CHAPTER I_The atom and the Bohr theory of its structure

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THE ATOM AND THE BOHR THEORY

OF ITS STRUCTURE

_Original Title: “Bohr’s Atomteori, almenfatteligt fremstillet”_

_Translated from the Danish by $1

Fellow of the American-Scandinavian Foundation,

1923, and RACHEL T. LINDSAY_

[Illustration: _Niels Bohr_]

THE ATOM

AND

THE BOHR THEORY

OF ITS STRUCTURE

An Elementary Presentation

H. A. KRAMERS

LECTURER AT THE INSTITUTE OF THEORETICAL PHYSICS IN THE

UNIVERSITY OF COPENHAGEN

AND

HELGE HOLST

LIBRARIAN AT THE ROYAL TECHNICAL COLLEGE OF COPENHAGEN

WITH A FOREWORD BY

SIR ERNEST RUTHERFORD, F.R.S.

[Illustration]

NEW YORK

ALFRED A. KNOPF

1923

PRINTED IN GREAT BRITAIN BY MORRISON AND GIBB LTD., EDINBURGH

PREFACE

At the close of the nineteenth century and the beginning of the

twentieth, our knowledge of the activities in the interior of matter

experienced a development which surpassed the boldest hopes that

could have been entertained by the chemists and physicists of the

nineteenth century. The smallest particles of chemistry, the atoms of

the elements, which hitherto had been approached merely by inductive

thought, now became tangible realities, so to speak, which could be

counted and whose tracks could be photographed. A series of remarkable

experimental investigations, stimulated largely by the English

physicist, J. J. Thomson, had disclosed the existence of negatively

charged particles, the so-called electrons, ¹/₂₀₀₀ the mass of the

smallest atom of the known elements. A theory of electrons, based

on Maxwell’s classical electrodynamical theory and developed mainly

through the labours of Lorentz in Holland and Larmor in England,

had brought the problem of atomic structure into close connection

with the theory of radiation. The experiments of Rutherford proved,

beyond a doubt, that atoms were composed simply of light, negative

electric particles, and small heavy, positive electric particles.

The new “quantum theory” of Planck was proving itself very powerful

in overcoming grave difficulties in the theory of radiation. The time

thus seemed ripe for a comprehensive investigation of the fundamental

problem of physics—the constitution of matter, and an explanation in

terms of simple general laws of the physical and chemical properties of

the atoms of the elements.

During the first ten years of the new century the problem was attacked

with great zeal by many scientists, and many interesting atomic models

were developed and studied. But most of these had more significance for

chemistry than for physics, and it was not until 1913 that the work of

the Danish physicist, Niels Bohr, paved the way for a really physical

investigation of the problem in a remarkable series of papers on the

spectrum and atomic structure of hydrogen. The ideas of Bohr, founded

as they were on the quantum theory, were startling and revolutionary,

but their immense success in explaining the facts of experience after

a time won for them the wide recognition of the scientific world, and

stimulated work by other investigators along similar lines. The past

decade has witnessed an enormous development at the hands of scientists

in all parts of the world of Bohr’s original conceptions; but through

it all Bohr has remained the leading spirit, and the theory which, at

the present time, gives the most comprehensive view of atomic structure

may, therefore, most properly bear the name of Bohr.

It is the object of this book to give the reader a glimpse of the

fundamental conceptions of this theory, together with some of the most

significant results it has attained. The book is designed to meet

the needs of those who wish to keep abreast of modern developments

in science, but have neither time nor inclination to delve into the

highly mathematical abstract literature in which the developments are

usually concealed. It is with this in mind that the first four chapters

have been devoted to a general survey of those parts of physics and

chemistry which have close connection with atomic theory. No attempt

has been made at a mathematical development, and the physical meaning

of such mathematical formulæ as do occur has been clearly emphasized

in the text. It is hoped, however, that even those readers whose

acquaintance with atomic theory is more than casual, will find the book

a stimulus to further study of the Bohr theory.

Here we wish to record our best thanks to Mr. and Mrs. Lindsay for

the ability and the great care with which they have carried out the

translation from the Danish original.

FOREWORD

During the last decade there has been a great advance in our knowledge

of the structure of the atom and of the relation between the atoms of

the chemical elements. In the later stages, science owes much to the

remarkable achievements of Professor Niels Bohr and his co-workers in

Copenhagen. For the first time, we have been given a consistent theory

to explain the arrangement and motion of the electrons in the outer

atom. The theory of Bohr is not only able to account in considerable

detail for the variation in the properties of the elements exemplified

by the periodic law, but also for the main features of the spectra,

both X-ray and optical, shown by all elements.

This volume, written by Dr. Kramers and Mr. Holst, gives a simple

and interesting account of our knowledge of atomic structure, with

special reference to the work of Professor Bohr. Dr. Kramers is in

an especially fortunate position to give a first-hand account of

this subject, for he has been a valued assistant to Professor Bohr

in developing his theories, and has himself made important original

contributions to our knowledge in this branch of inquiry.

I can confidently recommend this book to English readers as a clearly

written and accurate account of the development of our ideas on atomic

structure. It is written in simple language, and the essential ideas

are explained without mathematical calculations. This book should prove

attractive not only to the general scientific reader, but also to the

student who wishes to gain a broad general idea of this subject before

entering into the details of the mathematical theory.

E. RUTHERFORD.

CAVENDISH LABORATORY,

CAMBRIDGE, _8th October 1923_.

CONTENTS

PAGE

PREFACE vii

FOREWORD xi

CHAP.

I. ATOMS AND MOLECULES 1

II. LIGHT WAVES AND THE SPECTRUM 34

III. IONS AND ELECTRONS 61

IV. THE NUCLEAR ATOM 83

V. THE BOHR THEORY OF THE HYDROGEN SPECTRUM 105

VI. VARIOUS APPLICATIONS OF THE BOHR THEORY 153

VII. ATOMIC STRUCTURE AND THE CHEMICAL PROPERTIES

OF THE ELEMENTS 180

INTERPRETATION OF SYMBOLS AND PHYSICAL CONSTANTS 209

COLOURED PLATES

PLATE

I. SPECTRUM PLATES ACCORDING TO THE ORIGINAL

DRAWINGS OF BUNSEN AND KIRCHHOFF _At end_

II. PRINCIPAL FEATURES OF ATOMIC STRUCTURE IN

SOME OF THE ELEMENTS—ATOMIC STRUCTURE

OF RADIUM _At end_

THE ATOM AND THE BOHR THEORY OF ITS STRUCTURE

CHAPTER I

ATOMS AND MOLECULES

Introduction.

As early as 400 B.C. the Greek philosopher, Democritus, taught

that the world consisted of empty space and an infinite number of small

invisible particles. These particles, differing in form and magnitude,

by their arrangements and movements, by their unions and disunions,

caused the existence of physical bodies with different characteristics,

and also produced the observed variations in these bodies. This

theory, which no doubt antedated Democritus, later became known as the

Atomic Theory, since the particles were called atoms, _i.e._ the

“indivisible.”

But the atomic conception was not the generally accepted one in

antiquity. Aristotle (384-322 B.C.) was not an atomist, and

denied the existence of discontinuous matter; his philosophy had a

tremendous influence upon the ideas of the ancients, and even upon the

beliefs of the Middle Ages. It must be confessed that his conception

of the continuity of matter seemed to agree best with experiment,

because of the apparent homogeneity of physical substances such as

metal, glass, water and air. But even this apparent homogeneity could

not be considered entirely inconsistent with the atomic theory, for,

according to the latter, the atoms were so small as to be invisible.

Moreover, the atomic theory left the way open for a more complete

understanding of the properties of matter. Thus when air was compressed

and thereafter allowed to expand, or when salt was dissolved in water

producing an apparently new homogeneous liquid, salt water, or when

silver was melted by heat, or light changed colour on passing through

wine, it was clear that something had happened in the interior of the

substances in question. But complete homogeneity is synonymous with

inactivity. How is it possible to obtain a definite idea of the inner

activity lying at the bottom of these changes of state, if we do not

think of the phenomenon as an interplay between the different parts of

the apparently homogeneous matter? Thus, in the examples above, the

decrease in the volume of the air might be considered as due to the

particles drawing nearer to each other; the dissolving of salt in water

might be looked upon as the movement of the salt particles in between

the water particles and the combination of the two kinds; the melting

of silver might naturally appear to be due to the loosening of bonds

between the individual silver particles.

The atomic theory had thus a sound physical basis, and proved

particularly attractive to those philosophers who tried to explain

the mysterious activity of matter in terms of exact measurements. The

atomic hypothesis was never completely overthrown, being supported

after the time of Aristotle by Epicurus (_c._ 300 B.C.),

who introduced the term “atom,” and by the Latin poet, Lucretius

(_c._ 75 B.C.) in his _De Rerum Natura_. Even in the Middle Ages it was

supported by men of independent thought, such as Nicholas of Autrucia,

who assumed that all natural activities were due to unions or disunions

of atoms. It is interesting to note that in 1348 he was forced to

retract this heresy. With the impetus given to the new physics by

Galileo (1600) the atomic view gradually spread, sometimes explicitly

stated as atomic theory, sometimes as a background for the ideas of

individual philosophers. Various investigators developed comprehensive

atomic theories in which they attempted to explain nearly everything

from purely arbitrary hypotheses; they occasionally arrived at very

curious and amusing conceptions. For example, about 1650 the Frenchman,

Pierre Gassendi, following some of the ancient atomists, explained the

solidity of bodies by assuming a hook-like form of atom so that the

various atoms in a solid body could be hooked together. He thought of

frost as an element with tetrahedral atoms, that is, atoms with four

plane faces and with four vertices each; the vertices produced the

characteristic pricking sensation in the skin. A much more thorough

treatment of the atomic theory was given by Boscovich (1770). He saw

that it was unnecessary to conceive of the atoms as spheres, cubes, or

other sharply defined physical bodies; he considered them simply as

points in space, mathematical points with the additional property of

being centres of force. He assumed that any two atoms influenced each

other with a force which varied, according to a complicated formula,

with the distance between the centres. But the time was hardly ripe

for such a theory, inspired as it evidently was by Newton’s teachings

about the gravitational forces between the bodies of the universe.

Indeed there were no physical experiments whose results could, with

certainty, be assumed to express the properties of the individual atoms.

The Atomic Theory and Chemistry.

[Illustration: FIG. 1.—The four elements and the four fundamental

characteristics.]

In the meantime atomic investigations of a very different nature had

been influencing the new science of chemistry, in which the atomic

theory was later to prove itself extraordinarily fruitful. It was

particularly unfortunate that in chemistry, concerned as it is with

the inner activities of the elements, Aristotle’s philosophy was

long the prevailing one. He adopted and developed the famous theory

of the four “elements,” namely, the dry and cold earth, the cold

and damp water, the damp and warm air, the warm and dry fire. These

“elements” must not be confused with the chemical elements known at

the present day; they were merely representatives of the different

consistent combinations of the four fundamental qualities, dryness

and wetness, heat and cold. From the symmetry in the system these were

supposed to be the principles by means of which all the properties of

matter could be explained. Neither the four “elements” nor the four

fundamental qualities could be clearly defined; they were vague ideas

to be discussed in long dialectic treatises, but were founded upon no

physical quantities which could be measured.

A system of chemistry which had its theoretical foundations in

the Greek elemental conceptions naturally had to work in the

dark. Undoubtedly this uncertainty contributed to the relatively

insignificant results of all the labour expended in the Middle Ages

on chemical experiments, many of which had to do with the attempt

to transmute the base metals into gold. Naturally there were many

important contributions to chemistry, and the theories were changed

and developed in many ways in the course of time. The alchemists of

the Middle Ages thought that metal consisted only of sulphur and

quicksilver; but the interpretation of this idea was influenced by

the Greek elemental theory which was maintained at the same time;

thus these new metal “elements” were considered by many merely as the

expressions of certain aspects of the metallic characteristics, rather

than as definite substances, identical with the elements bearing these

names. It is, however, necessary to guard against attributing to a

single conception too great influence on the historical development

of the chemical and physical sciences. That the growth of the latter

was hindered for so long a time was due more to the uncritical faith

in authority and to the whole characteristic psychological point of

view which governed Western thought in the centuries preceding the

Renaissance.

Robert Boyle (1627-1691) is one of the men to whom great honour is

due for brushing aside the old ideas about the elements which had

originated in obscure philosophical meditations. To him an element was

simply a substance which by no method could be separated into other

substances, but which could unite with other elements to form chemical

compounds possessing very different characteristics, including that

of being decomposable into their constituent elements. Undoubtedly

Boyle’s clear conception of this matter was connected with his

representation of matter as of an atomic nature. According to the

atomic conception, the chemical processes do not depend upon changes

within the element itself, but rather in the union or disunion of the

constituent atoms. Thus when iron sulphide is produced by heating iron

and sulphur together, according to this conception, the iron atoms

and the sulphur atoms combine in such a way that each iron atom links

itself with a sulphur atom. There is then a definite meaning in the

statement that iron sulphide consists of iron and sulphur, and that

these two substances are both represented in the new substance. There

is also a definite meaning, for instance, in the statement that iron

is an element, namely, that by no known means can the iron be broken

down into different kinds of atoms which can be reunited to produce a

substance different from iron.

The clarity which the atomic interpretation gave to the conception of

chemical elements and compounds was surely most useful to chemical

research in the following years; but before the atomic theory could

play a really great rôle in chemistry, it had to undergo considerable

development. In the time of Boyle, and even later, there was still

uncertainty as to which substances were the elements. Thus, water

was generally considered as an element. According to the so-called

phlogiston theory developed by the German Stahl (1660-1734), a theory

which prevailed in chemistry for many years, the metals were chemical

compounds consisting of a gaseous substance, phlogiston, which was

driven off when the metals were heated in air, and the metallic

oxide which was left behind. It was not until the latter half of the

eighteenth century that the foundation was laid for the new chemical

science by a series of discoveries and researches carried on by the

Swedish scientist Scheele, the Englishmen Priestley and Cavendish,

and particularly by the Frenchman Lavoisier. It was then discovered

that water is a chemical compound of the gaseous elements oxygen

and hydrogen, that air is principally a mixture (not a compound) of

oxygen and nitrogen, that combustion is a chemical process in which

some substance is united with oxygen, that metals are elements, while

metallic oxides, on the other hand, are compounds of metal and oxygen,

etc. Of special significance for the atomic theory was the fact that

Lavoisier made weighing one of the most powerful tools of scientific

chemistry.

Weighing had indeed been used previously in chemical experiments, but

the experimenters had been satisfied with very crude precision, and

the results had little influence on chemical theory. For example, the

phlogiston theory was maintained in spite of the fact that it was well

known that metallic oxide weighed more than the metal from which it

was obtained. Lavoisier now showed, by very careful weighings, that

chemical combinations or decompositions can never change the total

weight of the substances involved; a given quantity of metallic oxide

weighs just as much as the metal and the oxygen taken individually, or

_vice versa_. From the point of view of the atomic theory, this

obviously means that the weight of individual atoms is not changed in

the combinations of atoms which occur in the chemical processes. In

other words, _the weight of an atom is an invariable quantity_.

Here, then, we have the first property of the atom itself to be

established by experiment—a property, indeed, which most atomists had

already tacitly assumed.

Moreover, by the practice of weighing it was determined that _to

every chemical combination there corresponds a definite weight ratio

among the constituent parts_. This also had been previously accepted

by most chemists as highly probable; but it must be admitted that the

law at one time was assailed from several sides.

In comparing the weight ratios in different chemical compounds certain

rules were, in the meantime, obtained. In many ways the most important

of these, the so-called _law of multiple proportions_, was

enunciated in the beginning of the last century by the Englishman,

John Dalton. As an example of this law we may take two compounds of

carbon and hydrogen called methane or marsh gas and ethylene, in which

the quantities of hydrogen compounded with the same quantity of carbon

are as two is to one. Another example may be seen in the compounds of

carbon and oxygen. In the two compounds of carbon and oxygen, carbon

monoxide and carbon dioxide, the weight ratios between the carbon

and oxygen are respectively as three to four and three to eight. A

definite quantity of carbon has thus in carbon dioxide combined with

just twice as much oxygen as in carbon monoxide. No less than five

oxygen compounds with nitrogen are known, where with a given quantity

of nitrogen the oxygen is combined in ratios of one, two, three, four

and five.

These simple number relations can be explained very easily by the

atomic theory, by assuming, first, that all atoms of the same element

have the same weight; and second, that in a chemical combination

between two elements the atoms combine to form an atomic group

characteristic of the compound in question—a _compound atom_, as

Dalton called it, or a _molecule_, as the atomic group is now

called. These molecules consist of comparatively few atoms, as, for

example, one of each kind, or one of one kind and two, three or four

of another, or two of one kind and three or four of another, etc. When

three elements are involved in a chemical compound the molecule must

contain at least three atoms, but there may be four, five, six or

more. The law of multiple proportions thus takes on a more complicated

character, but it remains apparent even in this case.

When Dalton in the beginning of last century formulated the theory of

the formation of chemical compounds from the atoms of the elements, he

at once turned atomic theory into the path of more practical research,

and it was soon evident that chemical research had then obtained a

valuable tool. It may be said that Dalton’s atomic theory is the firm

foundation upon which modern chemistry is built.

[Illustration]

[Illustration:

FIG. 2.—Representation of a part of Dalton’s atomic

table (of 1808) where the atom of each element

has its own symbol, and chemical compounds

are indicated by the union of the atoms of the

elements into groups by 2, 3, 4 ... (binary,

ternary, quaternary ... atoms). Below are given

the designations of the different atoms, and in

parentheses the atomic weight given by Dalton with

that of hydrogen as unity and the designations of

the indicated atomic groups.

_Atoms of the Elements._—1. Hydrogen (1); 2. Azote (5); 3. Carbon

(5); 4. Oxygen (7); 5. Phosphorus (9); 6. Sulphur (13); 7. Magnesia

(20); 8. Lime (23); 9. Soda (28); 10. Potash (42); 11. Strontites

(46); 12. Barytes (68); 13. Iron (38); 14. Zinc (56); 15. Copper (56);

16. Lead (95); 17. Silver (100); 18. Platina (100); 19. Gold (140);

20. Mercury (167).

_Chemical Compounds._—21. Water; 22. Ammonia; 23. 26. 27. and

30. Oxygen compounds of Azote; 24. 29. and 33. Hydrogen compounds

of Carbon; 25. Carbon monoxide; 28. Carbon dioxide; 31.

Sulphuric acid; 32. Hydro-sulphuric acid.]

While Dalton’s theory could not give information about the absolute

weights in grams of the atoms of various elements, it could say

something about the relative atomic weights, _i.e._, the ratios of

the weights of the different kinds of atoms, although it is true that

these ratios could not always be determined with certainty. If, for

example, the ratio between the oxygen and hydrogen in water is found

to be as eight to one, then the weight ratio between the oxygen atom

and the hydrogen atom will be as eight to one, if the water molecule is

composed of one oxygen atom and one hydrogen atom (as Dalton supposed,

see Fig. 2). But it will be as sixteen to one, if the water molecule is

composed of one oxygen and two hydrogen atoms (as we now know to be the

case). On the other hand, a ratio of seven to one will be compatible

with the experimental ratio of eight to one only if we assume that the

water molecule consists of fifteen atoms, eight of oxygen and seven of

hydrogen, a very improbable hypothesis. In another case let us compare

the quantities of oxygen and of hydrogen which are compounded with the

same quantities of carbon in the two substances, carbon monoxide and

methane respectively. On the assumption that the molecules in question

have a simple structure, we can draw conclusions about the ratio of the

atomic weights of hydrogen and oxygen. Now, if a ratio such as seven

to one or fourteen to one is obtained while the analysis of water

gives eight to one or sixteen to one, then either the structure of the

molecule is more complicated than was assumed, or the analyses must be

improved by more careful experiments. We can thus understand that the

atomic theory can serve as a controlling influence on the analysis of

chemical compounds.

In order to choose between the different possible ratios of atomic

weights, for example, the eight to one or the sixteen to one in the

case of oxygen and hydrogen, Dalton had to make certain arbitrary

assumptions. The first of these is that two elements of which only

one compound is known appear with but one atom each in a molecule.

Partly on account of this assumption and partly on account of the

incompleteness of his analyses, Dalton’s values of the ratios of the

atomic weights of the atoms and his pictures of the structure of

molecules differ from those of the present day, as is obvious from Fig.

A much firmer foundation for the choice made appears later in the

_Avogadro Law_; starting with the fact that different gases show

great similarity in their physical conduct—for instance, all expand by

an increase of ¹⁄₂₇₃ of their volume with an increase in temperature

from 0° C. to 1° C.—the Italian, Avogadro, in 1811, put forward the

hypothesis that equal volumes of all gases at the same temperature and

pressure contain equal numbers of molecules. A few examples suffice to

show the usefulness of this rule.

When one volume of the gas chlorine unites with one volume of hydrogen

there result two volumes of the gas, hydrogen chloride, at the same

temperature and pressure. According to Avogadro’s Law one molecule of

chlorine and one molecule of hydrogen unite to become two molecules of

hydrogen chloride, and since each of these two molecules must contain

at least one atom of hydrogen and one atom of chlorine, it follows

that one molecule of chlorine must contain two atoms of chlorine and

that one molecule of hydrogen must contain two atoms of hydrogen. From

this one can see that even in the elements the atoms are united into

molecules. It is now well established that most elements have diatomic

molecules, though some, including mercury and many other metals, are

monatomic. When oxygen and hydrogen unite to form water, one litre of

oxygen and two litres of hydrogen produce two litres of water vapour at

same temperature and pressure. Accordingly, one molecule of oxygen and

two molecules of hydrogen form two molecules of water. If the oxygen

molecule is diatomic like the hydrogen, then one molecule of water

contains one atom of oxygen and two atoms of hydrogen. Since the weight

ratio between the oxygen and hydrogen in water is eight to one, the

atomic weight of oxygen must be sixteen times that of hydrogen.

Through such considerations, supported by certain other rules, it has

gradually proved possible to obtain reliable figures for the ratios

between the atomic weights of all known elements and the atomic weight

of hydrogen. For convenience it was customary to assign the number 1 to

the latter and to call the ratio between the weight of the atom of a

given element and the weight of the hydrogen atom the atomic weight of

the element in question. Thus the atomic weight of oxygen is 16, that

of carbon 12, because one carbon atom weighs as much as 12 hydrogen

atoms. Nitrogen has the atomic weight 14, sulphur 32, copper 63.6, etc.

A summary of the chemical properties and chemical compounds was greatly

facilitated by the symbolic system initiated by the Swedish chemist,

Berzelius. In this system the initial of the Latin name of the element

(sometimes with one other letter from the Latin name) is made to

indicate the element itself, an atom of the element, and its atomic

weight with respect to hydrogen as unity, while a small subscript to

the initial designates the number of atoms to be used. For example, in

the chemical formula for sulphuric acid, H₂SO₄, the symbolic formula

means that this substance is a chemical compound of hydrogen, sulphur

and oxygen, that the acid molecule consists of two atoms of hydrogen,

one atom of sulphur and four atoms of oxygen, and that the weight

ratios between the three constituent parts is as 2×1 = 2 to 32 to 4×16

= 64, or as 1:16:32. To say that the chemical formula of zinc chloride

is ZnCl₂ means that the zinc chloride molecule consists of one atom of

zinc and two atoms of chlorine. Furthermore the changes which take

place in a chemical process may be indicated in a very simple way. Thus

the decomposition of water into hydrogen and oxygen may be represented

by the so-called chemical “equation” 2H₂O ⇾ 2H₂+O₂, where H₂ and O₂

signify the molecules of hydrogen and oxygen respectively. Conversely,

the combination of hydrogen and oxygen to form water will be given by

the equation 2H₂+O₂ ⇾ 2H₂O.

As a consequence of the development of the atomic theory the atoms of

the elements became, so to speak, the building stones of which the

elements and the chemical compounds are built. It can also be said that

the atoms are the smallest particles which the chemists reckon with in

the chemical processes, but it does not follow from the theory that

these building stones in themselves are indivisible. The theory leaves

the way open to the idea that they are composed of smaller parts. A

belief founded on such an idea was indeed enunciated by the Englishman,

Prout, a short time after Dalton had developed his atomic theory.

Prout assumed that the hydrogen atoms were the fundamental ones, and

that the atoms of the other elements consisted of a smaller or larger

number of the atoms of hydrogen. This might explain the fact that

within the limits of experimental error, many atomic weights seemed

to be integral multiples of that of hydrogen—16 for oxygen, 14 for

nitrogen, and 12 for carbon, etc. This led to the possibility that the

same might hold for all elements, and this hypothesis gave impetus to

very careful determinations of atomic weights. These, however, showed

that the assumption of the integral multiples could not be verified. It

therefore seemed as if Prout’s hypothesis would have to be given up. It

has, however, recently come into its own again, although the situation

is more complicated than Prout had imagined (see p. 97).

Dalton’s atomic theory gave no information about the atoms except that

the atoms of each element had a definite constant weight, and that

they could combine to form molecules in certain simple ratios. What

the forces are which unite them into such combinations, and why they

prefer certain unions to others, were very perplexing problems, which

could only be solved when chemical and physical research had collected

a great mass of information as a surer source of speculation.

From the knowledge of atomic weights it was easy to calculate what

weight ratios might be found to exist in chemical compounds, the

molecules of which consisted of simple atomic combinations. Thus many

compounds which were later produced in the laboratory were first

predicted theoretically, but only a small part of the total number of

possible compounds (corresponding to simple atomic combinations) could

actually be produced. Clearly it was one of the greatest problems of

chemistry to find the laws governing these cases.

It had early been known that the elements seemed to fall into two

groups, characterized by certain fundamental differences, the

metals and the metalloids. In addition, there were recognized two

very important groups of chemical compounds, _i.e._ acids and

bases, possessing the property of neutralizing each other to form a

third group of compounds, the so-called salts. The phenomenon called

electrolysis, in which an electric current separates a dissolved

salt or an acid into two parts which are carried respectively with

and against the direction of the current, indicates strongly that

the forces holding the atoms together in the molecule are of an

electrical nature, _i.e._ of the same nature as those forces

which bring together bodies of opposite electrical charges. One is

led to denote all metals as electropositive and all metalloids as

electronegative, which means that in a compound consisting of a

metal and a metalloid the metal appears with a positive charge and

the metalloid with a negative charge. The chemist Berzelius did a

great deal to develop electrical theories for chemical processes.

Great difficulties, however, were encountered, some proving for the

time being insurmountable. Such a difficulty, for example, is the

circumstance that two atoms of the same kind (like two hydrogen atoms)

can unite into a diatomic molecule, although one might expect them to

be similarly electrified and to repel rather than attract each other.

Another circumstance playing a very important part in determining the

chemical compounds which are possible, is the consideration of what is

called _valence_.

As mentioned above, one atom of oxygen combines with two atoms of

hydrogen to form water, while one atom of chlorine combines with but

one atom of hydrogen to form hydrogen chloride. The oxygen atom thus

seems to be “equivalent” to two hydrogen atoms or two chlorine atoms,

while one chlorine atom is “equivalent” to one hydrogen atom. The atoms

of hydrogen and chlorine are for this reason called monovalent, while

that of oxygen is called divalent. Again an acid is a chemical compound

containing hydrogen, in which the hydrogen can be replaced by a metal

to produce a metallic salt. Thus, when zinc is dissolved by sulphuric

acid to form hydrogen and the salt zinc sulphate, the hydrogen of the

acid is replaced by the zinc and the chemical change may be expressed

by the formula

Zn+H₂SO₄ ⇾ H₂+ZnSO₄

In this, one atom of zinc changes place with two atoms of hydrogen. The

zinc atom is therefore divalent. This is consistent with the fact that

one zinc atom will combine with one oxygen atom to form zinc oxide. To

take another example, if silver is dissolved in nitric acid, one atom

of silver is exchanged for one atom of hydrogen. Silver, therefore, is

monovalent, and we should expect that one atom of oxygen would unite

with two atoms of silver. Some elements are trivalent, as, for example,

nitrogen, which combines with hydrogen to form ammonia, NH₃; others,

again, are tetravalent, such as carbon, which unites with hydrogen

to form marsh gas CH₄, and with oxygen to form carbon dioxide CO₂. A

valence greater than seven or eight has not been found in any element.

[Illustration: FIG. 3.—Rough illustrations of the valences of

the elements.

A. Hydrogen chloride (HCl); B. Water (H₂O); C. Methane (CH₄); D.

Ethylene (C₂H₄).]

If we consider the matter rather roughly and more or less as Gassendi

did, we can explain the concept of valence by assuming that the atoms

possess hooks; thus hydrogen and chlorine are each furnished with one

hook, oxygen and zinc with two hooks, nitrogen with three hooks, etc.

When a hydrogen atom and a chlorine atom are hooked together, there

are no free hooks left, and consequently the compound is said to be

saturated. When one hydrogen atom is hooked into each of the hooks of

an oxygen or carbon atom the saturation is also complete (see Fig. 3,

A, B, C).

The matter is not so simple as this, however, since the same element

can often appear with different valences. Iron may be divalent,

trivalent or hexavalent in different compounds. In many cases,

however, where an examination of the weight ratios seems to show that

an element has changed its valence, this is not really true. It was

mentioned previously that carbon forms another compound with hydrogen

in addition to CH₄, namely, ethylene, containing half as much hydrogen

in proportion to the same amount of carbon. With the aid of Avogadro’s

Law, it is found that the ethylene molecule is not CH₂ but C₂H₄. Thus

we can say that the two carbon atoms in the molecule are held together

by two pairs of hooks, and consequently the compound can be expressed

by the formula

H-C-H

‖

H-C-H

where the dashes correspond to hooks (cf. Fig. 3, D). Such a formula is

called a _structural formula_.

Even if we are not allowed to think of the atoms in the molecules

as held together by hooks, it is well to have some sort of concrete

picture of molecular structure. It is possible to represent the

tetravalent carbon atom in the form of a tetrahedron, and to consider

the united atoms or atomic groups as placed at the four vertices. With

such a spatial representation we can get an idea about many chemical

questions which otherwise would be difficult to explain. We know, for

example, that two compound molecules having the same kind and number of

atoms and the same bonds (and hence the same structural formulæ), may

yet be different in that they are images of each other like a pair of

gloves. Substances whose molecules are symmetrical in this way can be

distinguished from each other by their different action on the passage

of light. This molecular chemistry of space, or stereo-chemistry as

it is called, has proved of great importance in explaining difficult

problems in organic chemistry, _i.e._ the chemistry of carbon.

Although there have never been many chemists who really have believed

the carbon atom to be a rigid tetrahedron, we must admit that in this

way it has been possible to get on the track of the secrets of atomic

structure.

In comparing the properties of the elements with their atomic weights,

there has been discovered a peculiar relation which remained for a

long time without explanation, but which later suggested a certain

connection between the inner structure of an atom and its chemical

properties. We refer to the _natural or periodic system of the

elements_ which was enunciated in 1869 by the Russian chemist,

Mendelejeff, and about the same time and independently by the German,

Lothar Meyer. This system will be understood most clearly by examining

the table on p. 23, where the elements with their respective atomic

weights and chemical symbols are arranged in numbered columns so that

the atomic weights increase upon reading the table from left to right

or from top to bottom. It will be seen that in each of the nine columns

there are collected elements with related properties, forming what may

be called chemical families. The table as here given is of a recent

date and differs from the old table of Mendelejeff, both in the greater

number of elements and in the particulars of the arrangement. With each

element there is associated a number which indicates its position in

the series with respect to increasing atomic weight. Thus hydrogen has

the number 1, helium 2, etc., up to uranium, the atom of which is the

heaviest of any known element, and to which the number 92 is given. In

each of the columns the elements fall naturally into two sub-groups,

and this division is indicated in the table by placing the chemical

symbols to the right or left in the column.

On close examination it becomes evident that the regularity in the

system is not entirely simple. First of all some cases will be found

where the atomic weight of one element is greater than that of the

following element. (The cases of argon and potassium on the one hand

and cobalt and nickel on the other are examples.) Such an interchange

is absolutely necessary if the elements which belong to the same

chemical family are to be placed in the same column. As a second

instance of irregularity, attention must be called to Column VIII. in

the table. While in the first score or so of elements it is always

found that two successive elements have different properties and

clearly belong to distinct chemical families, in the so-called iron

group (iron, cobalt and nickel) we meet with a case where successive

elements resemble each other in many respects (for instance, in their

magnetic properties). Since there are two more such “triads” in the

periodic system, however, we cannot properly call this an irregularity.

But in addition to these difficulties there is what we may even

call a kind of inelegance presented by the so-called “rare earths”

group. In this group there follow after lanthanum thirteen elements

whose properties are rather similar, so that it is very difficult to

separate them from each other in the mixtures in which they occur in

the minerals of nature. (In the table these elements are enclosed in a

frame.)

On the other hand, the apparent absence of an element in certain places

in the table (indicated by a dash) cannot by any means be looked upon

as irregular. In Mendelejeff’s first system there were many vacant

spaces. With the help of his table Mendelejeff was, to some extent,

able to predict the properties of the missing elements. An example of

this is the case of the element between gallium and arsenic. This is

called germanium, and was discovered to have precisely the properties

which had been predicted for it—a discovery which was one of the

greatest triumphs in favour of the reality of the periodic system. On

the whole, the elements discovered since the time of Mendelejeff have

found their natural positions in the table. This is seen, for example,

in the case of the so-called “inactive gases” of the atmosphere,

helium, argon, neon, xenon, krypton and niton, which have the common

property of being able to form no chemical combinations whatever.

Their valence is therefore zero, and in the table they are placed by

themselves in a separate column headed with zero.

To explain the mystery of the periodic system, it was necessary to

make clear not only the regularity of it, but also the apparent

irregularities which seemed to be arbitrary individual peculiarities of

certain elements or groups. In the periodic system, chemistry laid down

some rather searching tests for future theories of atomic structure.

THE PERIODIC OR NATURAL SYSTEM OF THE ELEMENTS

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+-------------------------+

| 0 | I. | II. | III. | IV. | V. | VI. | VII. | VIII. |

+==========+============+============+===============+============+==============+=============+===============+=========================+

| | H 1·008 | | | | | | | |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+-------------------------+

| He 4·00 | Li 6·94 | Be 9·1 | B 11·0 | C 12·0 | N 14·0 | O 16 | F 19·0 | |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+------------------------+

| Ne 20·2 | Na 23·0 |Mg 24·3 | Al 27·1 | Si 28·3 | P 31·0 | S 32·1 | Cl 35·5 | |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+------------------------+

| A 39·9 | K 39·1 | Ca 40·1 | Sc 44·1 | Ti 48·1 | V 51·0 | Cr 52·0 | Mn 54·9 | Fe 55·8 Co 59·0 |

| | | | | | | | | Ni 58.7 |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+------------------------+

| | Cu 63·6 | Zn 65·4 | Ga 69·9 | Ge 72·5 | As 75·0 | Se 79·2 | Br 79·9 | |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+------------------------+

| Kr 82·9 | Rb 85·4 |Sr 87·6 | Y 88·7 |Zr 90·6 | Nb 93·5 |Mo 96·0 | | Ru 101·7 Rh 102·9 |

| | | | | | | | | Pd 106·7 |

+----------+------------+------------+---------------+------------+--------------+-------------+---------------+------------------------+

| | Ag 107·9 | Cd 112·4 | In 114·8 | Sn 118·7 | Sb 120·2 | Te 127·5 | J 126·9 | |

+----------+------------+------------+--------------=====================================================================================

| 54 Xenon | 55 Caesium | 56 Barium | 57 Lanthanum ||58 Cerium 59 Praseodymium 60 Neodymium 61 -- 62 Samarium ||

| X 130·2 | Cs 132·8 | Ba 137·3 | La 139·0 || Ce 140·2 Pr 140·6 Nd 144·3 Sm 150·4 ||

| | | | || 63 Europium 64 Gadolinium 65 Terbium 66 Dysprosium ||

| | | | || Eu 152·0 Gd 157·3 Tb 159·2 Dy 162·5 ||

| | | | ||67 Holmium 68 Erbium 69 Thulium 70 Ytterbium 71 Cassiopeium ||

| | | | ||Ho 163·5 Er 167·7 Tm 168·5 Yb 173·0 Cp 175·0 ||

+----------+------------+------------+--------------=====================================================================================

| | | | | Hf 179 | Ta 181·5 | W 184·0 | | Os 190·9 Ir 192·1 |

| | | | | | | | | Pt 195·2 |

+----------+------------+------------+---------------+-----------+---------------+---------------+-------------+------------------------+

| | Au 197·2 | Hg 200·6 | Tl 204·0 | Pb 207·2 | Bi 209·0 | Po 210·0 | | |

+----------+------------+------------+---------------+-----------+---------------+---------------+-------------+------------------------+

| Ni 222·0 | | Ra 226·0 | Ac? | Th 232·1 | Pa? | U 238 | | |

+----------+------------+------------+---------------+-----------+---------------+---------------+-------------+------------------------+

The Molecular Theory of Physics.

From a consideration of the chemical properties of the elements we

shall now turn to an examination of the physical characteristics,

although in a certain sense chemistry itself is but one special phase

of physics.

If matter is really constructed of independently existing

particles—atoms and molecules—the interplay of the individual parts

must determine not only the chemical activities, but also the other

properties of matter. Since most of these properties are different for

different substances, or in other words are “molecular properties,” it

is reasonable to suppose that in many cases explanations can be more

readily given by considering the molecules as the fundamental parts.

It is natural that the first attempts to develop a molecular theory

concerned gases, for their physical properties are much simpler than

those of liquids or solids. This simplicity is indeed easily understood

on the molecular theory. When a liquid by evaporation is transformed

into a gas, the same weight of the element has a volume several hundred

times greater than before. The molecules, packed together tightly in

the liquid, in the gas are separated from each other and can move

freely without influencing each other appreciably. When two of them

come very close to each other, mutually repulsive forces will arise to

prevent collision. Since it must be assumed that in such a “collision”

the individual molecules do not change, they can then to a certain

extent be considered as elastic bodies, spheres for instance.

From considerations of this nature the kinetic theory of gases

developed. According to this a mass of gas consists of an immense

number of very small molecules. Each molecule travels with great

velocity in a straight line until it meets an obstruction, such as

another molecule or the wall of the containing vessel; after such an

encounter the molecule travels in a second direction until it collides

again, and so on. The pressure of the gas on the wall of the container

is the result of the very many collisions which each little piece

of wall receives in a short interval of time. The magnitude of the

pressure depends upon the number, mass and velocity of the molecules.

The velocity will be different for the individual molecules in a

gas, even if all the molecules are of the same kind, but at a given

temperature an average velocity can be determined and used. If the

temperature is increased, this average molecular velocity will be

increased, and if at the same time the volume is kept constant, the

pressure of the gas on the walls will be increased. If the temperature

and the average velocity remain constant while the volume is halved,

there will be twice as many molecules per cubic centimetre as before.

Therefore, on each square centimetre of the containing wall there will

be twice as many collisions, and consequently the pressure will be

doubled. Boyle’s Law, that the pressure of a gas at a given temperature

is inversely proportional to its volume, is thus an immediate result of

the molecular theory.

The molecular theory also throws new light upon the correspondence

between heat and mechanical work and upon the law of the conservation

of energy, which about the middle of the nineteenth century was

enunciated by the Englishman, Joule, the Germans, Mayer and Helmholtz,

and the Dane, Colding. A brief discussion of heat and energy will be

given here, since some conception of these phenomena is necessary in

understanding what follows.

To lift a stone of 5 pounds through a distance of 10 feet demands an

expenditure of work amounting to 5 × 10 = 50 foot-pounds; but the stone

is now enabled to perform an equally large amount of work in falling

back these 10 feet. The stone, by its height above the earth and by

the attraction of the earth, now has in its elevated position what is

called _“potential” energy_ to the amount of 50 foot-pounds. If

the stone as it falls lifts another weight by some such device as a

block and tackle, the potential energy lost by the falling stone will

be transferred to the lifted one. If the apparatus is frictionless, the

falling stone can lift 5 pounds 10 feet or 10 pounds 5 feet, etc., so

that all the 50 foot-pounds of potential energy will be stored in the

second stone. If instead of being used to lift the second stone, the

original stone is allowed to fall freely or to roll down an inclined

plane without friction, the velocity will increase as the stone falls,

and, as the potential energy is lost, another form of energy, known

as energy of motion or _kinetic energy_, is gained. Conversely,

a body when it loses its velocity can do work, such as stretching a

spring or setting another body in motion. Let us suppose that the stone

is fastened to a cord and is swinging like a pendulum in a vacuum where

there is no resistance to its motion. The pendulum will alternately

sink and rise again to the same height. As the pendulum sinks, the

potential energy will be changed into kinetic energy, but as it rises

again the kinetic will be exchanged for potential. Thus there is no

loss of energy, but merely a continuous exchange between the two forms.

If a moving body meets resistance, or if its free fall is halted by

a fixed body, it might seem as if, at last, the energy were lost.

This, however, is not the case, for another transformation occurs.

Every one knows that heat is developed by friction, and that heat

can produce work, as in a steam-engine. Careful investigations have

shown that a given amount of mechanical work will always produce a

certain definite amount of heat, that is, 400 foot-pounds of work,

if converted into heat, will always produce 1 B.T.U. of heat, which

is the amount necessary to raise the temperature of 1 pound of water

1° F. Conversely, when heat is converted into work, 1 B.T.U. of heat

“vanishes” every time 400 foot-pounds of work are produced. Heat then

is just a special form of energy, and the development of heat by

friction or collision is merely a transformation of energy from one

form to another.

With the assistance of the molecular theory it becomes possible to

interpret as purely mechanical the transformation of mechanical work

into _heat energy_. Let us suppose that a falling body strikes a

piston at the top of a gas-filled cylinder, closed at the bottom. If

the piston is driven down, the gas will be compressed and therefore

heated, for the speed of the molecules will be increased by collisions

with the piston in its downward motion. In this example the kinetic

energy given to the piston by the exterior falling body is used to

increase the kinetic energy of the molecules of the gas. When the

molecules contain more than one atom, attention must also be given to

the rotations of the atoms in a molecule about each other. A part of

any added kinetic energy in the gas will be used to increase the energy

of the atomic rotations.

The next step is to assume that, in solids and liquids, heat is

purely a molecular motion. Here, too, the development of heat after

collision with a moving body should be treated as a transformation

of the kinetic energy of an individual, visible body into an inner

kinetic energy, divided among the innumerable invisible molecules of

the heated solid or liquid. In considering the internal conduct of

gases it is unnecessary (at least in the main) to consider any inner

forces except the repulsions in the collisions of the molecules. In

solids and liquids, however, the attractions of the tightly packed

molecules for each other must not be neglected. Indeed the situation

is too complicated to be explained by any simple molecular theory. Not

all energy transformations can be considered as purely mechanical. For

instance, heat can be produced in a body by rays from the sun or from a

hot fire, and, conversely, a hot body can lose its heat by radiation.

Here, also, we are concerned with transformations of energy; therefore

the law for the conservation of energy still holds, _i.e._

the total amount of energy can neither be increased nor decreased

by transformations from one form to another. For the production of

1 B.T.U. of heat a definite amount of _radiation energy_ is

required; conversely, the same amount of radiation energy is produced

when 1 B.T.U. of heat is transformed into radiation. This change

cannot, however, be explained as the result of mechanical interplay

between bodies in motion.

The mechanical theory of heat is very useful when we restrict ourselves

to the transfer of heat from one body to another, which is in contact

with it. When applied to gases the theory leads directly to Avogadro’s

Law. If two masses of gas have the same temperature, _i.e._,

if no exchange of heat between them takes place even if they are

in contact with each other, then the average value of the kinetic

energy of the molecules must be the same in both gases. If one gas is

hydrogen and the other oxygen, the lighter hydrogen molecules must have

a greater velocity than the heavier oxygen molecules; otherwise they

cannot have the same kinetic energy (the kinetic energy of a body is

one-half the product of the mass and the square of the velocity). Since

the pressure of a gas depends upon the kinetic energy of the molecules

and upon their number per cubic centimetre, at the same temperature

and pressure equal volumes must contain equal numbers of oxygen and of

hydrogen molecules. As Joule showed in 1851, from the mass of a gas

per cubic centimetre and from its pressure per square centimetre, the

average velocity of the molecules can be calculated. For hydrogen at 0°

C. and atmospheric pressure the average velocity is about 5500 feet per

second; for oxygen under the same conditions it is something over 1300

feet per second.

All these results of the atomic and molecular theory, however, gave

no information about the absolute weight of the individual atoms and

molecules, nor about their magnitude nor the number of molecules in a

cubic centimetre at a given temperature and pressure. As long as such

questions were unsolved there was a suggestion of unreality in the

theory. The suspicion was easily aroused that the theory was merely

a convenient scheme for picturing a series of observations, and that

atoms and molecules were merely creations of the imagination. The

theory would seem more plausible if its supporters could say how large

and how heavy the atoms and molecules were. The molecular theory of

gases showed how to solve these problems which chemistry had been

powerless to solve.

Let us assume that the temperature of a mass of gas is 100° C. at a

certain altitude, and 0° C. one metre lower, _i.e._, the molecules

have different average velocities in the two places. The difference

between the velocities will gradually decrease and disappear on account

of molecular collisions. We might expect this “levelling out” process

or equilibration to proceed very rapidly because of the great velocity

of the molecules, but we must consider the fact that the molecules are

not entirely free in their movements. In reality they will travel but

very short distances before meeting other molecules, and consequently

their directions of motion will change. It is easy to understand that

the difference between the velocities of the molecules of the gas will

not disappear so quickly when the molecules move in zigzag lines with

very short straight stretches. The greater velocity in one part of the

gas will then influence the velocity in the other part only through

many intermediate steps. Gases are therefore poor conductors of heat.

When the molecular velocity of a gas and its conductivity of heat are

known, the average length of the small straight pieces of the zigzag

lines can be calculated—in other words, the length of the _mean free

path_. This length is very short; for oxygen at standard temperature

and pressure it is about one ten-thousandth of a millimetre, or 0·1 μ,

where μ is 0·001 millimetre or one _micron_.

In addition to the velocity of the molecules, the length of the mean

free path depends upon the average distance between the centres of two

neighbouring molecules (in other words, upon the number of molecules

per cubic centimetre) and upon their size. There is difficulty in

defining the size of molecules because, as a rule, each contains

at least two atoms; but it is helpful to consider the molecules,

temporarily, as elastic spheres. Even with this assumption we cannot

yet determine their dimensions from the mean free path, since there

are two unknowns, the dimensions of the molecules and their number

per cubic centimetre. Upon these two quantities depends, however,

also the volume which will contain this number of molecules, if they

are packed closely together. If we assume that we meet such a packing

when the substance is condensed in liquid form, this volume can be

calculated from a knowledge of the ratio between the volume in liquid

form and the volume of the same mass in gaseous form (at 0° C. and

atmospheric pressure). Then from this result and the length of the mean

free path the two unknowns can be determined. Although the assumptions

are imperfect, they serve to give an idea about the dimensions of

the molecules; the results found in this way are of the same order

of magnitude as those derived later by more perfect methods of an

electrical nature.

The radius of a molecule, considered as a sphere, is of the order of

magnitude 0·1 μμ, where μμ means 10⁻⁶ millimetre or 0·001 micron. Even

if a molecule is by no means a rigid sphere, the value given shows that

the molecule is almost unbelievably small, or, in other words, that it

can produce appreciable attraction and repulsion in only a very small

region in space.

The number of molecules in a cubic centimetre of gas at 0° C. and

atmospheric pressure has been calculated with fair accuracy as

approximately 27 × 10¹⁸. From this number and from the weight of a

cubic centimetre of a given gas the weight of one molecule can be

found. One hydrogen molecule weighs about 1·65 × 10⁻²⁴ grams, and

one gram of hydrogen contains about 6 × 10²³ atoms and 3 × 10²³

molecules. The weight of the atoms of the other elements can be found

by multiplying the weight of the hydrogen atom by the relative atomic

weight of the element in question—16 for oxygen, 14 for nitrogen, etc.

If the pressure on the gas is reduced as much as possible (to about one

ten-millionth of an atmosphere) there will still be 3 × 10¹² molecules

in a cubic centimetre, and the average distance between molecules will

be about one micron. The mean free path between two collisions will be

considerable, about two metres, for instance, in the case of hydrogen.

The values found for the number, weight and dimensions of molecules

are either so very large or so extremely small that many people,

instead of having more faith in the atomic and molecular theory,

perhaps may be more than ever inclined to suppose the atoms and

molecules to be mere creations of the imagination. In fact, it is only

two or three decades ago that some physicists and chemists—led by the

celebrated German scientist, Wilhelm Ostwald—denied the existence of

atoms and molecules, and even went so far as to try to remove the

atomic theory from science. When these sceptics, in defence of their

views, said that the atoms and molecules were, and for ever would be,

completely inaccessible to observation, it had to be admitted at that

time that they were seemingly sure of their argument, in this one

objection at any rate.

A series of remarkable discoveries at the close of the nineteenth

century so increased our knowledge of the atoms and improved the

methods of studying them that all doubts about their existence had to

be silenced. However incredible it may sound, we are now in a position

to examine many of the activities of a single atom, and even to

count atoms, one by one, and to photograph the path of an individual

atom. All these discoveries depend upon the behaviour of atoms as

electrically charged, moving under the influence of electrical forces.

This subject will be developed in another section after a discussion of

some phenomena of light, an understanding of which is necessary for the

appreciation of the theory of atomic structure proposed by Niels Bohr.

In the molecular theory of gases, where we have to do with neutral

molecules, much progress has in the last years been made by the Dane,

Martin Knudsen, in his experiments at a very low pressure, when the

molecules can travel relatively far without colliding with other

molecules. While his researches give information on many interesting

and important details, his work gives at the same time evidence of a

very direct nature concerning the existence of atoms and molecules.