SCIENCE.
Science, 309—Counting and Arithmetic, 310—Measuring
and Weighing, 316—Geometry, 318—Algebra, 322—Physics,
323—Chemistry, 328—Biology, 329—Astronomy, 332—Geography and
Geology, 335—Methods of Reasoning, 336—Magic, 338.
Science is exact, regular, arranged knowledge. Of common knowledge
savages and barbarians have a vast deal, indeed the struggle of life
could not be carried on without it. The rude man knows much of the
properties of matter, how fire burns and water soaks, the heavy sinks and
the light floats, what stone will serve for the hatchet and what wood
for its handle, which plants are food and which are poison, what are
the habits of the animals that he hunts or that may fall upon him. He
has notions how to cure, and much better notions how to kill. In a rude
way he is a physicist in making fire, a chemist in cooking, a surgeon
in binding up wounds, a geographer in knowing his rivers and mountains,
a mathematician in counting on his fingers. All this is knowledge, and
it was on these foundations that science proper began to be built up,
when the art of writing had come in and society had entered on the
civilized stage. We have to trace here in outline the rise and progress
of science. And as it has been especially through counting and measuring
that scientific methods have come into use, the first thing to do is to
examine how men learnt to count and measure.
Even those who cannot talk can count, as was well shown by the
deaf-and-dumb lad Massieu, who wrote down among the recollections of his
childhood before the Abbé Sicard educated him, “I knew the numbers before
my instruction; my fingers had taught me them.” We ourselves as children
began arithmetic on our fingers and now and then take to them still, so
that there is no difficulty in understanding how a savage whose language
has no word for a number above three will manage to reckon perhaps a list
of fifteen killed and wounded, how he will check off one finger for each
man, and at last hold up his hand three times to show the result. The
next question is, how numeral words came to be invented. This is answered
by many languages, which show in the plainest way how counting on fingers
and toes led to making numerals. When a Zulu wants to express the number
six, he says _tatisitupa_, which means “taking the thumb;” this signifies
that the speaker has counted all the fingers of his left hand, and begun
with the thumb of the right. When he comes to seven, for instance when
he has to express that his master bought seven oxen, he will say _u
kombile_, that is, “he pointed”; this signifies that in counting he had
come to the pointing-finger or forefinger. In this way the words “hand,”
“foot,” “man,” have in various parts of the world become numerals.
An example how they are worked may be taken from the language of the
Tamanacs of the Orinoco; here the term for five means “whole hand,” six
is “one of the other hand,” and so on up to ten or “both hands”; then
“one to the foot” is eleven, and so on to “whole foot” or fifteen, “one
to the other foot” or sixteen, and thence to “one man,” which signifies
twenty, “one to the hands of the next man” being twenty-one, and the
counting going on in the same way to “two men” which stands for forty,
&c. &c. Now this state of things teaches a truth which has sometimes been
denied, that the lower races of men have, like ourselves, the faculty of
progress or self-improvement. It is evident that there was a time when
the ancestors of these people had in their languages no word for fifteen
or sixteen, nor even for five or six, for if they had they could not have
been so stupid as to change them for their present clumsy phrases about
hands and feet and men. We see back to the time when, having no means of
reckoning such numbers except on their fingers and toes, they found they
had only to describe in words what they were doing, and such a phrase
as “both hands” would serve them as a numeral for ten. Then they would
keep up these as numerals after their original sense was lost, like the
Vei negros who called the number twenty _mo bande_, but had forgotten
that this must have meant “a person finished.” The languages of nations
long civilized seldom show such plain meaning in their numerals, perhaps
because they are so ancient and have undergone such change. But all
through the languages of the world, savage or civilized, with exceptions
too slight to notice here, there is ineffaceable proof that the numerals
arose out of the primitive counting on fingers and toes. This always led
men to reckon by fives, tens, and twenties, and so they reckon still. The
quinary kind of counting (by fives) is that of tribes like the negros
of Senegal, who count one, two, three, four, five, five-one, five-two,
&c.; we never count numbers thus in words, but we write them so in the
Roman numerals. The decimal counting (by tens) is the most usual in the
world, and our ordinary counting is done by it, thus eighty-three is
“eight tens and three.” The vigesimal counting (by twenties) which is
the regular mode in many languages, has its traces left in the midst
of the decimal counting of civilized Europe, as in English “fourscore
and three,” French “quatre-vingt trois,” that is “four twenties and
three.” Thus it can hardly be doubted that the modern world has inherited
direct from primitive man his earliest arithmetic worked on nature’s
counting-board—the hands and feet. This also explains (p. 18) why the
civilized world uses a numeral system based on the inconvenient number
ten, which will not divide either by three or four. Were we starting
our arithmetic afresh, we should more likely base it on the duodecimal
notation, and use dozens and grosses instead of tens and hundreds.
To have named the numbers was a great step, but words hardly serve beyond
the very simplest arithmetic, as any one may satisfy himself by trying
to multiply “seven thousand eight hundred and three” by “two hundred
and seventeen” in words, without helping himself by turning them in
thought into figures. How did men come to the use of numeral figures?
To this question the beginning of an answer may be had from barbaric
picture-writing, as where a North American warrior will make four little
marks //// to show that he has taken four scalps. This is very well for
the small numbers, but becomes clumsy for higher ones. So already when
writing was in its infancy, the ancients had fallen upon the device of
making special marks for their fives, tens, hundreds, &c., leaving the
simple strokes to be used only for the few units over. This is well
seen in Fig. 76 which shows how numeration was worked in ancient Egypt
and Assyria. Nor has this old method died out in the world, for the
Roman numerals I., V., X., L., still in common use among ourselves, are
arranged on much the same principle. Another device, which arose out
of the alphabet, was to take the letters in their order to stand for
numbers. Thus the sections of Psalm CXIX. are numbered by the letters of
the Hebrew alphabet, and the books of the Iliad by the letters of the
Greek alphabet. By these various plans the arithmetic of the ancient
civilized nations made great progress. Still their numeration was very
cumbrous in comparison with that of the modern world. Let us put down
MMDCLXIX. and multiply by CCCXLVIII., or β͵χʹξʹθʹ by τʹμʹηʹ, and a few
minutes’ trial will not fail to convince us of the superiority of our
ciphers.
[Illustration: FIG. 76.—Ancient Egyptian and Assyrian numeration.]
[Illustration: FIG. 77.—Mode of calculation by counters and by figures on
Abacus.]
To understand how the art of ciphering came to be invented, it is
necessary to go back to a ruder state of things. In Africa, negro traders
may be seen at market reckoning with pebbles, and when they come to five,
putting them aside in a little heap. In the South Sea Islands it has been
noticed that people reckoning, when they came to ten, would not put aside
a heap of ten things, but only a single bit of coco-nut stalk to stand
for ten, and then a bigger piece when they wanted to represent ten tens
or a hundred. Now to us it is plain that this use of different kinds of
markers is unnecessary, but all that the reckoner with little stones or
beans has to do, is to keep separate his unit-heap, his ten-heap, his
hundred-heap, &c. This use of such things as pebbles for “counters,”
which still survives in England among the ignorant, was so common in the
ancient world, that the Greek word for reckoning was _psēphizein_, from
_psēphos_, a pebble, and the corresponding Latin word was _calculare_
from _calculus_, a pebble, so that our word _calculate_ is a relic of
very early arithmetic. Now to work such pebble-counting in an orderly
manner, what is wanted is some kind of abacus or counting-board with
divisions. These have been made in various forms, as the Roman abacus
with lines of holes for knobs or pegs, or the Chinese swan-pan with
balls strung on wires, on which the native calculators in the merchants’
counting-houses reckon with a speed and exactness that fairly beats the
European clerk with his pencil and paper. It may have been from China
that the Russian traders borrowed the ball-frame on which they also do
their accounts, and it is said that a Frenchman noticing it in Russia at
the time of Napoleon’s invasion was struck with the idea that it would
serve perfectly to teach little children arithmetic; so he introduced it
in France, and thence it found its way into English infants’ schools. Now
whatever sort of abacus is used, its principle is always the same, to
divide the board or tray into columns, so that in one column the stones,
beans, pegs, or balls, stand for units, in the next column they are tens,
in the next hundreds, and so on, Fig. 77. Here the three stones in the
right-hand column stand for 3, the nine in the next column for 90, the
one in the fourth column for 1,000 and so on. The next improvement was
to get rid of the troublesome stones or beans, and write down numbers in
the columns, as is here shown with Greek and Roman numerals. But now the
calculator could do without the clumsy board, and had only to rule lines
on his paper, to make columns for units, tens, hundreds, &c. The reader
should notice that it is not necessary to the principle of the abacus
that each column should stand for ten times the one next it. It may be
twelve or twenty or any other number of times, and in fact the columns in
our account-books for £ _s._ _d._ or _cwts._ _qrs._ _lbs._, are surviving
representatives of the old method of the abacus. Such reckoning had still
the defect that the numbers could not be taken out of the columns, for
even when each number from one to nine has a single figure to stand for
it, there would still be here and there an empty column (as is purposely
left in Fig. 77) which would throw the whole into confusion. To us now
it seems a very simple thing to put a sign to show an empty column, as
we have learned to do with the zero or 0, so that the number expressed
in the picture of the abacus can be written down without any columns,
241093. This invention of a sign for nothing, was practically one of the
greatest moves ever made in science. It is the use of the zero which
makes the difference between the old arithmetic and our easy ciphering.
We give the credit of the invention to the Arabs by using the term Arabic
numerals, while the Arabs call them Indian, and there is truth in both
acknowledgments of the nations having been scholars in arithmetic one
to the other. But this does not go to the root of the matter, and it is
still unsettled whether ciphering was first devised in Asia, or may be
traced further back in Europe to the arithmeticians of the school of
Pythagoras. As to the main point, however, there is no doubt, that modern
arithmetic comes out of ancient counting on the columns of the abacus,
improved by writing a dot or a round 0 to show the empty column, and by
this means young children now work calculations which would have been
serious labour to the arithmeticians of the ancient world.
Next as to the art of measuring. Here it may be fairly guessed that man
first measured, as he first counted, on his own body. When barbarians
tried by finger-breadths how much one spear was longer than another, or
when in building huts they saw how to put one foot before the other to
get the distance right between two stakes, they had brought mensuration
to its first stage. We sometimes use this method still for rough work,
as in taking a horse’s height by hands, or stepping out the size of a
carpet. If care is taken to choose men of average size as measurers,
some approach may be made to fair measurement in this way. That it was
the primitive way can hardly be doubted, for civilized nations who have
more exact means still use the names of the body-measures. Besides the
_cubit_, _hand_, _foot_, _span_, _nail_, already mentioned in p. 17, we
have in English the _ell_, (of which the early meaning of arm or fore-arm
is seen in _el_-bow, the arm-bend), also the _fathom_ or cord stretched
by the outspread arms in sailors’ fashion, and the _pace_ or double
step (Latin _passus_) of which a thousand (_mille_) made the _mile_.
But though these names keep up the recollection of early measurement by
men’s limbs, they are now only used as convenient names for standard
measures which they happen to come tolerably near to, as for instance
one may go a long way to find a man’s foot a foot long by the rule.
Our modern measurements are made by standard lengths, which we have
inherited with more or less change from the ancients. It was a great
step in civilization when nations such as the Egyptians and Babylonians
made pieces of wood or metal of exact lengths to serve as standards. The
Egyptian cubit-rules with their divisions may still be seen, and the
King’s Chamber in the Great Pyramid measures very exactly 20 cubits by
10, the cubit being 20·63 of our inches. Our foot has scarcely altered
for some centuries, and is not very different from the ancient Greek and
Roman feet. The French at the first Revolution made a bold attempt to
cast off the old traditional standards and go straight to nature, so they
established the _metre_, which was to be a ten-millionth of the distance
from the pole to the equator. The calculation however proved inexact,
so that the metre is now really a standard measure of the old sort, but
so great is the convenience of using the same measures, that the metre
and its fractions are coming more and more into use for scientific work
all over the world. The use of scales and weights, and of wet and dry
measures, had already begun among the civilized nations in the earliest
known times. Our modern standards can even to some extent be traced back
to those of the old world, as for instance the pound and ounce, gallon
and pint, come from the ancient Roman weights and measures.
[Illustration: FIG. 78.—Rudimentary practical Geometry. 1, scalene
triangle; 2, folded right angle; 3, folded triangle; 4, rectangle folded
in circle.]
From measuring feet in length, men would soon come to reckoning the
contents, say of an oblong floor, in square feet. But to calculate the
contents of less simple figures required more difficult geometrical
rules. The Greeks acknowledged the Egyptians as having invented
_geometry_, that is, “land-measuring,” and there may be truth in the
old story that the art was invented in order to parcel out the plots of
fertile mud on the banks of the Nile. There is in the British Museum
an ancient Egyptian manual of mensuration (the Rhind papyrus), one of
the oldest books in the world, originally written more than 1,000 years
before Euklid’s time, and which shows what the Egyptians then knew and
did not know about geometry. From its figures and examples it appears
that they used square measure, but reckoned it roughly; for instance,
to get the area of the triangular field ABC Fig. 78 (1) they multiplied
half AC by AB, which would only be correct when BAC is a right angle.
When the Egyptians wanted the area of a circular field, they subtracted
one-ninth from the diameter and squared; thus if the diameter were 9
perches, they estimated that the circle contained 64 square perches,
which the reader will find on trial is a good approximation. All this
was admirable for the beginnings of geometry, and the record may well
be believed that Greek philosophers such as Thales and Pythagoras, when
they came to Egypt, gained wisdom from the geometer-priests of the land.
But these Egyptian mathematicians, being a priestly order, had come to
regard their rules as sacred, and therefore not to be improved on, while
their Greek disciples, bound by no such scientific orthodoxy, were free
to go on further to more perfect methods. Greek geometry thus reached
results which have come down to us in the great work of Euklid, who used
the theorems known to his predecessors, adding new ones and proving the
whole in a logical series. It must be clearly understood that elementary
geometry was not actually invented by means of definitions, axioms, and
demonstrations like Euklid’s. Its beginnings really arose out of the
daily practical work of land-measurers, masons, carpenters, tailors.
This may be seen in the geometrical rules of the altar-builders of
ancient India, which do not tell the bricklayer to draw a plan of such
and such lines, but to set up poles at certain distances, and stretch
cords between them. It is instructive to see that our term _straight
line_ still shows traces of such an early practical meaning; _line_ is
_linen_ thread, and _straight_ is the participle of the old verb to
_stretch_. If we stretch a thread tight between two pegs, we see that the
stretched thread must be the shortest possible; which suggests how the
straight line came to be defined as the shortest distance between two
points. Also, every carpenter knows the nature of a right angle, and he
is accustomed to parallel lines, or such as keep the same distance from
one another. To the tailor, the right angle presents itself in another
way. Suppose him cutting a doubled piece of cloth to open out into the
gore or wedge-shaped piece BAC in Fig. 78 (2). He must cut ADB a right
angle, or his piece when he opens it will have a projection or a recess,
as seen in the figure. When he has cut it right, so that BDC opens in
a straight line, then he cannot but see that the sides AB, AC, and the
angles ABC, ACB must exactly match, having in fact been cut out on one
another. Thus he arrives, by what may be called tailor’s geometry, at the
result of Euklid I. 5, which now often goes by the name of the “asses’
bridge.” Such easy properties of figures must have been practically known
very early. But it is also true that the ancients were long ignorant of
some of the problems which now belong to elementary teaching. Thus it has
just been mentioned how the Egyptian land-surveyors failed to make out
an exact rule to measure a triangular field. Yet had it occurred to them
to cut out the diagram of a triangle from a sheet of papyrus, as we may
do with the triangle ABC in Fig. 78 (3), and double it up as shown in
the figure, then they would have found that it folds into the rectangle
EFHG, and, therefore, its area is the product of the height by half the
base. It would be seen that this is no accident, but a property of all
triangles, while at the same time it would appear that the three angles
at A, B, C, all folding together at D, make up two right angles. Though
the more ancient Egyptian geometers do not seem to have got at either of
these properties of the triangle, the Greek geometers had in some way
become well aware of them before Euklid’s time. The old historians who
tell the origin of mathematical discoveries do not always seem to have
understood what they were talking of. Thus it is said of Thales that
he was the first to inscribe the right-angled triangle in the circle,
and thereupon sacrificed a bull. But a mathematician of such eminence
could hardly have been ignorant of what any intelligent carpenter has
reason to know, how an oblong board fits into a circle symmetrically;
the problem of the right-angled triangle in the semicircle is involved
in this, as is seen by (4) in the present figure. Perhaps the story
really meant that Thales was the first to work out a strict geometrical
demonstration of the problem. The tale is also told of Pythagoras, and
another version is that he sacrificed a hekatomb on discovering that the
square on the hypothenuse of a right-angled triangle is equal to the sum
of the squares on the other two sides (Euklid I. 47). The story is not a
likely one of a philosopher who forbad the sacrifice of any animal. As
for the proposition, it is one which may present itself practically to
masons working with square paving-stones or tiles; thus, when the base
is 3 tiles long, and the perpendicular 4, the hypothenuse will be 5, and
the tiles which form a square on it will just be as many as together form
squares on the other two sides. Whether Pythagoras got a hint from such
practical rules, or whether he was led by studying arithmetical squares,
at any rate he may have been the first to establish as a general law this
property of the right-angled triangle, on which the whole systems of
trigonometry and analytical geometry depend.
The early history of mathematics seems so far clear, that its founders
were the Egyptians with their practical surveying, and the Babylonians
whose skill in arithmetic is plain from the tables of square and cube
numbers drawn up by them, which are still to be seen. Then the Greek
philosophers, beginning as disciples of these older schools, soon left
their teachers behind, and raised _mathematics_ to be, as its name
implies, the “learning” or “discipline” of the human mind in strict
and exact thought. In its first stages, mathematics chiefly consisted
of arithmetic and geometry, and so had to do with known numbers and
quantities. But in ancient times the Egyptians and Greeks had already
begun methods of dealing with a number without as yet knowing what it
was, and the Hindu mathematicians, going further in the same direction,
introduced the method now called algebra. It is to be noticed that the
use of letters as symbols in algebra was not reached all at once by a
happy thought, but grew out of an earlier and clumsier device. It appears
from a Sanskrit book that the venerable teachers began by expressing
unknown quantities by the term “so-much-as,” or by the names of colours,
as “black,” “blue,” “yellow,” and then the first syllables of these words
came to be used for shortness. Thus if we had to express twice the square
of an unknown quantity, and called it “so much squared twice,” and then
abbreviated this to _so sq 2_, this would be very much as the Hindus
did in working out the following problem, given in Colebrooke’s _Hindu
Algebra_: “The square root of half the number of a swarm of bees is gone
to a shrub of jasmin: and so are eight-ninths of the whole swarm: a
female is buzzing to one remaining male, that is humming within a lotus,
in which he is confined, having been allured to it by its fragrance
at night. Say, lovely woman, the number of bees.” This Hindu equation
is worked out clumsily from the want of the convenient set of signs =
+ -, which were invented later in Europe, but the minus numbers are
marked, and the solution is in principle an ordinary quadratic. The Arab
mathematicians learnt from India this admirable method, and through them
it became known in Europe in the middle ages. The Arabic name given to
it is _al-jabr wa-l-mukabalah_, that is, “consolidation and opposition,”
this meaning what is now done by transposing quantities on the two
sides of an equation; thence comes the present word _algebra_. It was
not till about the 17th century in Europe that the higher mathematics
were thoroughly established, when Descartes worked into a system the
application of algebra to geometry, and Galileo’s researches on the path
of a ball or flung stone brought in the ideas which led up to Newton’s
fluxions and Leibnitz’s differential calculus, with the aid of which
mathematics have risen to their modern range and power. Mathematical
symbols have not lost the traces of their first beginnings as abbreviated
words, as where _n_ still stands for _number_ and _r_ for _radius_,
while √, which is a running-hand _r_, does duty for root (_radix_),
and ∫, which is an old-fashioned _s_, stands for the sum (_summa_) in
integration.
Mechanics and Physics, worked mathematically, now form the very
foundation of our knowledge of the universe. But in the old barbaric
life, men had only rudimentary notions of them. The savage understands
the path of a projectile well enough to aim it, and how to profit by
momentum when he mounts his axe on a long rather than a short handle.
But he hardly comes to bringing these practical ideas to a principle or
law. Even the old civilized nations of the East, though they could lift
stones with the lever, set their masonry upright with the plumb-line,
and weigh gold in the balance, are not known to have come to scientific
study of mechanical laws. What makes this more sure is that if they had,
the Greeks would have learnt it of them, whereas it is among the Greek
philosophers that the science is found just coming into existence. In
Aristotle’s time they were thinking about mechanical problems, though by
no means always rightly; it was considered that a body is drawn toward
the centre of the world, but the greater its weight the faster it will
fall. The chief founder of mechanical science was Archimedes, who worked
out from the steel-yard the law of the lever, and deduced thence cases of
all the particles of a body balancing on a common centre, now called its
centre of gravity; he even gave the general theory of floating bodies,
which mathematicians far on in the middle ages could hardly be brought
to understand. Indeed, mechanical science, after the classical period,
shared the general fate of knowledge during the long dead time when so
much was forgotten, and what was left was in bondage to the theology of
the schoolmen. It sometimes surprises a modern reader that the “wisdom
of the ancients” should still now and then be set up as an authority in
science. But the scholars of the middle ages, who on many scientific
points knew less than the ancient Greeks, might well look up to them. It
is curious to look at the book of Gerbert (Pope Sylvester II.) who was
a leading mathematician in the tenth century, and who bungles like an
early Egyptian over the measurement of the area of a triangle, though
the exact method as stated by Euklid had been well known in classical
times. Physical science might almost have disappeared if it had not been
that while the ancient treasure of knowledge was lost to Christendom,
the Mohammedan philosophers were its guardians, and even added to its
store. For this they have not always had due praise. A pretty story is
told of Galileo inventing the pendulum, being led to it by watching the
great hanging lamp in the cathedral of Pisa swinging steadily to and
fro; but as a matter of fact, it appears that six centuries earlier Ebn
Yunis and other Moorish astronomers were already using the pendulum as a
time-measurer in their observations. Of all the services which Galileo
did for science, perhaps the greatest was his teaching clearer ideas of
force and motion. People had of old times been deceived by the evidence
of their senses into the belief that the force of a moving body would
gradually become exhausted and it would stop of itself, but this idea of
force was changed by the new principle that force is as much required to
stop a moving body as to set it in motion, and that did no opposing force
retard the arrow or the wheel, the one would fly and the other roll on
for ever. In that age of mathematics applied to science new discoveries
followed fast. If Archimedes could have come to life again, he would
have seen progress going on at last, when the pressure of the air was
weighed with Torricelli’s barometer, and Stevin of Bruges made out the
principle of the parallelogram of forces. The notion of an attractive
force had come into the minds of philosophers by observing how the magnet
attracts iron at a distance, and glass and other substances when rubbed
become attractive. Thus the way was open for Newton to calculate the
effect of gravitation as such an attractive force, and by it to explain
the movements of the heavenly bodies, thus bringing the visible world
within the sway of one universal law. In the present day, among the
great laws which have been established in physical science, is that of
the conservation of energy, that power is not created and destroyed in
the processes of nature or the machines of man, but is transformed into
new manifestations equivalent to those which were before. Philosophers’
minds used often to be set on the invention of a perpetual moving power,
that should go on creating its own force. But nowadays this idea is
so discarded that, when some projector plans an absurd machine, he is
sufficiently answered by being shown that if his machine could work,
the perpetual motion would be possible. The modern mechanician has
only to apply in the most desirable way the stores of force placed at
his disposal by nature, and within this well-understood boundary his
business flourishes more and more.
Among the forms or manifestations of energy are sound, light, heat,
electricity. The classic philosophers knew in a vague way that sound
spreads like waves; and the relation between the length of a harpstring
and its note was laid down in arithmetical rule by Pythagoras, who
measured it with the instrument we still use, the monochord. But it was
the moderns who measured the velocity of sound, explained musical pitch
by the rate of vibration, and made the science of tone. About light the
ancients knew more. Their polished metal mirrors, flat and curved, had
taught them the first principles of reflexion. Nor were they ignorant of
refraction; they already knew the familiar experiment of putting a ring
in a basin and pouring in water till it becomes visible. A rock-crystal
lens has been dug up at Nineveh, and the Greeks and Romans were well
acquainted with glass lenses. One is surprised that neither the Arab
astronomers, who knew a good deal of optics, nor Roger Bacon, who in the
thirteenth century gave an intelligent account of their science, ever
seem to have combined two lenses into a telescope. It was not till the
seventeenth century that a telescope is plainly mentioned in Holland,
and Galileo, hearing of it, made the famous instrument with which he saw
Jupiter’s moons, and revolutionized men’s ideas of the universe. The
microscope and telescope may be called inverted forms of one another,
and their inventions came nearly together. By these two instruments the
range of man’s vision has been so vastly extended beyond his unaided
eyesight, that animalcules under a ten-thousandth of an inch long can
now be watched through all the stages of their life, while stars whose
distance from the earth is hundreds of thousands of billions of miles,
are within the maps of the universe. The rainbow led to the problem of
the decomposition of light and the theory of colour. The doctrine that
light was as it were bright particles emitted in straight lines from the
luminous body, failed to explain effects such as light extinguishing
light by interference, and it has yielded to the undulatory theory, of
ethereal light-waves of extreme smallness and speed. In our own day the
lines of the spectrum have become the means of recognising a glowing
substance, so that the astronomer whose telescope reveals the faint
shine of a nebula in the depths of the heavens, may test its composition
with the spectroscope, as if it were a gas-jet on the laboratory table.
Closely connected with the science of light, is the science of heat. Not
only do heat and light proceed together from the sun or fire, but the two
were seen to be subject to the same laws, when it was noticed that the
mirror or lens which concentrated a bright spot of light, also brought
to the same focus heat that would set wood on fire. The great step in
the study of heat was the invention of the heat-measurer or thermometer.
Who first made it is not known, but it was about three centuries ago,
and its earliest form may have been the air-flask with its tube in which
coloured water rises and falls, which is still the most striking way of
showing a class the principle of thermometers. The doctrine of heat as
due to vibration explains how heat is transformed force, so that the
steam-hammer worked by the heat used in the furnace can be set to beat
cold iron till it is white-hot; thus part of the force which came from
heat has gone back into heat, and with the heat re-appears the other
form of radiant energy, light. Lastly, the history of electricity comes
from the time when the ancients wondered to see amber when rubbed pick
up morsels of straw, and the loadstone draw bits of iron. The pointing
of the loadstone south and north seems to have been earliest noticed
by the Chinese, whence in the middle ages came its world-wide use in
navigation. The electrical machine is only an enlarged form of the old
experiment of rubbing the bit of amber. But the discoveries associated
with the name of Volta and Galvani brought in a new method of generating
electricity by chemical action in the battery. Franklin’s kite proved the
lightning-flash to be but a great electric spark. Oersted’s current-wire
deflecting a magnetic needle showed the relation between electricity and
magnetism, and set on foot the line of invention to which the world owes
the electric telegraph and much besides.
Next, as to chemistry. Its beginnings lie in practical processes such as
smelting metal from the ore, fusing sand and soda into glass, and tanning
leather with astringent pods or bark. The oldest civilized nations knew
these and many other chemical arts, which not only were learnt by the
artificers of Greece and Rome, but from time to time new processes were
added to the store of knowledge, as when we hear of their distilling
mercury from cinnabar, or treating copper with vinegar to make verdigris.
In early civilized ages also there arose beside these practical recipes
the first dim outlines of scientific chemistry. The Greek philosophers
expressed their ideas of the states of matter by the four elements, fire,
air, water, earth; and they also had learnt or invented the doctrine of
matter being made up of atoms—a principle now more influential than ever
in modern lecture-rooms. The successors of the Greeks were the Arabic
alchemists, and their disciples in mediæval Christendom. Their belief
that matter might be transmuted or transformed led many of them to spend
their lives among their furnaces and alembics in the attempt to turn
baser metals into gold. To modern chemists, who would not be surprised to
find all the many so-called elements proved to be forms of one matter,
the alchemists’ idea does not seem quite unreasonable in itself, and
practically it led them to the pursuit of truth by experiment, so that
though they found no philosophers’ stone, they were repaid by discoveries
such as alcohol, ammonia, sulphuric acid. Their method, being founded on
trials of real fact, cleared itself more and more from the magical folly
it had grown up with, and the alchemist prepared the way for the later
chemist. What of all things brought on the new chemical knowledge, was
the explanation of what takes place in burning, rusting, and breathing.
How is it that the air in a receiver is spoilt by a burning candle or a
mouse within, so that it no longer allows flame or life? How is it that
while some substances, like charcoal, seem to be dissipated by fire,
others, like lead or iron, turn into matter heavier than before? The
answers to such questions led the way to clearer notions of chemical
combination, but it was long before it was understood by what fixed laws
of affinity and proportion this combination takes place. The advanced
student of chemistry may spend an instructive hour in looking over old
chemistry books, where the catalogue of substances is a confused chaos,
not as yet brought into form and order on the lines of Dalton’s atomic
theory.
From the chemical nature of matter we pass to the nature of living
things. The more evident parts of biology or the science of life, have
come under man’s attentive observation from the first. So far as zoology
and botany consist in noticing the forms and habits of animals and
plants, savages and barbarians are skilled in them. Such people, for
instance, as the natives of the South American forests, have names for
each bird and beast, whose voices, resorts, and migrations they know
with an accuracy that astonishes the European naturalist whom they
guide through the jungle. The catalogue of the Brazilian native names
of animals and plants, often curiously descriptive of their natures,
would make a small book. Thus the _jaguara pimina_ or painted jaguar
is distinguished from the _jaguarete_ or great jaguar; the _capybara_
signifies the creature “living in the grass,” the _ipe-caa-goene_, or
“little wayside-plant-emetic,” is our _ipecacuanha_. Mankind everywhere
possesses this sort of popular Natural History. So it is with anatomy.
When the savage kills a deer, cuts it up, cooks the joints, heart, and
liver, makes clothes and straps of the hide, cuts harpoon-heads and
awls out of the long bones, and uses the sinews for thread, it stands
to reason that he must have a good rough knowledge of the anatomy of
an animal. The barbaric warrior and doctor have beyond such butchers’
anatomy an acquaintance with the structure of man’s body, as may be
seen in the description of the wounds of the heroes in the Iliad, where
the spear takes one in the diaphragm below the heart, and another has
the shoulder-tendon broken which makes his arm drop helpless. Among
the Greeks such rough knowledge passed into the scientific stage when
Aristotle wrote his book on animals, and Hippokrates took medicine
away from the priests and sorcerers to make it a method of treatment
by diet and drugs. The action of the body came to be better understood
during this classical period, as, for instance, is seen in the nerves
leading to and from the brain being no longer confounded with the sinews
which pull the limbs, although the same Greek word _neuron_ (_nerve_)
still continued to be used for both. It is curious how long it took the
ancients to get at the notion of what muscle is, and how it acts. They
never understood the circulation of the blood, though they had ideas
about it, as in Plato’s celebrated passage in the Timaios which compares
the heart to a fountain sending the blood round to nourish the body,
which is like a garden laid out with irrigating channels. Imperfect as
ancient knowledge was, it may be plainly seen how modern science is
based upon it. Thus the medical terms of Galen’s system, such as the
_diagnosis_ of disease, are still used; and indeed many old physician’s
words have passed into common talk, as when one is said to be in a
_sanguine humour_, which carries us back to the time when the humours
or fluids of the body were thought to cause the state of mind, the
humour which is sanguine, or “of the blood,” being lively and impetuous.
But in knowledge of the body the moderns have left the ancients quite
behind, now that the microscope shows its minute vessels and tissues,
and there have been made out the circulation of the blood, the process
of respiration, the chemistry of digestion, and the travelling of
currents along the nerves. Natural History still goes on the principles
of Aristotle, when he traces life on from lifeless matter through the
series of plants and animals. Modern naturalists like Linnæus so improved
the old classification, that it became possible to take a plant or
animal one had never seen before and did not know the name of, and make
out by examination that it must belong to such and such a genus and
species. Moreover, naturalists have long been seeking to understand why
the thousands of species should arrange themselves in groups or genera,
the species in each genus being connected by a common likeness, and the
genera themselves falling into higher groups, or orders. The thought that
the likeness among the species forming a genus is a family likeness,
due to these species being in fact the varied descendants of one race
or stock, is the foundation of that theory of development or evolution
which for many ages has been in the minds of naturalists, and now so
largely prevails. This is not the place to discuss the doctrine of
descent or development (see page 38), but it is worth while to remember
that the very word _genus_ meant originally birth or race, so that the
naturalist who sets down the horse, ass, zebra, quagga, as all belonging
to one genus Equus, is really suggesting that they are all descended from
one kind of animal, and are in fact distant cousins, which is the first
principle of the development-theory.
The world we live in is the subject of astronomy, geography, geology. It
seems plain how the rudiments of these sciences began from the evidence
of men’s senses. Children living unschooled in some wild woodland would
take it as a matter of course that the earth is a circular floor, more
or less uneven, arched over with a dome or firmament springing from the
horizon. Thus the natural and primitive notion of the world is that it
is like a round dish with a cover. Rude tribes in many countries are
found thinking so, and working out the idea so as to account for such
phenomena as rain, which is water from above dripping in through holes
in the sky-roof. This firmament is studded with stars, and is a few
miles off. There is nothing to suggest to the savage that the sun should
be enormously more distant than the cloud it seems to plunge into. The
sun seems to go down in the west into the sea, or through an opening
in the horizon, and to rise in like manner in the east, so that sunset
and sunrise force on the minds of the first rude astronomers the belief
in an under-world or infernal region, through which the sun travels
in the night, and which to many a nation has seemed also the abode of
departed souls, when after their bright day of life they sink like the
sun into the night of death. The sun and moon move as living gods in the
heaven, or at least are drawn or driven by such celestial powers, while
the presence of living beings in the sky seems peculiarly manifest in
eclipses, when invisible monsters seize or swallow the sun and moon.
All this is very natural, so natural indeed that more correct astronomy
has not yet rooted it out of Europe. Not many years ago a schoolmaster
who ventured to lecture on astronomy in the west of England roused the
displeasure of the country folk, that this young man should tell them
the world was round and went about, when they had lived on it all their
lives and knew it was flat and stood still. One part of the earliest
astronomy, which was so sound as to have held its own ever since, was the
measurement of time by the sun, moon, and stars. The day and the month
fix themselves at once. In a less exact way the seasons of the year, such
as the rainy season, or the icy season, or the growing season, furnish
a means of reckoning, as where a savage tells of his father’s death
having been three rains or three winters ago. Rude tribes, who observe
the stars to find their way by, notice also that the rising and setting
of particular stars or constellations mark the seasons. Thus the natives
of South Australia call the constellation Lyra the Loan-bird, for they
notice that when it sets with the sun, the season for getting loan-birds’
eggs has begun. It stands to reason that the great facts of the year’s
course, the change of the sun’s height at noon, and the lengthening and
shortening of the days, would be noticed, so that even among people who
have not as yet measured them with any accuracy, there exists in a loose
way the notion of the year. Within the year, too, the successive moons
or months come to be arranged with some regularity, as where the Ojibwas
reckoned in order the wild-rice moon, the leaves-falling moon, the
ice-moon, the snow-shoes moon, and so forth. But such lunar months have
to be got into the year as they best may. Indeed what distinguishes the
uncivilized calendar, is that though days, months, and years are known,
the days are not yet fitted regularly into the months, nor is it settled
how many months, much less how many days, the year is to consist of.
When we look from this to the astronomy of the ancient cultured nations,
we find great progress made in observing and calculating. Yet the
astronomer-priests who for ages watched and recorded the aspect of
the heavens, had not yet cut themselves free from the ideas of their
barbarian forefathers as to what the world as a whole was like. In the
Egyptian Book of the Dead, the departed souls descend with the sun-god
through the western gate, and travel with him among the fields and rivers
of the under-world, and the Assyrian records also tell of the regions
below, where Ishtar descends into the dark abode of fluttering ghosts,
the house men enter but cannot depart from. Yet the Egyptians who held
to this primitive astronomy had set the Great Pyramid by the cardinal
points with remarkable exactness. In reckoning the year, they not only
added to the 12 solar months of 30 days 5 intercalary days to make
365, but becoming aware that even this was not accurate, they recorded
its variation till it should come round in a cycle of 1,461 years, as
determined by the rising of Sirius. Even more advanced was the astronomy
of the Chaldæans, with its records of eclipses extending over 2,000
years. In the astronomy of barbarians the five planets Mercury, Venus,
Mars, Jupiter, and Saturn, are not thought much of in comparison with the
Sun and Moon. But among the Chaldæans all the seven planets were classed
together as objects of worship and observation, starting the ideas of
the sacred number seven, which thence pervaded the mystical philosophy
of the ancients. It may have been among the Babylonian astronomers that
the study of the motions of the planets led to the theory that they were
carried round on seven crystal spheres; to this day people talk of being
“in the seventh heaven.” The next and great step in astronomy was when
the long-treasured knowledge of Babylon and Egypt was taken up by the
Greeks, to be carried on by the exact methods of the geometer. The Greek
astronomers were familiar with the idea of the earth being a sphere; they
calculated its circumference, and usually taking it as the centre of the
universe, they measured the apparent movements of the heavenly bodies.
This system, in its most perfect form known as the Ptolemaic, held its
place into the middle ages, when it came into rivalry with the Copernican
system of a central sun round which revolve the earth and other planets.
How this became in the hands of Kepler and Newton a mechanical theory of
the universe, and how man was at last stripped of the fond conceit that
his little planet was the centre of all things, need not be re-told here.
Geography is a practical kind of knowledge in which the rudest tribes
are well skilled, so far as it consists in the lie of their own land,
the course of the streams, the passes over the mountains, how many days’
marches through forest and desert to reach some distant hunting-ground,
or the hill-side where hard stone for hatchets is to be found. However
uncivilized a people may be, they name their mountains and rivers in such
terms as “red hill” or “beaver brook.” Indeed the atlas contains hundreds
of names of places that once had meanings in tongues which no man any
longer speaks. Scientific geography begins when men come to drawing maps,
an art which perhaps no savage takes to untaught, but which was known to
the early civilized nations; the oldest known map is an Egyptian plan of
the gold-mines of Æthiopia. The earliest known mention of a geographer
attempting a map of the world is by Herodotus, who tells of Aristagoras’s
bronze tablet inscribed with the circuit of the whole earth, the sea
and all rivers. But to the ancients the known world was a very limited
district round their own countries. It brings the growth of geography
well before our minds to look at the map in Gladstone’s _Juventus Mundi_,
representing the world according to the Homeric poems, with its group of
nations round the Mediterranean, and the great Ocean River encircling
the whole. Later, in the world as known to geographers such as Strabo,
the lands of men form a vast oval, reaching from the pillars of Herakles
across to far India, and from tropical Africa up to polar Europe. How
land and sea came to lie as they do, it is the business of geology to
explain. This is among the most modern of sciences, yet its problems
had long set rude men thinking. Even the Greenlanders and the South Sea
Islanders have noticed the fossils inland and high on the mountains, and
account for them by declaring that the earth was once tilted over, or
that the sea rose in a great flood and covered the mountains, leaving at
their very tops the remains of fishes. In the infancy of Greek science,
Herodotus speculated more rightly as to how the valley of Egypt had
been formed by deposits of mud from the Nile, while the shells on the
mountains proved to him that the sea had once been where dry land now is.
But two thousand years had to pass before these lines of thought were
followed up by the modern geologists, to whom the earth is now revealing
the long history of the deposit and removal, rising and sinking of its
beds, and the succession of plants and animals which from remote ages
have lived upon it.
From this survey of the various branches of science, it is clear that
their progress has been made in age after age by facts being more fully
observed and more carefully reasoned on. Reasoning or logic is itself a
science, but like other sciences, it began as an art which man practised
without stopping to ask himself why or how. He worked out his conclusions
by thinking and talking, untold ages before it occurred to him to lay
down rules how to argue. Indeed, speech and reason work together. A
language which distinguishes substantive, adjective, and verb, is already
a powerful reasoning-apparatus. Men had made no mean advance toward
scientific method when their language enabled them to class wood as heavy
or light, and to form such propositions as, light wood floats, heavy
wood sinks. The rise of reasoning into the scientific stage was chiefly
due to the Greek philosophers, and Aristotle brought argument into a
regular system by the method of syllogisms. Of course the simpler forms
of these had always belonged to practical reasoning, and a savage, aware
that red-hot coals burn flesh, would not thank a logician for explaining
to him that in consequence of this principle a particular red-hot coal
will burn his fingers. It must not be supposed that the introduction
of logic as a science had the effect of at once stopping bad argument,
and it was rather by setting practically to work on exact reasoning,
especially in mathematics, that the Greeks brought on a general advance
in knowledge. The importance of science was recognised when the famous
Museum of Alexandria flourished, the type of later universities, with its
great libraries, its laboratories, its zoological and botanical gardens.
Hither students came by thousands to follow mathematics, chemistry,
anatomy, under professors who resorted there at once to teach others
and to learn themselves. Looking at the history of science for eighteen
hundred years after this flourishing time, though some progress was made,
it was not what might have been expected, and on the whole things went
wrong. The so-called scholastic period which prevailed in Europe was
unfavourable, partly because excessive reverence for the authority of
the past fettered men’s minds, and partly because the learned successors
of Aristotle had come to believe so utterly in argumentation as to fancy
that the problems of the world could be dealt with by arguing about them,
without increasing the stock of real knowledge. The great movement of
modern philosophy with which the name of Bacon is associated as a chief
expounder, brought men back to the sound old method of working experience
and thought together, only now the experience was more carefully sought
and observed, and thought arranged it more systematically. We who live
in an age when every week shows new riches of nature’s facts, and new
shapeliness in the laws that connect them, have the best of practical
proof that science is now moving on a right track.
The student who wishes to compare the mental habits of rude and ancient
peoples with our own, may look into a subject which has now fallen into
contempt from its practical uselessness, but which is most instructive in
showing how the unscientific mind works. This is Magic. In the earlier
days of knowledge men relied far more than we moderns do on reasoning by
analogy or mere association of ideas. In getting on from what is known
already to something new, analogy or reasoning by resemblance always was,
as it still is, the mind’s natural guide in the quest of truth. Only its
results must be put under the control of experience. When the Australians
picked up the bits of broken bottles left by the European sailors, the
likeness of the new material to their own stone flakes at once led them
to try it for teeth to their spears; experience proved that in this
case the argument from analogy held good, for the broken glass answered
perfectly. So the North American Indian, in default of tobacco, finds
some more or less similar plant to serve instead, such as willow-bark.
The practical knowledge of nature possessed by savages is so great, that
it cannot have been gained by mere chance observations; they must have
been for ages constantly noticing and trying new things, to see how far
their behaviour corresponded with that of things partly like them. And
where the matter can be brought to practical trial by experiment, this is
a thoroughly scientific method. But the rude man wants to learn and do
far more difficult things—how to find where there is plenty of game, or
whether his enemies are coming, how to save himself from the lightning,
or how to hurt some one he hates, but cannot safely throw a spear at.
In such matters beyond his limited knowledge, he contents himself with
working on resemblances or analogies of thought, which thus become the
foundation of magic. On looking into the “occult sciences,” it is easy to
make out in them principles which are intelligible if one can only bring
one’s mind down to the childish state they belong to. Nothing shows this
better than the rules of astrology, although this is far from the rudest
kind of magic. According to the astrologers, a man born under the sign
Taurus is likely to have a broad brow and thick lips, and to be brutal
and unfeeling, but when enraged, violent and furious. If he had been born
under the sign Libra, he would have had a just and well-balanced mind.
All this is because two particular groups of stars happen to have been
called the bull and the balance; the child whose hour of birth has some
sort of astronomical relation to these constellations is imagined to have
a character resembling that of a real bull or a real pair of scales. So
with the planets. He over whom Mars presides in his better aspect will
be bold and fearless, but where the planet is “ill-dignified,” then he
will be a boastful shameless bully, ready to rob and murder. Had he but
been born when Venus was in the ascendant, how different would he have
been, with dimpled cheek and soft voice apt to speak of love. Practically
foolish as all this is, it is not unintelligible. There is in it a train
of thought which can be followed quite easily, though it is a train
of thought hardly strong enough for a joke, much less for a serious
argument. Yet such is the magic which still pervades the barbaric world.
The North American Indian, eager to kill a bear to-morrow, will hang up
a rude grass image of one and shoot it, reckoning that this symbolic act
will make the real one happen. The Australians at a burial, to know in
what direction they may find the wicked sorcerer who has killed their
friend, will take as their omen the direction of the flames of the
grave-fire. The Zulu who has to buy cattle may be seen chewing a bit of
wood, in order to soften the hard heart of the seller he is dealing with.
The accounts of such practices would fill a volume, and they do not seem
broken-down remains of old ideas, for there is no reason to suppose they
ever had more sense in them than is to be plainly seen now. They may be
derived from some such loose savage logic as this:—Things which are like
one another behave in the same way—shooting this image of a bear is like
shooting a real bear—therefore, if I shoot the image I shall shoot a
real bear. It is true that such magical proceedings, if tested by facts,
prove to be worthless. But if we wonder that nevertheless they should so
prevail among mankind, it may be answered that they last on even in our
own country among those who are too ignorant to test them by facts—the
rustics who believe a neighbour’s ill-wishing has killed their cow, and
who, on true savage principles, try to punish the evil-doer by putting
a heart spitefully stuck full of pins up the chimney to shrivel in the
smoke, that in like manner sharp pangs may pierce him and he may waste
away.
In another and very different way the student of science is interested
in magic. Loose and illogical as man’s early reasonings may be, and slow
as he may be to improve them under the check of experience, it is a law
of human progress that thought tends to work itself clear. Thus even
the fancies of magic have been sources of real knowledge. Few magical
superstitions are more troublesome than the Chinese geomancy or rules of
“wind and water,” by which a lucky site has to be chosen for building a
house. Absurd as this ancient art is, its professors appear to have been
the earliest to use the magnetic compass to determine the aspects of the
heavens, so that it seems the magician gave the navigator his guide in
exploring the world. What exact science owes to astrology is well known,
how in Chaldæa the places of the stars were systematically observed and
recorded for portents of battle and pestilence, and registers of lucky
and unlucky days. The old magical character hung to astronomy even into
modern ages, when astrologers like Tycho Brahe and Kepler, who believed
that the destinies of men were foretold by the planets, helped by their
observation and calculation to foretell the motions of the planets
themselves. Thus man has but to go on observing and thinking, secure that
in time his errors will fall away, while the truth he attains to will
abide and grow.