Ten Books on Architecture

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5. So, when the levers are raised, the elbows draw down the bottoms of
the cylinders as far as they can go; and the dolphins, which are mounted
on joints, let the cymbals fall into the cylinders, thus filling the
interiors with air. Then the elbows, raising the bottoms within the
cylinders by repeated and violent blows, and stopping the openings above
by means of the cymbals, compress the air which is enclosed in the
cylinders, and force it into the pipes, through which it runs into the
regulator, and through its neck into the windchest. With a stronger
motion of the levers, the air is still more compressed, streams through
the apertures of the cocks, and fills the channels with wind.

6. So, when the keys, touched by the hand, drive the sliders forward and
draw them back regularly, alternately stopping and opening the holes,
they produce resonant sounds in a great variety of melodies conforming
to the laws of music.

With my best efforts I have striven to set forth an obscure subject
clearly in writing, but the theory of it is not easy, nor readily
understood by all, save only those who have had some practice in things
of this kind. If anybody has failed to understand it, he will certainly
find, when he comes to know the thing itself, that it is carefully and
exquisitely contrived in all respects.

CHAPTER IX

THE HODOMETER

1. The drift of our treatise now turns to a useful invention of the
greatest ingenuity, transmitted by our predecessors, which enables us,
while sitting in a carriage on the road or sailing by sea, to know how
many miles of a journey we have accomplished. This will be possible as
follows. Let the wheels of the carriage be each four feet in diameter,
so that if a wheel has a mark made upon it, and begins to move forward
from that mark in making its revolution on the surface of the road, it
will have covered the definite distance of twelve and a half feet on
reaching that mark at which it began to revolve.

2. Having provided such wheels, let a drum with a single tooth
projecting beyond the face of its circumference be firmly fastened to
the inner side of the hub of the wheel. Then, above this, let a case be
firmly fastened to the body of the carriage, containing a revolving drum
set on edge and mounted on an axle; on the face of the drum there are
four hundred teeth, placed at equal intervals, and engaging the tooth of
the drum below. The upper drum has, moreover, one tooth fixed to its
side and standing out farther than the other teeth.

3. Then, above, let there be a horizontal drum, similarly toothed and
contained in another case, with its teeth engaging the tooth fixed to
the side of the second drum, and let as many holes be made in this
(third) drum as will correspond to the number of miles--more or less, it
does not matter--that a carriage can go in a day's journey. Let a small
round stone be placed in every one of these holes, and in the receptacle
or case containing that drum let one hole be made, with a small pipe
attached, through which, when they reach that point, the stones placed
in the drum may fall one by one into a bronze vessel set underneath in
the body, of the carriage.

4. Thus, as the wheel in going forward carries with it the lowest drum,
and as the tooth of this at every revolution strikes against the teeth
of the upper drum, and makes it move along, the result will be that the
upper drum is carried round once for every four hundred revolutions of
the lowest, and that the tooth fixed to its side pushes forward one
tooth of the horizontal drum. Since, therefore, with four hundred
revolutions of the lowest drum, the upper will revolve once, the
progress made will be a distance of five thousand feet or one mile.
Hence, every stone, making a ringing sound as it falls, will give
warning that we have gone one mile. The number of stones gathered from
beneath and counted, will show the number of miles in the day's journey.

5. On board ship, also, the same principles may be employed with a few
changes. An axle is passed through the sides of the ship, with its ends
projecting, and wheels are mounted on them, four feet in diameter, with
projecting floatboards fastened round their faces and striking the
water. The middle of the axle in the middle of the ship carries a drum
with one tooth projecting beyond its circumference. Here a case is
placed containing a drum with four hundred teeth at regular intervals,
engaging the tooth of the drum that is mounted on the axle, and having
also one other tooth fixed to its side and projecting beyond its
circumference.

6. Above, in another case fastened to the former, is a horizontal drum
toothed in the same way, and with its teeth engaging the tooth fixed to
the side of the drum that is set on edge, so that one of the teeth of
the horizontal drum is struck at each revolution of that tooth, and the
horizontal drum is thus made to revolve in a circle. Let holes be made
in the horizontal drum, in which holes small round stones are to be
placed. In the receptacle or case containing that drum, let one hole be
opened with a small pipe attached, through which a stone, as soon as the
obstruction is removed, falls with a ringing sound into a bronze vessel.

7. So, when a ship is making headway, whether under oars or under a gale
of wind, the floatboards on the wheels will strike against the water and
be driven violently back, thus turning the wheels; and they, revolving,
will move the axle, and the axle the drum, the tooth of which, as it
goes round, strikes one of the teeth of the second drum at each
revolution, and makes it turn a little. So, when the floatboards have
caused the wheels to revolve four hundred times, this drum, having
turned round once, will strike a tooth of the horizontal drum with the
tooth that is fixed to its side. Hence, every time the turning of the
horizontal drum brings a stone to a hole, it will let the stone out
through the pipe. Thus by the sound and the number, the length of the
voyage will be shown in miles.

I have described how to make things that may be provided for use and
amusement in times that are peaceful and without fear.

CHAPTER X

CATAPULTS OR SCORPIONES

1. I shall next explain the symmetrical principles on which scorpiones
and ballistae may be constructed, inventions devised for defence against
danger, and in the interest of self-preservation.

The proportions of these engines are all computed from the given length
of the arrow which the engine is intended to throw, and the size of the
holes in the capitals, through which the twisted sinews that hold the
arms are stretched, is one ninth of that length.

2. The height and breadth of the capital itself must then conform to the
size of the holes. The boards at the top and bottom of the capital,
which are called "peritreti," should be in thickness equal to one hole,
and in breadth to one and three quarters, except at their extremities,
where they equal one hole and a half. The sideposts on the right and
left should be four holes high, excluding the tenons, and five twelfths
of a hole thick; the tenons, half a hole. The distance from a sidepost
to the hole is one quarter of a hole, and it is also one quarter of a
hole from the hole to the post in the middle. The breadth of the post
in the middle is equal to one hole and one eighth, the thickness, to one
hole.

3. The opening in the middle post, where the arrow is laid, is equal to
one fourth of the hole. The four surrounding corners should have iron
plates nailed to their sides and faces, or should be studded with bronze
pins and nails. The pipe, called [Greek: syrigx] in Greek, has a length
of nineteen holes. The strips, which some term cheeks, nailed at the
right and left of the pipe, have a length of nineteen holes and a height
and thickness of one hole. Two other strips, enclosing the windlass, are
nailed on to these, three holes long and half a hole in breadth. The
cheek nailed on to them, named the "bench," or by some the "box," and
made fast by means of dove-tailed tenons, is one hole thick and seven
twelfths of a hole in height. The length of the windlass is equal
to...[12] holes, the thickness of the windlass to three quarters of a
hole.

[Note 12: The dots here and in what follows, indicate lacunae in
the manuscripts.]

4. The latch is seven twelfths of a hole in length and one quarter in
thickness. So also its socket-piece. The trigger or handle is three
holes in length and three quarters of a hole in breadth and thickness.
The trough in the pipe is sixteen holes in length, one quarter of a hole
in thickness, and three quarters in height. The base of the standard on
the ground is equal to eight holes; the breadth of the standard where it
is fastened into the plinth is three quarters of a hole, its thickness
two thirds of a hole; the height of the standard up to the tenon is
twelve holes, its breadth three quarters of a hole, and its thickness
two thirds. It has three struts, each nine holes in length, half a hole
in breadth, and five twelfths in thickness. The tenon is one hole in
length, and the head of the standard one hole and a half in length.

5. The antefix has the breadth of a hole and one eighth, and the
thickness of one hole. The smaller support, which is behind, termed in
Greek [Greek: antibasis], is eight holes long, three quarters of a hole
broad, and two thirds thick. Its prop is twelve holes long, and has the
same breadth and thickness as the smaller support just mentioned. Above
the smaller support is its socket-piece, or what is called the cushion,
two and a half holes long, one and a half high, and three quarters of a
hole broad. The windlass cup is two and seven twelfths holes long, two
thirds of a hole thick, and three quarters broad. The crosspieces with
their tenons have the length of... holes, the breadth of three quarters,
and the thickness of two thirds of a hole. The length of an arm is seven
holes, its thickness at its base two thirds of a hole, and at its end
one half a hole; its curvature is equal to two thirds of a hole.

6. These engines are constructed according to these proportions or with
additions or diminutions. For, if the height of the capitals is greater
than their width--when they are called "high-tensioned,"--something
should be taken from the arms, so that the more the tension is weakened
by height of the capitals, the more the strength of the blow is
increased by shortness of the arms. But if the capital is less
high,--when the term "low-tensioned" is used,--the arms, on account of
their strength, should be made a little longer, so that they may be
drawn easily. Just as it takes four men to raise a load with a lever
five feet long, and only two men to lift the same load with a ten-foot
lever, so the longer the arms, the easier they are to draw, and the
shorter, the harder.

I have now spoken of the principles applicable to the parts and
proportions of catapults.

CHAPTER XI

BALLISTAE

1. Ballistae are constructed on varying principles to produce an
identical result. Some are worked by handspikes and windlasses, some by
blocks and pulleys, others by capstans, others again by means of drums.
No ballista, however, is made without regard to the given amount of
weight of the stone which the engine is intended to throw. Hence their
principle is not easy for everybody, but only for those who have
knowledge of the geometrical principles employed in calculation and in
multiplication.

2. For the holes made in the capitals through the openings of which are
stretched the strings made of twisted hair, generally women's, or of
sinew, are proportionate to the amount of weight in the stone which the
ballista is intended to throw, and to the principle of mass, as in
catapults the principle is that of the length of the arrow. Therefore,
in order that those who do not understand geometry may be prepared
beforehand, so as not to be delayed by having to think the matter out at
a moment of peril in war, I will set forth what I myself know by
experience can be depended upon, and what I have in part gathered from
the rules of my teachers, and wherever Greek weights bear a relation to
the measures, I shall reduce and explain them so that they will express
the same corresponding relation in our weights.

3. A ballista intended to throw a two-pound stone will have a hole of
five digits in its capital; four pounds, six digits; and six pounds,
seven digits; ten pounds, eight digits; twenty pounds, ten digits; forty
pounds, twelve and a half digits; sixty pounds, thirteen and a half
digits; eighty pounds, fifteen and three quarters digits; one hundred
pounds, one foot and one and a half digits; one hundred and twenty
pounds, one foot and two digits; one hundred and forty pounds, one foot
and three digits; one hundred and sixty pounds, one foot and a quarter;
one hundred and eighty pounds, one foot and five digits; two hundred
pounds, one foot and six digits; two hundred and forty pounds, one foot
and seven digits; two hundred and eighty pounds, one foot and a half;
three hundred and twenty pounds, one foot and nine digits; three hundred
and sixty pounds, one foot and ten digits.

4. Having determined the size of the hole, design the "scutula," termed
in Greek [Greek: peritretos],... holes in length and two and one sixth
in breadth. Bisect it by a line drawn diagonally from the angles, and
after this bisecting bring together the outlines of the figure so that
it may present a rhomboidal design, reducing it by one sixth of its
length and one fourth of its breadth at the (obtuse) angles. In the
part composed by the curvatures into which the points of the angles run
out, let the holes be situated, and let the breadth be reduced by one
sixth; moreover, let the hole be longer than it is broad by the
thickness of the bolt. After designing the scutula, let its outline be
worked down to give it a gentle curvature.

5. It should be given the thickness of seven twelfths of a hole. The
boxes are two holes (in height), one and three quarters in breadth, two
thirds of a hole in thickness except the part that is inserted in the
hole, and at the top one third of a hole in breadth. The sideposts are
five holes and two thirds in length, their curvature half a hole, and
their thickness thirty-seven forty-eighths of a hole. In the middle
their breadth is increased as much as it was near the hole in the
design, by the breadth and thickness of... hole; the height by one
fourth of a hole.

6. The (inner) strip on the "table" has a length of eight holes, a
breadth and thickness of half a hole. Its tenons are one hole and one
sixth long, and one quarter of a hole in thickness. The curvature of
this strip is three quarters of a hole. The outer strip has the same
breadth and thickness (as the inner), but the length is given by the
obtuse angle of the design and the breadth of the sidepost at its
curvature. The upper strips are to be equal to the lower; the
crosspieces of the "table," one half of a hole.

7. The shafts of the "ladder" are thirteen holes in length, one hole in
thickness; the space between them is one hole and a quarter in breadth,
and one and one eighth in depth. Let the entire length of the ladder on
its upper surface--which is the one adjoining the arms and fastened to
the table--be divided into five parts. Of these let two parts be given
to the member which the Greeks call the [Greek: chelonion], its breadth
being one and one sixth, its thickness one quarter, and its length
eleven holes and one half; the claw projects half a hole and the
"winging" three sixteenths of a hole. What is at the axis which is
termed the... face... the crosspieces of three holes?

8. The breadth of the inner slips is one quarter of a hole; their
thickness one sixth. The cover-joint or lid of the chelonium is
dove-tailed into the shafts of the ladder, and is three sixteenths of a
hole in breadth and one twelfth in thickness. The thickness of the
square piece on the ladder is three sixteenths of a hole,... the
diameter of the round axle will be equal to that of the claw, but at the
pivots seven sixteenths of a hole.

9. The stays are... holes in length, one quarter of a hole in breadth at
the bottom, and one sixth in thickness at the top. The base, termed
[Greek: eschara], has the length of... holes, and the anti-base of four
holes; each is one hole in thickness and breadth. A supporter is jointed
on, halfway up, one and one half holes in breadth and thickness. Its
height bears no relation to the hole, but will be such as to be
serviceable. The length of an arm is six holes, its thickness at the
base two thirds of a hole, and at the end one half a hole.

I have now given those symmetrical proportions of ballistae and
catapults which I thought most useful. But I shall not omit, so far as I
can express it in writing, the method of stretching and tuning their
strings of twisted sinew or hair.

CHAPTER XII

THE STRINGING AND TUNING OF CATAPULTS

1. Beams of very generous length are selected, and upon them are nailed
socket-pieces in which windlasses are inserted. Midway along their
length the beams are incised and cut away to form framings, and in these
cuttings the capitals of the catapults are inserted, and prevented by
wedges from moving when the stretching is going on. Then the bronze
boxes are inserted into the capitals, and the little iron bolts, which
the Greeks call [Greek: epizygides], are put in their places in the
boxes.

2. Next, the loops of the strings are put through the holes in the
capitals, and passed through to the other side; next, they are put upon
the windlasses, and wound round them in order that the strings,
stretched out taut on them by means of the handspikes, on being struck
by the hand, may respond with the same sound on both sides. Then they
are wedged tightly into the holes so that they cannot slacken. So, in
the same manner, they are passed through to the other side, and
stretched taut on the windlasses by means of the handspikes until they
give the same sound. Thus with tight wedging, catapults are tuned to the
proper pitch by musical sense of hearing.

On these things I have said what I could. There is left for me, in the
matter of sieges, to explain how generals can win victories and cities
be defended, by means of machinery.

CHAPTER XIII

SIEGE MACHINES

1. It is related that the battering ram for sieges was originally
invented as follows. The Carthaginians pitched their camp for the siege
of Cadiz. They captured an outwork and attempted to destroy it. But
having no iron implements for its destruction, they took a beam, and,
raising it with their hands, and driving the end of it repeatedly
against the top of the wall, they threw down the top courses of stones,
and thus, step by step in regular order, they demolished the entire
redoubt.

2. Afterwards a carpenter from Tyre, Bright by name and by nature, was
led by this invention into setting up a mast from which he hung another
crosswise like a steelyard, and so, by swinging it vigorously to and
fro, he threw down the wall of Cadiz. Geras of Chalcedon was the first
to make a wooden platform with wheels under it, upon which he
constructed a framework of uprights and crosspieces, and within it he
hung the ram, and covered it with oxhide for the better protection of
the men who were stationed in the machine to batter the wall. As the
machine made but slow progress, he first gave it the name of the
tortoise of the ram.

3. These were the first steps then taken towards that kind of machinery,
but afterwards, when Philip, the son of Amyntas, was besieging
Byzantium, it was developed in many varieties and made handier by
Polyidus the Thessalian. His pupils were Diades and Charias, who served
with Alexander. Diades shows in his writings that he invented moveable
towers, which he used also to take apart and carry round with the army,
and likewise the borer, and the scaling machine, by means of which one
can cross over to the wall on a level with the top of it, as well as the
destroyer called the raven, or by others the crane.

4. He also employed the ram mounted on wheels, an account of which he
left in his writings. As for the tower, he says that the smallest should
be not less than sixty cubits in height and seventeen in breadth, but
diminishing to one fifth less at the top; the uprights for the tower
being nine inches at the bottom and half a foot at the top. Such a
tower, he says, ought to be ten stories high, with windows in it on all
sides.

5. His larger tower, he adds, was one hundred and twenty cubits high and
twenty-three and one half cubits broad, diminishing like the other to
one fifth less; the uprights, one foot at the bottom and six digits at
the top. He made this large tower twenty stories high, each story having
a gallery round it, three cubits wide. He covered the towers with
rawhide to protect them from any kind of missile.

6. The tortoise of the battering ram was constructed in the same way. It
had, however, a base of thirty cubits square, and a height, excluding
the pediment, of thirteen cubits; the height of the pediment from its
bed to its top was seven cubits. Issuing up and above the middle of the
roof for not less than two cubits was a gable, and on this was reared a
small tower four stories high, in which, on the top floor, scorpiones
and catapults were set up, and on the lower floors a great quantity of
water was stored, to put out any fire that might be thrown on the
tortoise. Inside of this was set the machinery of the ram, termed in
Greek [Greek: kriodoche], in which was placed a roller, turned on a
lathe, and the ram, being set on top of this, produced its great
effects when swung to and fro by means of ropes. It was protected, like
the tower, with rawhide.

7. He explained the principles of the borer as follows: that the machine
itself resembled the tortoise, but that in the middle it had a pipe
lying between upright walls, like the pipe usually found in catapults
and ballistae, fifty cubits in length and one cubit in height, in which
a windlass was set transversely. On the right and left, at the end of
the pipe, were two blocks, by means of which the iron-pointed beam,
which lay in the pipe, was moved. There were numerous rollers enclosed
in the pipe itself under the beam, which made its movements quicker and
stronger. Numerous arches were erected along the pipe above the beam
which was in it, to hold up the rawhide in which this machine was
enveloped.

8. He thought it needless to write about the raven, because he saw that
the machine was of no value. With regard to the scaling machine, termed
in Greek [Greek: epibathra], and the naval contrivances which, as he
wrote, could be used in boarding ships, I have observed that he merely
promised with some earnestness to explain their principles, but that he
has not done so.

I have set forth what was written by Diades on machines and their
construction. I shall now set forth the methods which I have learned
from my teachers, and which I myself believe to be useful.

CHAPTER XIV

THE TORTOISE

1. A tortoise intended for the filling of ditches, and thereby to make
it possible to reach the wall, is to be made as follows. Let a base,
termed in Greek [Greek: eschara], be constructed, with each of its sides
twenty-one feet long, and with four crosspieces. Let these be held
together by two others, two thirds of a foot thick and half a foot
broad; let the crosspieces be about three feet and a half apart, and
beneath and in the spaces between them set the trees, termed in Greek
[Greek: hamaxopodes], in which the axles of the wheels turn in iron
hoops. Let the trees be provided with pivots, and also with holes
through which levers are passed to make them turn, so that the tortoise
can move forward or back or towards its right or left side, or if
necessary obliquely, all by the turning of the trees.

2. Let two beams be laid on the base, projecting for six feet on each
side, round the projections of which let two other beams be nailed,
projecting seven feet beyond the former, and of the thickness and
breadth prescribed in the case of the base. On this framework set up
posts mortised into it, nine feet high exclusive of their tenons, one
foot and a quarter square, and one foot and a half apart. Let the posts
be tied together at the top by mortised beams. Over the beams let the
rafters be set, tied one into another by means of tenons, and carried up
twelve feet high. Over the rafters set the square beam by which the
rafters are bound together.

3. Let the rafters themselves be held together by bridgings, and covered
with boards, preferably of holm oak, or, this failing, of any other
material which has the greatest strength, except pine or alder. For
these woods are weak and easily catch fire. Over the boardings let there
be placed wattles very closely woven of thin twigs as fresh as possible.
Let the entire machine be covered with rawhide sewed together double and
stuffed with seaweed or straw soaked in vinegar. In this way the blows
of ballistae and the force of fires will be repelled by them.

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