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Transcriber’s note:
Text enclosed by underscores is in italics (_italics_).
However, to improve readability, italics notation has been
omitted from equations. If the variables are in italics in
the surrounding text, they were in italics in the equations.
TIME AND CLOCKS.
[Illustration:
[_Frontispiece._
NUREMBERG CLOCK. CONVERTED FROM A VERGE ESCAPEMENT TO A PENDULUM
MOVEMENT.]
TIME AND CLOCKS:
A Description of Ancient and Modern Methods of
Measuring Time.
by
H. H. CUNYNGHAME M.A. C.B. M.I.E.E.
With Many Illustrations.
London:
Archibald Constable & Co. Ltd.
16 James Street Haymarket.
1906.
Bradbury, Agnew, & Co. Ld., Printers,
London and Tonbridge.
CONTENTS.
PAGE
INTRODUCTION 1
CHAPTER I. 7
CHAPTER II. 50
CHAPTER III. 90
CHAPTER IV. 123
APPENDIX ON THE SHAPE OF THE TEETH OF WHEELS 187
INDEX 199
TIME AND CLOCKS.
INTRODUCTION.
When we read the works of Homer, or Virgil, or Plato, or turn to the
later productions of Dante, of Shakespeare, of Milton, and the host
of writers and poets who have done so much to instruct and amuse us,
and to make our lives good and agreeable, we are apt to look with some
disappointment upon present times. And when we turn to the field of art
and compare Greek statues and Gothic or Renaissance architecture with
our modern efforts, we must feel bound to admit our inferiority to our
ancestors. And this leads us perhaps to question whether our age is the
equal of those which have gone before, or whether the human intellect
is not on the decline.
This feeling, however, proceeds from a failure to remember that each
age of the world has its peculiar points of strength, as well as of
weakness. During one period that self-denying patriotism and zeal
for the common good will be developing, which is necessary for the
formation of society. During another, the study of the principles of
morality and religion will be in the ascendant. During another the arts
will take the lead; during another, poetry, tragedy, and lyric poetry
and prose will be cultivated; during another, music will take its turn,
and out of rude peasant songs will evolve the harmony of the opera.
To our age is reserved the glory of being easily the foremost in
scientific discovery. Future ages may despise our literature,
surpass us in poetry, complain that in philosophy we have done
nothing, and even deride and forget our music; but they will only
be able to look back with admiration on the band of scientific
thinkers who in the seventeenth century reduced to a system the
laws that govern the motions of worlds no less than those of atoms,
and who in the eighteenth and nineteenth founded the sciences of
chemistry, electricity, sound, heat, light, and who gave to mankind
the steam-engine, the telegraph, railways, the methods of making
huge structures of iron, the dynamo, the telephone, and the thousand
applications of science to the service of man.
And future students of history who shall be familiar with the
conditions of our life will, I think, be also struck with surprise at
our estimate of our own peculiar capabilities and faculties. They will
note with astonishment that a gentleman of the nineteenth century, an
age mighty in science, and by no means pre-eminent in art, literature
and philosophy, should have considered it disgraceful to be ignorant
of the accent with which a Greek or a Roman thought fit to pronounce
a word, should have been ashamed to be unable to construe a Latin
aphorism, and yet should have considered it no shame at all not to
know how a telephone was made and why it worked. They will smile when
they observe that our highest university degrees, our most lucrative
rewards, were given for the study of dead languages or archæological
investigations, and that science, our glory and that for which we have
shown real ability, should only have occupied a secondary place in our
education.
They will smile when they learn that we considered that a knowledge
of public affairs could only be acquired by a grounding in Greek
particles, or that it could ever have been thought that men could not
command an army without a study of the tactics employed at the battle
of Marathon.
But the battle between classical and scientific education is not in
reality so much a dispute regarding subjects to be taught, as between
methods of teaching. It is possible to teach classics so that they
become a mental training of the highest value. It is possible to teach
science so that it becomes a mere enslaving routine.
The one great requirement for the education of the future is firmly to
grasp the fact that a study of words is not a study of things, and that
a man cannot become a carpenter merely by learning the names of his
tools.
It was the mistake of the teachers of the Middle Ages to believe that
the first step in knowledge was to get a correct set of concepts of
all things, and then to deduce or bring out all knowledge from them.
Admirable plan if you can get your concepts! But unfortunately concepts
do not exist ready made—they must be grown; and as your knowledge
increases, so do your concepts change. A concept of a thing is not a
mere definition, it is a complete history of it. And you must build up
your edifice of scientific knowledge from the earth, brick by brick and
stone by stone. There is no magic process by which it can with a word
be conjured into existence like a palace in the Arabian Nights.
For nothing is more fatal than a juggle with words such as force,
weight, attraction, mass, time, space, capacity, or gravity. Words are
like purses, they contain only as much money as you put into them. You
may jingle your bag of pennies till they sound like sovereigns, but
when you come to pay your bills the difference is soon discovered.
This fatal practice of learning words without trying to obtain a
clear comprehension of their meaning, causes many teachers to use
mathematical formulæ not as mere steps in a logical chain, but like
magical chaldrons into which they put the premises as the witches put
herbs and babies’ thumbs into their pots, and expect the answers to
rise like apparitions by some occult process that they cannot explain.
This tendency is encouraged by foolish parents who like to see their
infant prodigies appear to understand things too hard for themselves,
and look on at their children’s lessons in mathematics like rustics
gaping at a fair. They forget that for the practical purposes of
life one thing well understood is worth a whole book-full of muddled
ill-digested formulæ. Unfortunately it is possible to cram boys up
and run them through the examination sieves with the appearance of
knowledge without its reality. If it were cricket or golf that were
being tested how soon would the fraud be discovered. No humbug would be
permitted in those interesting and absorbing subjects. And really, when
one reflects how easy it is to present the appearance of book knowledge
without the reality, one can hardly blame those who select men for
service in India and Egypt a good deal for their proficiency in sports
and games. Better a good cricketer than a silly pedant stuffed full of
learning that “lies like marl upon a barren soil encumbering what is
not in its power to fertilize.”
Another kindred error is to expect too much of science. For with all
our efforts to obtain a further knowledge of the mysteries of nature,
we are only like travellers in a forest. The deeper we penetrate it,
the darker becomes the shade. For science is “but an exchange of
ignorance for that which is another kind of ignorance”[A] and all
our analysis of incomprehensible things leads us only to things more
incomprehensible still.
[A] _Manfred_, Act II., scene iv.
It is, therefore, by the firm resolution never to juggle with words or
ideas, or to try and persuade ourselves or others that we understand
what we do not understand, that any scientific advance can be made.
CHAPTER I.
All students of any subject are at first apt to be perplexed with the
number and complication of the new ideas presented to them.
The need of comprehending these ideas is felt, and yet they are
difficult to grasp and to define. Thus, for instance, we are all apt
to think we know what is meant when force, weight, length, capacity,
motion, rest, size, are spoken of. And yet when we come to examine
these ideas more closely, we find that we know very little about
them. Indeed, the more elementary they are, the less we are able to
understand them.
The most primordial of our ideas seem to be those of number and
quantity; we can count things, and we can measure them, or compare
them with one another. Arithmetic is the science which deals with the
numbers of things and enables us to multiply and divide them. The
estimation of quantities is made by the application of our faculty of
comparison to different subjects. The ideas of number and quantity
appear to pervade all our conceptions.
The study of natural phenomena of the world around us is called the
study of physics from the Greek word φυσίς or “inanimate nature,”
the term physics is usually confined to such part of nature as is not
alive. The study of living things is usually termed biology (from βια,
life).
In the study of natural phenomena there are, however, three ideas which
occupy a peculiar and important position, because they may be used
as the means of measuring or estimating all the rest. In this sense
they seem to be the most primitive and fundamental that we possess.
We are not entitled to say that all other ideas are formed from and
compounded of these ideas, but we are entitled to say that our correct
understanding of physics, that is of the study of nature, depends
in no slight degree upon our clear understanding of them. The three
fundamental ideas are those of space, time and mass.
Space appears to be the universal accompaniment of all our impressions
of the world around us. Try as we may, we cannot think of material
bodies except in space, and occupying space. Though we can imagine
space as empty we cannot conceive it as destroyed. And this space has
three dimensions, length, breadth measured across or at right angles to
length, and thickness measured at right angles to length and breadth.
More dimensions than this we cannot have. For some inscrutable reason
it has been arranged that space shall present these three dimensions
and no more. A fourth dimension is to us unimaginable—I will not say
inconceivable—we can conceive that a world might be with space in four
dimensions, but we cannot imagine it to ourselves or think what things
would be like in it.
With difficulty we can perhaps imagine a world with space of only two
dimensions, a “flat land,” where flat beings of different shapes,
like figures cut out of paper, slide or float about on a flat table.
They could not hop over one another, for they would only have length
and breadth; to hop up you would want to be able to move in a third
dimension, but having two dimensions only you could only slide forward
and sideways in a plane. To such beings a ring would be a box. You
would have to break the ring to get anything out of it, for if you
tried to slide out you would be met by a wall in every direction. You
could not jump out of it like a sheep would jump out of a pen over the
hurdles, for to jump would require a third dimension, which you have
not got. Beings in a world with one dimension only would be in a worse
plight still. Like beads on a string they could slide about in one
direction as far as the others would let them. They could not pass one
another. To such a being two other beings would be a box one on each
side of him, for if thus imprisoned, he could not get away. Like a
waggon on a railway, he could not walk round another waggon. That would
want power of moving in two dimensions, still less could he jump over
them, that would want three.
We have not the smallest idea why our world has been thus limited. Some
philosophers think that the limitation is in us, not in the world, and
that perhaps when our minds are free from the limitations imposed by
their sojourn in our bodies, and death has set us free, we may see not
only what is the length and breadth and height, but a great deal more
also of which we can now form no conception. But these speculations
lead us out of science into the shadowy land of metaphysics, of which
we long to know something, but are condemned to know so little. Area
is got by multiplying length by breadth. Cubic content is got by
multiplying length by breadth and by height. Of all the conceptions
respecting space, that of a line is the simplest. It has direction, and
length.
The idea of mass is more difficult to grasp than that of space. It
means quantity of matter. But what is matter? That we do not know. It
is not weight, though it is true that all matter has weight. Yet matter
would still have mass even if its property of weight were taken away.
For consider such a thing as a pound packet of tea. It has size, it
occupies space, it has length, breadth, and thickness. It has also
weight. But what gives it weight? The attraction of the earth. Suppose
you double the size of the earth. The earth being bigger would attract
the package of tea more strongly. The weight of the tea, that is, the
attraction of the earth on the package of tea, would be increased—the
tea would weigh more than before. Take the package of tea to the planet
Jupiter, which, being very large, has an attraction at the surface 2½
times that of the earth. Its size would be the same, but it would feel
to carry like a package of sand. Yet there would be the same “mass”
of tea. You could make no more cups of tea out of it in Jupiter than
on earth. Take it to the moon, and it would weigh a little over two
ounces, but still it would be a pound of tea. We are in the habit of
estimating mass by its weight, and we do so rightly, for at any place
on the earth, as London, the weights of masses are always proportioned
to the masses, and if you want to find out what mass of tea you have
got, you weigh it, and you know for certain. Hence in our minds we
confuse mass with weight. And even in our Acts of Parliament we have
done the same thing, so that it is difficult in the statutes respecting
standard weights to know what was meant by those who drew them up, and
whether a pound of tea means the _mass_ of a certain amount of tea or
the _weight_ of that mass. For accurate thinking we must, of course,
always deal with masses, not with weights. For so far as we can tell
_mass_ appears indestructible. A mass is a mass wherever it is, and
for all time, whereas its weight varies with the attractive force of
the planet upon which it happens to be, and with its distance from that
planet’s centre. A flea on this earth can skip perhaps eight inches
high; put that flea on the moon, and with the expenditure of the same
energy he could skip four feet high. Put him on the planet Jupiter and
he could only skip 3⅕ inches high. A man in a street in the moon could
jump up into a window on the first floor of a house. One pound of tea
taken to the sun would be as heavy as twenty-eight pounds of it at the
earth’s surface; and weight varies at different parts of the earth.
Hence the true measure of quantity of matter is mass, not weight.
The mass of bodies varies according to their size; if you have the same
nature of material, then for a double size you have a double mass. Some
bodies are more concentrated than others, that is to say, more dense;
it is as though they were more tightly squeezed together. Thus a ball
of lead of an inch in diameter contains forty-eight times as much mass
as a ball of cork an inch in diameter. In order to know the weight of a
certain mass of matter, we should have to multiply the mass by a figure
representing the attractive force or pull of the earth.
In physics it is usual to employ the letters of the alphabet as a sort
of shorthand to represent words. So that the letter _m_ stands for
the mass of a body. So again _g_ stands for the attractive pull of the
earth at a given place. _w_ stands for the weight of the body. Hence
then, since the weight of a body depends on its mass and also on the
attractive pull of the earth, we express this in short language by
saying, w = m × g; or _w_ is equal to _m_ multiplied by _g_; the symbol
= being used for equality, and × the sign of multiplication. In common
use × is usually omitted, and when letters are put together they are
intended to be understood as multiplied. So that this is written
w = mg.
Of course by this equation we do not mean that weight is mass
multiplied into the force of gravity, we only mean that the number of
units of weight is to be found by multiplying the number of units of
mass into the number of units of the earth’s force of gravity.
In the same way, if when estimating the number of waggons, _w_, that
would be wanted for an army of men, _n_, which consumed a number of
pounds, _p_, of provisions a day, we might put
w = np.
But this would not mean that we were multiplying soldiers into food
to produce waggons, but only that we were performing a numerical
calculation.
Time is one of the most mysterious of our elementary ideas. It seems to
exist or not to exist, according as we are thinking or not thinking.
It seems to run or stand still and to go fast or slowly. How it drags
through a wearisome lesson; how it flies during a game of cricket; how
it seems to stop in sleep. If we measured time by our own thoughts it
would be a very uncertain quantity. But other considerations seem to
show us that Nature knows no such uncertainty as regards time, that she
produces her phenomena in a uniform manner in uniform times, and that
time has an existence independent of our thoughts and wills.
The idea of a state of things in which time existed no more was quite
familiar to mediæval thinkers, and was regarded by many of them as the
condition that would exist after the Day of Judgment. In recent times
Kant propounded the theory that time was only a necessary condition of
our thoughts, and had no existence apart from thinking beings—in fact,
that it was our way of looking at things.
Scientifically, however, we are warranted in treating time as perfectly
real and capable of the most exact measurement. For example, if we
arrange a stream of sand to run out of an orifice, and observe how
much will run out while an egg is being boiled hard, we find as a fact
that if the same quantity of sand runs out, the state of the egg is
uniform. If we walk for an hour by a watch, we find that we can go
half the distance that we should if we walked two hours. It is the
correspondence of these various experiments that gives us faith in the
treatment of time as a thing existing independently of ourselves, or,
at all events, independent of our transient moods.
The ideas of time acquired by the races of men that first evolved from
a state of barbarism were no doubt derived from the observation of day
and night, the month and the year.
[Illustration: FIG. 1.]
For, suppose that a shepherd were on the plains of Chaldea, or perhaps
on those mountains of India known as the roof of the world, which
according to some archæologists was the site of the garden of Eden and
the early home of the European race, what would he see?
He would see the sun rise in the east, slowly mount the heavens till it
stood over the south at middle day, then it would sink towards the west
and disappear. In summer the rising point of the sun would be more to
the northward than in winter, and so also would be its point of setting
_A´_. In winter it would rise a little to the south of east, and set
a little to the south of west, and not rise so high in the heavens at
midday, so that the summer day would be longer than the winter day.
If the day were always divided into twelve hours, whether it were long
or short, then in summer the hours of the day would be long; in winter
they would be short. This mode of dividing the day was that used by
the Greeks. The Egyptians, on the other hand, averaged their day by
dividing the whole round of the sun into twenty-four hours, so that the
summer day contained more hours than the winter day. Hence, for the
Egyptians, sun-rise did not always take place at six o’clock. For in
winter it took place after six, and in summer before six; and this is
the system that has descended to us.
The moon also would rise at different places, varying between _A_ and
_B_, and set at places varying between _A´_ and _B´_, but these would
be independent of those at which the sun rose and set.
Moreover, the moon each day would appear to get further and further
away from the sun in the direction of the arrow, as shown in the
sketch. If the moon rose an hour after the sun on one day, the next day
it would rise more than two hours after the sun, and so on. This delay
in rising of the moon would go on day by day till at last she came
right round to the sun again, as shown at _M´_. And in her path she
would change her form from a crescent, as at _M_, up to a full moon,
when she would be half way round from the sun, that is, when she would
rise twelve hours after him, or just be rising as the sun set. This
delay and accompanying change of form would go on, till after three
weeks she would have got round to a position _A´_, when she would rise
eighteen hours after the sun, and have become a crescent with her back
to the sun; in fact, she would always turn her convex side to the sun.
At length, when twenty-eight days had passed, she would be round again
about opposite to the sun, and consequently her pale light would be
extinguished in his beams, and she would gradually reappear as a new
moon on the other side of him. This series of changes of the moon takes
place once every twenty-eight days, and is called a lunar or “moon”
month, and was used as a division of time by very early nations. The
changes of the seasons recurred with the changes in the times of rising
of the sun, and took a year to bring about. And there were nearly
thirteen moon changes in the year.
It was also observed that during its cycle of changes, the sun was
slowly moving round backwards among the stars in the same direction as
the moon, only it made its retrograde cycle in a year, and thus arose
the division of time into months and years. The stars turned round in
the heavens once in the complete day. The sun, therefore, appeared to
move back among them, passing successively through groups of stars, so
as to make the circuit of them all in a year. The stars through which
he passed in a year, and through which the moon travelled in a month,
were divided by the ancients into groups called constellations, and its
yearly path in the heavens was called the zodiac. There were twelve of
these constellations in the zodiac called the signs. Hence, then, the
sun passed through a sign in every month, making the tour of them all
in the year. To these signs fanciful names were given, such as “the
Ram,” “the Water-bearer,” “the Virgin,” “the Scorpion,” and so on, and
the sun and moon were then said to pass through the signs of the zodiac.
Hence, since the path of the sun marked the year, you could tell the
seasons by knowing what sign of the zodiac the sun was in. The age of
the moon was easily known by her form.
When the winter was over, then, just as the sun set the dog star would
be rising in the east, and this would show that the spring was at hand.
Then the peasants prepared to till the earth and sow the seed and lead
the oxen out to pasture, and celebrated with joyful mirth the glad
advent of the spring, corresponding to our Easter, when the sun had
run through three constellations of the zodiac. Then came the summer
heat, and with many a mystic rite they celebrated Midsummer’s Day. In
autumn, after three more signs of the zodiac have been traversed by the
sun, the sun again rises exactly in the east and sets in the west, and
the days and nights are equal. This is the autumnal equinox, and was
once celebrated by the feast which we now know as Michaelmas Day, and
the goose is the remnant of the ancient festival.
[Illustration: FIG. 2.]
And the great winter feast of the ancients is now known to us as
Christmas, and chosen to celebrate the birth of our Lord; for when
Christianity came into the world and the heathens were converted, the
old feast days were deliberately changed into Christian festivals.
To us, therefore, the whole heavens, and the fixed stars with them,
appear to turn from east to west, or from left to right, as we look
towards the south, as shown by the big arrow. But the moon and sun,
though apparently placed in the heavens, move backwards among the fixed
stars, as shown by the small arrows. The sun moves at such a rate that
he goes round the circle of the heavens in a year of three hundred and
sixty-five days. The moon goes round the circle in twenty-eight and a
half days, or a lunar month. Of course, in reality the sun is at rest,
and it is the earth that moves round the sun and spins on its axis
as it moves. But it will presently be shown that the appearance to a
person on the earth is the same whether the earth goes round the sun or
the sun round the earth.
From the works of Greek writers we know a good deal about the ideas of
the world that were entertained by the ancients. The most early notions
were, of course, connected with the worship of the gods. The sun was
considered as a huge light carried in a chariot, driven by Apollo, with
four spirited steeds. It descended to the ocean when the day declined,
and then the horses were unyoked by the nymphs of the ocean and led
round to the east, so as to be ready for the journey of the following
day. The Egyptians figured the sun as placed in a boat which sailed
over the heavens. At night the sun god descended into the infernal
regions, carrying with him the souls of those who had died during the
day. There they passed through different regions of hell, with portals
guarded by hideous monsters. Those who had well learned the ritual of
the dead knew the words of power wherewith to appease the demons. Those
unprovided with the watchwords were subjected to terrible dangers.
Then the soul appeared before Minos, and was weighed and dealt with
according to its deserts.
[Illustration: FIG. 3.]
The earth was considered as a huge island in the midst of a circular
sea. Gradually, however, astronomical ideas became subjected to
science. One of the first truths that dawned on astronomers was the
fact that the earth was a sphere. For they noticed that as people
went further and further to the north, the elevation of the sun at
midday above the horizon became smaller and smaller. This can easily
be seen from the diagram. When an observer is at _A_ the sun appears
at an altitude above the horizon equal to the angle α, but as he goes
along the curved surface of the earth to a point _B_ nearer to the
north pole, the sun appears to be lower and only to have an altitude
β. From this it was easy for men so skilled in geometry as the Greeks
to calculate how big the earth was. They did so, and it appeared to
have the enormous diameter of 8,000 miles. They only knew quite a
small portion of it. They thought that the rest was ocean. But they
had, of course, a clear idea of the “antipodes” or up-side-down side
of it, and they believed that if men were on the other side of it
that their feet must all point towards its centre. From this they
got the idea of the centre of the earth as a point of attraction for
all things that had an earth-seeking or earthy nature. Fire appeared
always to desire to go upwards, so they thought that fire had an
earth-repellent, heaven-seeking character. Water they thought partly
earth-seeking, partly heaven-seeking, for it appeared in the ocean or
floated as clouds. Air they thought to be indifferent. And out of the
four elements fire, water, earth, and air they believed the world was
made. The earth they thought must be at rest; for if it was in motion
things would fly off from it. They saw that either the sun must be
moving round the earth, or else the earth must be turning on its axis.
They chose the former hypothesis, because they argued that if the earth
were twisting round once in twenty-four hours then such a country as
Greece must be flying round like a spot on the surface of a top, at the
rate of about 18,000 miles in twenty-four hours, that is, at the rate
of about 180 yards in a second, or faster than an arrow from a bow.
But if that was the case then a bird that flew up from the earth would
be left far behind. If a ball were thrown up it would fall hundreds
of yards behind the person who threw it. They could not conceive how
it was possible for a ball thrown up by someone standing on a moving
object not to fall behind the thrower.
This decided them in their error. The mistaken astronomy of the Greeks
was also much forwarded by Aristotle, the tutor of Alexander the Great.
This great genius in politics and philosophy was only in the second
rank as a man of science, and, as I think, hardly equal to Archimedes
or Hipparchus, or even to Ptolemy. Aristotle wrote a book concerning
the heavens which bristles with the most wantonly erroneous scientific
ideas, such as, for instance, that the motion of the heavenly bodies
must be circular because the most perfect curve is a circle, and
similar assumptions as to the course of nature.
The earth, then, being fixed, they thought that the moon, the sun,
and the seven planets were carried round it, fixed each of them in
an enormous crystal spherical shell. These spheres, like coats of
an onion, slid round one upon another, each carrying his celestial
luminary. The moon was the nearest, then Mercury, then Venus, then the
sun, then Mars, Jupiter and Saturn. Outside them was the sphere of the
stars, and outside all the “_primum mobile_,” or great Prime Mover of
the universe. When one of the celestial bodies, such as the moon, got
in front of another, such as the sun, there was an eclipse. They soon
observed that the moon derived its light from the sun. As they knew
the size of the earth, by comparison they got some vague idea of the
huge distances that the heavenly bodies must be from us. In fact, they
measured the distance of the moon with approximate accuracy, making it
240,000 miles, or about thirty times the earth’s diameter.
This, of course, gave them the moon’s diameter, for they were easily
able to calculate how big an object must be, that looks as big as the
moon and is 240,000 miles away.
This large size of the moon gave them some idea of the distance of the
sun, but they failed to realise how big and far away he really is.
Several ancient nations used weeks as means of measuring time. They
made four weeks to the lunar month. The order of the days was rather
curiously arranged. For, assuming that the earth is the centre of the
planetary system, put the planets in a column, putting the nearest (the
moon) at the bottom and the furthest off at the top—
Saturn,
Jupiter,
Mars,
The Sun,
Venus,
Mercury,
The Moon.
Then divide the day into three watches of eight hours each, and let
each watch be presided over by one of the planet-gods: begin with
Saturn. We then have Saturn as the first god ruling Saturday, and
Jupiter and Mars, the two other gods, for that day. The first watch for
Sunday will be the sun; Venus and Mercury will preside over the next
two watches of that day. The planet that will preside over the first
watch of the next day will be the moon, and the day will, therefore, be
called Monday; Saturn and Jupiter will be the other gods for Monday.
The first watch of the next day will be presided over by Mars, and the
day will, therefore, be called Mars-day or Mardi, or, in the Teutonic
languages, Tuesday, after Tuesco, a Scandinavian god of war. Mercury
will give a name to Mercredi, or to Wednesday, or Wodin’s-day. Jupiter
to Jeudi, or “Thurs” day. Venus to Vendredi, or in the Scandinavian,
Friday, the day of the Scandinavian goddess Freya, the goddess of love
and beauty, who corresponds to Venus, and thus the week is completed.
[Illustration: FIG. 4.]
This weekly scheme came probably from the Chaldean astronomers. It
appears probable that the great tower of Babel, the ruins of which
exist to this day, consisted of seven stages, one over the other, the
top one painted white, or perhaps purple, to represent the Moon, the
next lower blue for Mercury, then green for Venus, yellow for the Sun,
red for Mars, orange for Jupiter, and black for Saturn. Unfortunately,
of the colours no trace now remains.
But nightly on the long terraces the Babylonian priests observed
eclipses and other celestial phenomena. Their records were afterwards
taken to Alexandria and kept in the great library that was subsequently
burned by the Turks. In that library they were seen by the astronomer
Ptolemy, who used them in the writing of his work on astronomy called
the “Great Syntaxis” or “Collection.” The original work perished, but
it had been translated into Arabic by the Arab astronomers, who called
it “Al Magest,” the Great Book. It was translated from Arabic into
Latin, and remained the textbook for astronomers in Europe quite down
to the time of Queen Elizabeth, when a better system took its place.
For the use of men engaged in practical astronomy, it is very
convenient to consider the sun, moon, stars, and planets as going
round the earth at rest. For instance, seamen use the heavenly bodies
as in a way hands of a huge clock from which they can know the time and
their position on the earth. “The Nautical Almanac,” which is printed
yearly, gives the true position of these heavenly bodies for every
hour, minute, and second of the year, and I will presently show how
useful this is to sailors.
We will deal with the sun first. From the motions of the sun we can
observe the time. This is done in every garden by means of sun-dials,
and I will now describe how they are constructed. If a light, such as
the light of a candle, be moved round in a circle at a uniform pace so
as to go round once in some given period, such as twenty-four hours, it
is obvious that it would serve to measure time. Thus, for example, if a
sheet of white paper be placed upon the table, and a pencil be stuck on
to it upright with some sealing wax, or a pen propped up in an ink-pot,
then a candle held by anyone will cast the shadow of the pen on the
paper.
[Illustration: FIG. 5.]
If the person holding the candle walk round the table at a uniform
speed, the shadow will go round like the hand of a clock, and might be
made to mark the time. If the candle took twenty-four hours to go round
the table, as the sun takes twenty-four hours to go round the earth,
then marks placed on the paper would serve to measure the hours, and
the paper and pen would serve as a sort of sun-dial.
But the sun does not go round the earth as the candle round the
table. Its path is an inclined one, like that shown by the dotted
line. Sometimes it is above the level of the table, sometimes below
it. And, moreover, its winter path is different from its summer path.
Whence then it follows that the hour-marks on the paper cannot be
put equidistant like the hours on the dial of a clock, and that some
arrangement must be made so that the line as shown by the summer sun
shall correspond with the time as shown by the winter sun.
[Illustration: FIG. 6.]
Let us suppose that _N O S_ is the axis of the heavens, and the lines
_N A S_, _N B S_, _N C S_, are meridian lines drawn from one of the
poles _N_ of the heavens round on the surface of a celestial sphere
whose centre is at _O_. Let _A B C_ be a circle also on this sphere,
passing through _O_, the centre of the sphere, in a plane at right
angles to _N S_, the axis. Then _A B C_ is called the equatorial. It
is a circle in the heavens corresponding to the equator on the earth.
At the vernal and autumnal equinox, namely on March 25 and September
25, the sun is in the equatorial. In midsummer and midwinter it is on
opposite sides of the equatorial. In midsummer it is nearer to _N_, as
at _V_; in midwinter it is nearer to _S_, as at _W_. Suppose we were
on an island in the midst of a surrounding ocean, we should only have
a limited range of view. If the highest point on the island were 100
feet, then from that altitude we should be able to see about thirteen
miles to the horizon. More than that could not be seen on account of
the rotundity of the earth.
Let us suppose then such an island surrounded for thirteen miles
distant on every side by an ocean, and let us consider what would be
the apparent motions of the sun when seen from such an island. At the
vernal and autumnal equinoxes, when the sun is on the equatorial, it
would appear to rise out of the ocean at a point _E_, due east; it
traverses half the equatorial and sets in the ocean at a point _W_, due
west. The day is twelve hours long, from 6 a.m. to 6 p.m.
[Illustration: FIG. 7.]
In summer the sun is higher, and nearer to the pole _N_, say at a point
_s_. It rises at a point _a_ in the ocean more to the north than _E_,
the eastern point, and sets at a point _b_, also more north than _W_,
the western point, and traverses the path _a s b_. But to traverse
this path it takes longer than twelve hours, for _a s b_ is more than
half the circle _a s b_. Hence then it rises say at 4.30 a.m. and
sets at 7.30 p.m. The night, during which the sun moves round the path
from _b_ to _a_, is correspondingly short, being only nine hours in
length, from 7.30 p.m. till 4.30 a.m. So you have a long summer day and
a short summer night. But in winter, when the sun gets nearer to the
south pole of the heavens, it rises at a point _C_ in the ocean at 7.30
a.m., and traverses the arc _c t d_, and sets at the point _d_ at 4.30
p.m. So that the winter day is only nine hours long. But the winter
night lasts from 4.30 p.m. till 7.30 a.m., and is therefore fifteen
hours long, the sun going round the path _d r c_ in the interval. It is
therefore the obliquity of the poles _N S_, coupled with the fact that
the sun’s position is nearer to one pole, _N_, in summer, and nearer to
the other pole, _S_, in winter, that produces the inequality of days
and nights in our latitudes. Suppose our island were on the equator.
The north pole and the south pole would appear to be on the horizon,
and then whether the sun moved in the circle _a s b_ in the summer, or
_E S W_ at the vernal or autumnal equinoxes, or _c t d_ in the winter,
in each of these cases, though the places of rising and setting in the
ocean might vary in summer from _a_ and _b_ to _c_ and _d_ in winter,
yet in each of these cases the path from _a_ to _b_, _A_ to _B_, and
_c_ to _d_ would still always be a half-circle and occupy twelve hours.
Hence at the equator the days and nights never vary in length, but the
sun always rises at six and sets at six. And, besides, it always rises
straight up from the ocean and plunges down vertically into it, so that
there is but little twilight and dawn.
[Illustration: FIG. 8.]
But now let us suppose we were living at the north pole. In this case
the north pole would be directly overhead, the south pole directly
under our feet. At the vernal and autumnal equinoxes the sun would
appear with half its disc above the ocean, and go round the ocean
horizon, always appearing with half its disc above the sea. In summer
it would appear at a point _s_ nearer to the pole _N_. It would go
round in the heavens, always appearing above the horizon, and would
never set at all. As the summer waned the sun would become lower and
lower, still, however, going round and round without setting till at
the autumn equinox it reached the horizon. So that for six months it
would never have set. But when it did set, there would then be six
months without a sun at all.
[Illustration: FIG. 9.]
Thus then all over the world the period of darkness and light is
equivalent. At the tropics the days and nights are always equal. At
the poles light for six months is followed by darkness for six months.
In the intermediate temperate regions nights of varying lengths follow
days of varying lengths, a short night following a long day and _vice
versâ_.
[Illustration: FIG. 10.]
It is evident that for a person living on the north pole a sun-dial
would be an easy thing to make. All that would be needful would be to
put a post vertically in the ground, and observe its shadow as the sun
went round (Fig. 10).
[Illustration: FIG. 11.]
In latitudes such as that of England, where the pole of the earth is
inclined at an angle to the horizon, it is necessary that the rod, or
“style” as it is called, of the sun-dial should be inclined to the
horizontal. For if we used an upright “style,” as _O A_, then when the
sun was in the south, at midday, the shadow would lie along the same
direction, _O B_, whether the sun were high in summer, as at _S_, or
low in winter, as at _s_. But at other hours, such as nine o’clock in
the morning, the shadow of the “style” _O A_ would, when the sun was
at its summer position _T_, lie along _O D_, whereas when the sun was
at its winter position _t_ the shadow would lie along _O C_. Thus the
time would appear different in summer and in winter; and the dial
would lead to errors. But if the “style” is inclined in the direction
of the poles, then, however, the sun moves from or towards the pole.
As its position varies in winter and summer, the shadow still remains
unchanged for any particular hour, and it is only the circular motion
of the sun round in its daily path that affects the position of the
shadows.
[Illustration: FIG. 12.]
Therefore the first condition of making a sun-dial is that the “style”
which casts the shadow should be parallel to the earth’s axis, that
is to say should point to the polar star. This is the case whether
the sun-dial is horizontal or is vertical, and whether it stands on a
pillar in the garden or is attached to the wall of a house.
To divide the dial, we have only to imagine it surrounded by a sort
of cage formed of twenty-four arcs drawn from the north pole to the
south pole, and equidistant from one another. In its course the sun
would cross one of them every hour. Hence the points to which the
shadows _o a_, _o b_, _o c_, _o d_, of the inclined “style” _O N_ would
point are the points where these arcs meet the horizontal circle. This
consideration leads to a simple method of constructing a sun-dial,
which is given at the end of this chapter in an appendix.
Sun-dials were largely in use in ancient times. It is thought that the
circular rows of stones used by the Druids were used to mark the sun’s
path, and indicate the times and seasons. Obelisks are also supposed
to have been used to cast sun-shadows. The Greeks were perfectly
acquainted with the method of making sun-dials with inclined “styles,”
or “gnomons.”
[Illustration: FIG. 13.]
Small portable sun-dials were once much used before the introduction of
watches, and were provided with compasses by which they could be turned
round, so that the “style” pointed to the north.
Sun-dials were only available during the hours of the day when the
sun was shining. The desire to mark the hours of the night led to
the adoption of water clocks, which measured time by the amount of
water which escaped from a small hole in a level of water. Some care,
however, is required to secure correct registration. For suppose that
we have a vessel with a small pipe leading out near the bottom, then
the amount of water which will run out of the pipe in a given time
depends upon the pressure of the water at the pipe, and this depends
in its turn upon _P Q_, the head of water in the vessel. Whence it
follows that the division _Q R_, due to say an hour’s run of the clock
at _Q R_, will be more than _q r_, the division corresponding to an
hour, at _q_, a point lower down between _P_ and _Q_, and hence the
divisions marked on the vessel to show the hours by means of the level
of the water would be uneven, becoming smaller and smaller as the water
fell in the vessel.
To avoid the inconvenience of unequal divisions, the water to be
measured was allowed to escape into an empty vessel from a vessel in
which its surface was always kept at a constant level. Inasmuch as the
pressure on the pipe or orifice in the vessel in which the water was
always kept at a constant level was always constant, it followed that
equal volumes of water indicated equal times, and the vessel into which
the water fell needed only to be equally divided.
As a measure of hours of the day in countries such as Egypt, where the
hours were always equal, and thus where the longer days contained more
hours, the water clock was very suitable; but in Greece and Rome, where
the day, whatever its length, was always divided into twelve hours, the
simple water clock was as unsuitable as a modern clock would be, for it
always divided the hours equally, and took no account of the fact that
by such a system the hours in summer were longer than in winter.
In order, therefore, to make the water clock available in Greece and
Italy, it became necessary to make the hours unequal, and to arrange
them to correspond with unequal hours of the Greek day. This plan was
accomplished as follows. Upon the water which was poured into the
vessel that measured the hours was placed a float; and on the float
stood a figure made of thin copper, with a wand in its hand. This wand
pointed to an unequally divided scale. A separate scale was provided
for every day in the year, and these scales were mounted on a drum
which revolved so as to turn round once in the year. Thus as the figure
rose each day by means of a cogwheel it moved the drum round one
division, or one three hundred and sixty-fifth part of a revolution.
By this means the scale corresponding to any particular day of winter
or summer was brought opposite the wand of the figure, and thus the
scale of hours was kept true. In fact, the water clock, which kept
true time, was made by artificial means to keep untrue time, in order
to correspond with the unequal hours of the Greek days. In the picture
_A_ is the receiving water vessel, _P_ the pipe through which the
water flows; _B_ is the figure, _C_ the rod; _D_ is the drum, made to
revolve by the cogwheel _E_, containing 365 teeth, of which one tooth
was driven forward at the close of each day. A syphon _G_ was fixed in
the vessel _A_, so that when the figure had risen to the top and pushed
forward the lever _F_, the syphon suddenly emptied the vessel through
the pipe _H_, and the figure fell to the bottom of the vessel _A_ and
became ready to rise and register another day. The divisions on the
drum are, of course, uneven. On one side, corresponding to the summer,
the day hours would reckon about seventy minutes each, the night hours
would be only about fifty minutes each, so that the day divisions on
the scale would be long, and the night divisions short. The reverse
would be the case in winter. And, therefore, the lines round the drum
would go in an uneven wavy form.
[Illustration: FIG. 14.]
Such water clocks as these were used by the ancient Romans.
Sand was also used to measure time. As soon as the art of blowing glass
had been perfected by the people of Byzantium, from whom the art passed
to the Venetians, sand-glasses were made. These glasses were used for
all sorts of purposes, for speeches and for cooking, but their most
important use was at sea. For it was very important in the early days
of navigation to know the speed at which the vessel was proceeding in
order that one’s place at sea might be calculated. The earliest method
was to throw over a heavy piece of wood of a shape that resisted being
dragged through the water, and with a string tied to it. The block of
wood was called the log, and the string had knots in it. The knots
were so arranged that when one of them ran through one’s fingers in
a half-minute measured by a sand-glass it indicated that the vessel
was going at the speed of one nautical mile in an hour. The nautical
mile was taken so that sixty of them constituted one degree, that is
one three hundred and sixtieth part of a great circle of the earth.
Each nautical mile has, therefore, 6,080 feet. This is bigger than an
ordinary mile on land, which has only 5,280 feet. The knots, therefore,
have to be arranged so that when the ship is going one nautical
mile—that is to say, 6,080 feet—in an hour, a knot shall run out during
the half-minute run of the minute glass. This is attained by putting
the knots 1/120 × 6,080 = 50 feet 7 inches apart. As one sailor heaved
the log over he gave a stamp on the deck and allowed the cord to run
out through his fingers. Another sailor then turned the sand-glass.
When the sand had all run out, showing that half a minute had passed,
the man who was letting the cord run through his fingers gripped it
fast, and observed how many knots or parts of knots of string had run
out, and thus was able to tell how many “knots” per half-minute the
vessel was going, that is to say, how many nautical miles an hour.
The modern plan of observing the speed of vessels is different. Now we
use a patent log, consisting of a miniature screw propeller tied to a
string and dragged through the water after the vessel. As it is pulled
through the water it revolves, and the number of revolutions it makes
shows how much water it has passed through, and thus what distance
it has gone. The number of revolutions is measured by a counting
mechanism, and can be read off when the log is pulled in. Or sometimes
the screw is attached to a stiff wire, and the counting mechanism is
kept on board the ship.
We use the expression “knots an hour” quite incorrectly. It should be
“knots per half-minute,” or “nautical miles an hour.”
It is easy to use the flow of sand for all sorts of purposes to measure
time. Thus, if sand be allowed to flow from a hopper through a fine
hole into a bucket, the bucket may be arranged so that when a given
time has elapsed, and a given weight of sand has therefore fallen, the
bucket shall tip over, and release a catch, which shall then allow
a weight to fall and any mechanical operation to be done that is
required. Thus, for example, we might put an egg in a small holder tied
to a string and lower it into a saucepan of boiling water. The string
might have a counter-weight attached to it, acting over a pulley and
thus always trying to pull it up out of the water. But this might be
prevented by a pin passing through a loop in the string and preventing
it moving. A hopper or funnel might be filled with sand which was
allowed gradually to escape into a small tip-waggon or other similar
device, so that when a given amount of sand had entered the tip-waggon
would tip over, lurch the pin out of the loop, and thus release the
weight, which in its turn would pull the egg up out of the water in
three minutes or any desired time after it had been put in, or a hole
could be made in the saucepan, furnished with a little tap, and the
water that ran out might be made to fall into a tip-waggon and tip it
over, and thus when it had run out to put an extinguisher on to the
spirit lamp that was heating the saucepan, and at the same time make
a contact and ring an electric bell. By this means the egg would be
always exactly cooked to the right amount, would be kept warm after it
was cooked, and a signal given when it was ready.
[Illustration: FIG. 15.]
The sketch shows such an arrangement. The saucepan is about three
inches in diameter and two inches high. When filled with water it will
hold an egg comfortably. The extinguisher _E_, mounted on a hinge _Q_,
is turned back, and the spirit lamp _L_ is lit. As soon as the water
boils, the tap _T_ is turned, and the water gradually trickles away
into the tip-waggon. As soon as it is full it tips over and strikes the
arm _X_ of the extinguisher, and turns the lamp out. The little hot
water left in the saucepan will keep the egg warm for some time. The
waggon _W_ must have a weight _P_ at one end of it, and the fulcrum
must be nearer to that end, so that when empty it rests with the end
_P_ down, but when full it tips over on the fulcrum, when the waggon
has received the right quantity of water. I leave to the ingenious
reader the task of working out the details of such a machine, which, if
made properly, will act very well and may be made for a number of eggs
and worked with very little trouble.
[Illustration: FIG. 16.]
Mercury has been used also as an hour-glass. The orifice must be
exceedingly fine. Or a bubble of mercury may be put into a tube which
contains air, and made gradually as it falls to drive the air out
through a minute hole. The difficulty is to get the hole fine enough.
All that can be done is to draw out a fine tube in the blow-lamp, break
it off, and put the broken point in the blow-lamp until it is almost
completely closed up. A tube may thus be made about twelve inches long
that will take twelve hours for a bubble of mercury to descend in it.
But the trouble of making so small a hole is considerable.
[Illustration: FIG. 17.]
King Alfred is said to have used candles made of wax to mark the time.
As they blew about with the draughts, he put them in lanterns of horn.
They had no glass windows in those days, but only openings closed
with heavy wooden shutters. These large shutters were for use in fine
weather. Smaller shutters were made in them, so as to let a little
light in in rainy weather without letting in too much wind and rain.
Rooms must then have been very draughty, so that people required to
wear caps and gowns, and beds had thick curtains drawn round them.
When glass was first invented it was only used by kings and princes,
and glass casements were carried about with them to be fixed into
the windows of the houses to which they came, and removed at their
departure.
Oil lamps were also used to mark the time. Some of them certainly as
early as the fifteenth century were made like bird-bottles; that is
to say, they consisted of a reservoir closed at the top with a pipe
leading out of the bottom. When full, the pressure of the external
atmosphere keeps the oil in the bottle, and the oil stands in the neck
and feeds the wick. As the oil is consumed bubbles of air pass back
along the neck and rise up to the top of the oil, the level of which
gradually sinks. Of course the time shown by the lamp varies with the
rate of burning of the oil, and hence with the size of the wick, so
that the method of measuring time is a very rough one.
APPENDIX.
To make a sun-dial, procure a circular piece of zinc, about ⅛ inch
thick, and say twelve inches in diameter. Have a “style” or “gnomon”
cast such that the angle of its edge equals the latitude of the place
where the sun-dial is to be set up. This for London will be equal to
51° 30´´. A pattern may be made for this in wood; it should then be
cast in gun-metal, which is much better for out-of-door exposure than
brass. On a sheet of paper draw a circle _A B C_ with centre _O_. Make
the angle _B O D_ equal to the latitude of the place for London = 51°
30´´. From _A_ draw _A E_ parallel to _O B_ to meet _O D_ in _E_, and
with radius _O E_ describe another circle about _O_. Divide the inner
circle _A B C_ into twenty-four parts, and draw radii through them
from _O_ to meet the larger circle. Through any divisions (say that
corresponding to two o’clock) draw lines parallel to _O B_, _O C_,
respectively to meet in _a_. Then the line _O a_ is the shadow line
of the gnomon at two o’clock. The lines thus drawn on paper may be
transferred to the dial and engraved on it, or else eaten in with acid
in the manner in which etchings are done.
[Illustration: FIG. 18.]
The centre _O_ need not be in the centre of the zinc disc, but may
be on one side of it, so as to give better room for the hours, etc.
A motto may be etched upon the dial, such as “Horas non numero nisi
serenas,” or “Qual ’hom senza Dio, son senza sol io,” or any suitable
inscription, and the dial is ready for use. It is best put up by
turning it till the hour is shown truly as compared with a correctly
timed watch. It must be levelled with a spirit level. It must be
remembered that the sun does not move quite uniformly in his yearly
path among the fixed stars. This is because he moves not in a circle,
but in an ellipse of which the earth is in one of the foci. Hence the
hours shown on the dial are slightly irregular, the sun being sometimes
in advance of the clock, sometimes behind it. The difference is never
more than a quarter of an hour. There is no difference at midsummer and
midwinter.
[Illustration: FIG. 19.]
Civil time is solar time averaged, so as to make the hours and days all
equal. The difference between civil time and apparent solar time is
called the equation of time, and is the amount by which the sun-dial is
in advance of or in retard of the clock. In setting a dial by means of
a watch, of course allowance must be made for the equation of time.