THE FOUNDATIONS
OF SCIENCE

BY WILLIAM CECIL DAMPIER

(WHETHAM,, M.A.,"F.R.S.

FELLOW AND TUTOR OF TRINITY COLLEGE, CAMBRIDGE

o

LONDON: T. C. & E. C. JACK
67 LONG ACRE, W.C., AND EDINBURGH
NEW YORK: DODGE PUBLISHING CO.

- 5

CONTENTS

CHAP.

PAGE

I. THE CLASSIFICATION OF KNOWLEDGE . . 7

H. PHYSICAL SCIENCE 16

HI. BIOLOGICAL SCIENCE 51

IV. PSYCHOLOGICAL SCIENCE . 71

THE
FOUNDATIONS OF SCIENCE

CHAPTER I

THE CLASSIFICATION OF KNOWLEDGE

THE Latin word scientia, from scire, to learn or knowL
signifies, broadly, learning or knowledge. But, in
general usage, the modern term science has come to
mean an ordered knowledge of the phenomena or
appearances of Nature, and of the connection or
relations which have been discovered between them.
Custom and_, convenience have divided science
into three main sections : physical science, bio-
logical science, and psychological science. Al-
though the Greek word <£wts (phusis) is perhaps
equivalent to the Latin word natura, the name
physical is confined, by general agreement, to that
part of science which deals wijhjnatter and energy^ (j
without reference to life. Biological science, on the s
other hand, treats of living things, and of those
special problems of matter and energy to which their , -
life gives rise. Psychological science is concerned ''.

8 THE FOUNDATIONS OF SCIENCE

with the phenomena of mind and the influences
affecting it — primarily, of course, with the mind of
man, but not exclusively so, since comparative
psychology is investigating also the minds of animals.

The relations between the sciences have been the
subject of discussion since philosophy, as the science
of the sciences, began. While the term science was
taken to include the whole of knowledge, the problem
of classification was more complicated, and perhaps
more important, than it is if we accept the modern
more limited view. The problem of the classifica-
tion of knowledge is one of much difficulty ; and
any scheme, such as that which is now suggested,
must not be regarded as final. The branches of
knowledge are not only growing within themselves,
but their relations to each other are continually
changing, so that the scheme of arrangement suitable
for one age may not be appropriate for another.

As regards science, the three main divisions
we have adopted seem to be related as follows.
Physical science, the knowledge of the phenomena
of matter and energy, on one side touches biology,
the science of living things. Biology, in its turn,
touches psychology, the science of mind, since mind,
as we can investigate it by scientific methods, is
always contained in living organisms, or, at all
events, is always investigated in relation to such
organisms.

So far all seems simple ; and we are inclined to

CLASSIFICATION OF KNOWLEDGE 9

represent our model of science as a sequence of sub-
jects, with physical science at one end, biology in
the middle, and psychology at the other end — a
sequence like that of the colours of the rainbow,
where red represents physics, green biology, and blue
psychology, physics appearing out of the invisible
as a faint, purplish glow, and psychology fading away
into a haze of violet, not very different from the
purple basis of physics.

Purple Red. Yellow Green Blue-Green Blue

FIG. 1.

And, indeed, we are led back by psychology to
approach logic, physics, and the other sciences we
have traced, from a new standpoint. Psychology
gives us insight into the theory of knowledge, and
leads us critically to examine how it is that we know
anything, either by logic or by the senses, or by that
fertile union of the two which breeds science. Thus,
by the road of psychology, we return once more to our
starting-point, ready to study fundamental, logical,
mechanical, and physical ideas from a critical point
of view.

We shall do well, then, to bend our spectrum round
so that the violet theory of knowledge, which lies
beyond the blue of psychology, shall be brought near
to the purple of logic, where fundamental scientific

10 THE FOUNDATIONS OF SCIENCE

ideas take their rise and pass into the red of definite
physics.

We may picture these relations to our eye in a
manner, originally suggested by Newton, and now
used to illustrate Maxwell's theory of colour vision.
On that theory, as we shall see later, there are three
primary colour sensations : red, green, and blue.
These colours are placed at the corners of a triangle,

FIG. 2.

and points within the triangle are tinged with com-
plex colours made up of the three primaries in
proportion to the nearness of the points to the three
corners.

Now, as before, let us take red to represent physical
science, green biology, and blue psychology. The
points of the triangle represent the purest sciences :
red represents physics in the strict sense, green the
natural history of plants and animals, and blue pure

CLASSIFICATION OF KNOWLEDGE 11

psychology. Moreover, a number of complex sciences
involve combinations of physics, biology, and psycho-
logy in different proportions, and are represented
by points within the triangle, where the colours are
mixtures of the primaries.

Let us begin a more detailed survey somewhere
in the purple region, at the beginnings of physical
science. Here we find the so-called laws of thought,
logic both verbal and symbolic, the latter contain-
ing the fundamental principles of mathematics. A
little further on are the developments of pure mathe-
matics leading to, and elsewhere lying side by side
with, the methods of applied mathematics ready for
use in physical problems. Then comes mechanics,
experimental in its principles, but largely formed in
detail by mathematical deduction from those prin-
ciples. The next region of our figure, the red corner,
contains, more or less side by side, the various
branches of physics proper : heat, light, sound,
electricity and magnetism. Here, too, we may
place chemistry, which in its essence is probably
only a branch of molecular physics, though it may
extend further along the length of the side of the
triangle, and run more into the biological region
than do some other subjects comprised in physics.

Next we pass into the yellow region — the physics
and chemistry of vital processes, one aspect of
physiology, animal and vegetable. With the other
aspect, that concerned first with the cell and then

12 THE FOUNDATIONS OF SCIENCE

with the living organisms as a whole, where green
first becomes visible, we come on a new factor, the
tremendous factor of life. Comparative physiology
introduces us to different types of animals and plants,
which are studied from another point of view in the
almost pure green of the natural history of the
zoologist and field botanist.

In contact with all the biological section devoted
to animals, and perhaps just touching that concerned
with plants, blue becomes visible in our diagram,
and we find once more a new phenomenon, which
transcends mere life as life transcends lifeless matter
— the phenomenon of mind and consciousness. Here
we enter psychology, that study of mind which is
of immemorial antiquity on the one side of intro-
spection, and is of the newest group of sciences on
the other, as a matter of experimental observation.
It touches physiology most closely of the biological
sciences, so that physiology, which comes in contact
with chemistry and physics, must be pictured in our
diagram as a region of space running across the whole
of that portion of the triangle given up to biology.

From psychology we pass to the theory of know-
ledge, and thus we complete the circuit of our figure.
We find ourselves once more at our starting-point of
logical principles, which, on one side, have affinities
with psychology, since they are apprehended by the
direct action of our minds, and on the other are the
basis of physics and all other sciences.

CLASSIFICATION OF KNOWLEDGE 13

The parts of the triangle lying nearer the centre
correspond with complex sciences, which need the
conceptions of all three primaries. Astronomy lies
in the purple region, where the chief elements are
mathematics and physics ; geology, in the yellow,
depends chiefly on physics and biology. Historical
and political science, a greenish-blue, is built up
chiefly on psychology and biology, but it is affected
by the physical structure of man, by the physical
conformation of the earth and heavens, and by
those mechanical laws in conformity with which
mankind always has had to live. Thus physical
science is also involved.

As we approach the white central point we come to
those great subjects which need a proportionate
knowledge of all sciences for their treatment, the
subjects of metaphysics, the study of the nature of
reality ; philosophy, the science of the co-ordination
of knowledge ; and theology, in its widest sense the
study of the meaning and purpose of the universe,
both external and internal.

But how are we to picture to ourselves the use of
this coloured triangle, this scheme of science, in the
examination of the knowable both within and
without ourselves ?

Let us suppose that we are placed in a room, the
only window of which is a triangle of glass coloured
in accordance with our diagram.

14 THE FOUNDATIONS OF SCIENCE

We examine objects in the room by light which
comes through the window, and we look at the land-
scape without through the same coloured glass.
Before the ages of accurate scientific experiment, no
precautions were taken to isolate different coloured
lights, or to look steadily for a time through one part
of the window. But gradually it was found that the
confusion of colour and light which had disturbed
man's vision could be obviated. By covering all
the window with a movable shutter in which a
single small hole was cut, and placing the hole at the
point corresponding to any one science, a view both
of the room and of the world without was obtained
by the light of that one science only — things were
seen steadily in one aspect.

Moreover, men slowly invented methods of exami-
nation of greater and greater power. These methods
we may illustrate in our analogy by the idea of
telescopes of gradually increasing magnification, with
which we may look through the hole in the shutter
at the outside world, and slowly improving lenses
and microscopes for the investigation of objects
within the room.

" To see life steadily and see it whole," we must
use successively light from all available sciences.
If we use but one colour we get a mental picture of
creation tinted by that light alone. If we use the
white light of the central metaphysical region only,
we fail to detect the complex nature of that white

CLASSIFICATION OF KNOWLEDGE 15

light itself, and fail also to discover a host of new
relations which are brought out successively as our
different coloured lights are employed one after
another.

Now, all this is only an allegory. It is not meant
that there is any real connection between knowledge
and a triangle, or that physicists in reality see things
red and psychologists blue. Yet analogies have
their uses. They prove nothing ; but they may
give clarity of vision to a mind which, without them,
would be confused ; they may even serve to suggest
new relations which perhaps, when suggested, can
be demonstrated and confirmed by more logical and
rigorous methods. Let our allegory be recognised
as such, and, however little it may help, it can da
no harm.

CHAPTER II

PHYSICAL SCIENCE

THE origin of mechanical science is to be sought in
the efforts to understand the tools and instruments
invented by man to supply his bodily needs, and the
phenomena of motion as seen in Nature.

The lever, the inclined plane, and the wedge are
pictured in the carved stone records of Egypt and
Assyria, and their practical use was known before
the dawn of history. But the first who attempted
to obtain a scientific explanation of the principles
which underlie their application was the Greek-
Sicilian philosopher, Archimedes of Syracuse, who
lived from the year 287 to the year 212 before
Christ.

Archimedes was educated at Alexandria, where
Euclid had taught fifty years earlier. And he threw
his investigations into the form which Euclid had used
with so much success in geometry.

He begins by laying down axioms, or what are
considered as self-evident propositions, and deduces
from them, in the Euclidean manner, the law of the
lever — a law that may be stated as' follows. If a

16

PHYSICAL SCIENCE 17

light bar be balanced over an edge, the weight at
the end of the shorter arm must be greater than
that at the end of the longer arm in the same pro-
portion as the greater length is to the shorter, or the
product of the weight and its distance from the point
of support is the same on each side.

But, if his proof of this proposition be examined
it will be found that he assumes a property, that of
the centre of gravity, which is, in reality, equivalent
to the principle of the lever. Moreover, some of
his axioms can only be justified by experiment. We
may, in fact, just as well investigate the law of the
lever directly by the experimental method, and use it,
when established, as the basis of further deductions.

Nevertheless, Archimedes' attempt to explain the
lever in terms of phenomena which he regarded as
better known, was an immense step in advance, and
is, in truth, the type of all scientific explanations,
which can consist only in expressing the less known
in terms of the better known. To the mind of
Archimedes and his contemporaries, his axioms
appeared better known than his conclusion, and his
proof was therefore to them a true explanation.

To us, steeped in the experimental method, it
seems better to base the subject on the law of the
lever, a law which lends itself readily to experimental
verification, than on the principle of the centre of
gravity, which, in its general form, cannot be demon-
strated so easily by experiment, though it may

B

18 THE FOUNDATIONS OF SCIENCE

appear more " self-evident " to minds unused to
experimental investigation. We see clearly from
this first illustration that a physical " explanation "
is merely a restatement of our result in terms of
others more familiar to the particular minds which
are dealing with the problem at the time.

It is to Archimedes, also, that we owe the first
clear ideas about the phenomena of floating bodies.
Before his work on weights in relation to volumes,
the conceptions which we call density and specific
gravity were unknown. He showed that when a
body floats in a liquid, partially or wholly immersed,
its own total weight must be equal to the weight
of that part of the liquid which it displaces.

Very little advance in mechanics was made from
the time of Archimedes till, nearly two thousand
years later, first that universal genius Leonardo da
Vinci (1452-1519) and then Simon Stevin of Bruges
(1548-1620) again took up the problem of the lever,
and dealt also with the inclined plane and the general
conditions of equilibrium of three forces acting in a
plane. Here again the form of the proof is that of
Euclidean geometry, the chief axiom being the in-
stinctive recognition that an endless chain, lying
along an inclined plane, hanging down from its top
and passing beneath it and so round, will not con-
tinue in perpetual motion. This is the real advance,
the increased insight into what is or is not experi-
mentally possible.

PHYSICAL SCIENCE 19

Thus Leonardo and Stevin had placed the science
of statics, or the knowledge of the laws of forces in
equilibrium, on a sound basis. But no correspond-
ing advance had been made in the subject of dynamics,
which deals with the phenomena and laws of motion ;
though here, too, some signs of progress appear in
the notebooks of Leonardo. The ideas current were
still held on the authority of the Greek philosopher
Aristotle, and it was believed that bodies fell to the
earth because each body sought its natural place
owing to an intrinsic property of heaviness or light-
ness, the " place " of heavy bodies being below and
that of light bodies being above. From these ideas
it followed that, the heavier a body, the faster it
must fall.

Galileo Galilei (1564-1642), with the instinctive
genius of the great man of science, saw that the whole
point of view must be changed. Instead of inquir-
ing with Greek philosophers and mediaeval school-
men why things fell, he set himself, in true modern
fashion, to examine experimentally how they fell.

For two thousand years men had tamely accepted
Aristotle's teaching, that heavy bodies fell faster
than light ones, when five minutes' experiment by
dropping lumps of stone and iron from a cliff or high
building would have sufficed to prove it erroneous.
Galileo showed his at first incredulous contemporaries
that heavy and light bodies, let fall simultaneously
from the top of the Leaning Tower of Pisa, reached

20 THE FOUNDATIONS OF SCIENCE

the ground together, so long 'as the lighter body was
not sufficiently light to be retarded seriously by
the resistance of the air. Aristotle was shown to
be wrong, and a new era had begun.

A falling body moves faster and faster as it travels
through space, and Galileo next set himself to examine
how this increase of velocity occurs. His first sup-
position was that the speed was proportional to the
distance travelled, but he soon convinced himself
that this idea was wrong. Then he tried the hypo-
thesis that the speed increased with the time of fall,
and cast about for a means of putting the relations
to the test of experiment.

Bodies falling freely moved too fast to be dealt
with by the primitive apparatus then available,
and, to get a manageable velocity, Galileo assumed
that a ball rolling down an inclined plane would
follow the same kind of rule as a ball falling freely,
though it would fall with less speed.

On the hypothesis that the speed of fall increased
with the time, he calculated the distance which the
ball should roll, and showed that it should be pro-
portional to the square of the time ; that is, if the
ball roll 1 foot in 1 second it will roll 4 feet in 2
seconds and 9 feet in 3 seconds. This result he
proceeded to test.

His clocks were not sufficiently accurate or con-
venient, and so, to measure times, he took a large
vessel with a small hole in the bottom which he closed

PHYSICAL SCIENCE 21

with his finger. The vessel was filled with water,
and the finger removed and replaced at the beginning
and the end of the time-interval to be measured. The
water flowing out was collected and weighed.

In this way, Galileo verified by experiment the
result of his assumption, and, in this case, no other
hypothesis would lead to the same result. Hence
the hypothesis that the speed is proportional to the
time of fall is confirmed in one instance. Further ex-
periments gave similar results, and general belief in
the hypothesis as true was established.

It remained to deal with the actual speed of a
body falling freely. This Galileo examined as follows.
He showed that a body sliding down one plane would
run up another of the same total height whatever
be the length of the slope of the planes. Hence it
followed that it was the height alone that mattered,
and that a body falling freely would acquire the
same velocity as a body sliding down an inclined
plane, provided that the total height descended were
the same in each case.

But an even more important result followed from
the investigation with the two planes. A body
sliding down one plane acquired velocity enough
to carry it up the other to an equal vertical height.
However long were the second plane, and however
gently inclined, if friction were negligible, the same re-
sult was obtained. It was the vertical rise alone that
destroyed the velocity. Hence it followed that, in

22 THE FOUNDATIONS OF SCIENCE

the extreme case, where the second plane was sup-
posed to be made horizontal, no destruction of velo-
city would occur, and, friction apart, the body would
move straight forward for ever with uniform velocity.

To appreciate the revolution in science which this
conclusion produced, it is necessary to describe shortly
the beliefs it displaced. In ordinary life, we are ac-
customed to see moving bodies brought to rest by
impact with the earth, or by friction, or by other
opposing agency ; and this experience led to the idea
that motion always required the continuous exertion
of some force to maintain it unimpaired. Hence
followed in astronomy the invention of vortices to
uphold the planetary motions, and in terrestrial
dynamics similar confusing conceptions had been
introduced.

At one blow Galileo destroyed all such theories,
and cleared the ground for new building.

But before we deal with those who, in this work,
entered into his labours, it is worth pausing to con-
sider the improvement in method as well as the
actual advance in knowledge effected by Galileo. To
study Galileo's researches after those of his pre-
decessors is like coming out into the light after
groping about in a dark room. In mechanical
science, he is the first of the moderns, and his methods
are a model of physical investigation for all time.
He uses experiment in its right place, and scientific

PHYSICAL SCIENCE 23

imagination also, to frame hypotheses to guide his
experiments, and to be checked, verified, or disproved
by his experiments.

Contemporary with Galileo, Lord Chancellor Bacon
(1561-1626) was philosophising in England over scien-
tific method. In a healthy reaction from the errors
of scholasticism, Bacon laid exclusive stress on ex-
periment. But he went too far, in teaching that by
experimenting in all directions, scientific laws will
appear without need of deductive reasoning. Galileo,
who did not philosophise, but had the true scientific
instinct for what was practicable and helpful, went
straight to the right method.

In the question of the fall of heavy and light
bodies, he saw at once that a crucial experiment
was possible. He dropped two bodies from the Lean-
ing Tower, and the question was settled. Here we
have the simplest kind of investigation. One thing
is believed on the word of authority. No one has
thought of testing it. Galileo, seeing reason to doubt,
is not content with the opinion of Aristotle as to what
ought to occur. He goes and tries what does occur.

In his work on the law of velocity of fall, we have
a more complicated problem. It was untouched
before ; any result was possible. If he had worked
by the Baconian method, Galileo would have made
endless experiments on falling bodies, till relations
forced themselves on his notice. He did nothing of
the kind. As a beginning, he sat and thought. He

24 THE FOUNDATIONS OF SCIENCE

then made a guess at a possible law : — that the speed
of fall was proportional to the distance fallen through.
He reasoned out the consequences of this hypothesis,
and found that they were self-contradictory. His
guess was clearly wrong.

He tried again. He tried the supposition that the
final speed varied as the time of fall. Here the con-
sequences deduced were consistent ; the hypothesis
was worth testing by experiment.

But the hypothesis itself was not fitted for direct
experiment — at all events, by means of Galileo's
apparatus. Therefore he took one of its conse-
quences, which he had obtained by deductive mathe-
matical reasoning — the consequence that the distance
fallen should be proportional to the square of the
time.

He had now formulated his experimental problem,
and had to face the practical mechanical difficulties.
First, he improved the conditions of the process from
the experimental point of view, reducing the velocity
by making the falling body run down an inclined
plane instead of fall freely through space. Secondly,
having no apparatus delicate enough to measure the
small intervals of time involved, he invented a new
form of water-clock for this special purpose. Thus,
the conditions being made favourable, and his appa-
ratus being made adequate, he measured the times
taken by the falling body to run over marked
distances on the inclined plane. Small divergences

PHYSICAL SCIENCE 25

in individual experiments appeared : but, on the
average, his results showed that the distances tra-
versed from rest were proportional to the squares
of the times of fall.

He had now verified one of the consequences of his
hypothesis. In this case it was enough, because, if
that consequence be assumed, the original hypothesis
may be shown to follow necessarily. Thus the original
hypothesis was verified also, and it was certain that,
as he supposed, the velocity of fall of his ball in-
creased with the time. Repetition of the experi-
ments has but served to confirm this result, and
gradually, by this process of induction, complete
conviction has been forced on us that it is a general
law of nature that the speed of falling bodies in-
creases in proportion to the time of fall.

In one respect all physicists are not so lucky as
Galileo. It cannot always be shown that the original
hypothesis is the only one consistent with the deduc-
tion from it which is chosen for submission to an
experimental test. If not, all verifiable consequences
of the original hypothesis must be deduced, and as
many of them as possible examined experimentally.
With each concordance the evidence in favour of the
original hypothesis is increased, till eventually a very
high degree of probability may be obtained.

Galileo's method, extended to cover this further
case, is that by which advance has been made in
physical science from his day to ours.

26 THE FOUNDATIONS OF SCIENCE

And now, let us return to Galileo's great discovery
that, left to itself, a body moves on in a straight
line with uniform velocity. The need for vortices
to maintain the motion of the planets was thus done
away, and it became clear that what cried for ex-
planation was not the continued motion, but the
continual deviation from the straight course involved
in circular or elliptical orbits. Some force must be
acting, drawing the planets towards the centre.

Isaac Newton (1642-1727), a young graduate of
Trinity College, Cambridge, had returned for a time
to his home in Lincolnshire, driven out of Cambridge
by the Great Plague of 1665. In this retirement he
set himself to apply Galileo's dynamical principles
to known astronomical events. At that time the
Ptolemaic system of astronomy, which made the
earth the centre of all things, had recently been
given up by all competent philosophers in favour of
Copernicus' (1473-1543) revival of the theory that the
sun is the centre of our system. Tycho Brahe (1546-
160i) had collected an immense number of observa-
tions on the motions of the planets, and, by a life-
long study of his data, John Kepler (1571-1630) had
formulated laws which described the motions: laws
such as the statement that the planets describe
ellipses with the sun in one focus.

Taking the simplest case, the revolution of the
moon in a nearly circular orbit round the earth, it
occurred to Newton that, as the moon moves in a

PHYSICAL SCIENCE 27

circle instead of in Galileo's straight course, perhaps
the familiar force of gravity, by which an apple falls
to the ground, might be the cause also of the moon's
continual fall towards the earth.

It was probable that any force directed towards a
central point, and operative throughout surrounding
space, would vary inversely as the square of the dis-
tance. And, on this hypothesis, Newton calculated
what the effect of gravity would be at the distance
of the moon. Misled at first by an inaccurate value
of this distance, he found that the actual fall of the
moon towards the earth was less than that calculated.
But, six years later, a redetermination of the size of
the earth gave a different value for the moon's
distance, and enabled Newton to show that gravity,
which is operative on the earth's surface, is the effec-
tive cause of the moon's circular motion.

Newton's next great achievement was the geo-
metrical proof that the inverse square law would
explain the motion of the planets in ellipses, and that
no other law would do so. Then, on the assumption
that each particle of matter produced its own effect,
he showed that a sphere attracted as though all
its mass were concentrated at a central point, and
was hence led to the final form of his theory, that
every particle of matter in the universe attracts
every other particle with a force that varies inversely
as the square of the distance between them.

For two years Newton was absorbed in the task

28 THE FOUNDATIONS OF SCIENCE

of working out the consequences of this theory, by
mathematical methods often invented by him in the
process. At the end of that time he had placed the
theory of the heavens on a mechanical basis, and the
publication of Newton's Principia in 1687 marks the
greatest step ever made in the advance of knowledge.
Besides the creation of gravitational astronomy,
Newton placed the science of mechanics firm on the
base prepared by Galileo. He first formulated
clearly the distinction between the mass of a body,
invariable and unalterable in all conditions of
mechanical experiment, and its weight, which de-
pends on the attraction of the earth, and would
vanish altogether at some point between the earth
and the moon where their pulls were equal as well
as opposite. He collected the principles of mechanics,
which had now become clear as the result of inductive
reasoning from experience, and expressed them in
three laws. These laws, the summit of the inductive
process, collect and state in short-hand form the
experimental knowledge of mechanical phenomena.
In turn, the laws are the starting-point of the de-
ductive science of mechanics, in which, by mathe-
matical reasoning, ideal cases of motion may be
investigated. These ideal cases may be suggested
by actual physical phenomena to which they may be
made to approach more or less nearly. The nearer
be the concordance between an actual case we wish
to investigate and the ideal and usually simplified

PHYSICAL SCIENCE 29

case we can examine mathematically, the closer is
the actual result found to conform with that pre-
dicted by calculation. Our imaginary mathematical
model seems to represent the observed mechanical
phenomena of Nature in a very accurate manner,
until, at all events, we have to take into account
velocities approaching that of light.

Let us now examine this picture or model of Nature
which mechanical science presents to our eyes.

In watching any motion we are conscious of two
main perceptions : those of space and time. The
moving body describes a certain length of path and
takes a certain time to do so — a time which our mind
measures in terms of its sequence of consciousness.
Length and Time, then, are taken as fundamental
concepts of the mind, corresponding to the direct
sense-perceptions of space and time.

From these fundamental concepts, others follow,
The Velocity of the moving body is measured by the
length moved over in a given time, or, writing the
result in the initial letters as symbols,

L

V=T

Again, if the velocity vary from instant to instant,
its change in unit time gives its rate of change, that
is, the acceleration of the moving body. Hence

L

80 THE FOUNDATIONS OF SCIENCE

and we have expressed acceleration in terms of our
fundamental concepts of length and time.

In order to co-ordinate these purely conceptional
relations with experimental quantities and to apply
them to practical measurement, we need units. The
units of length arose originally from the average
dimensions of the human body, the yard from a
convenient arm-span, the foot from the length of a
man's foot. But, as the need of accuracy increased,
mechanical models of the units in general use were
constructed, and the legal yard became the length
between two marks on a standard bar, and the foot
the third part of that length. The French units,
framed by the confident science of the revolutionary
period, took the dimensions of the earth as a standard.
But the legal metre is no longer the ten-millionth
part of one earth quadrant, but the length between
marks on a standard bar, which a re-measurement
of the earth has shown appreciably to differ from the
supposed relation.

The idea of time depends on human consciousness,
but as this differs from man to man, and even in one
man at different stages of his life, the periodicity of
astronomical phenomena was early taken as a better
practical standard. The day or the year may be
taken as our fundamental unit, and the second, or
practical scientific unit, defined as a fraction of either
of them. With the units of length and time, and the
derived units of velocity and acceleration, any system

PHYSICAL SCIENCE 31

of motion may be described. In these terms we may
specify the configuration of any system of moving
bodies at any instant and specify its changes. But
for a complete science of mechanics another concept
is needed.

Our sense of sight may give us an idea of motion,
but, if an external body comes in contact with us,
owing to relative motion, our sense of touch gives us
a new perception, that of force, and our muscular
sense gives us a rough measure of its intensity.

It would be possible to construct a scheme of
mechanics with force as a third fundamental unit,
but, as a matter of convenience, another procedure
is better. The concept of mass, which, in terms of
consciousness, may be taken as derived from that of
force, is a better basis for practical mechanics, be-
cause it may be imagined to keep constant for any
one body throughout a series of changes.

If we support two bodies so that their weights are
not operative — place two large stones, say, on smooth
ice — we shall find that if, being of identical sub-
stance, they differ in size, to set them in equal motion
requires either different forces or equal forces exerted
for different times. The same result holds with two
fly-wheels of the same size, one of iron and one of
wood. The iron wheel needs more force to set it in
motion, and more force to stop it when once set
going.

We express these facts by saying that the mass of

32 THE FOUNDATIONS OF SCIENCE

the large stone is greater than that of the small stone,
and the mass of the iron wheel greater than that of
the wooden one, in the proportion of the forces needed
to give them the same accelerations. Hence the
idea of the mass of a body is reached by considering
the force required to give it a certain acceleration.

It will be seen that in these relations the idea of
weight is not involved, and there is no reason to
predict that the weight of a body bears any simple
relation to its mass as defined above. It is a matter
of experiment to investigate the connection, if any,
between them. But the necessary experiment had
already been made by Galileo, before Newton placed
the concept of mass on a sound footing. Since
bodies, whether heavy or light, fall to the ground at
the same rate, their accelerations are the same.
Hence it follows that the forces acting, that is, the
weights of the bodies, are proportional to their
masses which those forces have to move.

The mass of a body, then, is proportional to its
weight, and the masses of bodies are compared,
accurately and easily, by the familiar process of
weighing them.

The unit of mass is defined, like that of length, in
terms of a standard. England has a standard pound
and France a standard kilogramme, with which other
pounds and kilogrammes can be compared and must
conform.

When we have added the unit of mass, M, to those

PHYSICAL SCIENCE 33

of length and time, we have the complete Newtonian
framework of mechanical science. From these
three units all other mechanical units may be
derived.

For instance, force, as we have seen, is a direct
sense-perception, and therefore might be made a
fundamental physical concept; but it is treated in
practical science as a unit derived from the unit of
mass, which, though theoretically derived, is more
convenient to take as fundamental. The mass of
a body is defined by the force required to produce
a given acceleration, and so force is measured by
the product of the acceleration and the mass of the
body on which it acts, or F = Ma.

Again, work or energy is defined as the product of
a force into the distance the force moves its point
of application, so that, in terms of fundamental units,
energy is FL = MaL, or since a is L/T2 we get

ML2
Energy = -?p-

Newton's formulation of dynamics has held undis-
puted sway till, in recent years, it has been shown
that the effective mass of an electrically charged body
in motion increases as the velocity of light is ap-
proached. But, whatever be the outcome of recent
discussion, at all velocities possible in mechanical
experiment, Newtonian results are in accordance

with practical observation.

o

34 THE FOUNDATIONS OF SCIENCE

Although the concept of mass was only formu-
lated clearly by Newton, the problem of matter,
the most characteristic property of which is mass,
is at least as old as the Greek philosophers. The
influence of this age-long familiarity is evident in
Newton's handling of the subject ; for, instead of
defining mass in terms of force, he defined it as " the
quantity of matter in a body," and treated force
as a derived unit. But, in truth, matter is best
known to us through its mass, though historically
matter itself seems the more familiar idea.

Even among the Greeks two views of the nature
of matter were held. One theory taught that it
was continuous and infinitely divisible into similar
parts, so that water was water however far the sub-
division went. But Leucippus and Democritus put
forward the opposite view that, at a certain stage,
division could go no further, and that there ultimate
particles or atoms would be reached. On this
atomic theory, the different properties of various
substances were due to differences in the size, struc-
ture, and arrangement of particles of the same
ultimate nature.

But this speculation was in advance of the age,
and no facts or experiments could then be adduced
in its verification. Hence, when it was criticised by
Aristotle in the light of his own preconceptions, it
withered away. It was revived by the Roman
poet Lucretius, but Aristotle's influence alone sur-

PHYSICAL SCIENCE 35

vived the Dark Ages, and dominated later medieeval
thought.

Galileo's experiments banished from mechanics the
conception of a body intrinsically light ; but, misled
by the phenomena of flame, chemists still repre-
sented burning as the loss of a substance, phlogiston,
which, since the balance showed a simultaneous
gain, must possess the Aristotelian property of a
negative weight. It was not till, towards the end
of the eighteenth century, the discovery and investi-
gation of several new gases had changed the point of
view, that burning was recognised as a combination
with oxygen, one of the gases of air, and phlogiston
vanished from the nomenclature of science.

Chemical change was then seen to be concerned
with bodies all essentially of the same nature, and
a detailed study of chemical combinations showed
that a compound always contained the same definite
proportions of its elements; while, if two elements
formed more than one compound, simple relations
held between the proportions in the different com-
pounds in which the elements combine.

In 1808 John Dalton (1766-1844) saw that these
relations were best explained by a revival of the old
atomic theory, the combining weights of the elements
giving a clue to the relative weights of their respec-
tive atoms. By the further investigation of the laws
of the combination of gases, the conception of the

36 THE FOUNDATIONS OF SCIENCE

chemical atom, as the smallest reacting particle, was
made more definite, and distinguished from the con-
ception of the physical molecule, the smallest particle
which could exist in the free state. In this form, the
theory is based on definite experimental evidence,
and not on speculative philosophical views about the
nature of matter, as it was in the days of the Greeks.
Chemistry is the direct descendant of mediaeval
alchemy, which sought to transmute base metals
into gold, and to prepare an elixir vitce or essence of
life, but in its search discovered many less harmful
things. By the investigation of the properties of
gases, and by the introduction of Dalton's atomic
theory, chemistry was placed firm on its modern
footing, where its conceptions have influenced all
other branches of science, and have become the basis
of the immense superstructure of molecular physics.

One of the earliest developments of molecular
physics was due to J. P. Joule (1818-1889), who from
1840 to 1850 revolutionised the theory of the nature
of heat. Boyle (1627-1691), Newton, and other
acute thinkers, had previously held the view that heat
was due to the agitation of the ultimate particles
of bodies; but, in the absence of the modern con-
ception of energy, such a theory gave no foundation
for the measurement of heat as a quantity constant
throughout a series of changes. Hence, as often
appears in the history of science, a theory which was

PHYSICAL SCIENCE 37

more nearly in accordance with the knowledge of a
later age was useless, and useful advance was made
in the light of a theory which after times rejected.
When Black (1728-1799) discovered the phenomena
of specific and latent heat — the different amounts of
heat needed to warm different substances, and the heat
required to melt solids and evaporate liquids — he
found a better working hypothesis in the rival theory
of heat as an imponderable, invisible fluid. This con-
ception suggested at once the idea of heat as a constant
measurable quantity, and on it the science of calori-
metry, or the measurement of heat, was founded.

However, observations accumulated rapidly which
pointed to another view of heat, and linked it with a
wider range of phenomena. Count Rumford (1753-
1814) by the boring of cannon, and Sir Humphry
Davy (1778-1829) by the friction of two pieces of
ice in a vacuum, showed that an unlimited amount
of heat could be obtained — an amount roughly, at
all events, proportional to the work expended.

But the fluid theory still persisted, and it was not
till Joule measured carefully the heat developed in
friction by known amounts of work that it was
generally relinquished. Joule found that the same
amount of work, whether mechanical or electrical,
and however expended, always developed exactly
the same amount of heat — that, in effect, heat and
work were equivalent and interchangeable. This
result gave definiteness and point to a vague fore-

38 THE FOUNDATIONS OF SCIENCE

shadowing of the theory of energy known as the
correlation of forces. Energy now emerged as an
exact conception — the power of doing work, to be
measured by the amount of work done. Moreover,
in Joule's experiments, if heat be taken as a form of
energy, the total energy is constant in amount, what
was lost in work being gained in heat. In this case,
then, we have definite experimental proof of the con-
servation of energy. Although no such exact proof
can be given in all cases, the cumulative evidence is
very strong that in all physical and chemical changes
we may imagine a quantity which is unchanged
in amount throughout the changes, a quantity which
may be transformed by friction into an equivalent
amount of heat, and may be identified with energy
as defined above.

While mass is constant at all moderate velocities,
and energy is conserved in all conditions known to
us, other quantities are conserved only in limited
conditions. Thus in pure Newtonian mechanics we
find a conservation of momentum ; and, in those
special changes which in thermodynamics are called
reversible, we recognise the constancy of another
quantity which is termed entropy. But neither
momentum nor entropy are conserved in physical
and chemical changes generally ; and we are hence
led to a cautious attitude in similar cases. While
energy is constant in all conditions known to science,
we must not be too sure that science has studied

PHYSICAL SCIENCE 39

all possible conditions in all possible depths of the
universe.

Mechanical and electrical work may be transformed
completely into heat by means of friction or resist-
ance ; but the reverse operation can only be com-
pleted in very special circumstances. The conditions
of the limited change which is usually alone possible
are of great importance in the theory of heat engines,
and are the subject of that branch of science known
as thermodynamics. All heat engines must possess
a hot body or source of heat and a cold body or
condenser, and the transformation of heat into work
will be more complete, and the engine therefore
more efficient, the greater the difference of tempe-
rature between the source and the condenser. The
change can only be complete if the temperature
ratio be infinity — that is, if the temperature of the
condenser be zero. Hence is reached the concep-
tion of a true absolute zero of temperature, un-
connected with the properties of any particular
thermometric substance like mercury, a zero which
has been approached more and more nearly as one
gas after the other has been liquefied.

Simultaneously with this development in the
science of heat, a great advance was made in the
kindred subject of light. Newton was the first to
give a satisfactory demonstration of the really com-
plex nature of white light, and to resolve it completely

40 THE FOUNDATIONS OF SCIENCE

into its coloured constituents by means of a prism.
Newton felt the necessity of imagining space to be
filled with a subtle medium or aether, though the
difficulty of accounting by any then known theory
of waves for the transfer of light in straight lines or
rays led him to suppose in addition that light con-
sisted of streams of minute particles or corpuscles shot
off from the luminous body with immense velocity.

The pure wave theory, however, had already been
developed by Huygens (1620-1695), but it was not
till a century later that Young (1773-1829) and
Fresnel (1788-1827) succeeded in establishing it in
general estimation. In their hands the new theory
explained satisfactorily all the phenomena then
known, especially those of the interference of two
rays of light to produce coloured fringes. When two
waves come together, if their crests coincide their
joint effect will be the sum of their individual effects ;
but, if the crests of one wave coincide with the
troughs of the other, their effects will be opposite and
may destroy each other. Hence some constituents
of a dual beam of white light may be destroyed, and
colour appear as the result of the remainder

Similarly, when the wave-length is very small
compared with the dimensions of the obstacles or
the distances concerned, the fact that light travels
in straight lines is explained by the interference of
all parts of the possible wave-front except a small
area which forms an advancing ray.

PHYSICAL SCIENCE 41

Thus the chief difficulty in the wave theory of
light was overcome, while the phenomena of polarisa-
tion, seen when light is passed through such bodies
as crystals of Iceland spar, showed that the direction
of vibration of the waves must be at right angles
to the direction of propagation of the light. This
observation indicated some of the properties with
which the hypothetical aether of space must be en-
dowed if it be to serve as the medium through
which these waves can travel.

The wave theory led directly to the explanation of
the black lines crossing the coloured band of light
or spectrum which is obtained by passing sunlight
through a glass prism. A theory of these lines had
been given by Sir George Stokes (1819-1903), but it
was not till the theory was reintroduced by the
German chemists Bunsen (1811-1898) and Kirchhoff
(1824-1887), and verified by experiment, that it was
generally accepted. A child's swing is set in motion
by giving it a series of gentle impulses in time with
its own natural period, and any mechanical system
will absorb energy which falls on it in similar periodic
unison with its own vibrations. The molecules of the
vapours in the outer envelope of the sun will absorb
the energy of particular rays coming from the hotter
interior when the waves coincide in oscillatory period
with the molecules. The light which passes on will
be deprived of those particular constituents — that is,
of those particular coloured rays — and black lines

42 THE FOUNDATIONS OF SCIENCE

corresponding to this omission will cross the solar
spectrum.

These conditions were reproduced in the laboratory
by Bunsen and Kirchhoff, who passed the intense
white light of an electric arc through sodium
vapour volatilised in the cooler flame of a spirit
lamp, and obtained the black absorption line of
sodium in the resulting spectrum.

By this discovery the whole new field of the consti-
tution of the sun and stars was opened to chemistry,
which found proof of the existence of its familiar
terrestrial elements in the depths of space. More-
over, spectrum analysis soon detected new elements
both on the earth, where rare alkalies came to light,
and in the sun, where an unknown spectral line
suggested a new element, helium, only afterwards
detected on the earth in the gases hidden in certain
minerals.

But these methods of research have done more than
reveal the chemical nature of celestial bodies. If the
source of light and the observer are approaching each
other, more waves per second reach the eye than if
they were relatively at rest. Hence the colour of a
simple ray and its position in the spectrum are slightly
changed. By measuring microscopically such dis-
placement of known lines in the spectra of stars, their
relative velocity of approach or recession in the line
of sight may be estimated — a feat which might well
have been thought impossible of attainment.

PHYSICAL SCIENCE 43

The most far-reaching development in physical
science during the nineteenth century was in the
domain of electricity. When the century opened,
the Italian Volta (1745-1827) had only just discovered
the pile or cell which enabled experimenters to ob-
tain a steady electric current instead of the isolated
charges alone available before.

It was soon found that these electric currents pro-
duced magnetic forces, and, by the invention of
galvanometers, instruments in which these forces were
used to deflect magnetised needles, the currents were
brought within the power of measurement, and the
electric telegraph made possible. The complemen-
tary discovery of Faraday (1791-1867), that the
movement of a magnet would produce an electric
current, barely perceptible to his apparatus, gave rise
to the astonishing development of electro-magnetic
machinery of the second half of the century.

Faraday's researches were largely inspired by his
repugnance to the idea of action at a distance, and
his consequent continual search into the properties
of the insulating medium through which electric
forces must exert themselves. Clerk-Maxwell (1831-
1879) interpreted and extended Faraday's ideas in
mathematical form, and showed that the properties
of the medium, which were necessary to explain the
electrical effects, were identical with those already
required to explain the propagation of light.

Hence it became possible to conceive of light as

44 THE FOUNDATIONS OF SCIENCE

a series of electro-magnetic waves, and this theory
was immensely strengthened by Hertz (1859-1894),
who, twenty years after Maxwell, succeeded in pro-
ducing long-wave electro-magnetic disturbances by
purely electrical means, and in demonstrating their
existence and properties. Improvements in the de-
tails of the apparatus soon made possible the use of
wireless telegraphy.

The chemical effects of electrical currents were
the first of their properties to be examined, and in
after years led to the most striking of the triumphs
of modern physics in the results of the study of the
conduction of electricity through gases.

When an electric current is passed between metallic
terminals or electrodes through the solution of a
salt, the salt is decomposed chemically. The products
of the decomposition appear at the electrodes only ;
the body of the solution is unaltered. To explain these
facts, it is necessary to suppose that a movement
in opposite directions of the opposite parts of the
salt is going on. From the conductivity of the
solution it is possible to calculate the relative velocity
with which these moving parts, or ions — travellers
— make their way through the liquid. The calculated
velocities have been confirmed experimentally by
watching the motion of coloured ions.

A relation discovered by Arrhenius, a Swedish
physicist, between the conductivities and the chemical
activities of solutions, made it plain that, in some

PHYSICAL SCIENCE 45

cases at all events, the ions which were effective
electrically were also the agents in chemical activity.
This discovery gave precision to the connection
long suspected between electric forces and chemical
affinity, and led to a great development in the theory
of physical chemistry, which, during late years, has
been largely inspired by the ideas of the ionic hypo-
thesis.

The conception of electric ions, originally due to
the investigation of the electrical properties of solu-
tions, has been used with striking success in the
explanation of the kindred phenomena of the con-
duction of electricity through gases.

When the air or other gas in a glass vessel with
metallic electrodes is gradually pumped out, an elec-
tric spark passed between the electrodes becomes a
broadened band of luminosity, separated from the
negative electrode or cathode by a narrow, dark space.
As the exhaustion of the gas proceeds, this dark space
grows till it fills the vessel, the walls of which then
show green phosphorescent effects, and become the
source of the remarkable rays discovered by Rontgen
and now used with great success in surgery.

At this stage the phosphorescence may be shown
to be due to the bombardment of the glass by streams
of minute particles, shot off from the cathode and
known as cathode rays. These particles may be
deflected by magnetic and also by electric forces,
and must therefore be charged electrically, the

46 THE FOUNDATIONS OF SCIENCE

direction of the deflection indicating a negative
charge. There is good reason to believe that the
charge is equal to that on the liquid ion, and hence,
from the measured values of the deflections, Sir J.
J. Thomson was able to calculate the mass of the
particles, as well as their velocities.

In this way Thomson made the remarkable dis-
covery that, whatever be the residual gas or the
material of the electrodes, the mass of these cathode
particles was the same, and equal to about the eight-
hundredth part of the mass of the lightest atom
known to chemistry — that of hydrogen. In these
ultra-atomic " corpuscles " the old conception of a
basis common to all types of matter has been realised
at length.

The corresponding positively electrified rays, on
the other hand, proceeding from the positive elec-
trode, are never of less than atomic dimensions, but
consist of streams of electrified atoms or molecules
derived mainly from the gas left in the vessel. From
the magnetic and electric deflections, the atomic
weight of these positive carriers may be measured,
and thus the particles identified among the atoms
and molecules of chemical substances.

The phosphorescence produced by the impact of
Rontgen rays on certain substances suggested that
these substances themselves might emit radiations.
In a search for such effects, Becquerel discovered
that salts of uranium emitted spontaneously rays

PHYSICAL SCIENCE 47

with a superficial resemblance to Rontgen rays, but
that there was no connection between this effect
and the phenomena of phosphorescence.

M. and Mme. Curie soon observed that certain ores
of uranium were more active than their contents of
uranium warranted, and, searching for the cause, they
gradually separated an intensely active salt, to the
metallic base of which they gave the name radium.

Radio-active substances, of which radium is the
most striking example yet discovered, emit at least
three kinds of radiation, now distinguished by the
Greek letters a, /3, y. The a radiation is easily ab-
sorbed by screens. It may, though with difficulty, be
deflected from its straight path by magnetic and elec-
tric forces, and is thereby shown to consist of posi-
tively electrified particles having the mass of helium
atoms. The /3 radiation is much more penetrative.
It is easily deflected, and shown to be identical in
nature with the cathode ray stream. It is made up
of negatively electrified projectiles like Thomson's
corpuscles, though the /5 rays possess higher velocities,
sometimes approaching that of light to within some five
per cent. The y rays seem to resemble Rontgen rays.

Radio-activity is always accompanied by chemical
change, and the rate of change indicates that it is
of the nature of a dissociation of particles acting singly.
The amounts of energy liberated are very much greater
than any connected with ordinary chemical actions,
and the whole of the evidence suggested to Rutherford

48 THE FOUNDATIONS OF SCIENCE

and Soddy the theory now accepted, that radio-
activity consists in the explosive disintegration of
isolated chemical atoms, atomic and sub-atomic
projectiles being shot off, till a simple atomic residue
is left behind.

All the types of radiation possess the power of
making a gas through which they pass a conductor
of electricity. The rays, as they impinge on the
molecules in their path, produce gaseous ions. It is
by this effect that they are chiefly investigated. Our
methods for the detection of electric effects are
so sensitive that Rutherford and C. T. R. Wilson
have been able to trace the effects of single a particles
as one by one they are shot off by disintegrating
radio-active atoms. In this marvellous way, by
watching the motions of the needle of an electro-
meter, or the formation of lines of cloud in the air
in a glass vessel, has the effect of the atomic structure
of matter been made visible to the human eye.

If, from one point of view, the cathode ray cor-
puscles and the /? particles of radio-active changes
can be regarded as sub-atomic particles of matter,
from another they are ultimate units of negative
electricity. An atom with one corpuscle too much
is an atom negatively electrified, while a defect of a
corpuscle from the normal number means positive
electrification.

But here we come in contact with another line of

PHYSICAL SCIENCE 49

inquiry. If light be an electro-magnetic wave, it
must originate in the vibrations of electric charges,
and from this idea a theory of matter was built up
by Lorentz and Larmor. The ultimate particle be-
came electrical in nature, and matter was resolved
into a collection of disembodied electric unit charges
or electrons. When Thomson's corpuscles became
known, they were identified with the electrons of
Lorentz and Larmor.

A moving electric charge is accompanied by electro-
magnetic energy and momentum in the surrounding
medium, and thus work must be done to set the
charge in movement or to stop it when travelling.
Here we have an explanation of the familiar pheno-
menon of mass or inertia — we explain, in fact, Galileo's
law of continued motion in terms of an electrical
theory of matter.

In this way the conception of matter has been
resolved into that of electricity, and a striking unity
reached between the two branches of science, dynamic
and electrical.

But, as we have no special electrical sense, mechani-
cal force is a more familiar conception to our minds
than electrical force. Hence, perhaps, arise the
efforts which have been made to express an electric
charge in its turn in mechanical conceptions, such
as a strain knot in the luminiferous aether.

Whatever be the fate of these attempts, there
seems no philosophical reason, save the structure of

D

50 THE FOUNDATIONS OF SCIENCE

our bodies and minds, for preferring a mechanical
explanation rather than an electrical one. To explain
everything in terms of aether is but to shift the
mystery of the physical universe on to the concep-
tion of a medium itself hypothetical.

Nevertheless, such a unification of physics, could
it be attained, would fulfil the highest aim of pure
science. Metaphysics is concerned with the ulti-
mate nature of reality, but the more modest aim of
science is the construction of a consistent model of
phenomena and their relations — a model which shall
be logically consistent when examined by our minds,
and consistent, according to its own convention, with
the observed appearances of Nature. Any simpli-
fication in that model is a step in advance, and a
unity such as that of which glimpses are now vouch-
safed to us would satisfy our legitimate desires for
scientific knowledge.

But it is not certain that unity will be obtained by
the conception of a luminiferous aether, which for
half a century has dominated physical science. It
is possible that the field of electro-magnetic energy
surrounding an electric charge in motion moves with
it, and that the vibrations of light travel through
this moving field, instead of through an ocean of
stagnant sether. These ideas, and the so-called
Principle of Relativity arising out of them, may be
the direction in which unity is next to be sought.

CHAPTER III

BIOLOGICAL SCIENCE

As the origins of physical science are found in the
observation of natural mechanical phenomena and
the use of primitive tools, so the beginnings of biology
are to be sought in the observation of wild animals
and plants, the gradual domestication of some of
them, and the rise of a rational medicine and surgery
from the chaos of ideas which preceded it.

The cultivation of plants, such as the cereals, most
of which seem to have been originally natives of the
lands round the Eastern Mediterranean, had not been
conducted entirely at haphazard. The writers of
classical times, who wrote on agricultural subjects,
laid great emphasis on the necessity of saving seed
from the largest and finest plants for next year's
crop ; showing that the effects of selection had been
noticed, and the idea of a progressive improvement
in natural qualities had been put in execution, some
two thousand years before the inward meaning of
such a conception affected the growth of knowledge
as a whole.

In the purely observational sciences of natural

52 THE FOUNDATIONS OF SCIENCE

history considerable progress was made by the Greeks.
Aristotle, for instance, gave an extended account of
the animals known in his day, with some details of
their anatomical structure. But in medicine, where
preconceived theories about the nature of man or
the origin of disease could be used as a basis of de-
ductive reasoning, the Greeks' love for this type of
philosophy led them astray. But even here, in the
school of Hippocrates (450 B.C.), rational ideas began
to emerge.

The first systematic study of human anatomy
appears to have arisen in Alexandria under the sway
of the Ptolemies, induced, perhaps, by the Egyptian
custom of embalming the bodies of the dead. From
Alexandria, too, a knowledge of Greek learning spread
among the Moors and Arabs, by them to be re-
imported into Western Europe when the chaos of
the dark ages which followed the decay and fall of
Rome was giving place to better days.

The great revival of thought and learning which
took place in Europe throughout the thirteenth
century proved singularly unfertile in the advance of
scientific knowledge. Francis, Lord Bacon, writing
three hundred years later, comments on the un-
serviceable character of the facts gleaned by the
men of learning up to that period, and calls attention
to the want of direction and organised system which
impeded mankind in the advance towards mastery
over the forces of nature.

BIOLOGICAL SCIENCE 53

When the full stream of the recovery of the ancient
writings reached Europe in the years of the Renais-
sance, it was thought that science would show the
same marvellous development that literature and
philosophy had undergone. Hence at first medicine
sought to solve all its problems by the wisdom of the
ancients rather than to build up a sound system by
the painfully slow methods of observation and ex-
periment. Isolated revolts were led, especially by
Leonardo da Vinci and Paracelsus (1490-1541),
against the tyranny of Greek authority, but it was
not till 1543, when Vesalius taught anatomy from his
own observations, that the true method was generally
used. In 1628 William Harvey applied the methods
of the new anatomy to the problems of physiology,
and, as a first-fruits, revealed the mechanism of the
circulation of the blood.

From that point growth was rapid, helped by the
new physical knowledge, by the application of the
microscope, by experiments on living animals, and
by the development of a less fantastic scheme of
chemical knowledge than that which had been
current among the earlier alchemists.

The growth of medicine and the demand for new
drugs reacted both on chemistry and botany. In
the former science it led to the discovery of many
substances before unknown, while in the latter,
besides inducing the cultivation of useful herbs, it
caused more intimate research into the structure and

54 THE FOUNDATIONS OF SCIENCE

uses of plant organs. The sexual functions of the
ovaries and anthers were made clear by Camerarius
in 1694, while the following century saw a complete
system of classification worked out by Linnaeus
(1707-1778).

Interest and curiosity about the animal world had
always been more marked than about plants, which
only attracted attention in so far as they were use-
ful or harmful in medicine or agriculture. From the
stories of Pliny and the anecdotes of beasts current
in the ancient world, some of which at least were
based on misconceptions or existed only in the
imagination, we pass to the Bestiaries, elaborately
written and illuminated in the monasteries of the
thirteenth and fourteenth centuries. Travellers such
as Marco Polo had brought back tales of animals
from India, China, and Africa, while the discovery
of America opened up a whole continent of unknown
animal and plant life. These stories were soon
followed by the capture and production of the animals
themselves, and natural history, from being too often
a collection of incredible marvels, took its place
among the recognised branches of systematic know-
ledge.

In the seventeenth century the study of animals
was stimulated by the foundation of Royal Mena-
geries, while improvements in the microscope led first
of all to a more detailed study of cell structure, and

BIOLOGICAL SCIENCE 55

afterwards disclosed the existence of multitudes of
micro-organisms, hitherto unsuspected.

But with all these studies of existing plants and
animals it was long before men fully realised that
authentic traces of extinct forms of life were to be
found in the fossils embedded in the rocks. Isolated
glimpses of this truth are seen here and there
in the fifteenth and following centuries, but it was
not till the eighteenth century that this view was
consistently advocated. Hutton's (1726-1797) Theory
of the Earth, published in 1785, taught that pro-
cesses still going on were adequate to explain the
formation of the stratified rocks, and the existence
of embedded fossils. But even then no general agree-
ment followed, and it was not till Lyell (1797-1875)
collected all the evidence that had accumulated in
his Principles of Geology (1830-33) that men of science
were convinced, and realised that ages must have
elapsed in geological processes, beside which the few
thousand years of the received Biblical chronology
were almost as nothing.

The long series of fossil animals and plants of
gradually increasing complexity, found by geologists
in strata of different ages, raised once more the ques-
tion of the evolution of species. The idea of the de-
velopment of all existing forms of life from a few
simple types had been held by some of the Greek
philosophers, but it had vanished in the ascendancy
of the Biblical story of the Creation, and been dis-

56 THE FOUNDATIONS OF SCIENCE

credited further by the scientific doctrine of fixity of
species prevalent in the eighteenth and early nine-
teenth centuries.

Lamarck (1744-1829), it is true, had advocated a
theory of evolution founded on the idea of the gradual
development of organs under the stimulus of special
use for many generations — the giraffe, for instance,
acquiring its long neck by the continual efforts of
its ancestors to browse on trees just beyond their
reach. But no evidence was forthcoming of the
inheritance of such acquired characters, and the
balance of scientific opinion was decidedly against
the evolutionary hypothesis.

In 1858, however, a new suggestion was made
independently by Charles Darwin (1809-1882) and
Alfred Russel Wallace (b. 1823), fortified in the
case of Darwin by illustrations drawn from many
years' observation and experiment. Impressed by
the severity of the struggle for life and for mates
among animals and plants in a state of nature,
Darwin and Wallace saw that a variation in struc-
ture or character which gave even a slight advantage
to any individual might determine the question
whether or not it was to survive, obtain a mate,
and rear offspring. Innate variations tend to be
inherited, and thus a favourable variation might be
perpetuated, developing in time into a new variety or
species. In this way, the pressure of natural selec-
tion might accentuate chance variations, and produce

BIOLOGICAL SCIENCE 57

from a few prototypes all the existing species of
living beings, gradually, throughout the long ages
of geological time, moulding each species to suit its
environment, and leaving it more fixed in type as
the need for variation disappeared.

When this theory had overcome the opposition of
those who held a too literal interpretation of the
book of Genesis, it became the dominating idea of
the second half of the nineteenth century. Its influ-
ence extended far beyond the confines of biological
science. By giving a reasonable explanation of bio-
logical development, it justified the conception of
evolution in general, and that conception was applied
with varying measures of success to co-ordinate the
phenomena of cosmical processes, the development
of the human race, historical change, and social
evolution. Even the specific idea of natural selec-
tion, or the survival of the fittest — the fittest for the
particular existing environment — found application
in other realms of thought. In especial it illuminated
the tendencies of sociology, or the science of human
societies, where progress has followed along much the
same lines previously trodden by natural history.
From the mere collection of tales of the marvellous
and surprising, such as were at first brought back by
travellers, traders, and missionaries — whose calling
took them among unknown peoples — the study of
mankind has advanced into the careful, sympathetic,
and intelligent stage, which is now characteristic of

58 THE FOUNDATIONS OF SCIENCE

anthropology and the allied subject of comparative
religion. The results of the patient labour of spade
and pick, among the sands of Egypt, and the waste
cities of Palestine and Asia Minor, by which the
relics of past civilisations have been brought to
light, may be compared with the unfolding of the
story of evolution by the study of the fossil contents
of rocks. But there are yet vast areas awaiting the
coming of the scientifically trained and equipped
explorer. The remains of the ancient peoples in the
central districts of Asia are still unmapped, and the
great inscriptions of Central America have so far
baffled all attempts to decipher their record. Never-
theless the causes which have contributed to the rise
and fall of civilisations are beginning to yield their
lessons for the future.

Mankind is subject to evolution, and the average
composition and character of each race is always
changing, not only absolutely but in relation to
other nations. Hence arises the importance of a
study of the comparative rates of reproduction of
different sections of a nation, and of other agencies
that may affect racial qualities — the subject-matter
of the study named Eugenics by the late Sir Francis
Galton (1822-1911), its founder.

While Darwin was still at work, another series of
researches was being carried out on inheritance,
which only became generally known many years

BIOLOGICAL SCIENCE 59

later. G. J. Mendel (1822-1884), Abbot of Briinn,
not satisfied with the theory of natural selection of
small variations as a sufficient cause of evolution,
investigated the effects of crossing different kinds of
green peas.

Mendel's discovery consists essentially in the dis-
closure that in heredity certain characters are trans-
mitted as indivisible units. In peas the tall and
dwarf varieties show these phenomena. Tallness and
dwarfness here are opposite unit qualities, and the
products of a cross between tall and dwarf parents
are not intermediate in character. In the first gene-
ration all the seedlings are outwardly like their tall
parents : hence tallness is said to be " dominant "
over the " recessive " dwarfness. But, when self-
fertilised, these tall hybrids reveal their difference
with their dominant parent. Instead of breeding
" true," and giving consistently tall offspring, the
second generation is found to consist of tails and
dwarfs in the ratio of three to one. All the dwarfs
breed true in future, but of the tails one-third only
breed true, while two-thirds reproduce in the third
generation the mixed result of the second.

These relations are explained directly and easily
by the supposition that the germ cells of the plants
are in character either " tall " or " dwarf," so that
a hybrid has some " tall " germ cells and some
" dwarf " but no intermediate variety. When a
dominant (D) tall plant is crossed with a recessive

60 THE FOUNDATIONS OF SCIENCE

(R) dwarf, its own germ cells are half D and half
R. If self-fertilised, or crossed with a similar plant,
on the average of large numbers, it must chance
that about half the unions will be between D's and
R's to form DR's, while half will be pure bred, being
divided equally between DD's and RR's.

But since " talhiess " is dominant, any plant which
contains " talhiess " at all in its composition grows
tall, and so all the DR's resemble the DD's outwardly,
and we get three-quarters of the seedlings apparently
tall. But, when crossed among themselves or self-
fertilised, these DR's reveal their true nature in their
offspring.

We may illustrate this scheme in a pedigree
diagram —

I I I

DR DR RR

In other cases, more complicated relations appear.
Qualities may be linked, so that one cannot appear
without the other, or may be antagonistic, and never
exist together. Other qualities may only be found
in one sex, or be dominant in one sex and recessive
in another.

Mendelian characters have been proved to exist in
many plants and animals. The insight which this

BIOLOGICAL SCIENCE 61

knowledge gives into the problems of cross-breeding
has already resulted in the raising of new and valuable
types of wheat, and bids fair to revolutionise the
arts of the stock-breeder and horticulturist. In
mankind Mendelian relations have been established
for eye colour, where brown pigment in the iris is
dominant, and in certain diseases and malformations.
In these cases, the probable result of marriages of
affected persons can be estimated accurately, and the
proportion of their children likely to show the special
characteristic has become a matter of exact calcu-
lation.

If our growing knowledge of heredity promises
greater final results, more practical gain has hitherto
been obtained from that branch of biology, which
has revealed to us the existence and life history of
those micro-organisms which have been proved so
powerful for good or ill to mankind.

The Greeks and Romans had noticed and specu-
lated on some of the diseases which we now know
are caused by microbic action. The connection be-
tween marshy districts and malarial fever seems
always to have been recognised. Mildew or rust in
wheat had also attracted attention, and the Romans,
after the beginning of our era, associated its preva-
lence with inclement and damp weather, and with
ground that lay low and was exposed to heavy dews.
The diagnosis so far was correct, as well as the

62 THE FOUNDATIONS OF SCIENCE

further idea that something from the outside had
come in and attacked the crop, which was expressed
in the view that either the moon, the Milky Way,
or some heavenly body had let fall an infecting sub-
stance. The remedy proposed, namely that a young
dog should be sacrificed, probably to conciliate the
constellation of Sirius (the dog-star), is however a
part of the classical treatment of the subject which
would find no analogue in modern science.

The putrefaction of decaying animal and vege-
table matter, also, had been a subject of speculation
from the earliest times, and the fermentation pro-
duced by yeast has also been known throughout
history. Yet it was not till about 1838 that Schwann
(1810-1882) discovered that the activity of yeast was
due to the growth and multiplication of living cells,
and that putrefaction was caused by a similar process.

These results were extended about 1855 by Pasteur
(1822-1895), who traced all such changes to the in-
troduction of living cells or germs of cells, and thus
destroyed the old idea of spontaneous generation.
Pasteur detected the specific microbes of chicken
cholera and the silk-worm disease, and gradually
our knowledge of microbic diseases has been ex-
tended, chiefly by inoculation experiments on living
animals, and we have learnt how to guard against
some of the worst of these microscopic but deadly
enemies. To this knowledge we can trace most of
the modern improvements in sanitation and hygiene.

BIOLOGICAL SCIENCE 63

In many cases the action of the microbe on the
body it attacks is directly due, not to the microbe
itself, but to a chemical substance, or enzyme, it pro-
duces. In 1897 this process was first demonstrated
by Biichner for the fermentation of yeast : its charac-
teristic effects could be induced by a substance
extracted from the cells. These enzymes seem them-
selves to remain unchanged at the end of the action,
their presence alone being sufficient to work the
changes.

The history of the discovery of the true nature
of malarial fever may be taken as a typical example
of the romance of modern biology. The forging of
the first link in the chain was due to Laveran, a
French army doctor, who, in 1880, detected living
parasites in the blood of a malarial patient. The
clue was followed up in Italy, where the life history
of these microbes was studied. Three distinct groups
were distinguished at first, corresponding to three
different forms of the disease prevalent at different
periods of the year. The interest now centred in
finding the means by which the infection was intro-
duced into the body of man ; naturally, some suctorial
insect was soon suspected. In 1895, Ross and Manson
were able to demonstrate the existence of the identical
parasites in mosquitoes which had fed on the blood
of infected persons, and showed how the parasites
increased in size, divided, and became full of thread-
like spores until their progeny filled the body cavity

64 THE FOUNDATIONS OF SCIENCE

of their insect host. By means of the bite of an
infected insect, the disease was recommunicated to a
human host, and a new cycle of existence was entered
upon.

Only one particular type of the mosquito or gnat
family, to which the name Anopheles has been given,
seems to serve in the distribution of malaria fever,
and among them the females are the bloodsuckers.
Species of this insect are found in almost every part
of the world, including England, and it is from the
study of their habits of life that malarial fever has
been swept away from many of its old haunts. These
gnats breed in stagnant water, and seldom fly about
except between sunset and sunrise. The breeding-
places can be destroyed by some system of drainage,
or by the filling in of places where pools of water are
apt to collect. Again, a thin layer of petroleum
oil over a sheet of water which cannot be drained,
will prevent the development of the larva. Wire
gauze screens to windows and doors and mosquito-
nets round beds will protect the inhabitants during
the period of the night, when these creatures are
active.

Malarial fever or ague was once well known in the
fen districts of England, but it was stamped out,
probably by the progressive drainage, and the suc-
cessful treatment of the occasional sufferer by quinine,
before the true cause of the disease had been ascer-
tained The mosquito which conveyed the infection

BIOLOGICAL SCIENCE 65

still exists, but it is no longer infected by the specific
parasite. Thus it seems possible to look forward
to the entire elimination at some time of any one
particular microbe, and so to remove its character-
istic disease from among the human race.

The success which attended the researches on
malaria has led to an extension of this branch
of preventive medicine in many directions. The
ravages of Mediterranean or Maltese fever among
the troops and crews of the men-of-war stationed in
those regions led to the appointment of a committee
of inquiry. A specific organism causing the disease
was again discovered ; and it was found that it
spent one of the necessary stages of its existence
in the goats, which form an important part of he
economic wealth of the Mediterranean agriculturist.
Thence the infection is transferred to men in the milk,
butter, or cheese derived from these animals. The
goats themselves, however, show no signs of feeling
any discomfort from the presence of the parasite.
This immunity of the animal host from any obvious
form of disease constitutes one of the most baffling
features in the pursuit of this class of knowledge.

Whole districts of Central and East Africa are
ravaged by epidemics and maladies in man and
beast, such as sleeping sickness, blackwater fever,
and others, by which some areas have been rendered
almost uninhabitable ; and various animals, pre-
viously unsuspected, have been shown to play their

66 THE FOUNDATIONS OF SCIENCE

part in spreading the infection. Moreover, the
various races of mankind manifest different degrees
of susceptibility to different forms of infection ; and
in a few cases persons have been found who, like
some animals, are apparently immune to the conse-
quences of infection, but are nevertheless acting as
hosts to the parasite, and are spreading the disease
amongst those with whom they come in contact.

The application of Pasteur's results to the pre-
vention of microbic infection in the operations of
surgery by Lord Lister (1827-1912), in conjunction
with the discovery of anaesthetics, made possible the
surgical advances which have done so much to
relieve human suffering, and have changed our hos-
pitals from institutions in which recovery was at
best doubtful into the most effective agencies for the
preservation of human life.

The result of the improvements in hygiene,
medicine, and surgery is best measured by the drop
in the annual death-rate in cities from some eighty
per thousand of the population two hundred years
ago to the present value of about fifteen per thousand.
Not only does this change mean lives prolonged
which otherwise would have been sacrificed, but it
means also increased health and strength for some
who, in old conditions, might have survived with
impaired vitality. Nevertheless, we must not forget
that this alteration in the incidence of death and
disease involves dangers of its own. Mental and

BIOLOGICAL SCIENCE 67

physical defects which in former ages would have
destroyed their owner, and with him ceased from
troubling the human race, are now sometimes per-
petuated in his offspring, whose existence has been
made possible by this same improvement in the con-
ditions of life. If the innate qualities of our race
are to improve in the future as they have done in
the past, if indeed the race is to be preserved from
decay, such problems will have to be faced.

We must now consider briefly the relations between
physics and chemistry on the one hand and the
biological sciences on the other.

The bodies of plants and animals are clearly
subject to the usual laws of mechanics. As wholes
they fall with the usual acceleration of gravity;
their limbs illustrate the mechanical principles of
the lever. The breathing of animals is analogous
chemically to the burning of a candle, and organic
bodies are composed of the same chemical elements
that are familiar in the inorganic world.

Nevertheless, carbon, which must be regarded as
the chief and most characteristic element in organic
matter, possesses properties more complicated than
those of other elements. A carbon atom is able to
combine with other carbon atoms, as well as with
those of different substances, to form very complex
molecules, and it is this property which makes pos-
sible the special chemistry of living processes.

68 THE FOUNDATIONS OF SCIENCE

Paracelsus (c. 1490-1541) and Stahl (1660-1735)
carried into modern times the old ideas of a distinct
vital principle, in opposition to the equally old theory
that the mechanism at work in the inorganic world
was sufficient completely to explain the phenomena
of life. Till comparatively recent times, the vitalist
thought that the characteristic organic compounds
could be produced by life alone, and were beyond
the resources of chemical laboratories.

But in 1828 Wohler (1800-1882) succeeded in
preparing artificially the typically organic compound
urea, and thereby threw doubt on the prevalent
vitalistic hypothesis. Other preparations followed,
till in 1887 Fischer and Tafel produced sugar from
its elements.

Simultaneously many physical processes have been
found operative in living tissues. In particular the
phenomena of solution have thrown light on many
of the physiological problems of living cells ; osmotic
pressure and the motion of electric ions are the means
by which many of the operations of living tissues are
carried on.

In this way much new insight has been obtained
on the mechanism, both physical and chemical, by
means of which the functions of life are maintained.
Nevertheless, the gap between the inorganic world
and the world of life shows no signs of being bridged.
We are still unable to produce the simplest living
cell from dead matter. All known organisms are

BIOLOGICAL SCIENCE 69

derived from parents of like nature. But, even
should " spontaneous generation " be discovered at
some future time, the gap would yawn as wide as
ever. We should still have to explain why matter
contained such tremendous potentialities that, in ap-
propriate conditions and under appropriate stimuli,
it should be capable of giving rise to the phenomena
of life. Even if that were explained, a yet wider
gap lies ahead, beyond which alone we touch the
still more tremendous fact of consciousness. If
dead matter could be made to live or simulate the
phenomena of life, there is no certainty that it would
think and feel. Here we are once more on a differ-
ent plane of being ; the phenomena on each side of
the gap are incommeasurable.

It is an appreciation of such logical chasms as
these that retains the conception of vitalism in modern
thought. After a period of discredit, due to a natural
exaggeration of the newly discovered power of re-
solving the processes of living cells into the physics
of colloids and the chemistry of the proteids, vitalism
is again in the ascendant. As long as it is not made
the excuse for ceasing to search for a physical or
chemical explanation in any possible case, its re-
surrection may be welcomed as a recognition of the
fact that first in life and then in consciousness we
have new phenomena, on a different scientific plane
to those of inorganic processes.

Thus vitalism does not depend on the difficulty

70 THE FOUNDATIONS OF SCIENCE

of preparing the more complex organic substances
which have hitherto defied the resources of our chemi-
cal laboratories. It does not depend on our failure
to explain the more recondite physical and electrical
phenomena of living cells, nor on our failure to manu-
facture life from inorganic matter. It is never safe
to build conclusions on the mere gaps in knowledge.
But it is required because we have to account for
phenomena which are different in kind to those
others — to account for growth, reproduction, for
the unity of a complex organism, for the transcen-
dent fact of consciousness, in short, for the problem
of life itself.

CHAPTER IV

PSYCHOLOGICAL SCIENCE

WE have now reached the last of our divisions of
science — that which deals with the phenomena of
mind, the organ by which we are enabled to appre-
hend the world as seen in the physical and biological
sciences.

In the history of human thought, we find that, for
a long while, the study of mind followed exclusively
the methods of introspection ; but in recent years
experiment has been applied to mental phenomena
also, and, for our purpose, it will be simpler to ap-
proach the subject from the experimental side.

We may begin by examining our sense-perceptions
— properties of the human body, varying from in-
dividual to individual, giving rise to the sensations
our minds experience when our senses are stimulated.

The sense of touch, by which we distinguish many
physical properties, varies greatly when different
parts of the body are affected, and for practical use
often seems to be concentrated in the finger-tips. The
sensitiveness of the nerves of the skin to a light touch
may be estimated by exploring the skin with a series

71

72 THE FOUNDATIONS OF SCIENCE

of fine hairs mounted on wooden handles. The
pressure which each hair is capable of exerting is
measured on a balance, and thus local differences
in sensibility may be mapped out. Again, by ex-
ploring the skin with blunt-pointed rods, either hot
or cold, the sensitiveness to heat and cold may be
determined. It is found that some areas are more
sensitive than others to each kind of stimulus, the
" touch spots " not coinciding either with the " heat
spots " or the " cold spots," and none of these being
coincident with the " pain spots," where painful
pressure is most easily felt.

If a nerve connected with a given sensory area of
the skin be cut, the sensations are destroyed, and
only return slowly as the injury is restored. The
sensibility to pain returns first, and the feeling of
cold before that of heat.

Thus we see that the extent to which the mind is
influenced by effects of pressure or of temperature
on the skin, does not depend alone on these outside
variables. The properties of the portion of the body
which is acting as receiving agent have to be taken
into account.

The sensation of sight, like those of touch and
hearing, is one which is possessed alike by mankind
and the upper members of the animal world ; though
the range of the sensations probably does not corre-
spond in the various instances.

PSYCHOLOGICAL SCIENCE 73

While intense radiant energy, such as powerful
direct sunlight, affects the whole surface of our body,
and gives to our minds the sensation of heat, the
sensation of light is excited only when radiation of
a certain type falls on our eyes. Their sensitiveness
to radiation within a limited range is extraordinarily
great, an infinitesimal amount of energy being enough
to produce the characteristic sensation ; but the kind
of radiation which is effective is strictly limited,
lying between definite limits of frequency of vibra-
tion of light waves from about 400 to 800 millions
of millions per second, the greatest sensitiveness
being about the middle of this range, in the yellow.

The sensations of light may be divided into colour-
less sensations — a white to grey and black linear
series — and colour sensations which are more com-
plex, and must be represented by some closed figure
such as a circle or triangle. Beginning with the
sensation of red, we may pass by insensible grada-
tions either towards orange or purple. If the former,
we reach successively, orange, yellow, green, blue,
violet, purple, and so complete our circuit and return
to red. If these colours be mixed with white or
grey, we get less pure shades. If red be mixed with
white or light grey, we get rose or pink ; if with dark
grey or black, the result is brown.

The sensation of white may be excited either by a
mixture in the eye of all coloured lights, as in sun-
light, which contains all the colours of the spectrum,

74 THE FOUNDATIONS OF SCIENCE

or by mixing in the eye pairs of colours which lie
opposite each other in our diagram — red and green,
blue and yellow, greenish blue and orange. It must
be noted that, in all these cases, rays of light must
be mixed so as to be blended when they enter the
eye. The mixture of pigments or paints outside the
eye is another and more complicated story.

As we have said, it is probable that the extent
and intensity of all sensations differ from person to
person, possibly from race to race, on the average
of large numbers of individuals. About four per
cent, of European men are colour-blind to red and
green, and see those colours as grey. Another much
rarer type of human being seems to be blind to blue
and yellow, while some others are totally colour-blind.

The common red-green blindness indicates that
red and green are primary colour sensations, and so
far all are agreed. But two explanations of the whole
of the phenomena are held: according to Hering's
theory, there are four primaries — red, green, blue,
and yellow; while, on Young and Helmholtz's
theory, all colour sensations are compounded of red,
green, and blue, as figured in the triangle we used to
illustrate another subject in Chapter I.

Primitive races seem to be much less sensitive to
blue and rather less sensitive to yellow than Euro-
peans, as though these sensations had not yet fully
developed. It is interesting to note that in the
Iliad of Homer colour terminology, except for red,

PSYCHOLOGICAL SCIENCE 75

and possibly yellow, is very vague, and we do not find
definite words expressing the ideas of blue or brown.

The sensations of hearing, taste, and smell, have
been less studied by experimental psychologists than
those of touch and sight. The sense of pitch in sound
is well known to vary largely in different individuals ;
a rough estimate of its delicacy is sometimes formed
by ability or inability to hear the squeak of the bat.
It may be measured scientifically by testing sensi-
bility with any source of sound in which the pitch is
under control.

Here again, the differences noted between the
powers of various individuals are probably at the
base of many differences of opinion and judgment,
believed to have a more intellectual " rationale."

Passing from direct sense-perceptions to the more
recondite powers of the mind, we are met at once by
the recognition of the importance of memory.
Without memory we should be unable to co-ordinate
our different states of consciousness; we should, in
fact, lose our personality.

The tendency of past events, particularly if
specially impressed on us at the time, to recur
spontaneously, has been termed " perseveration." A
thought that haunts us and prevents our sleep is a
good illustration of this tendency.

The form of perseveration differs among individuals.
Some recall a complete scene ; others visualise form

76 THE FOUNDATIONS OF SCIENCE

but not colour ; others revive most vividly sounds,
tastes, or smells. To others the past scene is pre-
sented in words, either imagined as heard or as spoken
in their minds. Finally, some remember in imageless
thoughts.

The simpler phenomena of memory have been
studied by measuring the number of repetitions
needed before a series of meaningless syllables
could be reproduced. The number requisite is found
to increase rapidly with the length of the series.
When, after a lapse of some time, they are partially
forgotten, new experiments may be made, and it is
now found that fewer repetitions are needed than at
first. By the elaboration of such experiments, the
effect of time, of new impressions, and of other com-
plications, may be investigated.

Light may also thus be thrown on that most im-
portant property of our minds known as association.
If the syllables be learnt in pairs, the first one of each
pair being accented, they are easier to learn. Here
a second sensation, that of rhythm, is probably
introduced. Moreover, if one of the accented syllables
be exhibited afterwards, it is easier to recall the one
that follows than if the non-accented syllable be
exhibited. More complex associations are also found
between groups of several syllables ; while the greater
rapidity and completeness with which syllables are
learnt when they make sense, shows the effect of
association between sounds and meaning. The ad-

PSYCHOLOGICAL SCIENCE 77

dition of rhythm, accent, and rhyme with sense,
complete the association which accounts for the
greater ease most people experience in committing
verse to memory rather than prose.

The most marked lapse of memory occurs im-
mediately after the impression has first been made.
Associations ten minutes old are less perfect than
those tested at once after learning, while the differ-
ences between ten minutes and twenty-four hours
are not so marked. Mere perseveration is especially
prone to lapse with time, much more so than the
complicated associations involved in rational learning
when the meaning of a lesson is fully grasped.

It is by association that much of our pnysical
and mental power is built up. An infant has no
power of co-ordinating the movements of its limbs,
and only gradually does the habit of associating ap-
propriate movements result in ability to walk and
speak. Increase, with practice, of skill in handi-
crafts, is another illustration of the same effect.

Part of education consists in the formation of
associations. From the simple effort of memory
involved in the association of five times seven with
thirty-five, to the facility of a more advanced mathe-
matician in the solution of differential equations by
the power of association, we save ourselves the
mental labour of working out problems each time
afresh from first principles.

The whole of that part of military training known

78 THE FOUNDATIONS OF SCIENCE

as discipline is an affair of association, whereby,
when orders are given, the obedience becomes
mechanical and independent of the will, and the
army becomes a tempered weapon in the hands of its
commander. Most of politics may be taken as an
illustration of the power of association. The art
of electioneering in especial consists in impressing
on the minds of the electors the association of their
ideas of the blue party and Smith, the blue candidate,
with the idea of peace, cheap food, and reform, or a
strong Empire and work for all, and connecting the
idea of Jones, the buff candidate, with Chinese
slavery, a dear loaf, a refusal to " tax the foreigner,"
or other unpopular and possibly irrelevant concep-
tions. The preliminary stage may involve a good
deal of more or less rational discussion ; but, as the
polling day approaches, excitement rises, and pre-
formed associations take most of those who vote to
the poll at the last.

In the methods of modern electioneering, elaborated
according to long experience in political psychology,
it is probable that there is an actual disadvantage in
having a candidate who is resident in the constitu-
ency, since he inevitably becomes associated in the
minds of the voters with commonplace occurrences
of daily life and useful enterprise, and consequently
the simplicity of association between the idea of the
candidate and the ideas of the electioneering virtues
tends to be obscured.

PSYCHOLOGICAL SCIENCE 79

The old intellectualist theory, the theory on which
indeed modern democracy was founded, taking no
account of the irrationality of mind under certain
stimuli, is more and more discredited by observa-
tion, though possibly other equally valid new founda-
tions may be discovered in the future for the system
to which it gave birth.

In the introspective part of psychology, though far
older in point of time, less general agreement has
been reached than in the experimental branch of
the subject. Since the time of Kant (1724-1804),
it has been usual to divide our direct mental relation
with objects into three types of conscious activity.
We know or apprehend an object, we feel pleased or
pained by our perception, and consequently we form
some wish or desire about it. These three states
are sometimes termed cognition (or knowing), feel-
ing, and conation (or willing). Since feeling and
willing seem more nearly allied than either of them
is to knowing, there is now a tendency to revert to
a dual classification, feeling and willing being grouped
as sub-divisions of interest.

The special characteristic of the human mind is
its power of constructing complex ideas and of follow-
ing trains of thought. In this process association
plays a part : association not only of impressions
which have chanced to coincide or follow each other
regularly in the past, but also association of similars

80 THE FOUNDATIONS OF SCIENCE

which may not have been associated before in time
or space. Here a new formative process appears —
the process of comparison. We see a tiger, and it
suggests to our mind the remembrance of a cat. We
thus consciously compare the cat and the tiger, and
form a concept of a feline or cat-class of animals
of which the tiger and the cat are varieties, and all
tigers and cats we know are members. Such a
concept also involves the possibility of the existence
of other animals of the class, unknown to us, and
assists us in any search for them and in the identi-
fication of them.

And here we see the psychological importance of
language : the possibility of giving all similar animals
the general name of cat, assists the mind to frame the
idea of a universal or general concept of cat. In
this it merely helps to clarify the results of sense-
perceptions ; but it may also be used to inform us
that cats have many interesting properties, such as
the possession of nine lives, which we have not our-
selves had the benefit of testing, and may incorporate
these qualities in our future concept of cat. Thus
may be elaborated a process of conceptual synthesis.

The mental processes of which we are conscious do
not represent the whole of the workings of our minds.
Sub-conscious changes, apparently independent of
voluntary control, may go on, and their results emerge
into consciousness at a future time. A problem

PSYCHOLOGICAL SCIENCE 81

studied unavailingly at night, and solved immedi-
ately on regaining consciousness after sleep, serves
as one example of this process. More striking cases
are shown in the phenomena of hypnotism, where
suggestions made by some outside person to the
subject during trance may affect his actions, not only
while in the hypnotic condition, but after recovering
therefrom and being apparently in a normal state
of self-control. Extreme instances are found in the
rare cases of dual or multiple personality, where an
injury to the brain or an unnatural sleep, or the
action of drugs, has resulted in complete loss of
memory of past life, and sometimes in the modifica-
tion of the old mental qualities. A return to the first
personality is not unknown, when forgetfulness of
the life of the second personality may ensue. Several
alternations between the two personalities have been
noted and described.

Evidence has been obtained that ideas may be
transmitted directly from mind to mind without the
use of normal sense-perception, while other pheno-
mena affecting mind in abnormal conditions have
been interpreted by some observers as indicating
the action on living minds of consciousness associated
with the personalities of the dead.

A close correspondence has been traced between
psychological states and changes in the nervous
system. Sensations are set up by the transfer of a

nervous impulse along one set of nerves from the

F

82 THE FOUNDATIONS OF SCIENCE

surface of the body to the brain, and movements
are carried out in response to other impulses which
travel from the brain along another set of nerves.

Different parts of the brain have been shown
by physiologists to play different functions. But
the co-ordination and harmonious use of different
functions needs a special nervous mechanism ; thus
the third convolution of one or other hemisphere
of the brain is concerned with the correlation of the
movements of the throat and larynx, which occur
in speech, and any injury to that convolution results
in aphasia, or loss of the power of speech. It seems
likely that the co-ordination and grouping of ideas
required in the high mental processes, is different in
kind to the simple constituents, and is more than
the mere aggregation of those constituents.

Evidence shows that to every psychological state
there exists a corresponding physiological process
in the brain, and to every physiological process
appropriate physical and chemical changes in nerve
substance.

This psycho-neural and psycho-physical parallelism
is a matter of observation and experiment, and is
one of the joint conclusions of psychology and physi-
ology. It is unnecessary for the purposes of science,
psychological or physiological, to frame any hypo-
thesis as to whether or no the subjective processes
of consciousness are directly connected with the
objective phenomena of nerve-change which accom-

PSYCHOLOGICAL SCIENCE 83

pany them. Such inquiries are of fundamental
importance to mankind, but they are problems of
that branch of philosophy known as metaphysics,
and are not problems which psychology or any
other science can answer or need ask. Just as
the function of physical science is to construct a
mental model of nature seen in a physical light, and
the function of biology is to represent it in a bio-
logical light, so psychology constructs a mental model
of that part of nature which involves mind from its
own special point of view. Its function is to con-
struct a consistent model, not to seek the answer to
the more fundamental question whether that model
corresponds completely with reality. That inquiry
is reserved for metaphysics. Moreover, psychology
cannot even rightly investigate the connection be-
tween its own model and that of physics or biology.
They are, so to speak, on different planes, and cannot
of themselves get into contact. The true connection,
or want of connection, between them is a part of the
study of reality — that is a problem of metaphysics.

Metaphysicians have formed four hypotheses on
this particular point. There is the metaphysical
theory of psycho-physical parallelism, which exalts
to the state of an ultimate truth that parallelism
of two independent series which psychologists take
merely as a convenient scientific working hypothesis.
According to this dualistic theory, our conscious
thoughts and our neural changes are for ever keeping

84 THE FOUNDATIONS OF SCIENCE

step, though between them is fixed an impassable
gulf, across which there is no possibility of interaction.

The second theory is that of the materialist, who
holds that the physical changes are the sole reality,
and that consciousness is merely a bye-product of
atomic and molecular rearrangements.

The third theory is called idealism, and, according
to it, mind is the only ultimate reality, and matter
is one of the manifestations of some finite or infinite
mind.

Finally, there is another dualistic theory which
regards mind and matter as distinct, but accepts the
common-sense view that our minds act on and are
acted on by matter, leaving undetermined as yet the
precise mode of interaction.

It is beyond our present purpose to discuss these
metaphysical theories.

We are now in a position to consider in more detail
the theory of knowledge, to ask, in fact, how know-
ledge becomes possible, whether in one way or in
more than one. Here we are on debatable, or, at all
events, debated, ground, and not all philosophers will
agree with the statements in the next paragraphs.

One kind of knowledge which we dealt with in the
chapters on physics and biology may be termed
knowledge by experience. It may be sub-divided
into knowledge by acquaintance and knowledge by
description. Knowledge by acquaintance may be

PSYCHOLOGICAL SCIENCE 85

acquired by direct sense-perception, when what we
know is the perception — the sensation of green when
we look at grass, or the sensation of force when we
stop a moving ball. But it may also be derived
from memory, which makes us aware of what we
remember by the direct action of the mind. Thirdly,
another sort of knowledge by acquaintance is ac-
quired by introspection, in what is called self-con-
sciousness. When we see the grass, we may be
aware of our seeing the grass, aware of our own
mental state and mental action. Self -consciousness
is the source of all our knowledge of our own mental
life.

The other division of knowledge by experience is
that kind which is acquired by description. Our
knowledge of the grass, as distinct from our know-
ledge of our sense-perceptions of it, is knowledge by
description. It involves the memory of a number
of descriptions of the qualities of the grass, either
discovered by ourselves or supplied to us by others
by the help of language. Our concept of grass
involves such properties as being green, of being good
food for cattle, of being made of growing vegetable
cells, themselves composed of molecules, atoms, or
electrons. We cannot be aware by acquaintance or
direct mental action of the grass, only of our sense-
perceptions ; we only know the grass, if we can be
said to know it at all, by consciously or unconsciously
putting together a number of descriptions of it.

86 THE FOUNDATIONS OF SCIENCE

We now pass to the consideration of a different
class of knowledge, where we come in contact with
the principles of logic and of pure mathematics or
symbolic logic. One school of philosophers — the
" empiricists " — hold that here too all our know-
ledge is acquired by experience. An opposing school,
the rationalists, hold that logical principles are grasped
by an intuitive action of the mind, and are not proved
by experience, though they may be and usually are
suggested by experience.

Thus the truth that two and two are four or the
axiom that things that are equal to the same thing
are equal to each other, may be suggested to a be-
ginner in mathematics by the process of counting
four real objects or by the actual measurement of
the equal lengths. As soon, however, as he has
grasped the meaning of these propositions, he recog-
nises general truths which are true not only of the
objects or lines used to illustrate them, but must be
true of all things at all times and in all conditions.

This result is different in kind to the propositions
which need the support of all possible instances for
their belief, such propositions as we meet with in
the subject-matter of natural science. The state-
ment that all chemical elements were unchangeable
was gradually established by a long series of failures
to transmute them one into the other, till it became
a principle universally accepted : the probability in
its favour was enormous. Yet the discovery of the

PSYCHOLOGICAL SCIENCE 87

spontaneous disintegration of radioactive elements
into simpler atoms shows that, in such matters,
certainty cannot be reached. We can conceive of a
woild where all chemical elements are unstable,
where energy is not constant, or where masses do
not gravitate; but we cannot conceive of a world
in which two and two do not make four, or where
things equal to the same thing are not equal to each
other.

Such logical principles, then, are known to us by
intuitive apprehension. They have often been
treated as laws of thought, and in this view are a
subject of psychology as well as the root of logic and
pure mathematics.

But, besides being laws of thought, in accordance
with which we are compelled to think, they are true
in the external world. Two shillings and two shillings
in actual experience always make four shillings, in
accordance with the general principle that two and
two make four. Hence, some philosophers hold that
the laws of thought give us certain knowledge about
a real world, the world of universals, and are laws of
nature rather than laws of thought. But others
would hold that the fact that our laws of thought are
in accordance with the particular instances that
happen in nature is a matter of experience, and might
conceivably fail us. On this view it seems better to
take such self-evident logical principles as a founda-
tion for our purely ideal and universal constructions

88 THE FOUNDATIONS OF SCIENCE

of logic and pure mathematics, and leave to experi-
ence and experiment the task of examining how far
they are true in substance and in fact in the concrete
cases of the external world of phenomena. Neverthe-
less, the evidence for the external particular truth of
such principles is greater in degree, perhaps different
in kind, to the evidence for the truth of any one
physical law, such as the proportionality between elec-
tromotive force and electric current, or any physical
theory such as Newton's theory of gravity. The
evidence for such laws and theories is special in kind,
though it may be of very great extent. But the
evidence that logical principles are of true applica-
tion in nature is not special but general. All our
experience of whatever kind is consistent with it,
and hopeless intellectual confusion would follow any
breach in its observance : no science, no ordered
knowledge would be possible.

Formal logic has made great progress since it
began to use symbols, already familiar in mathe-
matics. Symbols not only serve as a shorthand
method of writing down relations which it would
be tedious and cumbersome to express in words,
but also they represent an analysis of ideas and an
almost pictorial representation of them.

Thus it is one of the fundamental laws of algebra
that a first number (x) multiplied by a second number
(y) gives a product which is equal to the product
obtained by multiplying the second number by the

PSYCHOLOGICAL SCIENCE 89

first. This law is expressed not only more concisely
but also more clearly by the symbolic equation —

xy = yx.

In this way we can perform operations of reason-
ing almost mechanically, which otherwise would
require careful and tiring thought.

" Civilisation advances by extending the number
of important operations which we can perform with-
out thinking about them. Operations of thought
are like cavalry charges in a battle — they are strictly
limited in number, they require fresh horses, and must
only be made at decisive moments." x

Now, all this intuitive knowledge, whether ex-
pressed in words or symbols, is not knowledge about
things. It is knowledge about the relations between
universals. In our equation, x and y stand for any
two quantities whatever — any number of apples or
shillings or feet or hours. The ideas of multiplica-
tion also, and of equality, are general ideas, not con-
fined to a particular operation or a particular identity.

Thus the knowledge we gain intuitively is not
knowledge about natural objects or natural phe-
nomena. It is concerned with a purely ideal world,
a world of universals.

If we wish to apply this knowledge to natural
processes, we must turn to experience ; and here
we touch the experimental sciences with which we

1 Dr. A. N. Whitehead, Introduction to Mathematics.

90 THE FOUNDATIONS OF SCIENCE

began our survey. Our experience gives us data
on which to reason ; particular instances to which we
may apply our intuitive knowledge of the relations
between universals.

Our experience gives perceptions which suggest
the corresponding concepts of length, time, and
force, and from them we divine the secondary con-
cept of mass, related to force by the definition that
a mass (ra) is measured by the force (/) required to
give it unit acceleration. Hence we get the symbolic

statement —

/= mxa.

This relation is suggested by our experience of
the force required to set masses in motion, but, in
its accurate form, it is a consequence of our defini-
tion of mass. Thus, strictly, we can only know that
it applies to the conceptual world. Given our con-
cepts of length, time, and force, and our definition
of mass, the relation f= ma is a consequence of our
logical laws of thought, and gives only a necessary
relation between our ideal concepts of universals.

But, as a matter of experience, we find that this
relation serves as a valid basis for the practical
science of dynamics. To build that science, we
need further experience of actual cases. Newton,
associating the fall of an apple with the fall of the
moon, makes the hypothesis of an attracting force
between masses to explain both. Deducing by
logical intuitive principles the consequence of the

PSYCHOLOGICAL SCIENCE 91

hypothesis, he finds that they agree with observed
facts. The hypothesis is verified in one case.

Next it is shown sufficient to explain also the
motion of the planets round the sun in ellipses. It
is verified in a second case. It proves able to account
for all the complicated perturbations of the moon's
orbit, and even to disclose the existence of a hitherto
unknown planet from its disturbing effects on others.

Each new step in this process of induction gives the
mind a new feeling of security in further applications
of the theory. It becomes more and more probable
that the next test will again prove its power ; more
and more probable, indeed, that the theory is
of universal validity, that it represents a general
law of nature. Thus by induction we pass from
particular to particular and from particular to
general.

Nevertheless, we never reach logical certainty ;
we can only approach certainty more nearly, as
instances of the successful application of the theory
multiply under our hands. There is no such thing
as certainty in natural science ; it is an affair of
probabilities. A radium atom may behave as a
permanent institution for a thousand years, and
in one surprising moment explode into fragments
at the last.

Yet, in science no less than in practical life, we
are dependent on induction at every step. In
practice it is necessary to assume that because the

92 THE FOUNDATIONS OF SCIENCE

sun has risen every yesterday it will rise to-morrow,
and in science it is necessary to assume that an
electric current, as in the past, will always exert a
magnetic force. The inductive principle of pre-
diction cannot be proved by experience, for, as
regards future cases, it is the inductive principle
alone which can justify any inference from past cases.
The principle of induction, then, is itself involved in
any attempted proof of it which appeals to experi-
ence. Hence, like the laws of thought, it must be
accepted on its intrinsic evidence as a piece of in-
tuitive knowledge. We feel instinctively that any
event which has occurred before may recur again,
and that, the oftener it has occurred before with no
exception, the greater the probability of its recur-
rence : and there we must leave it.

We have now completed our circuit of the sciences,
and have returned to our starting-point, where logic
and mathematics are applied to the study of nature,
and especially, and in the first place, to that aspect
of nature given by mechanics.

And here our brief survey of an inexhaustible field
must close. It is contrary to our aim to examine
into the details of any one science. It is also beyond
our mark to deal with the metaphysical problems
of the nature of reality, which need all knowledge for
their study and are represented in our original
diagram by the spot of blinding white light at the
centre.

PSYCHOLOGICAL SCIENCE 93

Unlike natural science, metaphysics has yielded
no general agreement in results. Perhaps no definite
and certain results are possible, and the meta-
physician may be obliged to remain for ever upheld
by the conviction that it is better to learn how to
frame aright questions of high dignity and import,
than to solve successfully the lowlier problems of
natural science.

BIBLIOGRAPHY1

The Grammar of Science (Karl Pearson : A. & C. Black,
7s. 6d.), and Science and Hypothesis (Henri Poincare ;
Translation : Scott, 3s. 6d.), are two treatises on the
philosophy of science. The Preface to An Introduction
to the Theory of Optics (A. Schuster : Arnold, 15s. net)
is valuable as a general comment upon the limits of
scientific progress. These may be read for their treat-
ment of science in general.

The Recent Development of Physical Science (W. C. D.
Whetham : Murray, 5s.), gives a description of modern
work in physics suitable for the general reader. The
Science of Life (J. A. Thomson : Blackie, 2s. 6d.), an
historical account of the development of biology.

An introduction to the various branches of science
mentioned in this work will be found among " The
People's Books," each volume of which has been specially
written to be of use to general readers, and contains a
guide to further reading.

1 This list of books has been drawn up by the editor of " The
People's Books."

INDEX

50

, the, conception of, 49,

Anatomy, early researches in, 62
Astronomy, gravitational, 26-28
Atomic theory, 34, 35

BACTERIOLOGY, 61
Bequerel rays, 46
Biological science, 7, 8, 61-70
author's colour theory of,

9-12
Botany, early researches in, 53,

54
Burning, phenomena of, 35

CHEMISTRY, 35, 67

of celestial bodies, 42
Colour sensations, 73

DYNAMICS, early researches in,
16, 17, 19

ELECTRICAL science, develop-
ment of, 43

theory of matter, 49
Eugenics. 58
Evolution of species, 65

FARADAY'S researches in electri-
city, 43

GALILEO, on law of velocity of

fall, 19-27
Geology, early researches in, 55

HEAT, nature of, 36 et aeq.
Helium, 42

KNOWLEDGE, theory of, 85

LEVER, law of the, 16, 18
Light, nature of, 39 et seq.

sensations of, 73
Logic, inductive, 86, 91

MALARIA, 63

Malta fever, 65

Matter, electrical theory of, 49

nature of, 34

Mechanical science, 16, 29
Medical science, 62, 53, 65, 66
Memory, 75, 76
Mendelism, 59
Microbic diseases, 61
Microbiology, 61
Molecular theory, 34, 35

NATURAL Selection, 56
Newton, Sir Isaac, 26, 28, 32,
33, 34, 36, 39

PERSE VERATION, 75
Physical science, 7-11, 16-50
Physiology, 11, 12, 53
Psychological science, 9, 10, 12,
71-93

RADIO-ACTIVITY, 47

Radium, 47

Rontgen rays, 45, 46, 47

SCIENCES, the, author's colour
scheme of, 9-15
divisions of, 7
Sense perceptions, 71
Statics, 17, 18, 19

THERMODYNAMICS, 38, 39

VELOCITY, law of, 19-26, 29

of light, 33
Vitalism, 68, 69
Voltaic pile, the, 43

WAVE theory of light, 40
YEAST, fermentation of, 62, 63
ZOOLOGY, early researches in, 54

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