

E-text prepared by deaurider, Charlie Howard, and the Online Distributed
Proofreading Team (http://www.pgdp.net) from page images generously made
available by Internet Archive (https://archive.org)



Note: Project Gutenberg also has an HTML version of this
      file which includes the original illustrations.
      See 54546-h.htm or 54546-h.zip:
      (http://www.gutenberg.org/files/54546/54546-h/54546-h.htm)
      or
      (http://www.gutenberg.org/files/54546/54546-h.zip)


      Images of the original pages are available through
      Internet Archive. See
      https://archive.org/details/timeclocksdescri00cuny


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