B and once more be
fertilized with B pollen, and so continuously until finally a form is ar-
rived at which is like B and constant in its progeny. By this process the
species A would change into the species B. Gartner alone has effected
thirty such experiments with plants of genera Aquilegia, Dianthus, Geum,
Lavatera, Lychnis, Malva, Nicotianaf and Oenothera. The period of trans-
formation was not alike for all species. While with some a triple fertiliza-
tion sufficed, with others this had to be repeated five or six times, and
even in the same species fluctuations were observed in various experi-
ments. Gartner ascribes this difference to the circumstance that "the
specific [typische] power by which a species, during reproduction, effects
the change and transformation of the maternal type varies considerably
in different plants, and that, consequently, the periods within which the
one species is changed into the other must also vary, as also the number
of generations, so that the transformation in some species is perfected in
more, and in others in fewer generations." Further, the same observer
remarks "that in these transformation experiments a good deal depends
upon which type and which individual be chosen for further transforma-
tion."
If it may be assumed that in these experiments the constitution o£
the forms resulted in a similar way to that of Pisum, the entire process
of transformation would find a fairly simple explanation. The hybrid
forms as many kinds of egg cells as there are constant combinations pos-
sible of the characters conjoined therein, and one of these is always of
the same kind as that of the fertilizing pollen cells. Consequently there
always exists the possibility with all such experiments that even from the
second fertilization there may result a constant form identical with that
of the pollen parent. Whether this really be obtained depends in each
separate case upon the number of the experimental plants, as well as upon
532 MASTERWORKS OF SCIENCE
the number of differentiating characters which are united by the fertiliza-
tion. Let us, for instance, assume that the plants selected for experiment
differed in three characters, and the species ABC is to be transformed into
the other species abc by repeated fertilization with the pollen of the lat-
ter; the hybrids resulting from the first cross form eight different kinds
of egg cells, viz.:
ABC, ABc, AbC, dBC, Abe, aBc, abC, abc.
These in the second year of experiment are united again with the
pollen cells abc, and we obtain the series
AaBbCc+AaBbc+AabCc^BbCc+Aabc+aBbc+abCc+abc.
Since the form abc occurs once in the series of eight terms, it is con-
sequently little likely that it would be missing among the experimental
plants, even were these raised in a smaller number, and the transforma-
tion would be perfected already by a second fertilization. If by chance
it did not appear, then the fertilization must be repeated with one of
those forms nearest akin, Aabc, aBbc, abCc. It is perceived that such an
experiment must extend the farther the smaller the number of experi-
mental plants and the larger the number of differentiating characters in
the two original species; and that, furthermore, in the same species there
can easily occur a delay of one or even of two generations such as Gartner
observed. The transformation of widely divergent species could generally
only be completed in five or six years of experiment, since the number
of different egg cells which are formed in the hybrid increases as the
powers of two with the number of differentiating characters.
THE PERIODIC LAW
by
DMITRI IVANOVICH MtiNDELEYEV
CONTENTS
The Periodic Law
The Grouping of the Elements and the Periodic Law
DMITRI IVANOVICH MENDELEYEV
1834-190?
DMITRI IVANOVICH MENDELEYEV lived in a Russia not familiar
to the Western world. He was himself known, however, in
scientific circles all over continental Europe; he visited Eng-
land several times and the United States once. Westerners re-
membered his tall and slightly stooped figure, his deep-set,
bright blue eyes, his finely modeled, gesturing hands, and his
flowing hair — which he allowed a barber to cut only once a
year, in the spring. They recalled him as "patriarchal," or as
"a grand Russian of the province of Tver." His students at
the Technological Institute in St. Petersburg and at the Uni-
versity of St. Petersburg remembered less his personal appear-
ance than his talent for exposition in the lecture room and his
more remarkable talent for stirring in students an ambition
for knowledge. Several generations of them, including many
eminent chemists and teachers, have paid tribute to his abili-
ties. To them he said: "I do not wish to cram you with facts,
but I want you to understand chemistry. And you should re-
member that hypotheses are not theories. By a theory I mean
a conclusion drawn from the accumulated facts we now pos-
sess which enables us to foresee new facts which we do not
yet know."
Mendeleyev's name is inseparably associated with the
great generalization known as the periodic system of the ele-
ments. When he announced the generalization in 1869, it was,
according to his own definition, not a hypothesis, but a
theory. Subsequently, his own work and that of other chem-
ists has given to the theory the validity of a law; and the
Periodic Law is familiar to every student*
Mcndeleyev became a teacher partly by accident. His
father taught for many years, notably in the gymnasium at
Tobolsk, Siberia, where he met and married Maria Dmi-
trievna. Soon after the birth of his youngest son, Dmitri, in
536 MASTERWORKS OF SCIENCE
1834, he became wholly blind. He and his large family — there
were then eight children surviving of the fourteen Maria had
borne — had only his small pension to live on. But Maria had,
like her famous son, intelligence and energy. As a girl, she
had educated herself, in a time and a country where women
were not schooled, by repeating the lessons assigned to her
elder brother, Basil. With the same kind of directness, she
now set about the re-establishment of a glassworks once
owned by her family in Tobolsk. This she continued to man-
age and operate until after the death of her husband in 1847.
By this time young Dmitri had progressed through the
classes of the Tobolsk gymnasium. He had also met some of
the Decembrists in political exile in Tobolsk. They interested
him so much in natural science that he and his mother de-
cided that he should become a scientist. Some years later the
dying Maria said to Dmitri, "Refrain from illusions, insist on
work, and not on words. Patiently search divine and scientific
truth." She had perhaps already phrased for herself these in-
structions for her scientist son when he graduated from the
gymnasium. For then, not overcome by the death of her hus-
band or by the calamity of the fire which destroyed her glass-
works, she had gathered her scanty means and, with Dmitri
and her daughter Elizabeth, had made the long journey to
Moscow. Her design was to enter Dmitri at the university
there, to make a scientist of him. Official difficulties blocked
her way. After a year of effort, though she did not succeed in
entering her son at the University of Moscow, she did procure
government aid for his continued training at the Central
Pedagogic Institute in St. Petersburg, under the Physico-
Mathematical Faculty. The function of this school was to pre-
pare teachers for the imperial schools. Maria lived just long
enough to see her son complete his training and to graduate
as a teacher.
Young Mendeleyev showed symptoms of lung disorder
when he finished his course at the institute and was ordered
south. Fortunately he obtained a post as chief science master
in Simferopol, in the Crimea, and, during the Crimean War,
another teaching post in Odessa. Residence in this southern
climate cured his pulmonary trouble. In 1856, on his return to
St. Petersburg, he took his master's degree in chemistry and
became a privatdocent at the university. Three years later he
was permitted to go to Paris, and later to Heidelberg for
studies which he continued in St. Petersburg until he earned
his doctor's degree in 1861. In 1866 he was appointed profes-
sor of general chemistry in the university, and retained his
post there until a disagreement with the university adminis-
tration forced his retirement in 1 890. Three years later he was
MENDELEYEV — THE PERIODIC LAW 537
appointed Director o£ the Bureau of Weights and Measures,
and was still Director at his death in 1907.
Mendeleyev had a full life outside his profession. He
twice married, reared a family of five children, took decided
views on matters of education, art, and literature, wrote for
journals and newspapers on controversial artistic subjects,
and, though not a politician, showed himself a liberal in his
political thinking. Yet the bulk of his energy he devoted to
chemistry. Of his 262 printed publications, the majority are
on chemical subjects and on industrial subjects dependent
upon chemistry. His earliest paper dealt with the composition
of some specimens of orthite. Presently he began a long ex-
amination of the physical properties of liquids and a series of
experiments on the thermal expansion of liquids. In 1883 he an-
nounced as a result a simple expression for the expansion of
liquids between O° C. and the boiling point. By 1889 he had
closed an extended series of studies on the densities of various
solutions, he had studied the elasticity of gases minutely, he
had published papers on the nitriles, on fractional distillation,
on contact action, on the heat of combustion of organic sub-
stances, and on many other subjects in chemistry. He had also
published papers of interest to mineralogists and to chemical
geologists, had ascended in a balloon during the solar eclipse
of 1887 to make observations of the upper atmosphere, and
had so far developed his interest in and theories about petro-
leum that he had been commissioned by the government to
investigate the oil industry at Baku and the naphtha springs
in the Caucasus, and to study the operation of the oil fields
in Pennsylvania.
Much of the experimental and observational work Men-
deleyev accomplished in his career retains now only historical
interest. Even his great book, the two-volume Principles of
Chemistry (1869-71), for two generations the standard Rus-
sian textbook in chemistry, and a work several times trans-
lated into English, is outmoded in many chapters. It contains
in Chapter XV his first full statement of the Periodic Law
and his own account of the value and import of the law. This
is the chapter here reprinted (from the English edition of
In his later years Mendeleyev maintained the simplicity
of private life which had characterized his earlier days. He
spent the greater part of the year in St. Petersburg, occasion-
ally visiting his estates in Tver, where he carried on some
agricultural experiments. He dined always at six, usually in
the company of his family and friends, and he frequently
spent the evening reading James Fenimore Cooper and Jules
Verne. When he traveled, he chose to go third class so that he
538 MASTERWORKS OF SCIENCE
might meet plain people. Had he chosen, he could have lived
more elaborately. He had earned large sums by his industrial
work, he had been honored by the Czar, he had been awarded
the Davy Medal by the Royal Society, the Faraday Lecture-
ship by the Chemical Society, and, in 1905, the Copley Medal.
His renown as a teacher had attracted students from all over
the world to his classes, and his fame as the discoverer of th£
Periodic Law had made his name familiar wherever scientific
study flourished. By the time of his death his great generaliza-
tion was acknowledged to be the most important chemical
law put forward since the establishment of the atomic theory.
Though skilled and ingenious in experiment, Mende-
leyev's perspicacity made him pre-eminent in theoretical
work. Others' experiments and discoveries have confirmed his
theory; it continues to be a lasting influence in all research in
chemistry.
THE PERIODIC LAW
THE GROUPING OF THE ELEMENTS AND THE PERIODIC
LAW
THE SUM of the data concerning the chemical transformations proper to
the elements (for instance, with respect to the formation of acids, salts,
and other compounds having definite properties) is insufficient for accu-
rately determining the relationship of the elements, inasmuch as this may
be many-sided. Thus, lithium and barium are in some respects analogous
to sodium and potassium, and in others to magnesium and calcium. It is
evident, therefore, that for a complete judgment it is necessary to have,
not only qualitative, but also quantitative, exact and measurable, data.
When a property can be measured it ceases to be vague, and becomes
quantitative instead of merely qualitative.
Among these measurable properties of the elements, or of their cor-
responding compounds, are: (a) isomorphism, or the analogy of crystal-
line forms; and, connected with it, the power to form crystalline mixtures
which are isomorphous; (b) the relation of the volumes of analogous com-
pounds of the elements; (c) the composition of their saline compounds;
and (d) the relation of the atomic weights of the elements. In this chap-
ter we shall briefly consider these four aspects of the matter, which are
exceedingly important for a natural and fruitful grouping of the elements,
facilitating, not only a general acquaintance with them, but also their
detailed study.
Historically the first, and an important and convincing, method for
finding a relationship between the compounds of two different elements
is by isomorphism. This conception was introduced into chemistry by
Mitscherlich (in 1820), who demonstrated that the corresponding salts of
arsenic acid, H3AsO4, and the phosphoric acid, H3PO4, crystallise with an
equal quantity of water, show an exceedingly close resemblance in crystal-
line form (as regards the angles of their faces and axes), and are able to
crystallise together from solutions, forming crystals containing a mixture
of the isomorphous compounds. Isomorphous substances are those which,
with an equal number of atoms in their molecules, present an analogy in
their chemical reactions, a close resemblance in their properties, and a
similar or very nearly similar crystalline form: they often contain certain
elements in common, from which it is to be concluded that the remaining
elements (as in the preceding example of As and P) are analogous to each
other. And inasmuch as crystalline forms are capable of exact measure-
ment, the external form, or the relation of the molecules which causes
540 MASTERWORKS OF SCIENCE
their grouping into a crystalline form, is evidently as great a help in
judging of the internal forces acting between the atoms as a comparison
of reactions, vapour densities, and other like relations. It will be sufficient
to call to mind that the compounds of the alkali metals with the halogens
RX, in a crystalline form, all belong to the cubic system and crystallise in
octahedra or cubes — for example, sodium chloride, potassium chloride,
potassium iodide, rubidium chloride, &c. The nitrates of rubidium and
caesium appear in anhydrous crystals of the same form as potassium
nitrate. The carbonates of the metals of the alkaline earths are isomor-
phous with calcium carbonate — that is, they either appear in forms like
calc-spar or in the rhombic system in crystals analogous to aragonite. Fur-
thermore, sodium nitrate crystallises in rhombohedra, closely resembling
the rhombohedra of calc-spar (calcium carbonate), CaCO3, whilst potas-
sium nitrate appears in the same form as aragonite, CaCO3, and the num-
ber of atoms in both kinds of salts is the same. They all contain one atom
of a metal (K, Na, Ca), one atom of a non-metal (C, N), and three atoms
of oxygen. The analogy of form evidently coincides with an analogy of
atomic composition. But there is not any close resemblance in their prop-
erties. It is evident that calcium carbonate approaches more nearly to
magnesium carbonate than to sodium nitrate, although their crystalline
forms are all equally alike. Isomorphous substances which are perfectly
analogous to each other are not only characterised by a close resemblance
of form (homeomorphism), but also by the faculty of entering into analo-
gous reactions, which is not the case with RNO3 and RCO3. The most
important and direct method of recognising perfect isomorphism — that
is, the absolute analogy of two compounds — is given by that property of
analogous compounds of separating from solutions in homogeneous crys-
tals, containing the most varied proportions of the analogous substances
which enter into their composition. These quantities do not seem to be
in dependence on the molecular or atomic weights, and if they are gov-
erned by any laws they must be analogous to those which apply to indefi-
nite chemical compounds. This will be clear from the following examples.
Potassium chloride and potassium nitrate are not isomorphous with each
other, and are in an atomic sense composed in a different manner. If these
salts be mixed in a solution and the solution be evaporated, independent
crystals of the two salts will separate, each in that crystalline form which
is proper to it. The crystals will not contain a mixture of the two salts.
But if we mix the solutions of two isomorphous salts together, then,
under certain circumstances, crystals will be obtained which contain both
these substances. However, this cannot be taken as an absolute rule, for if
we take a Solution saturated at a high temperature with a mixture of
potassium and sodium chlorides, then on evaporation sodium chloride
only will separate, and on cooling only potassium chloride. The first will
contain very little potassium chloride, and the latter very little sodium
chloride. But if we take, for example, a mixture of solutions of magnesium
sulphate and zinc sulphate, they cannot be separated from each other by
evaporating the mixture, notwithstanding the rather considerable differ-
MENDELEYEV — THE PERIODIC LAW 541
ence in the solubility of these salts. Again, the isomorphous salts, magne-
sium carbonate, and calcium carbonate are found together — that is, in one
crystal — in nature. The angle of the rhombohedron of these magnesia-lime
spars is intermediate between the angles proper to the two spars individu-
ally (for calcium carbonate, the angle of the rhombohedron is 105° 8';
magnesium carbonate, 107° 30'; CaMg(CO3)2, 106° ic/). Certain of these
isomorphous mixtures of calc and magnesia spars appear in well-formed
crystals, and in this case there not unfrequently exists a simple molecular
proportion of strictly definite chemical combination between the compo-
nent salts — for instance, CaCO3,MgCO3 — whilst in other cases, especially
in the absence of distinct crystallisation (in dolomites), no such simple
molecular proportion is observable: this is also the case in many artifi-
cially prepared isomorphous mixtures. The microscopical and crystallo-
optical researches of Professor Inostrantzoff and others show that in many
cases there is really a mechanical, although microscopically minute, juxta-
position in one whole of the heterogeneous crystals of calcium carbonate
(double refracting) and of the compound CaMgC2O6. If we suppose the
adjacent parts to be microscopically small (on the basis of the researches
of Mallard, Weruboff, and others), we obtain an idea of isomorphous mix-
tures. A formula of the following kind is given to isomorphous mixtures:
for instance, for spars, RCO3, where R=Mg, Ca, and where it may be
Fe, Mn . . . , &c. This means that the Ca is partially replaced by Mg or
another metal. Alums form a common example of the separation of iso-
morphous mixtures from solutions. They are double sulphates (or seleni-
ates) of alumina (or oxides isomorphous with it) and the alkalis, which
crystallise in well-formed crystals. If aluminium sulphate be mixed
with potassium sulphate, an alum separates, having the composition
KA1S2O8,I2H2O. If sodium sulphate or ammonium sulphate, or rubidium
(or thallium) sulphate be used, we obtain alums having the composition
RA1S2O8,I2H2O. Not only do they all crystallise in the cubic system, but
they also contain an equal atomic quantity of water or crystallisation
(i2H2O). Besides which, if we mix solutions of the potassium and ammo-
nium (NH4A1S2O8?I2H2O) alums together, then the crystals which sepa-
rate will contain various proportions of the alkalis taken, and separate
crystals of the alums of one or the other kind will not be obtained, but
each separate crystal will contain both potassium and ammonium. Nor is
this all; if we take a crystal of a potassium alum and immerse it in a
solution capable of yielding ammonia alum, the crystal of the potash alum
will continue to grow and increase in size in this solution — that is, a layer
of the ammonia or other alum will deposit itself upon the planes bound-
ing the crystal of the potash alum. This is very distinctly seen if a colour-
less crystal of a common alum be immersed in a saturated violet solution
of chrome alum, KCrS2O8,i2H2O, which then deposits itself in a violet
layer over the colourless crystal of the alumina alum, as was observed even
before Mitscherlich noticed it. If this crystal be then immersed in a solu-
tion of an alumina alum, a layer of this salt will form over the layer of
chrome alum, so that one alum is able to incite the growth of the other.
542 MASTERWORKS OF SCIENCE
If the deposition proceed simultaneously, the resultant intermixture may
be minute and inseparable, but its nature is understood from the pre-
ceding experiments; the attractive force of crystallisation of isornorphous
substances is so nearly equal that the attractive power of an isornorphous
substance induces a crystalline superstructure exactly the same as would
be produced by the attractive force of like crystalline particles. From this
it is evident that one isornorphous substance may induce the crystallisa-
tion of another. Such a phenomenon explains, on the one hand, the aggre-
gation of different isomorphous substances in one crystal, whilst, on the
other hand, it serves as a most exact indication of the nearness both of
the molecular composition of isomorphous substances and of those forces
which are proper to the elements which distinguish the isomorphous sub-
stances. Thus, for example, ferrous sulphate or green vitriol crystallises in
the monoclinic system and contains seven molecules of water, FeSO4,7H2O,
whilst copper vitriol crystallises with five molecules of water in the tri-
clinic system, CuSO4,5H2O; nevertheless, it may be easily proved that both
salts are perfectly isomorphous; that they are able to appear in identically
the same forms and with an equal molecular amount of water. For in-
stance, Marignac, by evaporating a mixture of sulphuric acid and ferrous
sulphate under the receiver of an air pump, first obtained crystals of the
hepta-hydrated salt, and then of the penta-hydrated salt FeSO4,5H2O,
which were perfectly similar to the crystals of copper sulphate. Further-
more, Lecoq de Boisbaudran, by immersing crystals of FeSO4,7H2O in a
supersaturated solution of copper sulphate, caused the latter to deposit in
the same form as ferrous sulphate, in crystals of the monoclinic system,
CuSO4,7H2O.
Hence" it is evident that isomorphism — that is, the analogy of forms
and the property of inducing crystallisation — may serve as a means for the
discovery of analogies in molecular composition. We will take an exam-
ple in order to render this clear. If, instead of aluminium sulphate, we add
magnesium sulphate to potassium sulphate, then, on evaporating the solu-
tion, the double salt K2MgS2Os,6H2O separates instead of an alum, and
the ratio of the component parts (in alums one atom of potassium per
2SO4, and here two atoms) and the amount of water of crystallisation (in
alums 12, and here 6 equivalents per aSO4) are quite different; nor is this
double salt in any way isomorphous with the alums, nor capable of form-
ing an isomorphous crystalline mixture with them, nor does the one salt
provoke the crystallisation of the other. From this we must conclude that
although alumina and magnesia, or aluminium and magnesium, resemble
each other, they are not isomorphous, and that although they give par-
tially similar double salts, these salts are not analogous to each other. And
this is expressed in their chemical formulas by the fact that the number of
atoms in alumina or aluminium oxide, A12O3, is different from the num-
ber in magnesia, MgO. Aluminium is trivalent and magnesium bivalent*
Thus, having obtained a double salt from a given metal, it is possible to
judge of the analogy of the given metal with aluminium or with magne-
sium, or of the absence of such an analogy, from the composition and
MENDELEYEV — THE PERIODIC LAW 543
P bJD 3
u < <«
1
22 fi
CO
1
O
1 I
o §
t* feO
C o
O 3 oo
to I"*! O
H (5 "5.
ffi £ 3
'
* . 1 . 1 . . | . |
P? f^
'
C/3 • O • <u
CO JH "
o . 6 . I . . £ . D
Q o t?
fgj PH P^
P-i • *2 • ja • •-
<C c/D W
Q0 1 HH
!5 • > • z . S . £ .
| ffi
fc
' a ' (S ' 5 • ' £ •
Q 6 £
o . P . ^3 . 8 . 1 . p
^ ^
£
• < • cS ' * ' \ • P •
°" I
PQ -co • >^ • 2 • >«
«
B
• I5 • ts • s • • g •
n . a . & . z .
4! g
„
w'z'5'|'''|'
9, |
. a . « . a . 3 .
a,
3
O
O
M ' M M
«
-^
to
544 MASTERWORKS OF SCIENCE
form of this salt. Thus zinc, for example, does not form alums, but forms
a double salt with potassium sulphate, which has a composition exactly
like that of the corresponding salt of magnesium. It is often possible to
distinguish the bivalent metals analogous to magnesium or calcium from
the trivalent metals, like aluminium, by such a method. Furthermore, the
specific heat and vapour density serve as guides. There are also indirect
proofs. Thus iron gives ferrous compounds, FeX2, which are isomorphous
with the compounds of magnesium, and ferric compounds, FeX3, which
are isomorphous with the compounds of aluminium; in this instance the
relative composition is directly determined by analysis, because, for a
given amount of iron, FeCl2 only contains two thirds of the amount of
chlorine which occurs in FeCl3, and the composition of the correspond-
ing oxygen compounds, i.e. of ferrous oxide, FeO, and ferric oxide, Fe2O3,
clearly indicates the analogy of the ferrous oxide with MgO and of the
ferric oxide with A12O3.
Thus in the building up of similar molecules in crystalline forms we
see one of the numerous means for judging of the internal world of mole-
cules and atoms, and one of the weapons for conquests in the invisible
world of molecular mechanics which forms the main object of physico-
chemical knowledge. This method has more than once been employed for
discovering the analogy of elements and of their compounds; and as
crystals are measurable, and the capacity to form crystalline mixtures can
be experimentally verified, this method is a numerical and measurable
one, and in no sense arbitrary.
The regularity and simplicity expressed by the exact laws of crystal-
line form repeat themselves in the aggregation of the atoms to form
molecules. Here, as there, there are but few forms which are essentially
different, and their apparent diversity reduces itself to a few fundamental
differences of type. There the molecules aggregate themselves into crystal-
line forms; here, the atoms aggregate themselves into molecular forms or
into the types of compounds. In both cases the fundamental crystalline or
molecular forms are liable to variations, conjunctions, and combinations.
If we know that potassium gives compounds of the fundamental type KX,
where X is a univalent element (which combines with one atom of hydro-
gen, and is, according to the law of substitution, able to replace it), then
we know the composition of its compounds: K2O, KHO, KC1, NH2K,
KN03, K2SO4, KHS04, K2Mg (SO4)2,6H2O, &c. All the possible deriva-
tive crystalline forms are not known. So also all the atomic combinations
are not known for every element. Thus in the case of potassium, KCH3,
K3P, K2Pt, and other like compounds which exist for hydrogen or chlo-
rine, are unknown.
Only a few fundamental types exist for the building up of atoms into
molecules, and the majority of them are already known to us. If X stands
for a univalent element, and R for an element combined with it, then
eight atomic types may be observed: —
RX, RX2, RX3, RX4, RX5, RX6, RX7, RX8.
MENDELEYEV — THE PERIODIC LAW 545
Let X be chlorine or hydrogen. Then as examples of the first type we
have: H2, C12) HC1, KC1, NaCl, &c. The compounds of oxygen or calcium
may serve as examples of the type RX2: OH2, OC12, OHC1, CaO,
Ca(OH)2, CaCl2, &c. For the third type RX3 we know the representative
NH3 and the corresponding compounds N2O3, NO(OH), NO(OK), PClSr
P2O3, PH35 SbH3, Sb2O3, B2O3, BC13, A12O3, &c. The type RX4 is known
among the hydrogen compounds. Marsh gas, CH4, and its corresponding
saturated hydrocarbons, CnH2n4_2, are the best representatives. Also CH3Ci,
CC14, SiCl4, SnCl4, SnO2, CO2, SiO2 and a whole series of other com-
pounds come under this class. The type RX5 is rlso already familiar to us,
but there are no purely hydrogen compounds among its representatives.
Sal-ammoniac, NH4C1, and the corresponding NH4(OH), NO2(OH),
C1O2(OK), as well as PC15, POC13, &c., are representatives of this type. In
the higher types also there are no hydrogen compounds, but in the type
RX6 there is the chlorine compound WC16. However, there are many
oxygen compounds, and among them SO3 is the best known representa-
tive. To this class also belong SO2(OH)2, SO2, CL>, SO2(OH)C1, CrO3>
&c., all of an acid character. Of the higher types there are in general only
oxygen and acid representatives. The type RX7 we know in perchloric
acid, C1O3(OH), and potassium permanganate, MnO3(OK), is also a
member. The type RX8 in a free state is very rare; osmic anhydride, OsO4,
is the best known representative of it.
The four lower types RX, RX2, RX3, and RX4 are met with in com-
pounds of the elements R with chlorine and oxygen, and also in their
compounds with hydrogen, whilst the four higher types only appear for
such acid compounds as are formed by chlorine, oxygen, and similar
elements.
Among the oxygen compounds the saline oxides which are capable <5£
forming salts either through the function of a base or through the function
of an acid anhydride attract the greatest interest in every respect. Certain
elements, like calcium and magnesium, only give one saline oxide — for
example, MgO, corresponding with the type MgX2. But the majority of
the elements appear in several such forms. Thus copper gives CuX and
CuX2, or Cu2O and CuO. If an element R gives a higher type RXn, then
there often also exist, as if by symmetry, lower types, RX^_2, RXn_4, and
in general such types as differ from RXW by an even number of X. Thus
in the case of sulphur the types SX2, SX4, and SX6 are known — for
example SH2, SO2, and SO3. The last type is the highest, SXg. The types
SX5 and SX3 do not exist. But even and uneven types sometimes appear
for one and the same element. Thus the types RX and RX2 are known for
copper and mercury.
Among the saline oxides only the eight types enumerated below are
known to exist. They determine the possible formulae of the compounds
of the elements, if it be taken into consideration that an element which
gives a certain type of combination may also give lower types. For this
reason the rare type of the sub oxides or quaternary oxides R4O (for in-
stance, Ag4O, Ag2Cl) is not characteristic; it is always accompanied by
O Q «*^C
£88?
i-VXn «5C
fS r-. «og
r- p y^ <p yi o\ >o o\ p o\r
•g
-
1 1 IQQ6
OSS
1^
O
II
X
s
"i
o
u
ill
31
S co
* I I 11 IN
nt*k^nO«9<'>w .*?
XXQXijgX^X ^
SpSu^cilcSg O
ights of the
Ss
u
5 S
PC
lasi la ^ I M I la
u u* 2 <j
Us
i I I
»| I I
N
iT
§5^00000000 O . £
oooo^oc-ic*i«/*t-i<f r~- c
f er\ ii-t ol c*"i 4»- !•«•. OO I rMosl^OOOr-f-^'oCD-if CNfrr-iM
I $<$ I 1 1 3 II I
S
I 9 ! I 1 1 9 I I if I I I i I I I I I g
2
1 II
ili
tsj X I I
!S -^ ' '
M .
I'
M 1 I
N
-)
I
t>5^
b
•
g M| 1 1 1 Ig I ;
M i EM i M ¥
II <!
"B
S
o I
g 1 g g
- 1 X I I
2 I ?N I I
' S i ' i I
CX|
< J i I I
:|
n K \: c,^ x
• • 's : : . • ;-$ :^ : : : §^ . i
; ' *PO S S .?_ . .11 c !
v^ vo NO i-* r-- r^
^F
•^o^r-cvo^-i^r^w C^TT^T4 r^oc<pr^py^«/^r-i^cN.>;-^-Grp
II i i i
M
o cj u
li 1
"8-w
•IS
75-1^
.5 "3 a a^
"" av dt'ri u
l
ifcj
Illll itiil!3fil!i31lJi
1t'a-a1lrt-6^'s-8«-
.a.a « S Si'S^-a « >>o a
3-?«§«!a^
ff-S^afll
iji'^iiii
[w!3 G *J Q
0"7? ?. ^£
^•^~^^^^o^^^
^^^^^ 3^^ O g2 oo*S §.9
S*S|8iaJ2S j*^-
£ S*3.§ a ^x rt-£XD.ti=!^^.
>s
aiJgJ
^S^^"
^ « 2 o..
gT-s-s-
|->^ S
S7^S^
n 9 H^ d
1 1 1 w
«|Hs
J8
•&•;
o r.g s Mt^|.| c
0 S S-o o u.s 8'S^ "°o
B*S.JI -o a j( . *- « — a a
Jp j'S I § §3 a.s^ a i ^| »|| se^-a a-s^g ^ |j
t.^1-^ 8-g - g^i- f 548|| fe§ si *a «-5 1 -
MENDELEYEV — THE PERIODIC LAW 549
one of the higher grades of oxidation, and the compounds of this type
are distinguished by their great chemical instability, and split up into an
element and the higher compound (for instance, Ag4O=2Ag+Ag2O).
Many elements, moreover, form transition oxides whose composition is
intermediate, which are able, like N2O4, to split up into the lower and
higher oxides. Thus iron gives magnetic oxide, Fe3O4, which is In all
respects (by its reactions) a compound of the suboxide FeO with the
oxide Fe2O3. The independent and more or less stable saline compounds
correspond with the following eight types: —
R2O; salts RX, hydroxides ROH. Generally basic like K2O, Na2O, Hg2O,
Ag2O, Cu2O; if there are acid oxides of this composition they are
very rare, are only formed by distinctly acid elements, and even then
have only feeble acid properties; for example, C12O and N2O.
R2O2 or RO; salts RX2, hydroxides R(OH)2. The most simple basic salts
R2OX2 or R(OH)X; for instance, the chloride Zn2OQ2; also an
almost exclusively basic type; but the basic properties are more feebly
developed than in the preceding type. For example, CaO, MgO, BaO,
PbO, FeO, MnO, &c.
R9O3; salts RX3, hydroxides R(OH)3, RO(OH), the most simple basic
salts ROX, R(OH)X3. The bases are feeble, like A12O3, Fe2O3, T12O8,
Sb2O3. The acid properties are also feebly developed; for instance, in
B2O3; but with the non-metals the properties of acids are already
clear; for instance, P2O3, P(OH)3.
R2O4 or RO2; salts RX4 or ROX2, hydroxides R(OH)4, RO(OH)2. Rarely
bases (feeble), like ZrO2, PtO2, more often acid oxides; but the acid
properties are in general feeble, as in CO2> SO2, SnO2. Many inter-
mediate oxides appear in this and the preceding and following types.
R2O5; salts principally of the types ROXS, RO2X, RO(OH)3, RO2(OH),
rarely RX5. The basic character (X, a halogen, simple or complex; for
instance, NO3, Cl, &c.) is feeble, the acid character predominates, as
is seen in N2O5, P0O5, C10OB, then X=OH, OK, &c., for example,
N02(OK).
R2O6 or RO3; salts and hydroxides generally of the type RO2X2, RO2-
(OH)2. Oxides of an acid character, as SO3, CrO3, MnO3. Basic
properties rare and feebly developed as in UO3.
R2O7; salts of the form RO3X, RO3(OH), acid oxides; for instance, C12O7>
Mn2O7. Basic properties as feebly developed as the acid properties in
the oxides R2O.
R2O8 or RO4. A very rare type, and only known in OsO4 and RuO4.
It is evident from the circumstance that in all the higher types the
acid hydroxides (for example, HC1O4, H2SO4, H3PO4) and salts with a
single atom of one element contain, like the higher saline type RO4, not
more than jour atoms of oxygen; that the formation of the saline oxides
is governed by a certain common principle which is best looked for in the
fundamental properties of oxygen, and in general of the most simple com-
pounds. The hydrate of the oxide RO2 is of the higher type RO22H2O =
RH4O4 = R(HO)4. Such, for example, is the hydrate of silica and the salts
550 MASTERWORKS OF SCIENCE __^
(orthosilicates) corresponding with it, Si(MO)4. The oxide R2O5 corre-
sponds with the hydrate R2O53H2O = 2RH3O4 = 2RO(OH)3. Such is or-
thophosphoric acid, PH3O3. The hydrate of the oxide RO3 is RO3H2O =
RH2O4 = RO2(OH)2 — for instance, sulphuric acid. The hydrate corre-
sponding to R2O7 is evidently RHO = RO3(OH) — for example, perchloric
acid. Here, besides containing O4, it must further be remarked that
the amount of hydrogen in the hydrate is equal to the amount of hydro-
gen in the hydrogen corn-found. Thus silicon gives SiH4 and SiH4O4,
phosphorus PH3 and PH3O4, sulphur SH2 and SH2O4, chlorine C1H and
C1HO4. This, if it does not explain, at least connects in a harmonious and
general system the fact that the elements are capable of combining with
a greater amount of oxygen, the less the amount of hydrogen which they
are able to retain. In this the key to the comprehension of all further
deductions must be looked for, and we will therefore formulate this rule
in general terms. An element R gives a hydrogen compound RHM, the
hydrate of its higher oxide will be RHWO4, and therefore the higher oxide
will contain 2RHWO4 — #H2O = R2O8_n. For example, chlorine gives C1H,
hydrate C1HO4, and the higher oxide C12O7. Carbon gives CH4 and CO2.
So also, SiO2 and SiH4 are the higher compounds of silicon with hydrogen
and oxygen, like CO2 and CH4. Here the amounts of oxygen and hydrogen
are equivalent. Nitrogen combines with a large amount of oxygen, form-
ing N2O5, but, on the other hand, with a small quantity of hydrogen in
NH3. The sum of the equivalents of hydrogen and oxygen, occurring in
combination with an atom of nitrogen, is, as always in the higher types,
equal to eight. It is the same with the other elements which combine with
hydrogen and oxygen. Thus sulphur gives SO3; consequently, six equiva-
lents of oxygen fall to an atom of sulphur, and in SH2 two equivalents of
hydrogen. The sum is again equal to eight. The relation between C12O7
and C1H is the same. This shows that the property of elements of com-
bining with such different elements as oxygen and hydrogen is subject to
one common law, which is also formulated in the system of the elements
presently to be described.1
aThe hydrogen compounds, RaH, in equivalency correspond with the type of the
suboxides, IUO. Palladium, sodium, and potassium give such hydrogen compounds, and
it is worthy of remark that according to the periodic system these elements stand near
to each other, and that in those groups where the hydrogen compounds R2H appear, the
quaternary oxides R*O are also present.
Not wishing to complicate the explanation, I here only touch on the general fea-
tures of the relation between the hydrates and oxides and of the oxides among them-
selves. Thus, for instance, the conception of the ortho-acids and of the normal acids
will be considered in speaking of phosphoric and phosphorous acids.
As in the further explanation of the periodic law only those oxides which give salts
will be considered, I think it will not be superfluous to mention here the following facts
relative to the peroxides. Of the peroxides corresponding with hydrogen peroxide, the
following are at present known: HaOs, Na2O2, S2O7 (as HSCX,?), KaO*, KaOa, CaO2)
Ti03, Cr207, CuQa(?), Zn02, Rb2O3, SrO2, Ag2O2, CdO2, Cs02, Cs2O2, BaO2, Mo2Or,
SnOs, WsOr, UO*. It is probable that the number of peroxides will increase with further
investigation. A periodicity is seen in those now known, for the elements (excepting
MENDELEYEV — THE PERIODIC LAW g51
In the preceding we see not only the regularity and simplicity which
govern the formation and properties of the oxides and of all the com-
pounds of the elements, but also a fresh and exact means for recognising
the analogy of elements. Analogous elements give compounds of analo-
gous types, both higher and lower. If CO2 and SO2 are two gases which
closely resemble each other both in their physical and chemical properties,
the reason of this must be looked. for not in an analogy of sulphur and
carbon, but in that identity of the type of combination, RX4, which both
oxides assume, and in that influence which a large mass of oxygen always
exerts on the properties of its compounds. In fact, there is little resem-
blance between carbon and sulphur, as is seen not only from the fact that
CO2 is the higher form of oxidation, whilst SO2 is able to further oxidise
into SO3, but also from the fact that all the other compounds — for example,
SH2 and CH4, SC12 and CC14, &c. — are entirely unlike both in type and
in chemical properties. This absence of analogy in carbon and sulphur is
especially clearly seen in the fact that the highest saline oxides are of
different composition, CO2 for carbon, and SO3 for sulphur. Previously
we considered the limit to which carbon tends ifi its compounds, and in
a similar manner there is for every element in its compounds a tendency
to attain a certain highest limit RXW. This view was particularly "de-
veloped in the middle of the present century by Frankland in studying
the metallo-organic compounds, i.e. those in which X is wholly or partially
a hydrocarbon radicle; for instance, X=CH3 or C2H5 &c. Thus, for ex-
ample, antimony, Sb, gives, with chlorine, compounds SbCl and SbCl5
and corresponding oxygen compounds Sb2O3 and Sb2O5, whilst under the
action of CH3I, C2H3I, or in general El (where E is a hydrocarbon radicle
of the paraffin series), upon antimony or its alloy with sodium there are
formed SbE3 (for example, Sb(CH3)3, boiling at about 81°), which, cor-
responding to the lower form of combination SbX3, are able to combine
further with El, or C12, or O, and to form compounds of the limiting type
SbX5; for example, SbE4Cl corresponding to NH4C1 with the substitution
of nitrogen by antimony, and of hydrogen by the hydrocarbon radicle.
The elements which are most chemically analogous are characterised by
the fact of their giving compounds of similar form RXW. The halogens
which are analogous give both higher and lower compounds. So also do
Li) o£ the first group, which give RsO, form peroxides, and then the elements of the
sixth group seem also to be particularly inclined to form peroxides, RaO?; but at present
it is too early, in my opinion, to enter upon a generalisation of this subject, not only
because it is a new and but little studied matter (not investigated for all the elements),
but also, and more especially, because in many instances only the hydrates are known —
for instance, MoaHaOs — and they perhaps are only compounds of peroxide of hydrogen
— for example, MoaH^Os = 2MoOs + HaOa — since Professor Schone has shown that
HaOa and BaOa possess the property of combining together and with other oxides.
Nevertheless, I have, in the general table expressing the periodic properties of the
elements, endeavoured to sum up the data respecting all the known peroxide compounds
whose characteristic property is seen in their capability to form peroxide of hydrogen
under many circumstances.
552 MASTERWORKS OF SCIENCE
the metals of the alkalis and of the alkaline earths. And we saw that this
analogy extends to the composition and properties of the nitrogen and
hydrogen compounds of these metals, which is best seen in the salts. Many
such groups of analogous elements have long been known. Thus there
are analogues of oxygen, nitrogen, and carbon, and we shall meet with
many such groups. But an acquaintance with them inevitably leads to the
questions, what is the cause of analogy and what is the relation of one
group to another? If these questions remain unanswered, it is easy to fall
into error in the formation of the groups, because the notions of the
degree of analogy will always be relative, and will not present any accuracy
or distinctness. Thus lithium is analogous in some respects to potassium
and in others to magnesium; beryllium is analogous to both aluminium
and magnesium. Thallium has much kinship with lead and mercury, but
some of its properties appertain to lithium and potassium. Naturally,
where it is impossible to make measurements one is reluctantly obliged to
limit oneself to .approximate comparisons, founded on apparent signs
which are not distinct and are wanting in exactitude. But in the elements
there is one accurately measurable property, which is subject to no doubt
— namely, that property which is expressed in their atomic weights. Its
magnitude* indicates the relative mass of the atom, or, if we avoid the
conception of the atom, its magnitude shows the relation between the
masses forming the" chemical and independent individuals or elements.
And according to the teaching of all exact data about the phenomena of
nature, the mass of a substance is that property on which all its remaining
properties must be dependent, because they are all determined by similar
-conditions or by those forces which act in the weight of a substance, and
this is directly proportional to its mass. Therefore it is most natural to
seek for a dependence between the properties and analogies of the ele-
ments on the one hand and their atomic weights on the other.
This is the fundamental idea which leads to arranging all the dements
according to their atomic weights. A periodic repetition of properties is
then immediately observed in the elements. We are already familiar with
examples of this: —
F =19, 01=35.5, Br=8o, I =127,
Na=23, K =39, Rb=85, Cs=i33,
Mg=24, Ca=40, Sr=87, Ba=i37*
The essence of the matter is seen in these groups. The halogens have
smaller atomic weights than the alkali metals, and the latter than the
metals of the alkaline earths. Therefore, // all the elements be arranged in
the order of their atomic weights, a periodic repetition of properties is
obtained. This is expressed by the law of periodicity; the properties of
the elements, as well as the forms and properties of their compounds, are
in periodic dependence or (expressing ourselves algebraically} form a peri-
odic function of the atomic weights of the elements? Table I of the
sln laying out the accumulated information respecting the elements, I had occasion
to reflect on their mutual relations. At the beginning of 1869 I distributed among many
MENDELEYEV--THE PERIODIC LAW 553
periodic system of the elements is designed to illustrate this law. It is
arranged in conformity with the eight types of oxides described in the
preceding pages, and those elements which give the oxides, R2O and
consequently salts RX, form the ist group; the elements giving R2O2 or
RO as their highest grade of oxidation belong to the 2nd group, those
giving R2O3 as their highest oxides form the 3rd group, and so on; whilst
the elements of all the groups which are nearest in their atomic weights
are arranged in series from i to 12. The even and uneven series of the
same groups present the same forms and limits, but differ in their
properties, and therefore two contiguous series, one even and the other
uneven — for instance, the 4th and 5th — form a period. Hence the elements
of the 4th, 6th, 8th, loth, and i2th, or of the 3rd, 5th, 7th, 9th, and nth,
chemists a pamphlet entitled 'An Attempted System of the Elements, based on their
Atomic Weights and Chemical Analogies,' and at the March meeting of the Russian
Chemical Society, 1869, I communicated a paper 'On the Correlation of the Properties
and Atomic Weights of the Elements.' The substance of this paper is embraced in the
following conclusions: (i) The elements, if arranged according to their atomic weights,
exhibit an evident periodicity of properties. (2) Elements which are similar as regards
their chemical properties have atomic weights which are either of nearly the same value
(platinum, iridium, osmium) or which increase regularly (e.g. potassium, rubidium,
csesium). (3) The arrangement of the elements or of groups of elements in the order of
their atomic weights corresponds with their so-called valencies. (4) The elements, which
are the most widely distributed in nature, have small atomic weights, and all the ele-
ments of small atomic weight are characterised by sharply defined properties. They are
therefore typical elements. (5) The magnitude of the atomic weight determines the
character of an element. (6) The discovery of many yet unknown elements may be
expected. For instance, elements analogous to aluminium and silicon, whose atomic
weights would be between 65 and 75. (7) The atomic weight of an element may some-
times be corrected by aid of a knowledge of those of the adjacent elements. Thus the
combining weight of tellurium must lie between 123 and 126, and cannot be 128. (8)
Certain characteristic properties of the elements can be foretold from their atomic
weights.
The entire periodic law is included in these lines. In the series of subsequent papers
(1870—72, for example, in the Transactions of the Russian Chemical Society, of the
Moscow Meeting of Naturalists, of the St. Petersburg Academy, and Liebig's Annalen)
on the same subject we only find applications of the same principles, which were after-
wards confirmed by the labours of Roscoe, Carnelley, Thorpe, and others in England; of
Rammelsberg (cerium and uranium), L. Meyer (the specific volumes of the elements),
Zimmermann (uranium), and more especially of C. Winkler (who discovered germanium,
and showed its identity with ekasilicon), and others in Germany; of Lecoq de Boisbau-
dran in France (the discoverer of gallium == ekaaluminium) ; of Cleve (the atomic
weights of the cerium metals), Nilson (discoverer of scandium = ekaboron), and Nilson
and Pettersson (determination of the vapour density of beryllium chloride) in Sweden;
and of Brauner (who investigated cerium, and determined the combining weight of
tellurium = 125) in Austria, and Piccini in Italy.
I consider it necessary to state that, in arranging the periodic system of the ele-
ments, I made use of the previous researches of Dumas, Gladstone, Pettenkofer, Kremers,
and Lenssen on the atomic weights of related elements, but I was not acquainted with
the works preceding mine of De Chancourtois (vis tellurique, or the spiral of the ele-
ments according to their properties and equivalents) in France, and of J. Newlands
554 MASTERWORKS OF SCIENCE
series form analogues, like the halogens, the alkali metals, &c. The con-
junction of two series, one even and one contiguous uneven series, thus
forms one large period. These periods, beginning with the alkali metals,
end with the halogens. The elements of the first two series have the lowest
atomic weights, and in consequence of this very circumstance, although
they bear the general properties of a group, they still show many peculiar
and independent properties. Thus fluorine, as we know, differs in many
points from the other halogens, and lithium from the other alkali metals,
and so on. These lightest elements may be termed typical elements. They
include —
H.
Li, Be, B, C, N, O, F.
Na, Mg
In the annexed table all the remaining elements are arranged, not in
groups and series, but according to periods. In order to understand the
essence of the matter, it must be remembered that here the atomic weight
gradually increases along a given line; for instance, in the line commencing
with K=39 and ending with Br=8o, the intermediate elements have
intermediate atomic weights, as is clearly seen in Table II, where the
elements stand in the order of their atomic, weights.
Rb
Cs
The same degree of analogy that we know to exist between potas-
sim, rubidium, and caesium; or chlorine, bromine, and iodine; or calcium,
(Law of Octaves — for instance, H, F, Cl, Co, Br, Pd, I, Pt form the first octave, and
O, S, Fe, Se, Rh, Te, Au, Th the last) in England, although certain germs of the periodic
law are to be seen in these works. With regard to the work of Professor Lothar Meyer
respecting the periodic law (Notes 5 and 6), it is evident, judging from the method of
investigation, and from his statement (Liebig's Annalen, Supt. Band 7, 1870, 354), at
the very commencement of which he cites my paper of 1869 above mentioned, that he
accepted the periodic law in the form which I proposed.
In concluding this historical statement I consider it well to observe that no law
of nature, however general, has been established all at once; its recognition is always
preceded by many hints; the establishment of a law, however, does not take place when
its significance is recognised, but only when it has been confirmed by experiment, which
the man of science must consider as the only proof of the correctness of his conjecture
and opinions. I therefore, for my part, look upon Roscoe, De Boisbaudran, Nilson,
Wirikler, Brauner, Carnelley, Thorpe, and others who verified the adaptability of the
periodic law to chemical facts, as the true founders of the periodic law, the further
development of which still awaits fresh workers.
II
'•••"'"ilium,
Sr
fta
Ill IV V VI VII
Even Series.
»•* ^ — — ' -^
Y Zr Nb Mo —
T a fY Dt ?
Fe
Ru
Co
Rh
Ni
Pd
i
Cu
Ag
ii
Mg
Zn
Cd
in
Al
Ga
In
IV
Si
Ge
Sn
v
p
As
Sb
VI
S
Se
Te
VII
Cl
Br
I
JLJd
Yb — Ta W —
_ Th— U
Os
Ir
Pt
Au,
"-— *—
Tl
m~»
TT
Pb
-x^--
n
Bi
— •-••,
••••i
— — -
MENDELEYEV — THE PERIODIC LAW 555
strontium, and barium, also exists between the elements of the other ver-
tical columns. Thus, for example, zinc, cadmium, and mercury present a
very close analogy with magnesium. For a true comprehension of the
matter3 it is very important to see that all the aspects of the distribution
8Besides arranging the elements (a) in a successive order according to their atomic
weights, with indication o£ their analogies by showing some of the properties — for
instance, their power of giving one or another form of combination — both of the ele-
ments and of their compounds (as is done in Table II), (b) according to periods (as
in Table I), and (c) according to groups and series or small periods (as in the same
tables), I am acquainted with the following methods of expressing the periodic relations
of the elements: (i) By a curve drawn through points obtained in the following manner:
The elements are arranged along the horizontal axis as abscissae at distances from zero
proportional to their atomic weights, whilst the values for all the elements of some
property — for example, the specific volumes or the melting points, are expressed by the
ordinates. This method, although graphic, has the theoretical disadvantage that it does
not in any way indicate the existence of a limited and definite number of elements in
each period. There is nothing, for instance, in this method of expressing the law of
periodicity to show that between magnesium and aluminium there can be no other
element with an atomic weight of, say, 25, atomic volume 13, and in general having
properties intermediate between those of these two elements. The actual periodic law
does not correspond -with a continuous change of properties, with a continuous variation
of atomic weight — in a word, it does not express an uninterrupted function — and as
the law is purely chemical, starting from the conception of atoms and molecules which
combine in multiple proportions, with intervals (not continuously), it above all depends
on there being but few types of compounds, which are arithmetically simple, repeat
themselves, and offer no uninterrupted transitions, so that each period can only contain
a definite number of members. For this reason there can be no other elements between
magnesium, which gives the chloride MgCls, and aluminium, which forms AlXs; there
is a break in the continuity, according to the law of multiple proportions. The periodic
law ought not, therefore, to be expressed by geometrical figures in which continuity is
always understood. Owing to these considerations I never have and never will express
the periodic relations of the elements by any geometrical figures. (2) By a plane spiral.
Radii are traced from a centre, proportional to the atomic weights; analogous elements
lie along one radius, and the points of intersection are arranged in a spiral. This
method, adopted by De Chancourtois, Baumgauer, E. Huth, and others, has many of
the imperfections of the preceding, although it removes the indefmiteness as to the
number of elements in a period. It is merely an attempt to reduce the zomplex relations
to a simple graphic representation, since the equation to the spiral and the number of
radii are not dependent upon anything. (3) By the lines of atomicity, either parallel, as
in Reynolds's and the Rev. S. Haughton's method, or as in Crookes's method, arranged
to the right and left of an axis, along which the magnitudes of the atomic weights are
counted, and the position of the elements marked oil, on the one side the members of
the even series (paramagnetic, like oxygen, potassium, iron), and on the other side the
members of the uneven series (diamagnetic, like sulphur, chlorine, zinc, and mercury).
On joining up these points a periodic curve is obtained, compared by Crookes to the
oscillations of a pendulum, and, according to Haughton, representing a cubical curve.
This method would be very graphic did it not require, for instance, that sulphur should
be considered as bivalent and manganese as univalent, although neither of these ele-
ments gives stable derivatives of these natures, and although the one is taken on the
basis of the lowest possible compound 8X2, and the other of the highest, because
manganese can be referred to the univalent elements only by the analogy of KMnO* to
556 MASTERWORKS OF SCIENCE
of the elements according to their atomic weights essentially express one
and the same fundamental dependence — periodic properties.4" The follow-
ing points then must be remarked in it.
KC1CX, Furthermore, Reynolds and Crookes place hydrogen, iron, nickel, cobalt, and
others outside the axis o£ atomicity, and consider uranium as bivalent without the least
foundation. (4) Rantsheff endeavoured to classify the elements in their periodic rela-
tions by a system dependent on solid geometry. He communicated this mode of expres-
sion to the Russian Chemical Society, but his communication, which is apparently not
void of interest, has not yet appeared in print. (5) By algebraic formula?: for example,.
E. J. Mills (1886) endeavours to express all the atomic weights by the logarithmic
function A=:i5 (n — 0-93 752), in which the variables n and t are whole numbers. For
instance, for oxygen 72=2, t=i; hence A=i5'94; for antimony n=$, /=ro; whence
A=i20, and so on, n varies from i to 16 and t from o to 59. The analogues are hardly-
distinguishable by this method: thus for chlorine the magnitudes of n and t are 3 and 7;
for bromine 6 and 6; for iodine 9 and 9; for potassium 3 and 14; for rubidium 6 and
1 8; for caesium 9 and 20; but a certain regularity seems to be shown. (6) A more
natural method of expressing the dependence of the properties of elements on their
atomic weights is obtained by trigonometrical functions, because this dependence is
periodic like the functions of trigonometrical lines, and therefore Ridberg in Sweden
(Lund, 1885) and F. Flavitzky in Russia (Kazan, 1887) have adopted a similar method
of expression, which must be considered as worthy of being worked out, although it
does not express the absence of intermediate elements — for instance, between magne-
sium and aluminium, which is essentially the most important part of the matter. (7)
The investigations of B. N. Tchitcherin (1888, Journal of the Russian Physical and
Chemical Society) form the first effort in the latter direction. He carefully studied the
alkali metals, and discovered the following simple relation between their atomic
volumes: they can all be expressed by A(2 — 0-0428 An), where A is the atomic weight
and n=.i for lithium and sodium, % for potassium, % for rubidium, and % for caesium.
If n always = I, then the volume of the atom would become zero at A— 46%, and
would reach its maximum when A=23%, and the density increases with the growth of
A. In order to explain the variation of n, and the relation of the atomic weights of the
alkali metals to those of the other elements, as also the atomicity itself, Tchitcherin
supposes all atoms to be built up of a primary matter; he considers the relation of the
central to the peripheric mass, and, guided by mechanical principles, deduces many of
the properties of the atoms from the reaction of the internal and peripheric parts of
each atom. This endeavour offers many interesting points, but it admits the hypothesis
of the building up of all the elements from one primary matter, and at the present time
such an hypothesis has not the least support either in theory or in fact.
4Many natural phenomena exhibit a dependence of a periodic character. Thus the
phenomena of day and night and of the seasons of the year, and vibrations of all kinds,
exhibit variations of a periodic character in dependence on time and space. But in
ordinary periodic functions one variable varies continuously, whilst the other increases
to a limit, then a period of decrease begins, and having in turn reached its limit a,
period of increase again begins. It is otherwise in the periodic function of the elements,
Here the mass of the elements does not increase continuously, but abruptlys by steps, as
from magnesium to aluminium. So also the valency or atomicity leaps directly from
i to 2 to 3, &c., without intermediate quantities, and in my opinion it is these proper-
ties which are the most important, and it is their periodicity which forms the substance
of the periodic law. It expresses the properties of the real elements, and not of what
may be termed their manifestations visually known to us. The external properties o£
MENDELEYEV — THE PERIODIC LAW 557
1. The composition of the higher oxygen compounds is determined
by the groups: the first group gives R2O, the second R2O2 or RO, the
third R2O3, &c. There are eight type of oxides and therefore eight groups.
Two series give a period, and the same type of oxide is met with twice
in a period. For example, in the period beginning with potassium, oxides
of the composition RO are formed by calcium and zinc, and of the com-
position RO3 by molybdenum and tellurium. The oxides of the even series,
of the same type, have stronger basic properties than the oxides of the
uneven series, and the latter as a rule are endowed with an acid character.
Therefore the elements which exclusively give bases, like the alkali metals,
will be found at the commencement of the period, whilst such purely acid
elements as the halogens will be at the end of the period. The interval
will be occupied by intermediate elements. It must be observed that the
acid character is chiefly proper to the elements with small atomic weights
in the uneven series, whilst the basic character is exhibited by the heavier
elements in the even series. Hence elements which give acids chiefly pre-
dominate among the lightest (typical) elements, especially in the last
groups; whilst the heaviest elements, even in the last groups (for instance,
thallium, uranium), have a basic character. Thus the basic and acid char-
acters of the higher oxides are determined (a) by the type of oxide, (b)
by the even or uneven series, and (c) by the atomic weight. The groups
are indicated by Roman numerals from I to VIII.
2. The hydrogen compounds being volatile or gaseous substances
which are prone to reaction — such as HC1, H2O, H3N, and H4C — are only
formed by the elements of the uneven series and higher groups giving
oxides of the forms R2On, RO3, R2O5, and RO2.
3. If an element gives a hydrogen compound, RXm, it forms an
organo-metallic compound of the same composition, where X=CnH2n4_1;
that is, X is the radicle of a saturated hydrocarbon. The elements of the
uneven series, which are incapable of giving hydrogen compounds, and
give oxides of the forms RX, RX2, RX3, also give organo-metallic com-
pounds of this form proper to the higher oxides. Thus zinc forms the
oxide ZnO, salts ZnX2, and zinc ethyl Zn (C2H5)2. The elements -of the
even series do not seem to form organo-metallic compounds at all; at
elements and compounds are in periodic dependence on the atomic weight o£ the
elements only because these external properties are themselves the result o£ the proper-
ties of the real elements which unite to form the "free" elements and the compounds.
To explain and express the periodic law is to explain and express the cause of the law
of multiple proportions, of the difference of the elements, and the variation of their
atomicity, and at the same time to understand what mass and gravitation are. In my
opinion this is still premature. But just as without knowing the cause of gravitation, it
is possible to make use of the law of gravity, so for the aims of chemistry it is possible
to take advantage of the laws discovered by chemistry without being able to explain
their causes. The above-mentioned peculiarity of the laws of chemistry respecting defi-
nite compounds and the atomic weights leads one to think that the time has not yet
come for their full explanation, and I do not think that it will come before the
explanation of such a primary law of nature as the law o£ gravity.
558 MASTERWORKS OF SCIENCE
least all efforts for their preparation have as yet been fruitless — for in-
stance, in the case of titanium, zirconium, or iron.
4. The atomic weights of elements belonging to contiguous periods
differ approximately by 45; for example, K<Rb, Cr<Mo, Br<I. But the
elements of the typical series show much smaller differences. Thus the
difference between the atomic weights of Li, Na, and K, between Ca, Mg,
and Be, between Si and C, between S and O, and between Cl and F, is 16.
As a rule, there is a greater difference between the atomic weights of two
elements of one group and belonging to two neighboring series (Ti — Si
ssrV— P=Cr— S=Mn— Cl=Nb— As, &c.=2o); and this difference attains
a maximum with the heaviest elements (for example, Th — Pb=26, Bi — Ta
=26, Ba — Cd=25, &c.). Furthermore, the difference between the atomic
weights of the elements of even and uneven series also increases. In fact,
the differences between Na and K, Mg and Ca, Si and Ti, are less abrupt
than those between Pb and Th, Ta and Bi, Cd and Ba, &c. Thus even in
the magnitude of the differences of the atomic weights of analogous ele-
ments there is observable a certain connection with the gradation of their
properties.5
5. According to the periodic system every element occupies a certain
position, determined by the group (indicated in Roman numerals) and
series (Arabic numerals) in which it occurs. These indicate the atomic
weight, the analogues, properties, and type of the higher oxide, and of
the hydrogen and other compounds — in a word, all the chief quantitative
and qualitative features of an element, although there yet remains a
whole series of further details and peculiarities whose cause should per-
haps be looked for in small differences of the atomic weights. If in a
certain group there occur elements, R, R2, R3, and if in that series which
contains one of these elements, for instance R23 an element Q2 precedes
it and an element T2 succeeds it, then the properties of R2 are determined
by the properties of RI} R3, Q2> and T2. Thus, for instance, the atomic
weight of R2= %(Ri+R3+Q2+T2). For example, selenium occurs in
the same group as sulphur, S = 32, and tellurium, Te = 125, and, in the
^The relation between the atomic weights, and especially the differ ence:=i6> was
observed in the sixth and seventh decades of this century by Dumas, Pettenkofer, L-
Meyer, and others. Thus Lothar Meyer in 1864, following Dumas and others, grouped
together the tetravalent elements carbon and silicon; the trivalent elements nitrogen,
phosphorus, arsenic, antimony, and bismuth; the bivalent oxygen, sulphur, selenium,
and tellurium; the univalent fluorine, chlorine, bromine, and iodine; the univalent
metals lithium, sodium, potassium, rubidium, caesium, and thallium, and the bivalent
metals beryllium, magnesium, strontium and barium — observing that in the first the
difference is, in generals 1 6, in the second about=46, and the last about= 87-90. The
first germs of the periodic law are visible in such observations as these. Since its estab-
lishment this subject has been most fully worked out by Ridberg (Note 3), who ob-
served a periodicity in the variation of the differences between the atomic weights of
two contiguous elements, and its relation to their atomicity. A. Bazaroff (1887) inves-
tigated the same subject, taking, not the arithmetical differences of contiguous and
analogous elements, but the ratio of their atomic weights; and he also observed that
this ratio alternately rises and falls with the rise of the atomic weights.
MENDELEYEV — THE PERIODIC LAW 559
7th series As = 75 stands before it and Br = 80 after it. Hence the atomic
weight of selenium should be % (32+125+75-1-80) = 78, which is near
to the truth. Other properties of selenium may also be determined in
this manner. For example, arsenic forms H3As, bromine gives HBr> and
it is evident that selenium, which stands between them, should form
H2Se, with properties intermediate between those of H3As and HBr.
Even the physical properties of selenium and its compounds, not to
speak of their composition, being determined by the group in which
it occurs, may be foreseen with a close approach to reality from the
properties of sulphur, tellurium, arsenic, and bromine. In this manner
it is possible to foretell the properties of still unknown elements. For
instance, in the position IV, 5 — that is, in the IVth group and 5th series
— an element is still wanting. These unknown elements may be named
after the preceding known element of the same group by adding to the first
syllable the prefix e\a-, which means one in Sanskrit. The element IV, 5,
follows after IV, 3, and this latter position being occupied by silicon, we
call the unknown element ekasilicon and its symbol Es. The following are
the properties which this element should have on the basis of the known
properties of silicon, tin, zinc, and arsenic. Its atomic weight is nearly 72,
higher oxide EsO2, lower oxide EsO, compounds of the general form
EsX4, and chemically unstable lower compounds of the form EsX2. Es
gives volatile organo-metallic compounds — for instance, Es(CH3)4, Es
(CH3)3 Cl, and Es(C2H5)4, which boil at about 160°, &c.; also a volatile
and liquid chloride, EsCl4, boiling at about 90° and of specific gravity
about 1-9. EsO2 will be the anhydride of a feeble colloidal acid, metallic
Es will be rather easily obtainable from the oxides and from K2EsF6 by
reduction, EsS2 will resemble SnS2 and SiS2, and will probably be soluble
in ammonium sulphide; the specific gravity of Es will be about 55, EsO2
will have a density of about 4-7, &c. Such a prediction of the properties
of ekasilicon was made by me in 1871, on the basis of the properties of
the elements analogous to it: IV, 3, = Si, IV, 7 = Sn, and also II, 5 = Zn
and V, 5 = As. And now that this element has been discovered by C.
Winkler, of Freiberg, it has been found that its actual properties entirely
correspond with those which were foretold,6 In this we see a most impor-
eThe laws of nature admit of no exceptions, and in this they clearly differ
from such rules and maxims as are found in grammar, and other inventions, methods,
and relations of man's creation. The confirmation of a law is only possible by deducing
consequences from it, such as could not possibly be foreseen without it, and by veri-
fying those consequences by experiment and further proofs. Therefore, when I conceived
the periodic law, I (1869-1871) deduced such logical consequences from it as could
serve to show whether it were true or not. Among them was the prediction of the
properties of undiscovered elements and the correction of the atomic weights of many,
and at that time little known, elements. Thus uranium was considered as trivalent,
U=i2o; but as such it did not correspond with the periodic law. I therefore proposed
to double its atomic weight — 11=240, and the researches of Roscoe, Zimmermann, and
others justified this alteration. It was the same with cerium, whose atomic weight it
was necessary to change according to the periodic law. I therefore determined its
specific heat, and the result I obtained was verified by the new determinations of
560 MASTERWORKS OF SCIENCE
tant confirmation of the truth of the periodic law. This element is now
called germanium,, Ge. It is not the only one that has been predicted by
the periodic law.7 Properties were foretold of an element ekaaluminium,
III, 5, El = 68, and were afterwards verified when the metal termed "gal-
lium" was discovered by De Boisbaudran. So also the properties of scan-
dium corresponded with those predicted for ekaboron, according to
Nilson.
6. As a true law of nature is one to which there are no exceptions, the
periodic dependence of the properties on the atomic weights of the ele-
ments gives a new means for determining by the equivalent the atomic
weight or atomicity of imperfectly investigated but known elements, for
which no other means could as yet be applied for determining the true
atomic weight. At the time (1869) when the periodic law was first pro-
posed there were several such elements. It thus became possible to learn
their true atomic weights, and these were verified by later researches.
Among the elements thus concerned were indium, uranium, cerium,
yttrium, and others.8
Hillebrand. I then corrected certain formula: of the cerium compounds, and the re-
searches o£ Rammelsberg, Brauner, Cleve, and others verified the proposed alteration.
It was necessary to do one or the other — either to consider the periodic law as com-
pletely true, and as forming a new instrument in chemical research, or to refute it.
Acknowledging the method of experiment to be the only true one, I myself verified
what I could, and gave everyone the possibility of proving or confirming the law, and
did not think, like L. Meyer (Liebig's Annalen, Supt. Band 7, 1870, 364), when writing
about the periodic law that "it would be rash to change the accepted atomic weights
on the basis of so uncertain a starting point." In my opinion, the basis offered by the
periodic law had to be verified or refuted, and experiment in every case verified it.
The starting point then became general. No law of nature can be established without
such a method of testing it. Neither De Chancourtois, to whom the French ascribe the
discovery of the periodic law, nor Newlands, who is put forward by the English, nor
L. Meyer, who is now cited by many as its founder, ventured to foretell the properties
of undiscovered elements, or to alter the "accepted atomic weights," or, in general, to
regard the periodic law as a new, stricdy established law of nature, as I did from the
very beginning (1869).
7When in 1871 I wrote a paper on the application of the periodic law to the deter-
mination of the properties of hitherto undiscovered elements, I did not think I should
live to see the verification of this consequence of the law, but such was to be the case.
Three elements were described — ekaboron, ekaaluminium, and ekasilicon — and now,
after the lapse of twenty years, I have had the great pleasure of seeing them discovered
and named Gallium, Scandium, and Germanium, after those three countries where the
rare minerals containing them are found, and where they were discovered. For my part
I regard L. de Boisbaudran, Nilson, and Winkler, who discovered these elements, as
the true corroborators of the periodic law. Without them it would not have been
accepted to the extent it now is.
^Taking indium, which occurs together with zinc, as our example, we will show
the principle of the method employed. The equivalent of indium to hydrogen in its
oxide is 37*7 — that is, if we suppose its composition to be like that of water; then
In:=37-7, and the oxide of indium is InsO. The atomic weight of indium was taken as
double the equivalent — that is, indium was considered to be a bivalent element — and
MENDELEYEV — THE PERIODIC LAW 561
7. The periodic variability of the properties of the elements in de-
pendence on their masses presents a distinction from other kinds of peri-
odic dependence (as, for example, the sines of angles vary periodically
and successively with the growth of the angles, or the temperature of
the atmosphere with the course of time), in that the weights of the atoms
do not increase gradually, but by leaps, that is, according to Dalton's law
of multiple proportions, there not only are not, but there cannot be, any
transitive or intermediate elements between two neighbouring ones (for
example, between K = 39 and Ca = 40, or Al = 27 and Si = 28, or C =
12 and N = 14, &c.). As in a molecule of a hydrogen compound there
may be either one, as in HF, or two, as in H2O, or three, as in NH3, &c.,
atoms of hydrogen; but as there cannot be molecules containing 2%
atoms of hydrogen to one atom of another element, so there cannot be
any element intermediate between N and O, with an atomic weight
greater than 14 or less than 16, or between K and Ca. Hence the periodic
dependence of the elements cannot be expressed by any algebraical con-
tinuous function in the same way that it is possible, for instance, to ex-
press the variation of the temperature during the course of a day or year.
8. The essence of the notions giving rise to the periodic law consists
in a general physico-mechanical principle which recognises the correla-
In=2X37F7:=75'4- If indium only formed an oxide, RO, it should be placed in group
II. But in this case it appears that there would be no place for indium in the system of
the elements, because the positions II, 5 = Zn = 65 and II, 6 = Sr = 87 were
already occupied by known elements, and according to the periodic law an element
with an atomic weight 75 could not be bivalent. As neither the vapour density nor the
specific heat, nor ' even the isomorphism (the salts of indium crystallise with great
difficulty), of the compounds of indium were known, there was no reason for consid-
ering it to be a bivalent metal, and therefore it might be regarded as trivalent, quad-
rivalent, &c. If it be trivalent, then In=3X377— I]C3» anc* the composition of the oxide
is InaOs, and of its salts InXs. In this case it at once Jails into its place in the system,
namely, in group III and 7th series, between Cd=ii2 and Sn=n8, as an analogue of
aluminium or dvialuminium (dvi = 2 in Sanskrit). All the properties observed in
indium correspond with this position; for example, the density, cadmium = 8-6,
indium = 7-4; tin =. 7-2; the basic properties of the oxides CdO, In^Os, SnOs, succes-
sively vary, so that the properties of In2Os are intermediate between those of CdO and
SnOa or CdsOa and SnsO*. That indium belongs to group III has been confirmed by the
determination of its specific heat, (0-057 according to Bunsen, and 0-055 according to
me) and also by the fact that indium forms alums like aluminium, and therefore
belongs to the same group.
The same kind of considerations necessitated taking the atomic weight of titanium
as nearly 48, and not as 52, the figure derived from many analyses. And both these
corrections, made on the basis of the law, have now been confirmed, for Thorpe found,
by a series of careful experiments, the atomic weight of titanium to be that foreseen
by the periodic law. Notwithstanding that previous analyses gave 05=1997, 11=198,
and Pt=i87, the periodic law shows, as I remarked in 1871, that the atomic weights
should rise from osmium to platinum and gold, and not fall. Many recent researches,
and especially those of Seubert, have fully verified this statement, based on the law.
Thus a true law of nature anticipates facts, foretells magnitudes, gives a hold on nature,
and leads to improvements in the methods of research, &c.
562 MASTERWORKS OF SCIENCE
tion, transmutability, and equivalence of the forces of nature. Gravitation,
attraction at small distances, and many other phenomena are in direct
dependence on the mass of matter. It might therefore have been expected
that chemical forces would also depend on mass. A dependence is in fact
shown, the properties of elements and compounds being determined by
the masses of the atoms of which they are formed. The weight of a mole-
cule, or its mass, determines many of its properties independently of
its composition. Thus carbonic oxide, CO, and nitrogen, N2, are two
gases having the same molecular weight, and many of their properties
(density, liquefaction, specific heat, &c.) are similar or nearly similar.
The differences dependent on the nature of a substance play another part,
and form magnitudes of another order. But the properties of atoms are
mainly determined by their mass or weight, and are in dependence upon
it. Only in this case there is a peculiarity in the dependence of the prop-
erties on the mass, for this dependence is determined by a periodic law.
As the mass increases the properties vary, at first successively and regu-
larly, and then return to their original magnitude and recommence a
fresh period of variation like the first. Nevertheless here as in other cases
a small variation of the mass of the atom generally leads to a small varia-
tion of properties, and determines differences of a second order. The
atomic weights of cobalt and nickel, of rhodium, ruthenium, and palla-
dium, and of osmium, indium, and platinum, are very close to each other,
and their properties are also very much alike — the differences are not very
perceptible. And if the properties of atoms are a function of their weight,
many ideas which have more or less rooted themselves in chemistry must
suffer change and be developed and worked out in the sense of this de-
duction. Although at first sight it appears that the chemical elements are
perfectly independent and individual, instead of this idea of the nature
of the elements, the notion of the dependence of their properties upon
their mass must now be established; that is to say, the subjection of the
individuality of the elements to a common higher principle which evinces
itself in gravity and in all physico-chemical phenomena. Many chemical de-
ductions then acquire a new sense and significance, and a regularity is
observed where it would otherwise escape attention. -This is more par-
ticularly apparent in the physical properties, to the consideration of
which we shall afterwards turn, and we will now point out that Gustav-
son first, and subsequently Potilitzin, demonstrated the direct dependence
of the reactive power on the atomic weight and that fundamental prop-
erty which is expressed in the forms of their compounds, whilst in a
number of other cases the purely chemical relations of elements proved
to be in connection with their periodic properties. As a case in point, it
may be mentioned that Carnelley remarked a dependence of the decom-
posability of the hydrates on the position of the elements in the periodic
system; whilst L. Meyer, Willgerodt, and others established a connection
between the atomic weight or the position of the elements in the periodic
system and their property of serving as media in the transference of the
halogens to the hydrocarbons. Bailey pointed out a periodicity in the sta-
ivi JS1N JJ JC, JL £, X £, V — 1JHLJ± J^ £ K I U JU 1 (J LAW 563
bility (under the action of heat) of the oxides, namely: (a) in the even
series (for instance, CrO3, MoO3, WO3, and UO3) the higher oxides of
a given group decompose with greater ease the smaller the atomic weight,
while in the uneven series (for example, CO2, GeO2, SnO23 and PbO2) the
contrary is the case; and (b) the stability of the higher saline oxides in
the even series (as in the fourth series from K2O to Mn2O7) decreases
in passing from the lower to the higher groups, while in the uneven
series it increases from the 1st to the IVth group, and then falls from the
IVtrh to Vllth; for instance, in the series Ag9O, CdO, In0O3, SnO0? and
then SnO2, Sb2O5, TeO3, I2O7. K. Winkler looked for and" actually found
(1890) a dependence between the reducibility of the metals by mag-
nesium and their position in the periodic system of the elements. The
greater the attention paid to this field the more often is -a distinct con-
nection found between the variation of purely chemical properties of
analogous substances and the variation of the atomic weights of the con-
stituent elements and their position in the periodic system. Besides, since
the periodic system has become more firmly established, many facts have
been gathered, showing that there are many similarities between Sn and
Pb, B and Al, Cd and Hg, &c., which had not been previously observed,
although foreseen in some cases, and a consequence of the periodic law.
Keeping our attention in the same direction, we see that the most widely
distributed elements in nature are those with small atomic weights,
whilst in organisms the lightest elements exclusively predominate (hydro-
gen, carbon, nitrogen, oxygen), whose small mass facilitates those trans-
formations which are proper to organisms. Poluta (of Kharkoff), C. C.
Botkin, Blake, Brenten, and others even discovered a correlation between
the physiological action of salts and other reagents on organisms and the
positions occupied in the periodic system by the metals contained in
them.
As, from the necessity of the case, the physical properties must be
in dependence on the composition of a substance, i.e. on the quality and
quantity of the elements forming it, so for them also a dependence on
the atomic weight of the component elements must be expected, and
consequently also on their periodic distribution. We will content our-
selves with citing the discovery by Carnelley in 1879 of the dependence
of the magnetic properties of the elements on the position occupied by
them in the periodic system. Carnelley showed that all the elements of
the even series (beginning with lithium, potassium, rubidium, caesium)
belong to the number of magnetic (paramagnetic) substances; for exam-
ple, according to Faraday and others, C, N, O, K, Ti, Cr, Mn, Fe, Co, Ni,
Ce, are magnetic; and the elements of the uneven series are diamagnetic,
H, Na, Si, P, S, Cl, Cu, Zn, As, Se, Br, Ag, Cd, Sn, Sb, I, Au, Hg, H,
Pb, Bi.
Carnelley also showed that the melting point of elements varies peri-
odically, as is seen by the figures in Table II (nineteenth column), where
all the most trustworthy data are collected, and predominance is given
to those having maximum and minimum values.
564 MASTERWORKS OF SCIENCE
There Is no doubt that many other physical properties will, when
further studied, also prove to be in periodic dependence on the atomic
weights, but at present only a few are known with any completeness,
and we will only refer to the one which is the most easily and frequently
determined — namely, the specific gravity in a solid and liquid state, the
more especially as its connection with the chemical properties and rela-
tions of substances is shown at every step. Thus, for instance, of all the
metals those of the alkalis, and of all the non-metals the halogens, are
the most energetic in their reactions, and they have the lowest specific
gravity among the adjacent elements, as is seen in Table II, column 17.
Such are sodium, potassium, rubidium, caesium among the metals, and
chlorine, bromine, and iodine among the non-metals; and as such less
energetic metals as iridium, platinum, and gold (and even charcoal or
the diamond) have the highest specific gravity among the elements near
to them in atomic weight; therefore the degree of the condensation of
matter evidently influences the course of the transformations proper to a
substance, and furthermore this dependence on the atomic weight, al-
though very complex, is of a clearly periodic character. In order to ac-
count for this to some extent, it may be imagined that the lightest ele-
ments are porous, and, like a sponge, are easily penetrated by other sub-
stances, whilst the heavier elements are more compressed, and give way
with difficulty to the insertion of other elements. These relations are best
understood when, instead of the specific gravities referring to a unit of
volume, the atomic volumes of the elements — that is, the quotient A/d
of the atomic weight A by the specific gravity d — are taken for compari-
son. As, according to the entire sense of the atomic theory, the actual
matter of a substance does not fill up its whole cubical contents, but is
surrounded by a medium (ethereal, as is generally imagined), like the
stars and planets which travel in the space of the heavens and fill it,
with greater or less intervals, so the quotient A/d only expresses the mean
volume corresponding to the sphere of the atoms, and therefore ^ A/d
is the mean distance between the centres of the atoms. For compounds
whose molecules weigh M, the mean magnitude of the atomic volume is
obtained by dividing the mean molecular volume M/d by the number
of atoms n in the molecule. The above relations may easily be expressed
from this point of view by comparing the atomic volumes* Those com-
paratively light elements which easily and frequently enter into reaction
have the greatest atomic volumes: sodium 23, potassium 45, rubidium
57, caesium 71, and the halogens about 27; whilst with those elements
. which enter into reaction with difficulty, the mean atomic volume is small;
for carbon in the form of a diamond it is less than 4, as charcoal about 6,
for nickel and cobalt less than 7, for iridium and platinum about 9. The
remaining elements having atomic weights and properties intermediate
between those elements mentioned above have also intermediate atomic
volumes. Therefore the specific gravities and specific volumes of solids
and liquids stand in periodic dependence on the atomic weights, as is
MENDELEYEV — THE PERIODIC LAW 565
seen in Table II, where both A (the atomic weight) and d (the specific
gravity), and A/d (specific volumes of the atoms) are given (column 18).
Thus we find that in the large periods beginning with lithium,
sodium, potassium, rubidium, caesium, and ending with fluorine, chlorine,
bromine, iodine, the extreme members (energetic elements) have a small
density and large volume, whilst the intermediate substances gradually
increase in density and decrease in volume — that is, as the atomic weight
increases the density rises and falls, again rises and falls, and so on.
Furthermore, the energy decreases as the density rises, and the greatest
density is proper to the atomically heaviest and least energetic elements;
for example, Os, Ir, Pt, Au, U.
In order to explain the relation between the volumes of the elements
and of their compounds, the densities (column S) and volumes (column
M/.?) of some of the higher saline oxides arranged in the same order as
in the case of the elements are given on p. 566. For convenience of com-
parison the volumes of the oxides are all calculated per two atoms of an
element combined with oxygen. For example, the density of Al2O3=4*o,
weight Al2O3=i02, volume A12O3=25'5. Whence, knowing the volume of
aluminium to be n, it is at once seen that in the formation of aluminium
oxide, 22 volumes of it give 255 volumes of oxide. A distinct periodicity
may also be observed with respect to the specific gravities and volumes of
the higher saline oxides. Thus in each period, beginning with the alkali
metals, the specific gravity of the oxides first rises, reaches a maximum,
and then falls on passing to the acid oxides, and again becomes a mini-
mum about the halogens. But it is especially important to call attention to
the fact that the volume of the alkali oxides is less than that of the metal
contained in them, which is also expressed in the last column, giving this
difference for each atom of oxygen. Thus 2 atoms of sodium, or 46 vol-
umes, give 24 volumes of Na2O, and about 37 volumes of 2NaHO — that is,
the oxygen and hydrogen in distributing themselves in the medium of
sodium have not only not increased the distance between its atoms, but
have brought them nearer together, have drawn them together by the force
of their great affinity, by reason, it may be presumed, of the small mutual
attraction of the atoms of sodium. Such metals as aluminium and zinc, in
combining with oxygen and forming oxides of feeble salt-forming capac-
ity, hardly vary in volume, but the common metals and non-metals, and es-
pecially those forming acid oxides, always give an increased volume when
oxidised — that is, the atoms are set further apart in order to make room
for the oxygen. The oxygen in them does not compress the molecule as
in the alkalis; it is therefore comparatively easily disengaged.
As the volumes of the chlorides, organo-metallic and all other corre-
sponding compounds, also vary in a like periodic succession with a change
of elements, it is evidently possible to indicate the properties of sub-
stances yet uninvestigated by experimental means, and even those of yet
undiscovered elements. It was possible by following this method to fore-
tell, on the basis of the periodic law, many of the properties of scandium,
gallium, and germanium, which were verified with great accuracy after
566
MASTERWORKS OF SCIENCE
HaO
LiaO
BsOa
GO*
Na*O
MgaOa
ALOa
SbO*
PaOs
CLO*
K*0
ScaOa
Cu^O
ZnaOa
GasOa
AssO5
SraOa
TeOo
BaaOa
LaaOa
TaaOs
Hg202
PbaO*
I'O
2-0
3-06
1-8
1-6
1-64
2-6
3'5
4-0
2-65
2'39
1-96
2-7
3*25
3
4-2
3
2
5
86
49
74
9
NbaOs ....
MoOo ....
Ag20 ....
5'7
4'7
4'7
5-0
5'5
4*7
4*4
7'5
8-0
7-18
7-0
6-5
5-i
5*7
6-5
6-74
7'5
6-8
n-i
8-9
9*86
M/J
18
15
16
39
55
66
24
23
26
45
59
82
95
35
34
35
38
52
73
24
23
36
44
56
44
45
44
57
65
3i
32
38
43
49
52
50
50
59
68
39
53
54
Volume of Oxygen
? —22
— 9
+ 2-6
-J- 10*0
+ 10-6
? + 4
22
— 4'5
+ 5*2
+ 6-2
+ 8-7
+ 6
— 35
— 8
? o
+ 3
+ 6-7
+ 9'5
+ 9'6
+ 4'8
+ 4
+ 4'5
+ 6-0
— 13
? — 2
0
6
6-8
+
+
+
+
+
+
3
2-7
2-7
2-6
4.7
— 10
+ i
+ 2
+ 4-6
+ 8-2
+ 4-5
+ 4-2
+ 2
MENDELEYEV — THE PERIODIC LAW 567
these metals had been discovered. The periodic law, therefore, has not
only embraced the mutual relations of the elements and expressed their
analogy, but has also to a certain extent subjected to law the doctrine of
the types of the compounds formed by the elements: it has enabled us to
see a regularity in the variation of all chemical and physical properties of
elements and compounds, and has rendered it possible to foretell the
properties of elements and compounds yet uninvestigated by experimen-
tal means; thus it has prepared the ground for the building up of atomic
and molecular mechanics.
RADIOACTIVITY
MARIE CURIE
CONTENTS
Radioactivity
The Discovery of Radioactivity and of the Radioelements
The Rays of Uranium. The Rays of Thorium
Radioactivity an Atomic Property. New Method of Chemical Analy-
sis Based on Radioactivity. Discovery of Radium and Polonium
Spectrum and Atomic Weight of Radium. Metallic Radium
The Radioelements
The Derivatives of Uranium: A. The Radium Branch
B. The Actinium Branch
The Derivatives of Thorium
The Radioactive Ores and the Extraction of the Radioelements
The Radioactive Ores
Ores of Thorium and Uranium
MARIE CURIE
1867-1934
MARIE CUKIE was born Marie Sklodovska in Warsaw, in 1867,
the youngest child of a poorly paid Polish teacher in the Rus-
sian-controlled schools of Warsaw. At three she had learned
by herself to read; from an early age she displayed an infalli-
ble memory, quick comprehension, unbelievable powers of
concentration. This precocity her parents, particularly her
father, after his wife's death when Marie was scarcely more
than an infant, tried to curb. But the four other children in
the family also had great gifts, and the atmosphere of the
household encouraged intellectual striving. At sixteen Marie
had finished the course at the gymnasium and had there won
the gold medal — the third to be carried off by the Sklodovski
children. And after a year of visiting her relatives in rural
Poland, she began earning her living as a private teacher in
Warsaw.
Like the other young people of her set, she devoted her-
self to Comte, read Darwin and Pasteur, made an effort — pa-
triotic in origin — to educate the illiterate poor, and joined
secret classes for the study of science. The local university
being open only to men, she and her favorite sister, Bronya,
yearned to go to Paris to study. Finally she persuaded Bronya
to take their slender resources and to proceed to the Sor-
bonne. Their plan was that once Bronya had qualified for her
degree, she would aid Marie. Meantime, Marie would con-
tribute what she could earn to Bronya' s support.
There followed several years of service as a governess,
now in Warsaw, now in a country village miles from a town.
In the intervals of her exacting duties Marie found time to
organize secret Polish classes for the children of the poor, to
study mathematics, and to teach herself such chemistry and
physics as she could dig out of textbooks without the aid of
either teacher or laboratory. The dream of getting to Paris
572 MASTERWORKS OF SCIENCE
faded. Then Bronya finished her medical course, married a
fellow Pole in Paris, and began to practice. Suddenly Marie
was summoned to her opportunity.
In 1889, almost without financial resources, Marie was
living in Paris with her sister and was entered at the Sor-
bonne. Presently she felt that the gaiety of her sister's Polish
friends — even the occasional concert and the occasional thea-
ter— interfered with her work. She moved to a lodging in the
Latin Quarter. In that neighborhood, in one poor, unheated,
almost barren room or another, she lived her student days.
There, unable to cook, too poor to buy food and fuel, she
studied early and late until she almost succumbed to over-
work and malnutrition. In 1893, at the top of her class, she
took her master's degree in physics; in 1894, her master's
degree in mathematics.
About this time Marie undertook her first commission:
to study the magnetic properties of steels. In the course of this
work she met Pierre Curie. He was a man of thirty-five, al-
ready a highly esteemed physicist. Like Marie, he came of a
most cultivated, middle-class family; like her, he was devoted
to his science to the exclusion of people. The two were
quickly in sympathy, and shortly they were close friends. Two
years later they married.
The Curies now began an amazing collaborative work at
the School of Physics and Chemistry of the City of Paris,
where Pierre was chief of laboratory. Marie, searching for a
subject for a doctoral dissertation, had become interested in
Becquerel rays and their sources. As she systematically exam-
ined all known elements and minerals, she began to sus-
pect that in the pitchblende (uranium ore) she had studied
there was a hitherto-unidentified element capable of radia-
tion far stronger than that from - uranium. Pierre at once
abandoned his work with crystals to join in the study of the
Becquerel rays. In 1898 they together announced the probable
existence of polonium; a few months later they announced
radium.
From 1898 to 1902 they devoted themselves to the long,
arduous task of preparing a sample of pure radium from the
masses of pitchblende they were, with difficulty, able to ob-
tain. Together they studied the physical and chemical proper-
ties of the new element. Finally, in 1902, Marie isolated pure
radium salt and determined its atomic weight, 225.
Meantime, Pierre had become a teacher at the P.C.N., an
annex of the Sorbonne, and Marie had become a lecturer in
physics at the girls' normal school at Sevres. Though these
teaching duties constantly drained their energies, though
CURIE — RADIOACTIVITY 573
their earnings scarcely paid their modest bills, though Pierre's
health failed, they never halted in their research. By 1904 they
had published twenty-nine papers on radioactivity, most of
them so completely joint products that the work of one is
indistinguishable from that of the other.
For her work on radium Marie won her doctoral degree
in 1903; in the same year the Curies began to receive the
honors which, until Marie's death in 1934, never stopped
coming. They visited London to present the results of their
studies to the Royal Society, and Marie attended the meeting
— the first woman ever admitted; they were jointly awarded
the Davy Medal in 1903, and a few months later, together
with Becquerel, the Nobel Prize for Physics, Even this tri-
umph scarcely persuaded them to pause in their labors long
enough to visit Stockholm for the presentation of the prize
money. They scarcely paused to celebrate Pierre's election to
the Academy of Science, or his elevation to a professorship at
the Sorbonne. Suddenly, in 1906, after an idyllic Easter holi-
day in the country, Pierre died, the victim of a street accident.
The great collaboration was ended.
The tremendous official and the genuine friendly sym-
pathy which rose round Marie meant nothing to her. She was
sustained only by that devotion to science which had per-
suaded her and Pierre several years before to refuse to patent
their process for refining radium: by that devotion, and by
her ingrained habit of work. Within a few months the Sor-
bonne entrusted her with Pierre's course, as his successor. She
labored upon her lectures, and in November she delivered the
first of them, beginning exactly where Pierre had left off. The
first woman ever to lecture at the Sorbonne, she soon began to
give the first — and for long the only — course in the world on
radioactivity.
From 1906 to 1914, as the fame of Marie Curie grew, she
never stopped working — hardly even for an occasional visit to
Warsaw, such as that in 1913 to inaugurate a laboratory for
the study of radioactivity, or for a quick trip to a foreign uni-
versity to receive an honorary degree, or for a summer walk-
ing tour in the Engadine, or for a second excursion to Stock-
holm to receive in 1911 the Nobel Prize for Chemistry. She
studied polonium exhaustively; she administered the fellow-
ships for the study of radioactivity established by Carnegie;
she prepared the first and only sample of pure metallic radium
and redetermined its atomic weight; when the University of
Paris and the Pasteur Institute jointly undertook the construc-
tion of an Institute for Radium, she supervised the execution
of the scheme.
574 MASTERWQRKS OF SCIENCE
This building was just ready for occupancy when World
War I broke out in 1914. For the next five years Mme. Curie
was occupied constantly with the war work she made pecul-
iarly hers. She observed at once that the army hospitals were
not equipped to use radiology. Almost unaided, and fre-
quently in the face of official lethargy, by the end of the war
she had equipped two hundred radiological rooms, most of
them in field hospitals, and twenty radiological cars. She her-
self performed prodigies in the field as an X-ray technician;
she trained one hundred and fifty X-ray technicians, and she
organized and operated the radium emanation service. Her
patriotic fervor blazed: not only her services — and those of
all the scientists she could commandeer — but her prize win-
nings and her whole fortune, she put at the disposal of the
government. But immediately the war ended, she resumed her
investigative studies.
Though the hard work never ended, nor her eagerness for
it, Mme. Curie's life for the next fifteen years had a brighter
tone than before. She had wonderful summer holidays at Lar-
couest, a quiet spot in Brittany, with a group of congenial
academic people from the Sorbonne. She watched the prog-
ress of her daughter and her son-in-law, the Joliot-Curies, who
were rising to eminence in the world of science. She even oc-
casionally accepted the world's homage; for she came to be-
lieve that whatever was offered her was in reality a tribute to
science. Thus in 1921 she made a trip to America, an almost
royal progress, to receive from the women of America the gift
of a gram of radium, and repeated the same tour for the same
reason in 1929. (The first gift she immediately transferred to
the Paris Radium Institute, and the second to the Warsaw
Institute, founded in 1925.) Thus she journeyed to Rio de
Janeiro, to Italy, to Holland, to England, to Czechoslovakia,
to Spain. The learned societies of the world elected her to
membership; the universities of the world conferred their
honorary degrees upon her. She accepted everything with
complete self-effacement. It even seemed to her that these ex-
peditions, pleasurable as they sometimes were, cost overmuch
in their interruptions of her work. Even when her health de-
clined and her sight dimmed, her energy did not. Almost
until the day of her death she was busy writing her last, her
greatest, book. It was just finished when she died.
Mme. Curie's story has been so colorfully told by her
daughter Eve — and so vividly presented on the movie screen —
that everyone knows of her, and thinks of her, probably, as a
fairy-tale heroine of science. Yet her genius was not romantic.
It was a genius for hard work. She had a passionate devotion
to accuracy, to truth, to science — a devotion which made her
CURIE — RADIOACTIVITY 575
all but selfless. Even when she must credit herself with her
own achievements, as in the pages here translated from her
last book, Radioactivity, she speaks of herself in the third
person. For she cared nothing for personal glory, everything
for labor and knowledge.
RADIOACTIVITY
THE DISCOVERY OF RADIOACTIVITY AND OF THE
RADIOELEMENTS
THE STUDY of radioactivity includes the study of the chemistry of the
radioelements, the study of the rays emitted by these elements, and the
conclusions to be drawn from such studies relative to the structure of the
atom. The radioelements can be defined as particular elements from
which there emanate, spontaneously and atomically, rays designated as
alpha, beta, and gamma — positive corpuscular rays, negative corpuscular
rays (electrons in motion), and electromagnetic radiations. The emission
is accompanied by an atomic transformation. Arranged according to their
respective abilities to penetrate matter, the alpha rays are the weakest:
they are stopped by a sheet of paper or by a leaf of aluminum o.i mm. in
thickness; they travel through air a few centimeters. The beta rays travel
farther in air and can penetrate several millimeters of aluminum. The
gamma rays can penetrate several centimeters of relatively opaque ma-
terial such as lead.
. The Rays of Uranium. The Rays of Thorium.
Henri Becquerel discovered radioactivity in 1896.
After the discovery of Roentgen rays, Becquerel began his researches
upon the photographic effects of phosphorescent and fluorescent sub-
stances.
The first tubes which produced Roentgen rays had no metallic anti-
cathode. The source of the rays was the glass wall of the tube, rendered
fluorescent by the action of the cathode rays. It was natural to inquire
whether the emission of Roentgen rays did not necessarily accompany the
production of fluorescence, whatever might be the cause of the latter,
Henri Poincare suggested that it did, and various attempts were made to
obtain photographic impressions on plates shielded in black paper, using
zinc sulphide and calcium sulphide previously exposed to light; the re-
sults were finally negative.
H. Becquerel made similar experiments with the salts of uranium,
some of which are fluorescent. He obtained impressions on photographic
plates wrapped in black paper with the double sulphate of uranyl and
potassium. Subsequent experiment showed that the phenomenon ob-
CURIE — RADIOACTIVITY 577
served was not linked to that of fluorescence. The salt used need not be
activated by sunlight; further, uranium and all of its compounds, whether
fluorescent or not, act on the photographic plate in the same way, and
metallic uranium is the most active of all. Becquerel eventually discovered
that compounds of uranium, placed in complete darkness, continued for
a period of years to make impressions on photographic plates wrapped in
black paper. He then affirmed that uranium and its compounds emit spe-
cial rays: uranium rays. These rays can penetrate thin metallic screens; as
they pass through gases, they ionize them and render them conductors of
electricity. The radiation from uranium is spontaneous and constant; it is
independent of external conditions of light and temperature.
The electrical conductivity caused in the air or other gases by the
uranium rays is the same as that caused by Roentgen rays. The ions pro-
duced in both cases have the same mobility and the same coefficient of
diffusion. Measurement of the current for saturation provides a conven-
ient means of measuring the intensity of radiation under given conditions.
The Thorium Rays. Researches made simultaneously by C. Schmidt and
Marie Curie have shown that the compounds of thorium emit rays like
the uranium rays. Such rays are usually called Becquerel rays. The sub-
stances which emit Becquerel rays are called radioactive, and the new
property of matter revealed by that emission has been named by Marie
Curie radioactivity. The elements which so radiate are called radio-
elements.
Radioactivity an Atomic Property. New Method of Chemical Analysis
Based on Radioactivity. Discovery of Radium and Polonium.
From BecquereFs researches, it was clear that the radiation from
uranium is more intense than that from its compounds. Marie Curie made
a systematic study of all known metallic elements and their compounds to
investigate the radioactivity of various materials. She pulverized the vari-
ous substances and spread them in uniform layers on plates of the same
diameter which could be inserted into an ionization chamber. Using the
piezo-electric quartz method, she measured the saturation current pro-
duced in the chamber between the plates A and B (see p. 578). With
plates 3 cm. in diameter, placed three centimeters apart, an even layer of
uranium oxide gives a current of about 2Xio~n amperes, which scarcely
increases as the thickness of the layer increases after it exceeds a fraction
of a millimeter; the emanations are almost all alpha rays of uranium,
easily absorbed. Measurements made upon the compounds of uranium
have certified that the intensity of radiation increases with the uranium
content. The same thing is true for the thorium compounds. The radio-
activity of these elements is therefore an atomic property.
On the contrary, a substance such as phosphorus cannot be consid-
ered radioactive because to produce ionization it must be in the state of
578
MASTERWORKS OF SCIENCE
white phosphorus; in the red state, or in a compound such as sodium
phosphate, it does not produce ionization. Similarly, quinine sulphate,
which produces ionization only while it is being heated or cooled, is not
radioactive, for the emission of ions is produced here by the variation in
temperature and is not an indication of radioactivity of any one of the
constituent elements. It is, indeed, a fundamental characteristic of radio-
activity that it is a spontaneous phenomenon and an atomic property.
These considerations played an important part in the discovery of radium.
Marie Curie carried on her measurements, using both the widely dis-
tributed elements and the rare elements, and as many of their compounds
as possible. In addition to pure substances, she also examined a great
many samples of various rocks and ores. For simple substances and their
compounds, she demonstrated that none except thorium showed an ac-
tivity equal to i% of that of uranium.
Among the ores examined, several were radioactive: pitchblende,
chalcolite, autunite, thorite, and some others. Since all of these contain
either uranium or thorium, it was natural to find them active; but the
intensity of the phenomenon with certain minerals was unexpected. Thus
some pitchblendes (oxide of uranium) were four times as active as me-
tallic uranium. Chalcolite (copper phosphate and crystalline uranium)
was twice as active as uranium. These facts did not agree with the results
from the study of simple substances and their compounds, according to
which none of these minerals should have shown more activity than
uranium or thorium. Furthermore, double phosphate of copper and
uranium, of the same formula as chalcolite, prepared from uranium salts
CURIE — RADIOACTIVITY 579>
and pure copper, showed an activity quite normal (less than half that of
uranium). Marie Curie formed the hypothesis that pitchblende, chalco-.
lite, and autunite each contain a very small quantity of a very strongly-
active material, different from uranium, from thorium, and from already-
known elements. She undertook to extract that substance from the ore by-
the ordinary processes of chemical analysis. The analysis of these ores,,
previously made in general to an accuracy of nearly i% or 2%, did not
destroy the possibility that there might occur in them, in a proportion of:
that order, a hitherto unknown element. Experiment verified the proph-.
ecy relative to the existence of new, powerfully radioactive radioelements;
but their quantity turned out to be much smaller than had been sup--
posed. Several years were required to extract one of them in a state of-"
purity.
The research upon the radioelement hypothesized was made first by-
Pierre Curie and Marie Curie together, using pitchblende.
The research method had to be based upon radioactivity, for no other*
property of the hypothesized substance was known.
Radioactivity is used in a research of this kind in the following way:;
the activity of a product is measured; it is then subjected to chemical,
separation; the radioactivity of each resulting product is measured, and
it is observed whether the radioactive substance now remains integrally-
in one of the products or is divided among them, and if so, in what pro-,
portion. The first chemical operations carried out showed that an enrich-,
ment in active material was possible. The activity of the solid products — .
well-dried and spread in a powdered state on plates — was measured under-
comparable conditions. As more and more active products are obtained,,
it is necessary to modify the technique of measurements. Some methods,
of quantitative analysis for radioactive materials will be described later-
on in this work.
The method of analysis just described is comparable to spectrum,
analysis from low to high frequencies. It not only discovers a radioactive-,
material, but also distinguishes between the various radioactive elements,.
For they differ from one another in the quality of their radiations and in
their length of life.
The pitchblende from St. Joachimstahl which was used in the first
experiments is an ore of uranium oxide. Its greatest bulk is uranium
oxide, but it contains also a considerable quantity of flint, of lime, of
magnesia, of iron, and of lead, and smaller quantities of some other ele-.
ments: copper, bismuth, antimony, the rare earth elements, barium, silver^
and so on. Analysis made by using the new method showed a concentra-,
tion of the radioactive property in the bismuth and in the barium ex-,
tracted from the pitchblende. Yet the bismuth and the barium in com-,
mercial use, which are extracted from non-jradioactive ores, are not them-
selves active. In agreement with the original hypothesis, Pierre and Marie
Curie concluded that there were in the pitchblende two new radioactive
elements: polonium and radium. The first of these they took to be analog
gous in its chemical properties to bismuth, and, tb,e_ second to barium,.
580 MASTERWORKS OF SCIENCE _^
They announced these conclusions in 1898. At the same time, they indi-
cated that polonium could be separated from the bismuth by such chemi-
cal treatments as the fractional precipitation of the sulphides or the
nitrites, and that radium could be separated from barium by the frac-
tional crystallization of the chlorides in water, or their fractional precipi-
tation by alcohol. Theoretically, they claimed, such processes should lead
to the isolation of the new radioelements.
A specimen of radium-bearing barium chloride, sixty times as active
as the oxide of uranium, was submitted to spectral analysis by Demargay.
He found, accompanying the spectrum of barium, a new line of 3815
Angstrom units. Later, examining a specimen nine hundred times as
active as the oxide of uranium, he found the line of 3815 A. much
strengthened, and two other new lines. Examination of polonium-bearing
bismuth, though the specimen was very active, revealed no new lines.
It had become clear that the new elements occurred in the ore in very
small proportions, and that they could be isolated only by treating hun-
dreds or even thousands of kilograms of the ore. To accomplish this labor,
it was necessary to have recourse to industrial operations, and to treat the
concentrated products thus obtained. After several years, Marie Curie suc-
ceeded in obtaining several decigrams of a pure radium salt, in deter-
mining the atomic weight of that element, and in assigning to it a place
in the periodic table hitherto vacant. Still later, Marie Curie and A.
Debierne isolated radium in the metal state. Thus the chemical individu-
ality of radium was established in the most complete and rigorous way.
The application of the new method of investigation later led to the
discovery of other new radioelements: first, actinium (discovered by A.
Debierne), then ionium (by Boltwood), then mesothorium and radio-
thorium (by O. Hahn), then protoactinium (by O. Hahn and L. Meit-
ner), etc. There have also been identified radioactive gases called emana-
tions.
Among all these substances, radium is the most widely known and most
widely used. Practically unvarying because of the slowness of its transfor-
mation, it is now industrially prepared, especially because of the medical
applications of the gamma radiations to which it apparently gives rise,
and which are, in reality, only indirectly attributable to it. Radium pro-
duces, apparently continuously, a radioactive gas named radon, and this
gas gives birth to a series of substances: radium A, radium B, radium C.
The last of these emits particularly penetrating gamma rays. Radium and
the derivatives which usually accompany it furnish intense sources of
alpha, beta, and gamma radiations. These have been and are the principal
ones used in researches upon such radiations. From the point of view of
chemistry, the studies of radium have confirmed the atomic theory of
radioactivity and have provided a solid foundation for a theory of radio-
active transformation.
CURIE — RADIOACTIVITY 581
Spectrum and Atomic Weight of Radium. Metallic Radium.
Since radium is an alkaline-earth metal, it is extracted from its ores
simultaneously with the barium also found there, or combined with it.
The mixture of radium and barium is submitted to a series of operations
of which the result is the separation of the radium from the barium in
the form of a pure salt.
As the products of these operations are successively enriched in ra-
dium, their radioactivity increases, the intensity of the spectral lines for
radium increases — as compared with the barium lines — and the mean
atomic weight increases. When the radium salt is wholly pure, the pho-
tographed spark spectrum shows only the lines characteristic of radium;
the strong 4554.4 A line of barium, of such sensitivity that it is extremely
hard to elimina-te, is now scarcely discernible.
A radium salt introduced into a flame gives it a carmine-red color,
and produces a visible spectrum composed of the characteristic radium
lines (Giesel).
In general, the appearance of the radium spectrum resembles that of
the alkaline-earth metals. It includes bright, narrow lines and also cloudy
bands. The principal lines of the spark spectrum and of the flame spec-
trum follow:
Spectrum Flame Spectrum
4821.1 faint 6653
4682.3 very bright 6700-6530 band
4533*3 faint 6329
4340.8 bright 6330-6130 band
3814.6 very bright 4826
3649.7 bright
2814.0 bright
2708.6 bright
The spark spectrum shows two bright, nebulous bands, with maximum
intensity at 4627.5 and 4455.2 A respectively.
The spectral reaction of radium is very sensitive. It makes possible
the identification of radium present in a substance in the proportion of
io~5. But the radioactive reaction is still more sensitive; it makes possible
the identification of the radium when its concentration is no more than
io~~12.
The atomic weight of radium, or the mean atomic weight of a mix-
ture of radium and barium, can be determined, as for barium, with pre-
cision. Although the radioactivity of the mixture is not less than 1000
times that of uranium, its atomic weight differs only negligibly from that
of barium. ,
The method used to make this determination is as follows: chloride
of radium, the purity of which had been certified by spectral analysis, was
582 MASTERWQRKS OF SCIENCE
deprived of its water of crystallization at a temperature of about 150° C.
and was carefully weighed in the state of an anhydrous salt. From a clear
solution of this salt, the chlorine was precipitated as silver chloride, and
the silver chloride was weighed. From the relation of that second weight
to the first, supposing that the formula for anhydrous chloride of radium
is RaCl2 — by analogy with the formula BaCl2, accepted for barium chlo-
ride— and using the accepted atomic weights of chlorine and silver, the
atomic weight of radium could be calculated.
The details of this technique have been explained in special reports
(Marie Curie, E. Hoenigschmid). The quantities of the chloride of ra-
dium used have varied from o.i gm. to i.o gm., and the various determi-
nations have resulted uniformly. Taking the atomic weight of silver as
107.88 and that of chlorine as 35.457, the atomic weight of radium is 226
( Hoenigschmid ) .
To isolate radium in its metallic state, the amalgam of radium was
prepared by electrolyzing, with a cathode of mercury, a solution con-
taining o.i gm. of pure radium chloride. The resulting liquid amalgam
decomposes water and is modified by air. It was dried, placed in a vessel
of pure iron, and distilled in an atmosphere of pure hydrogen obtained
by osmosis through incandescent platinum. The amalgam solidified at
about 400° C. The metal, cleared of mercury, melts at 700° C. and begins
to volatilize. Radium is a white, shining metal which rapidly alters in air,
and which decomposes water energetically.
In accord with its atomic weight, radium has been placed in the peri-
odic table of the elements as a higher homologue of barium, in the last
line of the table; its atomic number is 88; its spectrum and its chemical
properties accord with its position; similarly with its high-frequency
spectra (values of L^ and L2 levels) (Maurice de Broglie).
Here is a resume of the chemical properties of the radium salts: the
sulphate is insoluble in water and the common acids (solubility in water
at 20° C. is i.4XIO~3 £m« Per liter); the carbonate is insoluble in water
and in solutions of alkaline carbonates; the chloride is soluble in water
(at 20° C., 245 gm. of RaCl2 per liter), insoluble in concentrated hydro-
chloric acid and in pure alcohol; the bromide behaves similarly (at 20° C.,
706 gm. of RaBr2 per liter); the hydrate and the sulphide are soluble. The
separation of radium from barium by fractional crystallization depends
upon the fact that the chloride and the bromide of radium are less soluble
than the corresponding salts of barium (at 20° C., 357 gm. of BaCl2 and
1041 gm. of BaBr2 per liter of water).
The Radio elements
Each radioelement undergoes a transformation consisting of the suc-
cessive destruction of all its atoms, in accord with a law that half the
number existing at a given moment are transformed in a time T which is
characteristic of the radioelement under consideration, and which is called
CURIE — RADIOACTIVITY 583
its period. Measured by the magnitude of the period, radioelements have
a life which is more or less long. Some, like uranium and thorium, which
have survived several geological epochs in the ores which contain them>
have a very long life. Others, such as radium, actinium, polonium, meso-
thorium, radiothorium, and so on, would have disappeared wholly from
the ores if their decay had not been compensated for by their production
from uranium, and thorium. These two primary elements form, therefore,,
the heads of series or families to which belong all the other radioelements
— derivatives of the two, bound to one another by lines of descent. The
quantities of the derived elements which exist in untreated ores are pro-
portional to the quantities of the primary elements there, and to the
periods of the derivatives. Each derived element with a life sufficiently
long can be extracted from uranium and thorium ores, just as the primary
elements are; but sometimes it can be obtained by the decay of a more
or less distantly related element which has already been extracted from
the ore. For the radioelements of short life, only the latter method is.
available. In this chapter are given descriptions of the radioelements in
the order which they occupy in the several families.
The chemical properties of uranium and of thorium have been de-
scribed in treatises on chemistry, and will be omitted here. There exist at
least two isotopes of uranium, Ux (period of the order of io9 years) and
Ujj, a derivative with a very short life, existing in small proportion along
with Ur There is probably also a third isotope, AcU.
The Derivatives of Uranium
A. THE RADIUM BRANCH
Uranium X. The compounds of uranium emit alpha, beta, and gamma
rays; always, the alpha rays come from the uranium itself (Uj and U^);
the penetrating beta and gamma rays are emitted by a group of deriva-
tives which together form Uranium X, discovered by Crookes. Experi-
ments show that the alpha-radiating material cannot be separated from
the uranium; but by various reactions, the material which emits the beta
and gamma radiations can be separated from the uranium. The methods
of operation most*employed are the following: fractional crystallization
of uranium nitrate, extraction of the uranium from solution by the addi-
tion of ammonium carbonate in excess, and the treatment with ether of a
highly concentrated solution of uranium nitrate. In the first process,,
uranium X is concentrated in the more soluble portions. In the second*
uranium passes into solution, and the uranium X remains, with insoluble
impurities such as iron, in the alkaline solution. In the third, two layers o£
the liquid form; the one richer in ether contains a solution of uranium,
without uranium X; the on^ richer in water contains uranium X in excess.
The active material thus separated has a period of twenty-four days.
Uranium X is not simple, but is composed of several radioelements*
584 MASTERWORKS OF SCIENCE
The substance with a period of twenty-four days, preparation of which
has just been described, is an isotope of thorium (atomic number, 90),
and is called uranium Xx; it is produced by Up and it emits a group of
beta rays only mildly penetrative.
Uranium "X^ gives rise to a derivative of very short life, uranium X2 or
brevium (Fajans and Goehring). Its period is 1.13 minutes; it is a higher
homologue of tantalum (atomic number, 91); it emits a group of pene-
trating beta rays. Finally, there are found in uranium X, in very small
proportions, two other radioelements: uranium Y (Antonoff), an isotope
of thorium (atomic number, 90; period, 25 hours); and uranium Z
(Hahn) (atomic number, 91; period, 6.7 hours).
Ionium. Ionium, discovered by Boltwood, is the derivative of uranium
which is transformed directly into radium. Its period is 83,000 years. Its
chemical properties are exactly those of thorium, the two elements being
isotopes (atomic number, 90). In the treatment of ores, ionium is found
in the same portions as the thorium, and it is separated at the same
time as that rare earth element. From the uranium ore, what is actually
extracted is, therefore, a mixture of thorium-ionium; and though the pro-
portion of ionium is generally smaller than that of thorium, it may be com-
parable to it.
The spectrum of a thorium-ionium mixture containing 30% of
ionium is identical with that of thorium. This fact has been taken as an
argument that the spectra of isotopes are identical. Later researches into
the isotopes of lead have shown, however, that the identity is not com-
plete; there are very minute differences.
Though ionium occurs in relatively important quantities in the ura-
nium ores (perhaps 20 gm. per ton of uranium), it cannot be extracted as
a pure salt because of its close association with thorium.
The radiation of ionium is simple; it is composed principally of alpha
rays accompanied by a weak gamma ray of little penetrative power.
Radium and its first derivatives. The chemical individuality of radium
has already been given in earlier sections. Its period is 1600 years. By
radioactive transformations, radium produces a series of short-lived radio-
elements by which it is generally accompanied. These are a radioactive
gas, or emanation from radium, called radon, and * the components
A,B,C,C',C" of the active deposit. The radiation of this group is complex,
and is composed of alpha, beta, and gamma rays.
Radium D. Radium E. Radium D is an isotope of lead (atomic number,
82; period, 22 years). It emits a beta radiation of which the ionizing
power is very small; its presence is revealed by the formation of deriva-
tives. Of these derivatives, the first, radium E (isotope of bismuth; atomic
number, 83; period, 5 days), has a beta radiation; the second, radium F,
identical with polonium, has an alpha radiation. Radium D can be ex-
tracted from uranium ores at the same time as the lead which they con-
CURIE — RADIOACTIVITY 585
tain, and cannot be separated from this lead. This radioactive lead — or
radiolead — can be used as the primary material for the preparation of
polonium. Radium D can also be obtained from radium, from which it
derives through the intermediary steps of radon and the materials of its
active deposit.
Polonium. Polonium is the first radioactive element discovered by the
new method of chemical analysis based on radioactivity. It is a derivative
of uranium through the intermediary stage of radium. It is characterized
by an alpha radiation, and by the absence of penetrating rays. Its presence
was recognized in the sulphides precipitated in an acid solution of pitch-
blende, and, in the analysis of these sulphides, it particularly clung to the
bismuth. By means of the fractional precipitation of the bismuth salts
from water, the polonium can be concentrated in the less soluble portions.
Later research has shown that this element occurs in the ores in a much
smaller proportion than radium, and that it decays, with a period of 140
days. Marckwald has demonstrated that in certain of its chemical proper-
ties, polonium is analogous to tellurium. It is characterized also by the
ease with which certain metals (iron, copper, silver) displace it from acid
solutions. It can be prepared either from ores or from radiolead or from
radium.
The largest quantity of polonium hitherto prepared (Marie Curie
and A. Debierne) consists of about o.i mg. mixed with several milligrams
of foreign metals easily reducible. The radiation of that sample was com-
parable to that of 0.5 gm. of radium. Among the lines in the spark spec-
trum, there was one (4170.5 A) which seems to belong to polonium. More
recently, there has been announced the existence of a line of 2450 A (A.
Czapek),
To polonium, in the periodic table, has been assigned a place, hith-
erto vacant, beside bismuth (atomic number, 84), as a higher -analogue of
tellurium.
The analogy which polonium presents in part with tellurium, in part
with bismuth, is explainable, apparently, on considerations of valency.
For the compounds in which polonium is trivalent (sulphide), the anal-
ogy with bismuth is valid; for those in which it is tetravalent (chloride,
hydroxide), the analogy with tellurium is valid (M. Guillot). Polonium is
soluble in acid solutions and also in concentrated soda solutions. It can
behave, then, like a metal, or it can enter, like tellurium, into an acid
radical. In solutions almost neutral, its compounds undergo hydrolysis
and the radioactive material is deposited on the walls of the container;
this process is hastened by centrifugation. Polonium appears to be sus-
ceptible to linkage in certain complexes such as chloropoloniate of am-
monia, an isomorph of the corresponding salts of iron, lead, strontium,
platinum; or the diethylthiosulfocarbonate of polonium, an isomorph of
the salt of cobalt having the same formula. Experiment in electrolysis
points to ions of complex form.
Polonium can be volatilized, and the distilled material can be caught
386 MASTERWQRKS OF SCIENCE
by a gas current. The purest preparation so far obtained upon a small
-surface corresponds, according to numerical evaluations, to more than
fifty molecular layers, superimposed; the color is gray or black, attributa-
ble to polonium or to one of its oxides. Some polonium compounds, such
«as the hydride and the polonium carbonyl have been reported to be par-
ticularly volatile.
B. THE ACTINIUM BRANCH
The elements of the actinium family are, in all probability, deriva-
tives of uranium; but they are not of the same linked series as radium
&nd its derivatives. It is supposed that the isotopes of uranium give rise
"to two lines of derivatives, of which the radium family forms one and the
actinium family the other. The first certainly known member of the latter
-family is protoactinium. The connection between protoactinium and ura-
nium is probably through the intermediary UY.
Protoactinium (Hahn and Meitner, Soddy and Cranston). Protoactinium
was discovered in the residue remaining from the treatment of pitch-
blende from St. Joachimstahl. It is the immediate parent of actinium. It
•emits alpha and beta rays, and it has a period of 30,000 years. In certain
•of its chemical properties it is analogous to tantalum, of which it is the
higher homologue (atomic number, 91). But according to the experi-
ments of Grosse, its oxide, instead of having the properties of an acid,
behaves rather like a weak base. Grosse has perfected a method of frac-
tional crystallization of the chlorides of zirconium and of protoactinium,
the latter concentrating in the solution, and has obtained several centi-
grams of the radioelement in a pure state. Protoactinium occurs in the
ores of uranium in a proportion comparable to that of radium, and can
be extracted in sufficient quantity to determine its atomic weight.
Like tantalum, protoactinium can easily be dissolved as an oxide or
hydrate in hydrofluoric acid. The oxide (probable formula, Pa2O5) is a
white powder with a high fusion point; calcined, it is insoluble in hydro-
chloric, nitric, sulphuric acids. By fusion with NaSO4 and recovery by
water and sulphuric acid, it can be dissolved and separated from tan-
talum. After fusion with K3CO3 and recovery by water, protoactinium re-
mains in the insoluble residue, whereas the tantalum dissolves. In a hydro-
chloric, nitric, or sulphuric solution, the protoactinium can be precipi-
tated entirely by an excess of phosphoric acid.
Actinium, Actinium (A. Debierne) belongs, according to its chemical
properties, among the rare earth elements. Extracted from ore at the same
time as the elements of this group, it can be separated only by laborious
fractionations. Its presence is revealed by the radiation of its successive
derivatives. These are formed so slowly that the activity of actinium
freshly prepared increases for several months. The period of actinium
CURIE — RADIOACTIVITY 587
being about ten years, it forms with its derivatives a relatively stable
group (actinium family) with a complex alpha, beta, gamma radiation.
Like polonium and radium, actinium was first found in pitchblende.
This generally contains, in a small proportion, rare earths, principally of
the cerium group: cerium, lanthanum, neodymium, praseodymium, sa-
marium; there are also always small quantities of thorium. In this mixture
of substances with neighboring properties, thorium is the element most
weakly basic, and lanthanum the one most strongly basic. Actinium is
especially close to lanthanum and is even more strongly basic.
Actinium is precipitated with thorium and with the rare earth ele-
ments in the state of hydrates, fluorides, or oxalates (the precipitation
being relatively less complete than for lanthanum). It remains with the
other rare earths when thorium and cerium are separated from them by
the usual methods. The rare earths can be separated from one another by
the methodical fractionation of their double ammoniacal nitrates in a
nitric solution. The actinium comes out at the same time as the lanthanum,
in the least soluble fractions. To enrich the actinium-bearing lanthanum in
actinium, there has been used successfully the fractional precipitation of
the oxalate in a nitric solution; the actinium concentrates in the solution
(Marie Curie and collaborators). By applying* this method to the ac-
tinium-bearing lanthanum extracted from uranium ore from Haut Ka-
tanga, several grams of the oxide, containing i to 2 milligrams of ac-
tinium, have recently been obtained; this quantity corresponds in the ore
to about ten tons of uranium. ^ •<
The isomorphism of the salts of actinium and lanthanum being dem-
onstrated by the regularity of the fractional crystallizations, it can be sup-
posed that the chemical formulas of the actinium compounds are of the
same type as the corresponding formulas for lanthanum.
In the periodic table, there has been assigned to actinium a place,
hitherto vacant, in the column of the trivalent elements, in the last line of
the table (atomic number, 89).
Radio actinium. Actinium X. These substances are the first derivatives of
actinium and are obtained by beginning with it. Radioactinium (Hahn)
is an isotope of thorium (atomic number, 90), with a period of 18.9 days;
it emits an alpha radiation and also weak beta and gamma radiations. It
can be separated from actinium by the same methods used to separate
thorium from lanthanum. It gives rise to the formation of actinium X
(Giesel, Godlewski), which has a period of 11.2 days and a radiation like
that of radioactinium. Actinium X is an isotope of radium (atomic num-
ber, 88). From a solution containing actinium, radioactinium, and ac-
tinium X, the first two can be separated by precipitating them with am-
monia; the actinium X remains in solution. Actinium X gives birth to
actinon (a radioactive gas), which produces an active deposit from
actinium composed of a number of constituents.
588 MASTERWORKS OF SCIENCE
The Derivatives of Thorium
Mesothorium /. This substance, discovered by O. Hahn, accompanies the
radium extracted from ores which contain uranium and thorium (thori-
anite, monazite). The beta and gamma radiations which it appears to
give really come from a short-lived derivative of it, mesothorium 2. The
latter can be separated from the former by precipitation by ammonia, and
it immediately re-forms. Mesothorium i gives off no measurable radiation.
It has not been separated from radium, of which it is an isotope (atomic
number, 88); its period is 6.7 years. Its use in medicine is analogous to
that of radium, and it has been industrially extracted as a by-product of
the preparation of thorium in the incandescent-mantle industry.
Mesothorium 2 is an isotope of actinium (atomic number, 89), and
though its period is only 6.2 hours, it has nevertheless been possible to
study its chemical properties (Yovanovitch). Thence has been learned
much about the chemical properties o£ actinium, the study of which, as
has been observed, involves great delays. This is an example of the
method of radioactive indicators.
To separate mesothorium 2 from mesothorium i, the method is cur-
rently used of crystallization in a strongly acid hydrochloric solution in
the presence o£ barium. This operation leaves mesothorium 2 in solution
while the chloride of mesothorium i crystallizes with the barium-chloride.
Mesothorium is a source of radiothorium. After the solution has been
for some time undisturbed, that substance accumulates, and can be sepa-
rated by NH3 after the addition of several milligrams of another reagent.
In the crystallization hitherto described, radiothorium accumulates in the
solution with mesothorium i; but if the operation is repeated several
times at intervals of a day, finally mesothorium 2 quite free of radio-
thorium collects, the speed of formation of these two being different,
Radiothorium. Thorium X. Radiothorium was found by O. Hahn in tho-
rianite from Ceylon of which some hundreds of kilos had been submitted
to treatment for the extraction of radium. This ore is composed chiefly of
thorium oxide, but contains also some uranium oxide, and, consequently,
some radium. When the chloride of radium-bearing barium coming from
this mineral was submitted to fractional crystallization, it was remarked
that at the same time that the radium concentrated in the less soluble
portions, another radioactive substance concentrated in the more soluble
portions. This material had the radioactive properties of thorium, but in
a heightened degree; in particular, it gave off in great quantities the
radioactive gas which is obtained from thorium compounds and which is
called thoront or thorium emanation. The new radioelement responsible
for this release of gas has been called radiothorium. It is now known- that
it is present in the compounds of thorium as a derivative. Radiothorium
has also been discovered in the deposits of some hot springs in Savoy
CURIE — RADIOACTIVITY 589
(Blanc). Radiothorium is an isotope of thorium (atomic number, 90); its
period is 1.9 years. Its radiation is made up chiefly of alpha rays, but it
also feebly gives off beta rays. It produces a short-lived derivative, thorium
X (Rutherford, Soddy) (isotope of radium, period of 3.64 days, alpha and
weak beta radiation), which is used in medicine. It can be separated from
a solution of radiothorium by precipitating the latter with ammonia or
with oxygenated water; thorium X remains in solution. Thorium X is
the direct parent of thoron, from which come other derivatives forming
its active deposit.
THE RADIOACTIVE ORES AND THE EXTRACTION OF THE
RADIOELEMENTS
The Radioactive Ores
THESE ORES, of which a large number are known, are all ores of uranium
and thorium, containing these two elements in varying proportions, in
association with inactive elements. Sought for more actively since the dis-
covery of radium, they have been found in different parts of the globe.
The radioelements, derivatives of uranium or of thorium, occur in the
ores in quantities proportional to those of the primary substances, respec-
tively. Among the exploitable ores of uranium, some are almost free of
thorium and contain only the series of derivatives which begin with ura-
nium; the radium which is extracted from them is free of mesothorium.
On the contrary, the commercial ores of thorium contain an appreciable
quantity of uranium; with the descendants of thorium there are also pres-
ent those of uranium. The mesothorium obtained in industry is therefore
always accompanied by radium. For equivalent radiation, such a mixture
is less valuable than radium, for mesothorium decays in accord with its
period of 6.7 years, whereas radium is practically constant, its period
being 1600 years.
The radioactive ores occur sometimes in a concentrated form, but
more frequently in a dispersed form. In the first case, they form crystals
of considerable volume, or compact masses which are found as threads or
beads embedded in massive rock. In the second case, they are intimately
mixed through rock or soil which they impregnate wholly, or through
which they are disseminated in the form of extremely tiny crystals. Indus-
trially, not only the rich ores — containing 50 milligrams or more of ra-
dium per ton — but also the poorer ores — containing only a few milligrams
of radium per ton — have been successfully used. In the ores, the relation
between the quantity of radium and that of uranium has a constant value
of 3.4Xio~7. Consequently, no ore can possibly contain more than 340
milligrams of radium per ton of uranium.
To recognize that an ore is radioactive, two simple processes are
available: i. A piece of the ore is placed on a photographic plate which
is kept entirely in darkness for a day before it is developed. In the image
590 MASTERWORKS OF SCIENCE
obtained, the dark portions correspond to the active portions of the speci-
men, and the light portions to the inactive parts, 2. A piece of the ore
may be pulverized, the powder so obtained placed upon a plate, and the
ionization produced by the specimen measured in an electrical apparatus.
Both processes are used in prospecting, and for that purpose there is avail-
able a portable electroscope. The primary, compact ores of uranium, com-
posed of uranium oxide more or less pure, are black and dense; those in
which the uranium is accompanied by acids — tantalic, niobic, titanic
(samarskite, betafite, etc.) — are similarly black or dark brown. But there
are also uranium ores of more recent origin, the result of the alteration of
primary ores (autunite, chalcolite, curite, etc.) which are vividly colored.
The thorium ores are generally of a more or less dark brown (thorite,
orangite, thorianite, monazite, etc.).
Below is given a table showing a certain number of the ores, and
later are recited the principal points in the treatment of first the uranium
ores and then the uranium and thorium ores,
A. Ores of the oxides of uranium or of uranium and thorium:
Pitchblende (uraninite), possibly containing 30% to 80% of uranium in the
form of the oxides UOa and UOs, with little or almost no thorium, but with
a great number of other materials in small quantities: SiOs, Fe, Ca, Ba, Sb,
Cu, Pb, Bi, etc. Compact or cryptocrystalline structure (St. Joachimstahl,
England, United States, Belgian Congo, Canada).
Broggerite, cleveite, etc. Ores of crystallized uranium oxide, possibly con-
taining thorium oxide, ThOa, in varying proportions (Norway, United
States).
Thorianite, an ore of the crystalline oxide of uranium and thorium with a
great predominance of thorium (e.g., Th, 65%, U, 10%) (Ceylon).
B. Ores of hydrated deterioration:
Bccquer elite (UOs 2HaO), 72% U (Belgian Congo).
Curite (zPbO 5UOa 4HaO), lead uranate, 55% uranium (Belgian Congo).
Kasolite (s?bO sUOs 3SiOa 4HaO), 40% uranium, silicouranate of lead
(Belgian Congo).
C. Hydrated silicates:
Soddite (i2UOa 5SiOa i4HaO), 72% uranium (Belgian Congo).
Qrangite, 66% thorium, i% uranium (Norway).
Thorite, 45%-65% thorium, 9% uranium (Norway).
D. Phosphates:
Autunite (Ca 2UO* 2PO* 8HaO), phosphate of calcium and uranyl, about
50% uranium, in green crystalline spangles (Portugal, Tonkin).
Chalcolite, torbernite (Cu zUOa 2PO* 8HaO), phosphate of copper and
uranyl, about 50% uranium, in green crystals (Cornwall, England; Portugal).
Monazite, phosphate of rare earths, principally eerie (CePO*), containing
thorium (of the order of 10%) and a little uranium (of the order of i%)
(Brazil, United States, India).
E. Vanadates:
Carnotite, vanadate of UOa and hydrated K, about 50% uranium, in yellow
crystalline powder (United States).
Ferghanite, Tuyamunite, composed of UOa and VaOs, about 50% uranium
(Turkestan).
^ CURIE — RADIOACTIVITY 591
F. Niobates, tantalates, titanates:
Samars'kite, niobate and tantalate of rare earths (especially the yttrium
group), 3% to 15% uranium, 4% thorium (Russia, United States, India,
Madagascar) .
Euxenite, niobate and titanate of rare earths (yttrium), 3% to 15%
uranium, 6% thorium (Norway, United States, Madagascar).
Betafite, titanoniobate and tantalate of uranium, crystallized, 25% uranium,
i% thorium (Madagascar).
Uranium Ores Containing a little Thorium. Treatment of Pitchblende
The principal ores which the radium industry has used are pitch-
blende, autunite, carnotite, betafite. Some of these contain so little tho-
rium that the Th/U ratio is of the order of io~5 (pitchblendes from St.
Joachimstahl and from Haut Katanga). In betafite, the ratio is higher, i
to 4%. The St. Joachimstahl pitchblende is the ore in which were discov-
ered polonium and radium; exploited first for uranium, it was later ex-
ploited for radium. It occurs in association with dolomite and quartz in
veins located at great depths (500 meters and more) in the granite mass
of the region. Its composition is complex and variable; here is an ex-
ample:
UsOs 76.82
FsOs 4.0
PbO 4.63
BiaOa .67
ASaOs 82
ZnO 22
MnO 04
SiOa 5.07
CaO 245
MgO 19
KsO .28
NasO 1.19
Rare earths 52
HsO 3-25
S 1-15
Thorium traces
The pitchblende from the Belgian Congo (Haut Katanga) occurs in
nuggets within sedimentary rocks; it is accompanied by ores resulting
from the alteration of pitchblende under the action of various physical
and chemical agents: chalcolite, kasolite, etc. These ores are treated in the
Oolen plant in Belgium and actually provide the chief source of radium.
In Canada, pitchblende has been found in lengthy veins, in ancient sedi-
mentary rock near the Arctic Circle.
The principal phases in the extraction of radium are the following:
i. Reduction of the ore to which has been added previously a proper
amount of barium to serve as a radium capturer. 2. Separation of the
592 MASTERWORKS OF SCIENCE ^
crude sulphates containing the radium-bearing barium. 3. Purification of
the crude sulphates and transformation of the radium-bearing barium into
a chloride. 4. Fractional crystallization of the chloride to obtain a salt
enriched in radium. 5. Purification of the enriched chloride and final frac-
tional crystallization of the chlorides or bromides.
These operations are represented in the accompanying table with an
indication of the products of the treatment in which certain radioele-
ments are concentrated. It must be observed that this treatment is adapted
to its principal objective — the extraction of radium and of uranium. The
other radioelements, of which less accurate account is given, are dispersed
in the course of the operations. (See Table I.)
TABLE I
Pitchblende +
I I
residue (Ra, RaD, Pa) solution U, Fe(Pa, lo, Ac, Po)
-f- hot solution NaCl 4. Na-jCOa
.[ ~I I 1
residue solution precipitated solution
hot solution Na2CO3 treated with Fc U
NasCOa
residue precipitated Pb
solution HC1 -f RaD
I 1
residue solution Ba -f- impure Ra
silica, Pa coarse fractional crystallization
I I
less soluble fraction more soluble fraction,
treatment with HaS lo. Ac
precipitated Pb solution
-j- RaD, Po peroxidized -f NHa
hydrates solution
Ac. lo precipitated by
(NH<)* C0a
precipitated.
dissolved HBr
fine fractional crystallization
less soluble fraction Ra
Pitchblende is generally reduced by the use of weak sulphuric acid;
but that operation must sometimes be preceded by a preliminary treat-
ment such as the roasting of the ore finely ground and mixed with car-
bonate of soda.
CURIE — RADIOACTIVITY . 593
The fractional crystallization of the chlorides (the method originated
by Marie Curie) is a fundamental step in the treatment. It is accomplished
at first in an aqueous solution. As the extraction of the radium salt ad-
vances, it is desirable to crystallize it in a solution of increasing acidity,
partly to decrease its solubility, partly to aid in the elimination of various
impurities (iron, calcium, rare earth elements). Generally, the fractional
crystallization is not continued until a pure radium salt is obtained, but is
stopped when a concentration fixed by the use to which the product is to
be put (50% to 90%) has been reached. To enrich the concentrated prod-
ucts, fractional crystallization of bromides replaces that of chlorides
(Giesel).
The method of treating pitchblende in order to obtain polonium,
used in some attempts in that direction, is given in an accompanying
table. The separation of polonium with lead, bismuth, and other easily
reducible metals is accomplished by making use of the chemical and
electrochemical properties of polonium described earlier. (See Table II.)
TABLE II
Pitchblende + hot solution of HCl
I I
residue solution + HaS
to be treated for I
extraction of radium precipitate
dissolved in HNOs + HCl +
Solution precipitated by NHa
I I
hydrates Pb, Bi, Po solution Cu
treated to concentrate Po
From Table I, it is clear that radiolead (lead + RaD) is a by-product
in the preparation of radium; its separation from the ore is generally
sufficiently complete, and the concentration in Radium D is greater as the
ore contains less inactive lead. This radiolead may be conserved for the
preparation of polonium. The method of concentration involves the fol-
lowing steps: i. The precipitation of lead in a nitric solution by concen-
trated hydrochloric acid, leaving the polonium in solution; 2. The deposit
of polonium by electrochemical means upon copper or silver leaves
plunged into the solution of radiolead; 3. The capture of polonium with a
precipitate of colloidal ferric hydrate.
Among the other by-products in the preparation of radium, proto-
actinium occurs either with the final residue of the reduction — composed
principally of silica — or in the sulphuric solution of uranium. Ionium and
actinium also occur — in part in that same solution, in part in the insoluble
sulphates. The accompanying table records the method used to extract
that material, on one hand the mixture thorium-ionium, on the other,
actinium associated with lanthanum. In this treatment, hydrofluoric acid
may be substituted for the oxalic acid. (See Table III.)
594 MASTERWORKS OF SCIENCE
TABLE III
More soluble fraction o£ solution
resulting from the coarse fractional crystallization
of radium (Ba, lo, Ac)
treated by H*S
| — 1
sulphides pcroxidizcd solution
y
hydrates dissolved in solution Ba
HCl + oxalic acid
oxalates solution Fe
4- hot solution NaOH
I
hydrates dissolved in HCl, treatment
with NaaCOs
I — 1
solution Th. To precipitates Ac -f La, Nd, Pr, Cc, etc.
separation or Ce
then fractional precipitation of
the oxalates in a nitric solution
Only a few indications of the treatment used for other ores which
have been exploited industrially are given here. The principal phases of
the treatment are the same as for pitchblende, but the processes employed
for the reduction of the ore and the obtaining of the crude sulphates may
vary from one ore to another.
Carnotite — a vanadate of uranium found principally in the United
States — and autunite — a phosphate of uranium and lime which has been
mined principally in Portugal — can both, in certain cases, be treated with
weak, hot hydrochloric acid; from that solution, the crude sulphates are
precipitated. In other cases there is an advantage in treating the ore with
carbonate of soda prior to dissolving it in acid.
Betafite — an ore from Madagascar which contains uranium with nio-
bic, titanic, and tantalic acids — is reduced by fusion with soda and car-
bonate of soda in order to cause the rare acids to pass into solution. The
reduction can also be accomplished with bisulphate of soda and recla-
mation with water; the sulphate of radium-bearing barium then remains in
the residue with the rare acids. These latter can be separated by treatment
with soda or with weak hydrofluoric acid.
Ores of Thorium and Uranium
Some ores of thorium are poor in uranium, and consequently have a
scientific interest from the fact that they contain almost solely the deriva-
tives of thorium; this is the situation with certain thorites. But in the
CURIE — RADIOACTIVITY 595
ores which have been exploited (thorianite, monazite) the proportion of
uranium to thorium is sufficiently large for the derivatives of these two
elements to be represented by comparable radiations.
Thorianite is an ore rich in thorium, found in the island of Ceylon in
the form of small crystal cubes. By the treatment of several hundred kilo-
grams of that ore, mesothorium and radio thorium were discovered. The
proportion of thorium in this ore runs as high as 60 to 80%; that of
uranium, 10 to 20%. Monazite, though it is less rich in thorium, is never-
theless regularly exploited for the incandescent-mantle industry, because
it is found in great quantities in the so-called monazite sands of the
United States and of Brazil.
Monazite is a rare-earth phosphate, crystallized, containing generally
6 to 12% of thorium. It is reduced with hot sulphuric acid, and all the
soluble sulphates are extracted; in the insoluble sulphates, along with
barium, radium and mesothorium i occur. The latter treatment of these
crude sulphates does not differ in principle from that already described.
The fractional crystallization is undertaken to separate in the less soluble
portions the radium and the mesothorium i and, in the more soluble
portions, the radiothorium — a disintegration product of mesothorium.
The fractional crystallization can be continued until there is obtained a
chloride or a bromide of radium quite free of barium and containing a
negligible amount of mesothorium. After that, continued fractional crystal-
lization does not alter the product thus obtained. The effect of the meso-
thorium is, however, so important that in certain products a month old it
is estimated that about 75% of the most penetrating gamma rays are due
to the mesothorium (through its derivative MThll) and about 25% of the
most penetrating gamma rays to the radium (through its derivative RaC).
The gamma radiation increases constantly for about three years because
of the formation of radiothorium and its later derivatives. Having passed
a maximum, it lessens because of the destruction of the meso thorium^ i;
after about fifty years, the radiation is due almost solely to radium, with
a diminution of about 2% of the original quantity of radiation.
RELATIVITY: THE SPECIAL
AND GENERAL THEORY
by
ALBERT EINSTEIN
CONTENTS
Relativity: The Special and General Theory
Part One: The Special Theory of Relativity
I. Physical Meaning of Geometrical Propositions
II. The System of Co-ordinates
III. Space and Time in Classical Mechanics
IV. The Galileian System of Co-ordinates
V. The Principle of Relativity (in the Restricted Sense)
VI. The Theorem of the Addition of Velocities Employed in Classical
Mechanics
VII, The Apparent Incompatibility of the Law of Propagation of Light
with the Principle of Relativity
VIII. On the Idea of Time in Physics
IX. The Relativity of Simultaneity
X* On the Relativity of the Conception of Distance
XL The Lorentz Transformation
XII. The Behaviour of Measuring Rods and Clocks in Motion
XIII. Theorem of the Addition of Velocities. The Experiment of Fizeau
XIV. The Heuristic Value of the Theory of Relativity
XV. General Results of the Theory
XVI. Expedience and the Special Theory of Relativity
XVII. Minkowski's Four-dimensional Space
Part Two: The General Theory of Relativity
XVIIL Special and General Principle of Relativity
XIX. The Gravitational Field
XX. The Equality of Inertial and Gravitational Mass as an Argument for
the General Postulate of Relativity
XXI. In What Respects Are the Foundations of Classical Mechanics and of
the Special Theory of Relativity Unsatisfactory?
XXII. A Few Inferences from the General Theory of Relativity
XXIII. Behaviour of Clocks and Measuring Rods on a Rotating Body of
Reference
XXIV. Euclidean and Non-Euclidean Continuum
XXV. Gaussian Co-ordinates
XXVI. The Space-time Continuum of the- Special Theory of Relativity Con-
sidered as a Euclidean Continuum
XXVII. The Space-time Continuum of the General Theory of Relativity Is Not
a Euclidean Continuum
XXVIIL Exact Formulation of the General Principle of Relativity
XXIX. The Solution of the Problem of Gravitation on the Basis of the Gen-
eral Principle of Relativity
Part Three: Considerations on the Universe as a Whole
XXX. Cosmological Difficulties of Newton's Theory
XXXI. The Possibility of a "Finite" and yet "Unbounded" Universe
XXXIL The Structure o£ Space according to the General Theory of Relativity
ALBERT EINSTEIN
1879-
EINSTEIN'S is undoubtedly the best known of contemporary
scientists* names. His love of music and his skill as a violinist
forgotten, his devotion to philanthropic causes and his serv-
ices to international order neglected, he has come to be re-
garded as the type of the scientist who lives in an intellectual
atmosphere so rarefied that the layman dare not enter it. He
is widely believed to have made science so abstruse and compli-
cated that it retreats ever farther from the ambitious grasp.
Yet he himself considers his object to be the increase of scienr
tific clarity and simplicity.
Einstein was born in 1879 in Ulm, Wiirttemberg, where
his father owned a small electric-technical plant. In Munich
he attended the Luitpold Gymnasium until 1894; then his
family moved to Milan, and he entered the Cantonal School at
Aarau, Switzerland., Two years later he began to attend lec-
tures at the Technical Academy in Zurich, and shortly after-
ward, while still a student, he taught mathematics and physics
in the same school. In 1901 he became a Swiss citizen, *thus
qualifying for a post as examiner of patents in Berne. He held
this position for eight years. Meantime he married a fellow
student, a Serbian girl; he served as an unsalaried lecturer in
the University of Berne; and he began publishing his first
important papers.
An early believer in Planck's quantum theory (1900), in
these early papers Einstein treated problems which invited
application of quantum mechanics. In one series (1905-09),
on the assumption that propagated radiation has a "quantum-
like" structure, he developed the light-quantum hypothesis,
and a law of photoelectric effects. He made the first real ex-
tension of Planck's fundamental hypothesis in a paper (1907)
on the variation of specific heat with temperature. Using the
generalized Bohr atom rather tjian Planck's linear oscillator as
600 MASTERWQRKS OF SCIENCE
his basic concept, he developed his Law of Radiation. Much
earlier he had exhaustively studied the Brownian Movements
— those erratic motions of microscopic particles of insoluble
matter in still water. Though these movements observably
demonstrated the kinetic theory of matter, they had puzzled
physicists for eighty years. Now Einstein published a com-
plete theory and working formulas to explain them.
Discussing the Brownian Movements when he was twenty-
six, Einstein wrote that "rest and equilibrium can only be an
outward semblance which marks a state of disorder and unrest
and prepares us for a profound alteration in the aspect of the
universe as soon as we alter the scale of our observations. . . .
Nature is such that it is impossible to determine absolute
motion by any experiment whatever." He was challenging the
three-century-long reign of Newton's concept of the universe,
signalizing the revolution in scientific thought which has
transferred the study of the inner workings of nature from the
engineering scientist to the mathematician.
The readers of these early papers recognized in them the
scope of imagination and the boldness of deduction of a new
master. In 1909 the University of Zurich, where shortly before
he had earned his doctoral degree, made him professor ex-
traordinary of theoretical physics; two years later he was
named professor of physics at the University of Prague; the
next year he returned to Zurich as professor of physics in the
Technical Academy; and in 1913, after becoming once more
a German citizen, he was named director of the Kaiser-
Wilhelm Physical Institute in Berlin. He had now a stipend
large enough to allow him to devote all his time, free of
routine duties, to research; and he published constantly in the
learned journals of Germany, Russia, Switzerland. The Acade-
mies of Copenhagen and of Amsterdam and the Royal Society
elected him to membership. In 1921, for his work on the photo-
chemical equivalent, the Nobel Prize was conferred upon him.
Six years prior to the award of the Nobel Prize, Einstein
had published his generalized theory of relativity, and ten
years before that, his restricted theory, with an account of its
consequences. The restricted theory had been generally ac-
cepted in Germany as early as 1912; but elsewhere it was
viewed skeptically. The complete theory made its way slowly,
only gradually winning British scientists. By their vote Ein-
stein was awarded the Copley Medal of the Royal Society in
1925, and the Davy Medal in the following year. Both awards
were for the relativity theory.
Einstein's growing fame brought him urgent invitations
to visit other countries. He had lectured in France in the early
19208, eager to further friendliness between French and Ger-
EINSTEIN — RELATIVITY 601
man scientists. Now he traveled to India, to China, Japan,
Palestine — where he seconded Zionist ambition — to Latin
America, England, the United States. Everywhere his vast
learning, his modesty, his humanity, his intellectual honesty im-
pressed his hearers. Universities everywhere conferred honor-
ary degrees upon him, and learned societies everywhere
pressed him for contributions to their journals. While he was
on the Pacific Coast in 1932, Hitler came to power in Germany.
When a "German physics" was promulgated, Einstein re-
signed his directorship of the Institute in Berlin. Almost im-
mediately he became professor of mathematics in the Institute
for Advanced Study of Princeton University. In Princeton —
an American citizen since 1940 — he now resides.
Einstein's theory of relativity grew out of his supposition
that the identity in our world of inertial mass as measured by
Galileo and of gravitational mass as measured by Newton is
not accidental. If it is not, the Newtonian physics does not ex-
plain as wide a range of physical phenomena as is desirable.
Classical, or Galilean-Newtonian, physics had explained many
natural phenomena in terms of simple forces acting along
straight lines, had triumphantly developed astronomy, and,
by assuming a mechanical "ether," had applied its principles
to problems apparently not mechanical. But the Michelson-
Morley experiment on the velocity of light propagation pro-
vided sound reasons for denying the existence of an "ether";
the planet Mercury did not behave quite according to the
predictions of Newtonian astronomy; electro-magnetic phe-
nomena could not be wholly explained in terms of simple
forces. Einstein weighed these difficulties, restudied the funda-
mental assumptions of physical science, and produced the
special theory of relativity.
The special theory makes it possible, by use of the Lorentz
transformation, to translate the phenomena of any given iner-
tial system into terms of any other similar system. But Einstein
was able to imagine a system not inertial — in fact, to question
whether an inertial system could really exist. In 1913, during
a walking tour in the Engadine with a party which included
Mme. Curie — one of the few mathematicians in Europe suf-
ficiently skilled to discuss his ideas with him — he remarked
to her, "What I need to know is what happens to the pas-
sengers in an elevator when it falls into emptiness." This
problem is not susceptible to experimental solution. But Ein-
stein is a mathematician, not an experimentalist. He did solve
the problem, and the answer is the general theory of relativity.
This theory requires that energy and mass being inter-
changeable and similar in properties, energy — in the form of
light, for example — must have weight. It will, therefore, be
602 MASTERWORKS OF SCIENCE
deflected in a strong gravitational field. During the eclipse of
the sun in 1919, observation startlingly confirmed ^the theory.
Light from the fixed stars was deflected in the neighborhood
of the sun, and exactly in the direction and to the amount
which Einstein had computed. The theory also satisfactorily
explained the aberration in the path of Mercury; using the
Maxwell equations, it accounted for the phenomena of electro-
magnetism. Further, it foretold atomic fission and the trans-
mutation of one element into another, ideas which later skilled
experimentation confirmed.
These triumphant demonstrations have led to general ac-
ceptance of the theory of relativity, and thus to modern
physics. But modern physics differs radically from Newtonian
physics. Indeed, it provides a wholly new concept of the physi-
cal universe — one in which a mechanical ether does not exist,
in which mass and energy are interchangeable, in which abso-
lute rest is impossible, and in which absolute time is unrecog-
nized. Properly the twentieth century may claim to add to the
list of builders of world concepts— Pythagoras, Copernicus,
Newton — one more: Einstein.
What follow! is a condensation of Einstein's Relativity:
The Special and General Theory, written while he was profes-
sor of physics in the University of Berlin.
RELATIVITY
PART ONE: THE SPECIAL THEORY
OF RELATIVITY
I. PHYSICAL MEANING OF GEOMETRICAL PROPOSITIONS
GEOMETRY sets out from certain conceptions such as "plane," "point," and
"straight line," with which we are able to associate more or less definite
ideas, and from certain simple propositions (axioms) which, in virtue of
these ideas, we are inclined to accept as "true." Then, on the basis of a
logical process, the justification of which we feel ourselves compelled to
admit, all remaining propositions are shown to follow from those axioms,
/.<?. they are proven.
If, in pursuance of our habit of thought, we now supplement the
propositions of Euclidean geometry by the single proposition that two
points on a practically rigid body always correspond to the same distance
(line-interval), independently of any changes in position to which we may
subject the body, the propositions of Euclidean geometry then resolve
themselves into propositions on the possible relative position of practically
rigid bodies. Geometry which has been supplemented in this way is then
to be treated as a branch of physics. We can now legitimately ask as to the
"truth" of geometrical propositions interpreted in this way.
//. THE SYSTEM OF CO-ORDINATES
EVERY DESCRIPTION of the scene of an event or of the position of an object
in space is based on the specification of the point on a rigid body (body
of reference) with which that event or object coincides. This applies not
only to scientific description, but also to everyday life. If I analyse the
place specification "Trafalgar Square, London," I arrive at the following
result. The earth is the rigid body to which the specification of place
refers; "Trafalgar Square, London" is a well-defined point, to which a
name has been assigned, and with which the event coincides in space. If
a cloud is hovering over Trafalgar Square, then we can determine its
position relative to the surface of the earth by erecting a pole perpendicu-
larly on the Square, so that it reaches the cloud. The length of the pole
measured with the standard measuring rod, combined with the specifi-
604 MASTERWORKS OF SCIENCE
cation of the position of the foot of the pole, supplies us with a complete
place specification.
(a) We imagine the rigid body, to which the place specification is
referred, supplemented in such a manner that the object whose position
we require is reached by the completed rigid body.
(£) In locating the position of the object, we make use of a number
(here the length of the pole measured with the measuring rod) instead
of designated points of reference.
(c) We speak of the height of the cloud even when the pole which
reaches the cloud has not been erected. By means of optical observations
of the cloud from different positions on the ground, and taking into
account the properties of the propagation of light, we determine the
length of the pole we should have required in order to reach the cloud.
From this consideration we see that it will be advantageous if, in
the description of position, it should be possible by means of numerical
measures to make ourselves independent of the existence of marked
positions (possessing names) on the rigid body of reference. In the physics
of measurement this is attained by the application of the Cartesian system
of co-ordinates.
This consists of three plane surfaces perpendicular to each other and
rigidly attached to a rigid body. Referred to a system of co-ordinates, the
scene of any event will be determined (for the main part) by the specifi-
cation of the lengths of the three perpendiculars or co-ordinates (x, y, z)
which can be dropped from the scene of the event to those three plane
surfaces.
We thus obtain the following result: Every description of events in
space involves the use of a rigid body to which such events have to be
referred. The resulting relationship takes for granted that the laws of
Euclidean geometry hold for "distances," the "distance" being represented
physically by means of the convention of two marks on a rigid body.
///. SPACE AND TIME IN CLASSICAL MECHANICS
"THE PURPOSE of mechanics is to describe how bodies change their position
in space with time."
It is not clear what is to be understood here by "position" and
"space." I stand at the window of a railway carriage which is travelling
uniformly, and drop a stone on the embankment, without throwing it.
Then, disregarding the influence of the air resistance, I see the stone
descend in a straight line. A pedestrian who observes the misdeed from
athe footpath notices that the stone falls to earth in a parabolic curve. I
now ask: Do the "positions" traversed by the stone lie "in reality" on a
straight line or on a parabola? Moreover, what is meant here by motion
"in space"? From the considerations of the previous chapter the answer
is self-evident. In the first place, we entirely shun the vague word "space,"
of which, we must honestly acknowledge, we cannot form the slightest
EINSTEIN — RELATIVITY 605
conception, and we replace it by "motion relative to a practically rigid-
body of reference." If instead of "body of reference" we insert "system of
co-ordinates/' which is a useful idea for mathematical description, we are
in a position to say: The stone traverses a straight line relative to a system
of co-ordinates rigidly attached to the carriage, but relative to a system
of co-ordinates rigidly attached to the ground (embankment) it describes
a parabola. With the aid of this example it is clearly seen that there is no
such thing as an independently existing trajectory (lit. "path-curve"), but
only a trajectory relative to a particular body of reference.
In order to have a complete description of the motion, we must
specify how the body alters its position with time; i.e. for every point on
the trajectory it must be stated at what time the body is situated there.
These data must be supplemented by such a definition of time that, in
virtue of this definition, these time-values can be regarded essentially as
magnitudes (results of measurements) capable of observation. If we take
our stand on the ground of classical mechanics, we can satisfy this require-
ment for our illustration in the following manner. We imagine two clocks
of identical construction; the man at the railway-carriage window is hold-
ing one of them, and the man on the footpath the other. Each of the
observers determines the position on his own reference-body occupied by
the stone at each tick of the clock he is holding in his hand. In this con-
nection we have, not taken account of the inaccuracy involved by the
finiteness of the velocity of propagation of light.
IV. THE GAL1LE1AN SYSTEM OF CO-ORDINATES
As is WELL KNOWN, the fundamental law of the mechanics of Galilei-
Newton, which is known as the law of inertia, can be stated thus: A body
removed sufficiently far from other bodies continues in a state of rest or
of uniform motion in a straight line. This law not only says something
about the motion of the bodies, but it also indicates the reference-bodies
or systems of co-ordinates, permissible in mechanics, which can be used
in mechanical description. The visible fixed stars are bodies for which the
law of inertia certainly holds to a high degree of approximation. Now if
we use a system of co-ordinates which is rigidly attached to the earth,
then, relative to this sytem, every fixed star describes a circle of immense
radius in the course of an astronomical day, a result which is opposed to
the statement of the law of inertia. So that if we adhere to this law we
must refer these motions only to systems of co-ordinates relative to which
the fixed stars do not move in a circle. A system of co-ordinates of which
the state of motion is such that the law of inertia holds relative to it is
called a "Galileian system of co-ordinates." The laws of the mechanics of
Galilei-Newton can be regarded as valid only for a Galileian system of
co-ordinates.
606 MASTERWORKS OF SCIENCE
V. THE PRINCIPLE OF RELATIVITY (IN THE
RESTRICTED SENSE)
IN ORDER TO ATTAIN the greatest possible clearness, let us return to our
example of the railway carriage supposed to be travelling uniformly. We
call its motion a uniform translation ("uniform" because it is of constant
velocity and direction, "translation" because although the carriage changes
its position relative to the embankment yet it does not rotate in so doing).
Let us imagine a raven flying through the air in such a manner that its
motion, as observed from the embankment, is uniform and in a straight
line. If we were to observe the flying raven from the moving railway
carriage, we should find that the motion of the raven would be one of
different velocity and direction, but that it would still be uniform and in
a straight line. Expressed in an abstract manner, we may say: If a mass m
is moving uniformly in a straight line with respect to a co-ordinate system
K, then it will also be moving uniformly and in a straight line relative
to a second co-ordinate system Kr, provided that the latter is executing a
uniform translatory motion with respect to K. In accordance with the
discussion contained in the preceding section, it follows that: If, relative
to K, K is a uniformly moving co-ordinate system devoid of rotation, then
natural phenomena run their course with respect to K? according to
exactly the same general laws as with respect to K. This statement is called
the principle of relativity (in the restricted sense).
As long as one was convinced that all natural phenomena were capa-
ble of representation with the help of classical mechanics, there was no
need to doubt the validity of this principle of relativity. But in view of
the more recent development of electrodynamics and optics it became
more and more evident that classical mechanics affords an insufficient
foundation for the physical description of all natural phenomena. At this
juncture the question of the validity of the principle of relativity became
ripe for discussion.
There are two general facts which at the outset speak very much in
favour of the validity of the principle of relativity. It supplies us with the
actual motions of the heavenly bodies with a delicacy of detail little short
of wonderful. The principle of relativity must therefore apply with great
accuracy in the domain of mechanics. But that a principle of such broad
generality should hold with such exactness in one domain of phenomena,
and yet should be invalid for another, is a priori not very probable.
We now proceed to the second argument. If the principle of relativity
(in the restricted sense) does not hold, we should be constrained to believe
that natural laws are capable of being formulated in a particularly, simple
manner, and of course only on condition that, from amongst all possible
Galileian co-ordinate systems, we should have chosen one (Ka) of a par-
ticular state of motion as our body of reference. We should then be
justified in calling this system "absolutely at rest/' and all other Galileian
EINSTEIN — RELATIVITY 607
systems K "in motion." If, for instance, our embankment were the system
K0f then our railway carriage would be a system Kt relative to which less
simple laws would hold than with respect to K0. This diminished sim-
plicity would be due to the fact that the carriage K would be in motion
(i.e. "really") with respect to K0. In the general laws of nature which have
been formulated with reference to K, the magnitude and direction of the
velocity of the carriage would necessarily play a part. Now in virtue of its
motion in an orbit round the sun, our earth is comparable with a railway
carriage travelling with a velocity of about 30 kilometres per second. If
the principle of relativity were not valid we should therefore expect that the
direction of motion of the earth at any moment would enter into the laws of
nature, and also that physical systems in their behaviour would be de-
pendent on the orientation in space with respect to the earth. For owing
to the alteration in direction of the velocity of revolution of the earth in
the course of a year, the earth cannot be at rest relative to the hypothetical
system K0 throughout the whole year. However, the most careful obser-
vations have never revealed such anisotropic properties in terrestrial physi-
cal space, Le. a physical non-equivalence of different directions. This is a
very powerful argument in favour of the principle of relativity.
VI. THE THEOREM OF THE ADDITION OF VELOCITIES
EMPLOYED IN CLASSICAL MECHANICS
LET us SUPPOSE our old friend the railway carriage to be travelling along
the rails with a constant velocity v, and that a man traverses the length
of the carriage in the direction of travel with a velocity w. With what
velocity W does the man advance relative to the embankment during the
process? If the man were to stand still for a second, he would advance
relative to the embankment through a distance v equal numerically to the
velocity of the carriage. As a consequence of his walking, however, he
traverses an additional distance u> relative to the carriage, and hence also
relative to the embankment, in this second, the distance w being numeri-
cally equal to the velocity with which he is walking. Thus in total he-
covers the distance W — v-\-w relative to the embankment in the second
considered.
VII. THE APPARENT INCOMPATIBILITY OF THE LAW OF
PROPAGATION OF LIGHT WITH THE PRINCIPLE
OF RELATIVITY
THERE is HARDLY a simpler law in physics than that according to which:
light is propagated in empty space. Every child at school knows, or
believes he knows, that this propagation takes place in straight lines with
a velocity c = 300,000 km./sec.
Of course we must refer the process of the propagation of light (and
indeed every other process) to a rigid reference-body (co-ordinate system)*
608 MASTERWORKS OF SCIENCE
As such a system let us again choose our embankment. We shall imagine
the air above it to have been removed. If a ray of light be sent along the
embankment, we see from the above that the tip of the ray will be trans-
mitted with the velocity c relative to the embankment. Now let us sup-
pose that our railway carriage is again travelling along the railway lines
with the velocity vf and that its direction is the same as that of the ray
of light, but its velocity of course much less. It is obvious that we can here
apply the consideration of the previous section, since the ray of light plays
the part of the man walking along relatively to the carriage, w is the re-
quired velocity of light with respect to the carriage, and we have
u> = c — v.
The velocity of propagation of a ray of light relative to the carriage thus
comes out smaller than c.
But this result comes into conflict with the principle of relativity set
forth in Chapter V. For, like every other general law of nature, the law
of the transmission of light in vacuo must, according to the principle of
relativity, be the same for the railway carriage as reference-body as when
the rails are the body of reference. But if every ray of light is propagated
relative to the embankment with the velocity c, then for this reason it
would appear that another law of propagation of light must necessarily
hold with respect to the carriage — a result contradictory to the principle
of relativity.
In view of this dilemma there appears to be nothing else for it than
to abandon either the principle of relativity or the simple law of the
propagation of light in vacuo. The epoch-making theoretical investiga-
tions of H. A. Lorentz on the electrodynamical and optical phenomena
•connected with moving bodies lead conclusively to a theory of electro-
magnetic phenomena, of which the law of the constancy of the velocity of
light in vacuo is a necessary consequence. Prominent theoretical physicists
were therefore more inclined to reject the principle of relativity.
At this juncture the theory of relativity entered the arena. As a result
of an analysis of the physical conceptions of time and space, it became
•evident that in reality there is not the least incompatibility between the
principle of relativity and the law of propagation of light, and that
by systematically holding fast to both these laws a logically rigid theory
could be arrived at. This theory has. been called the special theory of rela-
tivity.
VIII. ON THE IDEA OF TIME IN PHYSICS
LIGHTNING has struck the rails on our railway embankment at two places
A and B far distant from each other. I make the additional assertion that
these two lightning flashes occurred simultaneously. If I now approach
you with the request to explain to me the sense of the statement more
precisely, you find after some consideration that the answer to this ques-
tion is not so easy as it appears at first sight.
EINSTEIN — RELATIVITY 609
After thinking the matter over for some time you offer the following
suggestion with which to test simultaneity. By measuring along the rails,
the connecting line AB should be measured and an observer placed at
the mid-point M of the distance AB. This observer should be supplied
with an arrangement (e.g. two mirrors inclined at 90°) which allows him
visually to observe both places A and B at the same time. If the observer
perceives the two flashes of lightning at the same time, then they are
simultaneous.
I am very pleased with this suggestion. You declare: "There is only
one demand to be made of the definition of simultaneity, namely, that in
every real case it must supply us with an empirical decision as to whether
or not the conception that has to be defined is fulfilled. That light re-
quires the same time to traverse the path A >M as for the path
B >M is in reality neither a supposition nor a hypothesis about the
physical nature of light, but a stipulation!'
It is clear that this definition can be used to give an exact meaning
not only to two events, but to as many events as we care to choose, and
independently of the positions of the scenes of the events with respect
to the body of reference (here the railway embankment). We are thus
led also to a definition of "time" in physics. For this purpose we suppose
that clocks of identical construction are placed at the points A, B and C
of the railway line (co-ordinate system), and that they are set in such a
manner that the positions of their pointers are simultaneously (in the
above sense) the same. Under these conditions we understand by the
"time" of an event the reading (position of the hands) of that one of these
clocks which is in the immediate vicinity (in space) of the event. In this
manner a time-value is associated with every event which is essentially
capable of observation.
IX. THE RELATIVITY OF SIMULTANEITY
WE SUPPOSE a very long train travelling along the rails with the constant
velocity v and in the direction indicated in Fig. i. People travelling in
this train will with advantage use the train as a rigid reference-body (co-
u ^f ^ E, / 3rai-7*'
A M J3
FIG. i.
ordinate system); they regard all events in reference to the train. Then
every event which takes place along the line also takes place at a particu-
lar point of the train. *
Are two events (e.g. the two strokes of lightning A and B) which
are simultaneous with reference to the railway embankment also simul-
taneous relatively to the train?
610 MASTERWORKS OF SCIENCE
When we say that the lightning strokes A and B are simultaneous
with respect to the embankment, we mean: the rays of light emitted at the
places A and B, where the lightning occurs, meet each other at the mid-
point M of the length A >B of the embankment. But the events A
and B also correspond to positions A and B on the train. Let M' be the
mid-point of the distance A >J? on the travelling train. Just when the
flashes of lightning occur, this point Mf naturally coincides with the point
M, but it moves towards the right in the diagram with the velocity v
of the train. If an observer sitting in the position Mf in the train did not
possess this velocity, then he would remain permanently at M, and the
light rays emitted by the flashes of lightning A and B would reach him
simultaneously, i.e. they would meet just where he is situated. Now in
reality (considered with reference to the railway embankment) he is
hastening towards the beam of light coming from Bf whilst he is riding
on ahead of the beam of light coming from A. Hence the observer will
see the beam of light emitted from B earlier than he will see that emitted
from A. Observers who take the railway train as their reference-body
must therefore come to the conclusion that the lightning flash B took
place earlier than the lightning flash A. We thus arrive at the important
result:
Events which are simultaneous with reference to the embankment
are not simultaneous with respect to the train, and vice versa (relativity
of simultaneity). Every reference-body (co-ordinate system) has its own
particular time; unless we are told the reference-body to which the state-
ment of time refers, there is no meaning in a statement of the time of an
event.
We concluded that the man in the carriage, who traverses the dis-
tance tv per second relative to the carriage, traverses the same distance
also with respect to the embankment in each second of time. But, accord-
ing to the foregoing considerations, the time required by a particular
occurrence with respect to the carriage must not be considered equal to
the duration of the same occurrence as judged from the embankment (as
reference-body). Hence it cannot be contended that the man in walking
travels the distance tv relative to the railway line in a time which is equal
to one second as judged from the embankment.
X. ON THE RELATIVITY OF THE CONCEPTION OF DISTANCE
LET us CONSIDER two particular points on the train travelling along the
embankment with the velocity v, and inquire as to their distance apart.
It is the simplest plan to use the train itself as the reference-body (co-
ordinate system). An observer in the train measures the interval by mark-
ing off his measuring rod in a straight line (e.g. along the floor of the car-
riage) as many times as is necessary to take him* from the one marked
point to the other.
It is a different matter when the distance has to be judged from the
EINSTEIN — RELATIVITY 6H
railway line. If we call Af and Br the two points on the train whose dis-
tance apart is required, then both of these points are moving with the
velocity v along the embankment. In the first place we require to deter-
mine the points A and B of the embankment which are just being passed
by the two points A' and #' at a particular time t — judged from the em-
bankment. These points A and B of the embankment can be determined
by applying the definition of time given in Chapter VIIL The distance
between these points A and B is then measured by repeated application of
the measuring rod along the embankment.
A priori it is by no means certain that this last measurement will
supply us with the same result as the first. Thus the length of the train
as measured from the embankment may be different from that obtained
by measuring in the train itself. This circumstance leads us to a second
objection which must be raised against the apparently obvious considera-
tion of Chapter VI. Namely, if the man in the carriage covers the distance
w in a unit of time — measured from the train — then this distance — as
measured from the embankment — is not necessarily also equal to w.
XL THE LORENTZ TRANSFORMATION
THE RESULTS of the last three chapters show that the apparent incompati-
bility of the law of propagation of light with the principle of relativity
(Chapter VII) has been derived by means of a consideration which bor-
rowed two unjustifiable hypotheses from classical mechanics; these are
as follows:
(1) The time-interval (tirne) between two events is independent of
the condition of motion of the body of reference.
(2) The space-interval (distance) between two points of a rigid body
is independent of the condition of motion of the body of refer-
ence.
If we drop these hypotheses, then the dilemma of Chapter VII dis-
appears, because the theorem of the addition of velocities derived in
Chapter VI becomes invalid. The possibility presents itself that the law
of the propagation of light in vacua may be compatible with the principle
of relativity. In the discussion of Chapter VI we have to do with places
and times relative both to the train and to the embankment. Can we
conceive of a relation between place and time of the individual events
relative to both reference-bodies, such that every ray of light possesses the
velocity of transmission c relative to the embankment and relative to the
train?
Up to the present we have only considered events taking place
along the embankment, which had mathematically to assume the function
of a straight line. In the manner indicated in Chapter II we can imagine
this reference-body supplemented laterally and in a vertical direction by
means of a framework of rods, so that an event which takes place any-
612
MASTERWORKS OF SCIENCE
where can be localised with reference to this framework. Similarly, we
can imagine the train travelling with the velocity v to be continued across
the whole of space, so that every event, no matter how far off it may be,
could also be localised with respect to the second framework. In every
such framework we imagine three surfaces perpendicular to each other
marked out, and designated as "co-ordinate planes" ("co-ordinate sys-
tem"). A co-ordinate system K then, corresponds to tjie embankment, and
a co-ordinate system K' to the train. An event, wherever it may have taken
place, would be fixed in space with respect to K by the three perpendicu-
lars x, y, * on the co-ordinate planes, and with regard to time by a time-
value /. Relative to K , the same event would be fixed in respect of space
and time by corresponding values xff yf , zf, t', which o£ course are not
identical with x,y,z,t..
What are the values yf , /, sf, tf of an event with respect to K , when
the magnitudes x, y, z, t of the same event with respect to K are given?
The relations must be so chosen that the law of the transmission of light
-JT'
"JC
FIG. 2.
in vacuo is satisfied for one and the same ray of light (and of course for
every ray) with respect to K and Kf. For the relative orientation in space
of the co-ordinate systems indicated in the diagram (Fig. 2), this problem
is solved by means of the equations:
/ ,_.
x — vt
This system of equations is known as the "Lorentz transformation."
If in place of the law of transmission of light we had taken as our
basis the tacit assumptions of the older mechanics as to the absolute
_ EINSTEIN-— RELATIVITY _ 615
character of times and lengths, then instead of the above we should have
obtained the following equations:
= x — Vt
This system of equations is often termed the "Galilei transformation."'
The Galilei transformation can be obtained from the Lorentz transforma-
tion by substituting an infinitely large value for the velocity of light c
in the latter transformation.
XII. THE BEHAVIOUR OF MEASURING RODS AND CLOCKS
IN MOTION
I PLACE a metre-rod in the #'-axis of Kf in such a manner that one end
(the beginning) coincides with the point yf = o, whilst the other end
(the end of the rod) coincides with the point xf = i. What is the length
of the metre-rod relatively to the system K? In order to learn this, we
need only ask where the beginning of the rod and the end of the rod lie
with respect to K at a particular time t of the system K. By means of
the first equation of the Lorentz transformation the values of these two*
points at the time t = -o can be shown to be
^(beginning of rod) = o.^ / x fL
r(end of rod) = i.J I _ *
the distance between the points being %/ i §-. But the metre-rod
is moving with the velocity v relative to K. It therefore follows that the-
length of a rigid metre-rod moving in the direction of its length with a
velocity v is \/ i — v^/c2 of a metre. The rigid rod is thus shorter when
in motion than when at rest, and the more quickly it is moving, the*
shorter is the rod. For the velocity v = c we should have >/ i — t^/c2 = o,.
and for still greater velocities the square root becomes imaginary. From
this we conclude that in the theory of relativity the velocity c plays the
part, of a limiting velocity, which can neither be reached nor exceeded
by any real body.
If, on the contrary, we had considered a metre-rod at rest in the
#-axis with respect to K, then we should have found that the length of
the rod as judged from K! would have been \J i — tfi/c2; this is, quite
in accordance with the principle of relativity which forms the basis of our
614 MASTERWORKS OF SCIENCE
considerations. If we had based our considerations on the Galilei trans-
formation we should not have obtained a contraction of the rod as a con-
sequence of its motion.
Let us now consider a seconds clock which is permanently situated
at the origin (x' = o) of Kf; t' = o and / = i are two successive ticks of
this clock. The first and fourth equations of the Lorentz transformation
give for these two ticks:
t = o
and
As judged from Kf the clock is moving with the velocity v; as judged
from this reference-body, the time which elapses between two strokes of
the clock is not one second, but — \ , -: seconds, /. e. a somewhat
pr
\'— ?
larger time. As a consequence of its motion the clock goes more slowly
than when at rest. Here also the velocity c plays the part of an unattain-
able limiting velocity.
XIIL THEOREM OF THE ADDITION OF VELOCITIES.
THE EXPERIMENT OF FIZEAU
IN Chapter VI we derived the theorem of the addition of velocities in
one direction in the form which also results from the hypotheses of clas-
sical mechanics. This theorem can also be deduced readily from the
Galilei transformation (Chapter XI). In place of the man walking inside
the carriage, we introduce a point moving relatively to the co-ordinate
system K' in accordance with the equation
yf - wf.
By means of the first and fourth equations of the Galilei transformation
we can express x' and / in terms of x and t, and we then obtain
x = (v-\-w}t.
This equation expresses nothing else than the law of motion of the point
with reference to the system K (of the man with reference to the em-
bankment). We denote this velocity by the symbol Wf and we then
obtain, as in Chapter VI,
W = v + w (A).
^ EINSTEIN — RELATIVITY 615
But we can carry out this consideration just as well on the basis of
the theory of relativity. In the equation
y? = wf
we must then express xf and / in terms of x and t, making use of the
first and fourth equations of the Lorentz transformation. Instead of the
equation (A) we then obtain the equation
(B),
which corresponds to the theorem of addition for velocities in one direc-
tion according to the theory of relativity. The question now arises as to
which of these two theorems is the better in accord with experience. On
this point we are enlightened by a most important experiment which the
brilliant physicist Fizeau performed more than half a century ago.
The experiment is concerned with the following question. Light
travels in a motionless liquid with a particular velocity w. How quickly
does it travel in the direction of the arrow in the tube T (see the accom-
panying diagram. Fig. 3) when the liquid above mentioned is flowing
through the tube with a velocity v?
In accordance with the principle of relativity we shall certainly have
to take for granted that the propagation of light always takes place with
the same velocity w with respect to the liquid, whether the latter is in
motion with reference to other bodies or not. The velocity of light rela-
tive to the liquid and the velocity of the latter relative to the tube are
thus known, and we require the velocity of light relative to the tube.
/T
FIG. 3.
If we denote the velocity of the light relative to the tube by Wf then
this is given by the equation (A) or (B), according as the Galilei trans-
formation or the Lorentz transformation corresponds to the facts. Experi-
ment decides in favour of equation (B) derived from the theory of rela-
tivity, and the agreement is, indeed, very exact.
XIV. THE HEURISTIC VALUE OF THE THEORY OF
RELATIVITY
OUR TRAIN OF THOUGHT in the foregoing pages can be epitomised in the
following manner.
616 MASTERWORKS OF SCIENCE
Every general law of nature must be so constituted that it is trans-
formed into a law of exactly the same form when, instead of the space-
time variables x, y, z, t of the original co-ordinate system Kf we introduce
new space-time variables xf, yf , zf, tf of a co-ordinate system K'. In this
connection the relation between the ordinary and the accented magni-
tudes is given by the Lorentz transformation. Or, in brief: General laws
of nature are co-variant with respect to Lorentz transformations.
This is a definite mathematical condition that the theory of relativity
demands of a natural law, and in virtue of this, the theory becomes a
valuable heuristic aid in the search for general laws of nature. If a general
law of nature were to be found which did not satisfy this condition, then
at least one of the two fundamental assumptions of the theory would
have been disproved. Let us now examine what general results the latter
theory has hitherto evinced.
XV. GENERAL RESULTS OF THE THEORY
IT is CLEAR from our previous considerations that the (special) theory of
relativity has grown out of electrodynamics and optics. In these fields it
lias not appreciably altered the predictions of theory, but it has consider-
ably simplified the theoretical structure, i.e. the derivation of laws, and —
what is incomparably more important — it has considerably reduced the
number of independent hypotheses forming the basis of theory.
Classical mechanics required to be modified before it could come
into line with the demands of the special theory of relativity. For the
main part, however, this modification affects only the laws for rapid
motions, in which the velocities of matter v are not very small as com-
pared with the velocity of light. We have experience of such rapid mo-
tions only in the case of electrons and ions; for other motions the varia-
tions from the laws of classical mechanics are too small to make them-
selves evident in practice. In accordance with the theory of relativity the
kinetic energy of a material point of mass m is no longer given by the
well-known expression
v*
. m-9
but by the expression
me2
This expression approaches infinity as the velocity v approaches the veloc-
ity of light c. The velocity must therefore always remain less than c, how-
ever great may be the energies used to produce the acceleration. If we
EINSTEIN — RELATIVITY 617
develop the expression for the kinetic energy in the form of a series, we
r\r\i-rt IT*
obtain
_
V* .
When -g- is small compared with unity, the third of these terms is
always small in comparison with the second, which last is alone consid-
ered in classical mechanics. The first term me2 does not contain the
velocity, and requires no consideration if we are only dealing with the
question as to how the energy of a point-mass depends on the velocity.
Before the advent of relativity, physics recognised two conservation
laws of fundamental importance, namely, the law of the conservation of
energy and the law of the .conservation of mass;, these two fundamental
laws appeared to be quite independent of each other. By means of the
theory of relativity they have been united into one law.
The principle of relativity requires that the law of the conservation
of energy should hold not only with reference to a co-ordinate system K,
but also with respect to every co-ordinate system Kf which is in a state
of uniform motion of translation relative to K, or, briefly, relative to every
"Galileian" system of co-ordinates. In contrast to classical mechanics, the
Lorentz transformation isjie deciding factor in the transition from one
such system to another.
By means of comparatively simple considerations we are led to draw
the following conclusion from these premises, in conjunction with the
fundamental equations o£ the electrodynamics of Maxwell: A body mov-
ing with the velocity v, which absorbs an amount of energy EQ in the
form of radiation without suffering an alteration in velocity in the process,
has, as a consequence, its energy increased by an amount
In consideration of the expression given above for the kinetic energy
of the body, the required energy of the body comes out to be
(*+•!>
~
Thus the body has the same energy as a bo'dy of mass I m +" ~3 1
moving with the velocity v. Hence we can say: If a body takes up an
E
amount of energy E09 then its inertial mass increases by an amount -5;
the inertial mass of a body is not a constant, but varies according to the
618 MASTERWORKS OF SCIENCE
change in the energy of the body. The inertial mass of a system of bodies
can even be regarded as a measure of its energy. The law of the conserva-
tion of the mass of a system becomes identical with the law of the con-
servation of energy, and is only valid provided that the system neither
takes up nor sends out energy. Writing the expression for the energy in
the form
we see that the term me2 is nothing else than the energy possessed by the
body before it absorbed the energy EQ.
A direct comparison of this relation with experiment is not possible
at the present time, owing to the fact that the changes in energy E0 to
which we can subject a system are not large enough to make themselves
77
perceptible as a change in the inertial mass of the system. — | is too
small in comparison with the mass m, which was present before the al-
teration of the energy. It is owing to this circumstance that classical
mechanics was able to establish successfully the conservation of mass as a
law of independent validity.
XVL EXPERIENCE AND THE SPECIAL THEORY OF
RELATIVITY
IT is KNOWN that cathode rays and the so-called /?-rays emitted by radio-
active substances consist of negatively electrified particles (electrons) of
very small inertia and large velocity. By examining the deflection of these
rays under the influence of electric and magnetic fields, we can study the
law of motion of these particles very exactly.
In the theoretical treatment of these electrons, we are faced with the
difficulty that electrodynamic theory of itself is unable to give an account
of their nature. For since electrical masses of one sign repel each other,
the negative electrical masses constituting the electron would necessarily
be scattered under the influence of their mutual repulsions, unless there
are forces of another kind operating between them, the nature of which
has hitherto remained obscure to us. If we now assume that the relative
distances between the electrical masses constituting the electron remain
unchanged during the motion of the electron (rigid connection in the
sense of classical mechanics), we arrive at a law of motion of the electron
which does not agree with experience. Guided by purely formal points
of view, H. A. Lorentz was the first to introduce the hypothesis that the
particles constituting the electron experience a contraction in the direc-
tion of motion in consequence of that motion, the amount of this con-
traction being proportional to the expression «* / i — -5 . This hypothesis,
EINSTEIN — RELATIVITY 619
which is not justifiable by any electrodynatnical facts, supplies us then
with that particular law of motion which has been confirmed with great
precision in recent years.
The theory of relativity leads to the same law of motion, without
requiring any special hypothesis whatsoever as to the structure and the
behaviour of the electron.
XVII. MINKOWSKTS FOUR-DIMENSIONAL SPACE
SPACE is a three-dimensional continuum. By this we mean that it is pos-
sible to describe the position of a point (at rest) by means of three num-
bers (co-ordinates) x, y, z, and that there is an indefinite number of
points in the neighbourhood of this one, the position of which can be
described by co-ordinates such as xl9 yv zv which may be as near as we
choose to the respective values of the co-ordinates x, yf z of the first
point. In virtue of the latter property we speak of a "continuum," and
owing to the fact that there are three co-ordinates we speak of it as being
"three-dimensional."
Similarly, the world of physical phenomena which was briefly called
"world" by Minkowski is naturally four-dimensional in the space-time
sense. For it is composed of individual events, each of which is described
by four numbers, namely, three space co-ordinates x, y, z and a time co-
ordinate, the time-value t. The "world" is in this sense also a continuum;
for to every event there are as many "neighbouring" events (realised or
at least thinkable) as we care to choose, the co-ordinates x^9 yi9 z^ t± of
which differ by an indefinitely small amount from those of the event
xt y, zt t originally considered. As a matter of fact, according to classical
mechanics, time is absolute, /.<?. it is independent of the position and the
condition of motion of the system of co-ordinates. We see this expressed
in the last equation of the Galileian transformation (/ = /).
The four-dimensional mode of consideration of the "worl3" is natu-
ral on the theory of relativity, since according to this theory time is
robbed of its independence. But the discovery of Minkowski, which was
of importance for the formal development of the theory of relativity, does
not lie here. It is to be found rather in the fact of his recognition that the
four-dimensional space-time continuum of the theory of relativity, in its
most essential formal properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space. In order
to give due prominence to this relationship, however, we must replace
the usual time co-ordinate / by an imaginary magnitude \/ — i. ct pro-
portional to it. Under these conditions, the natural laws satisfying the
demands of the (special) theory of relativity assume mathematical forms,
in which the time co-ordinate plays exactly the same role as the three
space co-ordinates. Formally, these four co-ordinates correspond exactly
to the three space co-ordinates in Euclidean geometry. It must be clear
even to the non-mathematician that, as a consequence of this purely
620 MASTERWORKS OF SCIENCE
formal addition to our knowledge, the theory perforce gained clearness in
no mean measure.
PART TWO: THE GENERAL THEORY OF RELATIVITY
XVI1L SPECIAL AND GENERAL PRINCIPLE OF RELATIVITY
THE BASAL PRINCIPLE, which was the pivot of all our previous considera-
tions, was the special principle of relativity, i.e. the principle of the physi-
cal relativity of all uniform motion.
The principle we have made use of not only maintains that we may
equally well choose the carriage or the embankment as our reference-body
for the description of any event. Our principle rather asserts what fol-
lows: If we formulate the general laws of nature as they are obtained
from experience, by making use of
(a) the embankment as reference-body,
(&) the railway carriage as reference-body,
then these general laws of nature (e.g. the laws of mechanics or the law
of the propagation of light in vacuo) have exactly the same form in both
cases. This can also be expressed as follows: For the physical description
of natural processes, neither of the reference-bodies K, Kf is unique (lit.
"specially marked out") as compared with the other. Unlike the first, this
latter statement need not of necessity hold a priori; it is not contained in
the conceptions of "motion" and "reference-body" and derivable from
them; only experience can decide as to its correctness or incorrectness.
We started out from the assumption that there exists a reference-
body K, whose condition of motion is such that the Galileian law holds"
with respect to it: A particle left to itself and sufficiently far removed
from all other particles moves uniformly in a straight line. With refer-
ence to K (Galileian reference-body) the laws of nature were to be as
simple as possible. But in addition to K, all bodies of reference K! should
be given preference in this sense, and they should be exactly equivalent
to K for the formulation of natural laws, provided that they are in a state
of uniform rectilinear and non-rotary motion with respect to K; all these
bodies of reference are to be regarded as Galileian reference-bodies. The
validity of the principle of relativity was assumed only for these reference-
bodies, but not for others (e.g. those possessing motion of a different
kind). In this sense we speak of the special principle of relativity, or
special theory of relativity.
In contrast to this we wish to understand by the "general principle
of relativity" the following statement: All bodies of reference K, K', etc.,
are equivalent for the description of natural phenomena (formulation of
the general laws of nature), whatever may be their state of motion.
Let us imagine ourselves transferred to our old friend the railway car-
riage, which is travelling at a uniform rate. As long as it is moving uni-
formly, the occupant of the carriage is not sensible of its motion, and it
EINSTEIN — RELATIVITY 621
is for this reason that he can without reluctance interpret the facts of the
case as indicating that the carriage is at rest, but the embankment in
motion. Moreover, according to the special principle of relativity, this
interpretation is quite justified also from a physical point of view.
If the motion of the carriage is now changed into a non-uniform
motion, as for instance by a powerful application of the brakes, then the
occupant of the carriage experiences a correspondingly powerful jerk for-
wards. It is clear that the Galileian law does not hold with respect to the
non-uniformly moving carriage. Because of this, we feel compelled at the
present juncture to grant a kind of absolute physical reality to non-uni-
form motion, in opposition to the general principle of relativity.
XIX. THE GRAVITATIONAL FIELD
"!F WE PICK UP a stone and then let it go, why does it fall to the ground?"
The usual answer to this question is: "Because it is attractecl by the
earth." Modern physics formulates the answer rather differently for the
following reason. As a result of the more careful study of electromagnetic
phenomena, we have come to regard action at a distance as a process im-
possible without the intervention of some intermediary medium. If, for
instance, a magnet attracts a piece of iron, we cannot be content to
regard this as meaning that the magnet acts directly on the iron through
the intermediate empty space, but we are constrained to imagine — after
the manner of Faraday — that the magnet always calls into being some-
thing physically real in the space around it, that something being what
we call a "magnetic field." In its turn this magnetic field operates on the
piece of iron, so that the latter strives to move towards the magnet.
The action of the earth on the stone takes place indirectly. The earth
produces in its surroundings a gravitational field, which acts on the
stone and produces its motion of fall. As we know from experience, the
intensity of the action on a body diminishes according to a quite definite
law, as we proceed farther and farther away from the earth. From our
point of view this means: The body (e.g. the earth) produces a field ia
its immediate neighbourhood directly; the intensity and direction of the
field at points farther removed from the body are thence determined by
the law which governs the properties in space of the gravitational fields
themselves.
In contrast to electric and magnetic fields, the gravitational field ex-
hibits a most remarkable property, which is of fundamental importance
for what follows. Bodies which are moving under the sole influence of a
gravitational field receive an acceleration, which does not in the least
depend either on the material or on the physical state of the body. This
law, which holds most accurately, can be expressed in a different form
in the light of the following consideration.
According to Newton's law of motion, we have
(Force) = (inertial mass) X (acceleration),
622 MASTERWORKS OF SCIENCE
where the "inertial mass" is a characteristic constant of the accelerated
body. If now gravitation is the cause of the acceleration, we then have
(Force) = (gravitational mass) X (intensity of the
gravitational field),
where the "gravitational mass" is likewise a characteristic constant for
the body. From these two relations follows:
/ , . v (gravitational mass)vv/. . f ,
(acceleration) = ^-r-. n r— ~X (intensity of the
v ' (inertial mass) v 7
gravitational field).
If now, as we find from experience, the acceleration is to be inde-
pendent of the nature and the condition of the body and always the same
for a given gravitational field, then the ratio of the gravitational to the
inertial mass must likewise be the same for all bodies. By a suitable
choice of units we can thus make this ratio equal to unity. We then have
the following law: The gravitational mass of a body is equal to its Inertial
mass.
It is true that this important law had hitherto been recorded in me-
chanics, but it had not been interpreted. A satisfactory interpretation can
be obtained only if we recognise the following fact: The same quality of
a body manifests itself according to circumstances as "inertia" or as
"weight" (lit, "heaviness").
XX. THE EQUALITY OF INERTIAL AND GRAVITATIONAL
MASS AS AN ARGUMENT FOR THE GENERAL
POSTULATE OF RELATIVITY
WE IMAGINE a large portion of empty space, so far removed from stars and
other appreciable masses that we have before us approximately the condi-
tions required by the fundamental law of Galilei. As reference-body, let
us imagine a spacious chest resembling a room with an observer inside
who is equipped with apparatus. Gravitation naturally does not exist for
this observer. He must fasten himself with strings to the floor, otherwise
the slightest impact against the floor will cause him to rise slowly
towards the ceiling of the room.
To the middle of the lid of the chest is fixed externally a hook with
rope attached, and now a "being" (what kind of a being is immaterial to
us) begins pulling at this with a constant force. The chest together with
the observer then begins to move "upwards" with a uniformly accelerated
motion. In course of time its velocity will reach unheard-of values— pro-
vided that we are viewing all this from another reference-body which is
not being pulled with a rope.
But how does the man in the chest regard the process? The accelera-
tion of the chest will be transmitted to him by the reaction of the floor
of the chest. If he release a body which he previously had in his hand,
EINSTEIN — RELATIVITY 623
the acceleration of the chest will no longer be transmitted to this body,
and for this reason the body will approach the floor of the chest with an
accelerated relative motion. The observer will further convince himself
that the acceleration of the body towards the floor of the chest is always
of the same magnitude, whatever tynd of body he may happen to use for
the experiment.
Relying on his knowledge of the gravitational field (as it was dis-
cussed in the preceding chapter), the man in the chest will thus come to
the conclusion that he and the chest are in a gravitational field which is
constant with regard to time. Of course he will be puzzled for a moment
as to why the chest does not fall in this gravitational field. Just then, how-
ever, he discovers the hook in the middle of the lid of the chest and the
rope which is attached to it, and he consequently comes to the conclusion
that the chest is suspended at rest in the gravitational field.
Even though it is being accelerated with respect to the "Galileian
space" first considered, we can nevertheless regard the chest as being at
rest. We have thus good grounds for extending the principle of relativity
to include bodies of reference which are accelerated with respect to each
other, and as a result we have gained a powerful argument for a general-
ised postulate of relativity.
Suppose that the man in the chest fixes a rope to the inner side of the
lid, and that he attaches a body to the free end of the rope. The result of
this will be to stretch the rope so that it will hang "vertically" down-
wards. If we ask for an opinion of the cause of tension in the rope, the
man in the chest will say: "The suspended body experiences a downward
force in the gravitational field, and this is neutralised by the tension of
the rope; what determines the magnitude of the tension of the rope is
the gravitational mass of the suspended body." On the other hand, -an
observer who is poised freely in space will interpret the condition of
things thus: "The rope must perforce take part in the accelerated motion
of the chest, and it transmits this motion to the body attached to it. The
tension of the rope is just large enough to effect the acceleration of the
body. That which determines the magnitude of the tension of the rope
is the inertial mass of the body." Guided by this example, we see that our
extension of the principle of relativity implies the necessity of the law of
the equality of inertial and gravitational mass. Thus we have obtained a
physical interpretation of this law.
We can now appreciate why that argument is not convincing which
we brought forward against the general principle of relativity at the end
of Chapter XVIII. It is certainly true that the observer in the railway
carriage experiences a jerk forwards as a result of the application of the
brake, and that he recognises in this the non-uniformity of motion (re-
tardation) of the carriage. But he is compelled by nobody to refer this
jerk to a "real" acceleration (retardation) of the carriage. He might also
interpret his experience thus: "My body of reference (the carriage) re-
mains permanently at rest. With reference to it, however, there exists
(during the period of application of the brakes) a gravitational field
624 MASTERWQRKS OF SCIENCE
which is directed forwards and which is variable with respect to time*
Under the influence of this field, the embankment together with the earth
moves non-uniformly in such a manner that their original velocity in the
backwards direction is continuously reduced."
XXI. IN WHAT RESPECTS ARE THE FOUNDATIONS OF CLAS-
SICAL MECHANICS AND OF THE SPECIAL THEORY
OF RELATIVITY UNSATISFACTORY?
WE HAVE ALREADY STATED several times that classical mechanics starts out
from the following law: Material particles sufficiently far removed from
other material particles continue to move uniformly in a straight line or
continue in a state of rest. We have also repeatedly emphasised that this
fundamental law can only be valid for bodies of reference K which pos-
sess certain unique states of motion, and which are in uniform transla-
tional motion relative to each other. Relative to other reference-bodies K
the law is not valid. Both in classical mechanics and in the special theory
of relativity we therefore differentiate between reference-bodies K rela-
tive to which the recognised "laws of nature" can be said to hold and
reference-bodies K relative to which these laws do not hold.
But no person whose mode of thought is logical can rest satisfied
with this condition of things. He asks: "How does it come that certain
reference-bodies (or their states of motion) are given priority over other
reference-bodies (or their states of motion) ? What is the reason -for Ms
preference?"
I seek in vain for a real something in classical mechanics (or in the
special theory of relativity) to which I can attribute the different be-
haviour of bodies considered with respect to the reference-systems K and
Kf. Newton saw this objection and attempted to invalidate it, but with-
out success. It can only be got rid of by means of a physics which is con-
formable to the general principle of relativity, since the equations of such
a theory hold for every body of reference, whatever may be its state of
motion.
XXII. A FEW INFERENCES FROM THE GENERAL THEORY OF
RELATIVITY
THE CONSIDERATIONS of Chapter XX show that the general theory of rela-
tivity puts us in a position to derive properties of the gravitational field
in a purely theoretical manner. Let us suppose, for instance, that we know
the space-time "course" for any natural process whatsoever, as regards the
manner in which it takes place in the Galileian domain relative to a
Galileian body of reference K. By means of purely theoretical operations
(i.e, simply by calculation) we are then able to find how this known natu-
ral process appears, as seen from a reference-body K? which is accelerated
EINSTEIN — RELATIVITY 625
relatively to K. But since a gravitational field exists with respect to this
new body of reference K ', our consideration also teaches us how the
gravitational field influences the process studied.
For example, we learn that a body which is in a state of uniform
rectilinear motion with respect to K (in accordance with the law of
Galilei) is executing an accelerated and in general curvilinear motion
with respect to the accelerated reference-body K? (chest). This accelera-
tion or curvature corresponds to the influence on the moving body of the
gravitational field prevailing relatively to K. It is known that a gravita-
tional field influences the movement of bodies in this way, so that our
consideration supplies us with nothing essentially new.
However, we obtain a new result of fundamental importance when
we carry out the analogous consideration for a ray of light. With respect
to the Galileian reference-body K, such a ray of light is transmitted rec-
tilinearly with the velocity c. It can easily be shown that the path of the
same ray of light is no longer a straight line when we consider it with
reference to the accelerated chest (reference-body K'). From this we con-
clude that, in general, rays of light are propagated curvilinearly in gravi-
tational fields.
Although a detailed examination of the question shows that the
curvature of light rays required by the general theory of relativity is only
exceedingly small for the gravitational fields at our disposal in practice,
its estimated magnitude for light rays passing the sun at grazing incidence
is nevertheless 1.7 seconds of arc. This ought to manifest itself in the fol-
lowing way: As seen from the earth, certain fixed stars appear to be in the
neighbourhood of the sun, and are thus capable of observation during a
total eclipse of the sun. At such times, these stars ought to appear to be
displaced outwards from the sun by an amount indicated above, as com-
pared with their apparent position in the sky when the sun is situated at
another part of the heavens. The examination of the correctness or other-
wise of this deduction is a problem of the greatest importance, the early
solution of which is to be expected of astronomers.1
In the second place our result shows that, according to the general
theory of relativity, the law of the constancy of the velocity of light in
vacuo, which constitutes one of the two fundamental assumptions in the
special theory of relativity and to which we have already frequently re-
ferred, cannot claim any unlimited validity. A curvature of rays of light
can only take place when the velocity of propagation of light varies with
position. Now we might think that as a consequence of this, the special
theory of relativity and with it the whole theory of relativity would be laid
in the dust. But in reality this is not the case. We can only conclude that
the special theory of relativity cannot claim an unlimited domain of
validity; its results hold only so long as we are able to disregard the influ-
ences of gravitational fields on the phenomena (e.g. of light).
aBy means of the star photographs of two expeditions equipped by a Joint Com-
mittee of the Royal and Royal Astronomical Societies, the existence of the deflection
of light demanded by theory was confirmed during the solar eclipse of May 29, 1919.
626 MASTERWORKS OF SCIENCE
The most attractive problem, to the solution of which the general
theory of relativity supplies the key, concerns the investigation of the
laws satisfied by the gravitational field itself. Let us consider this for a
moment.
We are acquainted with space-time domains which behave (approxi-
mately) in a "Galileian" fashion under suitable choice of reference-body,
i.e. domains in which gravitational fields are absent. If we now refer such
a domain to a reference-body K? possessing any kind of motion, then
relative to K' there exists a gravitational field which is variable with re-
spect to space and time. According to the general theory of relativity,
the general law of the gravitational field must be satisfied for all gravi-
tational fields obtainable in this way.
XXIII. BEHAVIOUR OF CLOCKS AND MEASURING RODS ON A
ROTATING BODY OF REFERENCE
WE START OFF AGAIN from quite special cases, which we have frequently
used before. Let us consider a space-time domain in which no gravita-
tional field exists relative to a reference-body K whose state of motion has
been suitably chosen. K is then a Galileian reference-body as regards the
domain considered, and the results of the special theory of relativity hold
relative to K. Let us suppose the same domain referred to a second body
of reference K ', which is rotating uniformly with respect to K. In order
to fix our ideas, we shall imagine K' to be in the form of a plane circular
disc, which rotates uniformly in its own plane about its centre. An ob-
server who is sitting eccentrically on the disc K' is sensible of a force
which acts outwards in a radial direction, and which would be inter-
preted as an effect of inertia (centrifugal force) by an observer who was
at rest with respect to the original reference-body K. But the observer on
the disc may regard his disc'as a reference-body which is "at rest.'* The
force acting on himself, and in fact on all other bodies which are at rest
relative to the disc, he regards as the effect of a gravitational field.
The observer performs experiments on his circular disc with clocks
and measuring rods. In doing so, it is his intention to arrive at exact
definitions for the signification of time- and space-data with reference to
the circular disc Kf, these definitions being based on his observations.
To start with, he places one of two identically constructed clocks at
the centre of the circular disc, and the other on the edge, of the disc, so
that they are at rest relative to it. As judged from this body, the clock
at the centre of the disc has no velocity, whereas the clock at the edge of
the disc is in motion relative to K in consequence of the rotation. Ac-
cording to a result obtained in Chapter XII, it follows that the latter clock
goes at a rate permanently slower than that of the clock at the centre of
the circular disc, i.e. as observed from K. Thus on our circular disc, or, to
make the case more general, in every gravitational field, a clock will go
more quickly or less quickly, according to the position in which the
EINSTEIN — RELATIVITY 627
clock is situated (at rest). For this reason it is not possible to obtain a
reasonable definition of time with the aid of clocks which are arranged at
rest with respect to the body of reference.
If the observer applies his standard measuring rod (a rod which is
short as compared with the radius of the disc) tangentially to the edge
of the disc, then, as judged from the Galileian system, the length of this
rod will be less than i, since, according to Chapter XII, moving bodies
suffer a shortening in the direction of the motion. On the other hand, the
measuring rod will not experience a shortening in length, as judged from
K, if it is applied to the disc in the direction of the radius. If, then, the
observer first measures the circumference of the disc with his measuring
rod and then the diameter of the disc, on dividing the one by the other,
he will not obtain as quotient the familiar number TT = 3.14 . . . , but
a larger number, whereas of course, for a disc which is at rest with re-
spect to K, this operation would yield TT exactly. This proves that the
propositions of Euclidean geometry cannot hold exactly on the rotating
disc, nor in general in a gravitational field, at least if we attribute the
length i to the rod in all positions and in every orientation. Hence the
idea of a straight line also loses its meaning. We are therefore not in a
position to define exactly the co-ordinates x, y, z relative to the disc by
means of the method used in discussing the special theory, and as long as
the co-ordinates and times of events have not been defined we cannot
assign an exact meaning to the natural laws in which these occur.
XXIV. EUCLIDEAN AND NON-EUCLIDEAN CONTINUUM
THE SURFACE of a marble table is spread out in front of me. I can get from
any one point on this table to any other point by passing continuously
from one point to a "neighbouring" one, and repeating this process a
(large) number of times, or, in other words, by going from point to point
without executing "jumps." We express this property of the surface by
describing the latter as a continuum.
Let us now imagine that a large number of little rods of equal length
have been made, their lengths being small compared with the dimensions
of the marble slab. We next lay four of these little rods on the marble
slab so that they constitute a quadrilateral figure (a square), the diag-
onals of which are equally long. To this square we add similar ones, each
of which has one rod in common with the first. We proceed in like man-
ner with each of these squares until finally the whole marble slab is laid
out with squares.
If everything has really gone smoothly, then I say that the points of
the marble slab constitute a Euclidean continuum with respect to the
little rod, which has been used as a "distance" (line-interval). By choos-
ing one corner of a square as "origin," I can characterise every other
corner of a square with reference to this origin by means of two numbers.
I only need state how many rods I must pass over when, starting from the
628 MASTERWORKS OF SCIENCE
origin, I proceed towards the "right" and then "upwards," in order to
arrive at the corner of the square under consideration. These two num-
bers are then the "Cartesian co-ordinates" of this corner with reference
to the "Cartesian co-ordinate system" which is determined by the ar-
rangement of little rods.
We recognise that there must also be cases in which the experiment
would be unsuccessful. We shall suppose that the rods "expand" by an
amount proportional to the increase of temperature. We heat the central
part of the marble slab, but not the periphery, in which case two of our
little rods can still be brought into coincidence at every position on the
table. But our construction of squares must necessarily come into disor-
der during the heating, because the little rods on the central region of
the table expand, whereas those on the outer part do not.
With reference to our little rods — defined as unit lengths — the
marble slab is no longer a Euclidean continuum, and we are also no longer
in the position of defining Cartesian co-ordinates directly with their aid,
since the above construction can no longer be carried out.
If rods of every kind (i.e. of every material) were to behave in the
same way as regards the influence of temperature when they are on the
variably heated marble slab, and if we had no other means of detecting
the effect of temperature than the geometrical behaviour of our rods in
experiments analogous to the one described here, then our best plan
would be to assign the distance one to two points on the slab, provided
that the ends of one of our rods could be made to coincide with these
two points.
The method of Cartesian co-ordinates must then be discarded, and
replaced by another which does not assume the validity of Euclidean
geometry for rigid bodies. The reader will notice that the situation de-
picted here corresponds to the one brought about by the general postu-
late of relativity.
XXV. GAUSSIAN CO-ORDINATES
ACCORDING TO Gauss, this combined analytical and geometrical mode of
handling the problem can be arrived at in the following way. We im-
agine a system of arbitrary curves (see Fig. 4) drawn on the surface of
the table. These we designate as ^-curves, and we indicate each of them
by means of a number. The curves u = i, u = 2, and u = 3 are drawn in
the diagram. Between the curves u = i and u = 2 we must imagine an
infinitely large number to be drawn, all of which correspond to real num-
bers lying between i and 2. We have then a system of ^-curves, and this
"infinitely dense" system covers the whole surface of the table. These
w-curves must not intersect each other, and through each point of the
surface one and only one curve must pass. Thus a perfectly definite value
of u belongs to every point on the surface of the marble slab. In like man-
ner we imagine a system of ^-curves drawn on the surface. These satisfy
EINSTEIN — RELATIVITY 629
the same conditions as the w-curves, they are provided with numbers in a
corresponding manner, and they may likewise be of arbitrary shape. It
follows that a value of u and a value of v belong to every point on the
surface of the table. For example, the point P in the diagram has the
Gaussian co-ordinates u = 3, v = i. Two neighbouring points P and P'
on the surface then correspond to the co-ordinates
P: u, v
P': u + du, v + dv,
where du and dv signify very small numbers. In a similar manner we may
Indicate the distance" (line-interval) between P and P', as measured with
a little rod, by means of the very small number ds. Then according to
Gauss we have
ds* = £U du2 + 2£12 du dv + £22 dv*,
where g119 gi29 g22 are magnitudes which depend in a perfectly definite
way on u and v. The magnitudes gn, glZ9 and g22 determine the be-
haviour of the rods relative to the w-curves and ^-curves, and thus also
relative to the surface of the table.
For the case in which the points of the surface considered form a
Euclidean continuum with reference to the measuring rods, but only in
this case, it is possible to draw the ^-curves and ^-curves and to attach
numbers to them, in such a manner, that we simply have:
Under these conditions, the ^-curves and ^-curves are straight lines m
the sense of Euclidean geometry, and they are perpendicular to each
other. Here the Gaussian co-ordinates are simply Cartesian ones. It is
clear that Gauss co-ordinates are nothing more than an association of
two sets of numbers with the points of the surface considered, of such a
nature that numerical values differing very slightly from each other are
associated with neighbouring points "in space."
So far, these considerations hold for a continuum of two dimensions.
But the Gaussian method can be applied also to a continuum of three,
four, or more dimensions. If, for instance, a continuum of four dimen-
sions be supposed available, we may represent it in the following way.
With every point of the continuum we associate arbitrarily four numbers,
630 MASTERWORKS OF SCIENCE
*i> *2> XB> xv whicn are known as "co-ordinates." Adjacent points cor-
respond to adjacent values o£ the co-ordinates. If a distance ds is associated
with the adjacent points P and P', this distance being measurable and
well-defined from a physical point of view, then the following formula
holds:
d? = £11 <**i2 + 2£i2 dx-L dxz " ' * *+Siidx*>
where the magnitudes gll9 etc., have values which vary with the position
in the continuum.
We can sum this up as follows: Gauss invented a method for the
mathematical treatment of continua in general, in which "size-relations""
("distances'* between neighbouring points) are defined. To every point
of a continuum are assigned as many numbers (Gaussian co-ordinates) as
the continuum has dimensions. This is done in such a way that only one
meaning can be attached to the assignment and -that numbers (Gaussian
co-ordinates) which differ by an indefinitely small amount are assigned
to adjacent points. The Gaussian co-ordinate system is a logical generali-
sation of the Cartesian co-ordinate system. It is also applicable to non-
Euclidean continua, but only when, with respect to the defined "size" or
"distance," small parts of the continuum under consideration behave
more nearly like a Euclidean system, the smaller the part of the continuum
under our notice.
XXVI. THE SPACE-TIME CONTINUUM OF THE SPECIAL
THEORY OF RELATIVITY CONSIDERED AS A
EUCLIDEAN CONTINUUM
FOR THE TRANSITION from one Galileian system to another, which is moving
uniformly with reference to the first, the equations of the Lorentz trans-
formation are valid. These last form the basis for the derivation of de-
ductions from the special theory of relativity, and in themselves they are
nothing more than the expression of the universal validity of the law of
transmission of light for all Galileian systems of reference.
Minkowski found that the Lorentz transformations satisfy the fol-
lowing simple conditions. Let us consider two neighbouring events, the
relative position of which in the four-dimensional continuum is given
with respect to a Galileian reference-body K by the space co-ordinate
differences dx, dyf dz and the time-difference dt. With reference to a
second Galileian system we shall suppose that the corresponding differ-
ences for these two events are dx't dyf , dzf, dt'. The magnitude
d? = dx*m+ dy2 + da? — <r2 dt?9
which belongs to two adjacent points of the four-dimensional space-time
continuum, has the same value for all selected (Galileian) reference-
bodies. If we replace x, y, zf\/ — i ct, by xv x2> XB) #4, we also obtain the
result that
EINSTEIN — RELATIVITY 631
is independent of the choice of the body of reference. We call the magni-
tude ds the "distance" apart of the two events or four-dimensional points.
Thus, if we choose as time-variable the imaginary variable \/-i ct
instead of the real quantity /, we can regard the space-time continuum —
in accordance with the special theory of relativity — as a "Euclidean" four-
dimensional continuum.
XXVII. THE SPACE-TIME CONTINUUM OF THE GENERAL
THEORY OF RELATIVITY IS NOT A EUCLIDEAN
CONTINUUM
IN THE FIRST PART of this book we were able to make use of space-time
co-ordinates which allowed of a simple and direct physical interpretation,
and which, according to Chapter XXVI, can be regarded as four-dimen-
sional Cartesian co-ordinates. This was possible on the basis of the law
of the constancy of the velocity of light. But according to Chapter XXI,
the general theory of relativity cannot retain this law. On the contrary,
we arrived at the result that according to this latter theory the velocity
of light must always depend on the co-ordinates when a gravitational field
is present. In connection -with a specific illustration in Chapter XXIII, we
found that the presence of a gravitational field invalidates the definition
of the co-ordinates and the time, which led us to our objective in the
special theory of relativity.
We are led to the conviction that, according to the general principle
of relativity, the space-time continuum cannot be regarded as a Euclidean
one, but that here we have the general case, corresponding to the marble
slab with local variations of temperature. Just as it was there impossible to
construct a Cartesian co-ordinate system from equal rods, so here it is im-
possible to build up a system (reference-body) from rigid bodies and
clocks, which shall be of such a nature that measuring rods and clocks,
arranged rigidly with respect to one another, shall indicate position and
time directly.
But the considerations of Chapter XXV and XXVI show us the way
to surmount this difficulty. We refer the four-dimensional space-time
continuum in an arbitrary manner to Gauss co-ordinates. We assign to
every point of the continuum (event) four numbers, xv x2, XB, x4 (co-
ordinates), which have not the least direct physical significance, but only
serve the purpose of numbering the points of the continuum in a definite
but arbitrary manner. This arrangement does not even need to be of
such a kind that we must regard xv x2) xz as "space" co-ordinates and x±
as a "time" co-ordinate.
The only statements having regard to these points which can claim
a physical existence are in reality the statements about their encounters.
In our mathematical treatment, such an encounter is expressed in the fact
that the two lines which represent the motions of the points in question
have a particular system of co-ordinate values, xly x2, #3, #4, in common.
632 MASTERWQRKS OF SCIENCE
After mature consideration the reader will doubtless admit that in reality
such encounters constitute the only actual evidence of a time-space nature
with which we meet in physical statements.
The following statements hold generally: Every physical description
resolves itself into a number of statements, each of which refers to the
space-time coincidence of two events A and B. In terms of Gaussian co-
ordinates, every such statement is expressed by the agreement of their
four co-ordinates xI9 x2, #3, #4. Thus, in reality, the description of the
time-space continuum by means of Gauss co-ordinates completely replaces
the description with the aid of a body of reference, without suffering
from the defects of the latter mode of description; it is ndt tied down
to the Euclidean character of the continuum which has to be represented.
XXVIII. EXACT FORMULATION OF THE GENERAL
PRINCIPLE OF RELATIVITY
THE FOLLOWING STATEMENT corresponds to the fundamental idea of the
general principle of relativity: "All Gaussian co-ordinate systems are
essentially equivalent for the formulation of the general laws of nature."
If we desire to adhere to our "old-time" three-dimensional view of
things, then we can characterise the development which is being under-
gone by the fundamental idea of the general theory of relativity as follows:
The special theory of relativity has reference to Galileian domains, i.e. to
those in which no gravitational field exists. In this connection a Galileian
reference-body serves as body of reference, i.e. a rigid body the state of
motion of which is so chosen that the Galileian law of the uniform rec-
tilinear motion of "isolated" material points holds relatively to it.
In gravitational fields there are no such things as rigid bodies with
Euclidean properties; thus the fictitious rigid body of reference is of no
avail in the general theory of relativity. The motion of clocks is also
influenced by gravitational fields, and in such a way that a physical defi-
nition of time which is made directly with the aid of clocks has by no
means the same degree of plausibility as in the special theory of relativity.
For this reason non-rigid reference-bodies are used which are as a
whole not only moving in any way whatsoever, but which also suffer
alterations in form ad lib. during their motion. Clocks, for which the law
of motion is of any kind, however irregular, serve for the definition of
time. We have to imagine each of these clocks fixed at a point on the
non-rigid reference-body. These clocks satisfy only the one condition, that
the "readings" which are observed simultaneously on adjacent clocks (in
space) differ from each other by an indefinitely small amount. This non-
rigid reference-body,, which might appropriately be termed a "reference-
mollusk," is in the main equivalent to a Gaussian four-dimensional co-
ordinate system chosen arbitrarily. Every point on the mollusk is treated
as a space-point, and every material point which is at rest relatively to
it as at rest, so long as the mollusk is considered as reference-body. The
EINSTEIN — RELATIVITY 633
general principle of relativity requires that all these mollusks can be used
as reference-bodies with equal right and equal success in the formulation
of the general laws of nature; the laws themselves must be quite inde-
pendent of the choice of mollusk.
The great power possessed by the general principle of relativity lies
in the comprehensive limitation which is imposed on the laws of nature
in consequence of what we have seen above.
XXIX. THE SOLUTION OF THE PROBLEM OF GRAVITATION
ON THE BASIS OF THE GENERAL PRINCIPLE OF
RELATIVITY
FINALLY, the general principle of relativity permits us to determine the
influence of the gravitational field on the course of all those processes
which take place according to known laws when a gravitational field is
absent, i.e. which have already been fitted into the frame of the special
theory of relativity; it has also already explained a result of observation
in astronomy, against which classical mechanics is powerless. According
to Newton's theory, a planet moves round the sun in an ellipse, which
would permanently maintain its position with respect to the fixed stars,
if we could disregard the motion of the fixed stars themselves and the
action of the other planets under consideration. Thus, if we correct the
observed motion of the planets for these two influences, and if Newton's
theory be strictly correct, we ought to obtain for the orbit of the planet
an ellipse, which is fixed with reference to the fixed stars. This deduction,
which can be tested with great accuracy, has been confirmed for all the
planets save one. The sole exception is Mercury, the planet which lies
nearest the sun. Since the time of Leverrier, it has been known that the
ellipse corresponding to the orbit of Mercury, after it has been corrected
for the influences mentioned above, is not stationary with respect to the
fixed stars, but that it rotates exceedingly slowly in the plane of the orbit
and in the sense of the orbital motion. The value obtained for this rotary
movement of the orbital ellipse was 43 seconds of arc per century, an
amount ensured to be correct to within a few seconds of arc. This effect
can be explained by means of classical mechanics only on the assumption
of hypotheses which have little probability and which were devised solely
for this purpose.
On the basis of the general theory of relativity, it is found that the
ellipse of every planet round the sun must necessarily rotate in the man-
ner indicated above; that for all the planets, with the exception of
Mercury, this rotation is too small to be detected with the delicacy of
observation possible at the present time; but that in the case of Mercury
it must amount to 43 seconds of arc per century, a result which is strictly
in agreement with observation.
Apart from this one, it has hitherto been possible to make only two
deductions from the theory which admit of being tested by observation,
634 MASTERWORKS OF SCIENCE
to wit, the curvature of light rays by the gravitational field of the sun,
and a displacement of the spectral lines of light reaching us from large
stars, as compared with the corresponding lines for light produced in an
analogous manner terrestrially (*'.*. by the same kind of molecule).
PART THREE: CONSIDERATIONS ON THE UNIVERSE
AS A WHOLE
XXX COSMOLOGICAL DIFFICULTIES OF NEWTON'S
THEORY
IF WE PONDER over the question as to how the universe, considered as a
whole, is to be regarded, the first answer that suggests itself to us is
surely this: As regards space (and time) the universe is infinite. There
are stars everywhere, so that the density of matter, although very variable
in detail, is nevertheless on the average everywhere the same.
This view is not in harmony with the theory of Newton. The latter
theory rather requires that the universe should have a kind of centre in
which the density of the stars is a maximum, and that as we proceed out-
wards from this centre the group-density of the stars should diminish,
until finally, at great distances, it is succeeded by an infinite region of
emptiness. The- stellar universe ought to be a finite island in the infinite
ocean of space.
This conception is in itself not very satisfactory. It is still less satis-
factory because it leads to the result that the light emitted by the stars
and also individual stars of the stellar system are perpetually passing out
into infinite space, never to return, and without ever again coming into
interaction with other objects of nature. Such a finite material universe
would be destined to become gradually but systematically impoverished.
In order to escape this dilemma, Seeliger suggested a modification of
Newton's law, in which he assumes that for great distances the force of
attraction between two masses diminishes more rapidly than would result
from the inverse-square law. In this way it is possible for the mean density
of matter to be constant everywhere, even to infinity, without infinitely
large gravitational fields being produced.
XXXI THE POSSIBILITY OF A "FINITE" AND YET
"UNBOUNDED'' UNIVERSE
BUT SPECULATIONS on the structure of the universe also move in quite
another direction. The development of non-Euclidean geometry led to
the recognition of the fact that we can cast doubt on the infiniteness of
our space without coming into conflict with the laws of thought or with
experience (Riemann, Helmholtz).
In the first place, we imagine an existence in two-dimensional space.
EINSTEIN — RELATIVITY 635
Flat beings with flat implements, and in particular flat rigid measuring
rods, are free to move in a plane. For them nothing exists outside of this
plane: that which they observe to happen to themselves and to their flat
"things" is the all-inclusive reality of their plane. In particular, the con-
structions of plane Euclidean geometry can be carried out by means of
the rods, e.g. the lattice construction, considered in Chapter XXIV. In
contrast to ours, the universe of these beings is two-dimensional; but, like
ours, it extends to infinity. In their universe there is room for an infinite
number of identical squares made up of rods, i.e. its volume (surface)
is infinite. If these beings say their universe is "plane," there is sense in
the statement, because they mean that they can perform the constructions
of plane Euclidean geometry with their rods. In this connection the indi-
vidual rods always represent the same distance, independently of their
position.
Let us consider now a second two-dimensional existence, but this
time on a spherical surface instead of on a plane. The flat beings with
their measuring rods and other objects fit exactly on this surface and
they are unable to leave it. Their whole universe of observation extends
exclusively over the surface of the sphere. Are these beings able to regard
the geometry of their universe as being plane geometry and their rods
withal as the realisation of "distance"? They cannot do this. For if they
attempt to realise a straight line, they will obtain a curve, which we
"three-dimensional beings" designate as a great circle, i.e. a self-contained
line of definite finite length, which can be measured up by means of a
measuring rod. Similarly, this universe has a finite area that can be com-
pared with the area of a square constructed with rods. The great charm
resulting from this consideration lies in the recognition of the fact that
the universe of these beings is finite and yet has no limits.
But the spherical-surface beings do not need to go on a world tour
in order to perceive that they are not living in a Euclidean universe. They
can convince themselves of this on every part of their "world," provided
they do not use too small a piece of it. Starting from a point, they draw
"straight lines" (arcs of circles as judged in three-dimensional space) of
equal length in all directions. They will call the line joining the free ends
of these lines a "circle." For a plane surface, the ratio of the circumfer-
ence of a circle to its diameter, both lengths being measured with the
same rod, is, according to Euclidean geometry of the plane, equal to a
constant value TT, which is independent of the diameter of the circle. On
their spherical surface our flat beings would find for this ratio the value
sin/ — ]
\R)
7T
i.e. a smaller value than TT, the difference being the more considerable,
the greater is the radius of the circle in comparison with the radius R of
636 MASTERWORKS OF SCIENCE
the "world-sphere." By means of this relation the spherical beings can
determine the radius of their universe ("world"), even when only a
relatively small part of their world-sphere is available for their measure-
ments.
Thus if the spherical-surface beings are living on a planet of which
the solar system occupies only a negligibly small part of the spherical
universe, they have no means of determining whether they are living _
a finite or in an infinite universe, because the "piece of universe" to
which they have access is in both cases practically plane, or Euclidt *i.
It follows directly from this discussion that for our sphere-beings the
circumference of a circle first increases with the radius until the "circum-
ference of the universe" 'is reached, and that it thenceforward gradually
decreases to zero for still further increasing values of the radius. During
this process the area of the circle continues to increase more and more,
until finally it becomes equal to the total area of the whole "world-
sphere."
Perhaps the reader will wonder why we have placed our "beings" on
a sphere rather than on another closed surface. But this choice has" its
justification in the fact that, of all closed surfaces, the sphere is unique
in possessing the property that all points on it are equivalent. I admit
that the ratio of the circumference c of a circle to its radius r depends
on r, but for a given value of r it is the same for all points of the "world-
sphere"; in other words, the "world-sphere" is a "surface of constant
curvature."
To this two-dimensional sphere-universe there is a three-dimensional
analogy, namely, the three-dimensional spherical space which was dis-
covered by Biernann. Its points are likewise all equivalent. It possesses a
finite volume, which is determined by its "radius" (zi^R3).
Suppose we draw lines or stretch strings in all directions from a
point, and mark off from each of these the distance r with a measuring
rod. All the free end-points of these lengths lie on a spherical surface. We
can specially measure up the area (JP) of this surface by means of a square
made up of measuring rods. If the universe is Euclidean, then F = 4?rr2;
if it is spherical, then F is always less than ^r2. With increasing values
of rt F increases from zero up to a maximum value which is determined
by the "world-radius," but for still further increasing values of r, the area
gradually diminishes to zero. At first the straight lines which radiate
from the starting point diverge farther and farther from one another, but
later they approach each other, and finally they run together again at a
"counter-point" to the starting point. Under such conditions they have
traversed the whole spherical space. It is easily seen that the three-dimen-
sional spherical space is quite analogous to the two-dimensional spherical
surface. It is finite (i.e. of finite volume), and has no bounds.
It follows, from what has been said, that closed spaces without limits
are conceivable. From amongst these, the spherical space (and the ellipti-
cal) excels in its simplicity, since all points on it are equivalent. As a
result of this discus§ion? a most interesting question arises for astrono-
EINSTEIN — RELATIVITY 637
mers and physicists, and that is whether the universe in which we live is
infinite or whether it is finite in the manner of the spherical universe.
Our experience is far from being sufficient to enable us to answer this
question. But the general theory of relativity permits of our answering
it with a moderate degree of certainty.
i:; XXXII. THE STRUCTURE OF SPACE ACCORDING TO
THE GENERAL THEORY OF RELATIVITY
ACCORDING TO the general theory of relativity, the geometrical properties
of space are not independent, but they are determined by matter. Thus
we can draw conclusions about the geometrical structure of the universe
only if we base our considerations on the state of the matter as being
something that is known. We know from experience that, for a suitably
chosen co-ordinate system, the velocities of the stars are small as com-
pared with the velocity of transmission of light. We can thus as a rough
approximation arrive at a conclusion as to the nature of the universe as
a whole, if we treat the matter as being at rest.
We already know from our previous discussion that the behaviour
of measuring rods and clocks is influenced by gravitational fields, i.e. by
the distribution of matter. This in itself is sufficient to exclude the pos-
sibility of the exact validity of Euclidean geometry in our universe. But
it is conceivable that our universe differs only slightly from a Euclidean
one, and this notion seems all the more probable, since calculations show
that the metrics of surrounding space is influenced only to an exceedingly
small extent by masses even of the magnitude of our sun. We might
imagine that, as regards geometry, our universe behaves analogously to
a surface which is irregularly curved in its individual parts, but which
nowhere departs appreciably from a plane: something like the rippled
surface of a lake. Such a universe might fittingly be called a quasi-Euclid-
ean universe. As regards its space it would be infinite. But calculation
shows that in a quasi-Euclidean universe the average density of matter
would necessarily be nil. Thus such a universe could not be inhabited by
matter everywhere; it would present to us that unsatisfactory picture
which we portrayed in Chapter XXX.
If we are to have in the universe an average density of matter which
differs from zero, however small may be that difference, then the universe
cannot be quasi-Euclidean. On the contrary, the results of calculation
indicate that if matter be distributed uniformly, the universe would
necessarily be spherical (or elliptical). Since in reality the detailed distri-
bution of matter is not uniform, the real universe will deviate in indi-
vidual parts from the spherical, i.e. the universe will be quasi-spherical.
But it will be necessarily finite. In fact, the theory supplies us with a
simple connection between the space-expanse of the universe and the
average density of matter in it.
115484
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11