Introduction
1. In the famous and important Greek city of Ephesus there is said to be an
ancient ancestral law, the terms of which are severe, but its justice is not
inequitable. When an architect accepts the charge of a public work, he has to
promise what the cost of it will be. His estimate is handed to the magistrate,
and his property is pledged as security until the work is done. When it is
finished, if the outlay agrees with his statement, he is complimented by decrees
and marks of honour. If no more than a fourth has to be added to his estimate,
it is furnished by the treasury and no penalty is inflicted. But when more than
one fourth has to be spent in addition on the work, the money required to finish
it is taken from his property.
2. Would to God that this were also a law of the Roman people, not merely for
public, but also for private buildings. For the ignorant would no longer run
riot with impunity, but men who are well qualified by an exact scientific
training would unquestionably adopt the profession of architecture. Gentlemen
would not be misled into limitless and prodigal expenditure, even to ejectments
from their estates, and the architects themselves could be forced, by fear of
the penalty, to be more careful in calculating and stating the limit of expense,
so that gentlemen would procure their buildings for that which they had
expected, or by adding only a little more. It is true that men who can afford to
devote four hundred thousand to a work may hold on, if they have to add another
hundred thousand, from the pleasure which the hope of finishing it gives them;
but if they are loaded with a fifty per cent increase, or with an even greater
expense, they lose hope, sacrifice what they have already spent, and are
compelled to leave off, broken in fortune and in spirit.
3. This fault appears not only in the matter of buildings, but also in the
shows given by magistrates, whether of gladiators in the forum or of plays on
the stage. Here neither delay nor postponement is permissible, but the
necessities of the case require that everything should be ready at a fixed
time,—the seats for the audience, the awning drawn over them, and whatever, in
accordance with the customs of the stage, is provided by machinery to please the
eye of the people. These matters require careful thought and planning by a well
trained intellect; for none of them can be accomplished without machinery, and
without hard study skilfully applied in various ways.
4. Therefore, since such are our traditions and established practices, it is
obviously fitting that the plans should be worked out carefully, and with the
greatest attention, before the structures are begun. Consequently, as we have no
law or customary practice to compel this, and as every year both praetors and
aediles have to provide machinery for the festivals, I have thought it not out
of place, Emperor, since I have treated of buildings in the earlier books, to
set forth and teach in this, which forms the final conclusion of my treatise,
the principles which govern machines.
Chapter One
Machines and Implements
1. A machine is a combination of timbers fastened together, chiefly
efficacious in moving great weights. Such a machine is set in motion on
scientific principles in circular rounds, which the Greeks call κυλικη κἱνησις.
There is, however, a class intended for climbing, termed in Greek ἁκροβατικὁν,
another worked by air, which with them is called πνευματικὁν, and a third for
hoisting; this the Greeks named βαρουλκὁς. In the climbing class are machines so
disposed that one can safely climb up high, by means of timbers set up on end
and connected by crossbeams, in order to view operations. In the pneumatic
class, air is forced by pressure to produce sounds and tones as in an
ὁργανον.
2. In the hoisting class, heavy weights are removed by machines which raise
them up and set them in position. The climbing machine displays no scientific
principle, but merely a spirit of daring. It is held together by dowels and
crossbeams and twisted lashings and supporting props. A machine that gets its
motive power by pneumatic pressure will produce pretty effects by scientific
refinements. But the hoisting machine has opportunities for usefulness which are
greater and full of grandeur, and it is of the highest efficacy when used with
intelligence.
3. Some of these act on the principle of the μηχανἡ, others on that of the
ὁργανον. The difference between "machines" and "engines" is obviously this, that
machines need more workmen and greater power to make them take effect, as for
instance ballistae and the beams of presses. Engines, on the other hand,
accomplish their purpose at the intelligent touch of a single workman, as the
scorpio or anisocycli when they are turned. Therefore engines, as well as
machines, are, in principle, practical necessities, without which nothing can be
unattended with difficulties.
4. All machinery is derived from nature, and is founded on the teaching and
instruction of the revolution of the firmament. Let us but consider the
connected revolutions of the sun, the moon, and the five planets, without the
revolution of which, due to mechanism, we should not have had the alternation of
day and night, nor the ripening of fruits. Thus, when our ancestors had seen
that this was so, they took their models from nature, and by imitating them were
led on by divine facts, until they perfected the contrivances which are so
serviceable in our life. Some things, with a view to greater convenience, they
worked out by means of machines and their revolutions, others by means of
engines, and so, whatever they found to be useful for investigations, for the
arts, and for established practices, they took care to improve step by step on
scientific principles.
5. Let us take first a necessary invention, such as clothing, and see how the
combination of warp and woof on the loom, which does its work on the principle
of an engine, not only protects the body by covering it, but also gives it
honourable apparel. We should not have had food in abundance unless yokes and
ploughs for oxen, and for all draught animals, had been invented. If there had
been no provision of windlasses, pressbeams, and levers for presses, we could
not have had the shining oil, nor the fruit of the vine to give us pleasure, and
these things could not be transported on land without the invention of the
mechanism of carts or waggons, nor on the sea without that of ships.
6. The discovery of the method of testing weights by steelyards and balances
saves us from fraud, by introducing honest practices into life. There are also
innumerable ways of employing machinery about which it seems unnecessary to
speak, since they are at hand every day; such as mills, blacksmiths' bellows,
carriages, gigs, turning lathes, and other things which are habitually used as
general conveniences. Hence, we shall begin by explaining those that rarely come
to hand, so that they may be understood.
Chapter Two
Hoisting Machines
1. First we shall treat of those machines which are of necessity made ready
when temples and public buildings are to be constructed. Two timbers are
provided, strong enough for the weight of the load. They are fastened together
at the upper end by a bolt, then spread apart at the bottom, and so set up,
being kept upright by ropes attached at the upper ends and fixed at intervals
all round. At the top is fastened a block, which some call a "rechamus." In the
block two sheaves are enclosed, turning on axles. The traction rope is carried
over the sheave at the top, then let fall and passed round a sheave in a block
below. Then it is brought back to a sheave at the bottom of the upper block, and
so it goes down to the lower block, where it is fastened through a hole in that
block. The other end of the rope is brought back and down between the legs of
the machine.
2. Socket-pieces are nailed to the hinder faces of the squared timbers at the
point where they are spread apart, and the ends of the windlass are inserted
into them so that the axles may turn freely. Close to each end of the windlass
are two holes, so adjusted that handspikes can be fitted into them. To the
bottom of the lower block are fastened shears made of iron, whose prongs are
brought to bear upon the stones, which have holes bored in them. When one end of
the rope is fastened to the windlass, and the latter is turned round by working
the handspikes, the rope winds round the windlass, gets taut, and thus it raises
the load to the proper height and to its place in the work.
3. This kind of machinery, revolving with three sheaves, is called a
trispast. When there are two sheaves turning in the block beneath and three in
the upper, the machine is termed a pentaspast. But if we have to furnish
machines for heavier loads, we must use timbers of greater length and thickness,
providing them with correspondingly large bolts at the top, and windlasses turning at the
bottom. When these are ready, let forestays be attached and left lying slack in
front; let the backstays be carried over the shoulders of the machine to some
distance, and, if there is nothing to which they can be fastened, sloping piles
should be driven, the ground rammed down all round to fix them firmly, and the
ropes made fast to them.
4. A block should then be attached by a stout cord to the top of the machine,
and from that point a rope should be carried to a pile, and to a block tied to
the pile. Let the rope be put in round the sheave of this block, and brought
back to the block that is fastened at the top of the machine. Round its sheave
the rope should be passed, and then should go down from the top, and back to the
windlass, which is at the bottom of the machine, and there be fastened. The
windlass is now to be turned by means of the handspikes, and it will raise the
machine of itself without danger. Thus, a machine of the larger kind will be set
in position, with its ropes in their places about it, and its stays attached to
the piles. Its blocks and traction ropes are arranged as described above.
5. But if the loads of material for the work are still more colossal in size
and weight, we shall not entrust them to a windlass, but set in an axle-tree,
held by sockets as the windlass was, and carrying on its centre a large drum,
which some term a wheel, but the Greeks call it ἁμφἱεσις or περιθἡκιον.
6. And the blocks in such machines are not arranged in the same, but in a
different manner; for the rows of sheaves in them are doubled, both at the
bottom and at the top. The traction rope is passed through a hole in the lower
block, in such a way that the two ends of the rope are of equal length when it
is stretched out, and both portions are held there at the lower block by a cord
which is passed round them and lashed so that they cannot come out either to the
right or the left. Then the ends of the rope are brought up into the block at
the top from the outside, and passed down over its lower sheaves, and so return
to the bottom, and are passed from the inside to the sheaves in the lowest
block, and then
are brought up on the right and left, and return to the top and round the
highest set of sheaves.
7. Passing over these from the outside, they are then carried to the right
and left of the drum on the axle-tree, and are tied there so as to stay fast.
Then another rope is wound round the drum and carried to a capstan, and when
that is turned, it turns the drum and the axle-tree, the ropes get taut as they
wind round regularly, and thus they raise the loads smoothly and with no danger.
But if a larger drum is placed either in the middle or at one side, without any
capstan, men can tread in it and accomplish the work more expeditiously.
8. There is also another kind of machine, ingenious enough and easy to use
with speed, but only experts can work with it. It consists of a single timber,
which is set up and held in place by stays on four sides. Two cheeks are nailed
on below the stays, a block is fastened by ropes above the cheeks, and a
straight piece of wood about two feet long, six digits wide, and four digits
thick, is put under the block. The blocks used have each three rows of sheaves
side by side. Hence three traction ropes are fastened at the top of the machine.
Then they are brought to the block at the bottom, and passed from the inside
round the sheaves that are nearest the top of it. Then they are brought back to
the upper block, and passed inwards from outside round the sheaves nearest the
bottom.
9. On coming down to the block at the bottom, they are carried round its
second row of sheaves from the inside to the outside, and brought back to the
second row at the top, passing round it and returning to the bottom; then from
the bottom they are carried to the summit, where they pass round the highest row
of sheaves, and then return to the bottom of the machine. At the foot of the
machine a third block is attached. The Greeks call it ἑπἁγων, but our people
"artemon." This block fastened at the foot of the machine has three sheaves in
it, round which the ropes are passed and then delivered to men to pull. Thus,
three rows of men, pulling without a capstan, can quickly raise the load to the
top.
10. This kind of machine is called a polyspast, because of the many revolving
sheaves to which its dexterity and despatch are due. There is also this
advantage in the erection of only a single timber, that by previously inclining
it to the right or left as much as one wishes, the load can be set down at one
side.
All these kinds of machinery described above are, in their principles, suited
not only to the purposes mentioned, but also to the loading and unloading of
ships, some kinds being set upright, and others placed horizontally on revolving
platforms. On the same principle, ships can be hauled ashore by means of
arrangements of ropes and blocks used on the ground, without setting up
timbers.
11. It may also not be out of place to explain the ingenious procedure of
Chersiphron. Desiring to convey the shafts for the temple of Diana at Ephesus
from the stone quarries, and not trusting to carts, lest their wheels should be
engulfed on account of the great weights of the load and the softness of the
roads in the plain, he tried the following plan. Using four-inch timbers, he
joined two of them, each as long as the shaft, with two crosspieces set between
them, dovetailing all together, and then leaded iron gudgeons shaped like
dovetails into the ends of the shafts, as dowels are leaded, and in the woodwork
he fixed rings to contain the pivots, and fastened wooden cheeks to the ends.
The pivots, being enclosed in the rings, turned freely. So, when yokes of oxen
began to draw the four-inch frame, they made the shaft revolve constantly,
turning it by means of the pivots and rings.
12. When they had thus transported all the shafts, and it became necessary to
transport the architraves, Chersiphron's son Metagenes extended the same
principle from the transportation of the shafts to the bringing down of the
architraves. He made wheels, each about twelve feet in diameter, and enclosed
the ends of the architraves in the wheels. In the ends he fixed pivots and rings
in the same way. So when the four-inch frames were drawn by oxen, the wheels
turned on the pivots enclosed in the rings, and the architraves, which were
enclosed like axles in
the wheels, soon reached the building, in the
same way as the shafts. The rollers used for smoothing the walks in palaestrae
will serve as an example of this method. But it could not have been employed
unless the distance had been short; for it is not more than eight miles from the
stone-quarries to the temple, and there is no hill, but an uninterrupted
plain.
13. In our own times, however, when the pedestal of the colossal Apollo in
his temple had cracked with age, they were afraid that the statue would fall and
be broken, and so they contracted for the cutting of a pedestal from the same
quarries. The contract was taken by one Paconius. This pedestal was twelve feet
long, eight feet wide, and six feet high. Paconius, with confident pride, did
not transport it by the method of Metagenes, but determined to make a machine of
a different sort, though on the same principle.
14. He made wheels of about fifteen feet in diameter, and in these wheels he
enclosed the ends of the stone; then he fastened two-inch crossbars from wheel
to wheel round the stone, encompassing it, so that there was an interval of not
more than one foot between bar and bar. Then he coiled a rope round the bars,
yoked up his oxen, and began to draw on the rope. Consequently as it uncoiled,
it did indeed cause the wheels to turn, but it could not draw them in a line
straight along the road, but kept swerving out to one side. Hence it was
necessary to draw the machine back again. Thus, by this drawing to and fro,
Paconius got into such financial embarrassment that he became insolvent.
15. I will digress a bit and explain how these stone-quarries were
discovered. Pixodorus was a shepherd who lived in that vicinity. When the people
of Ephesus were planning to build the temple of Diana in marble, and debating
whether to get the marble from Paros, Proconnesus, Heraclea, or Thasos,
Pixodorus drove out his sheep and was feeding his flock in that very spot. Then
two rams ran at each other, and, each passing the other, one of them, after his
charge, struck his horns against a
rock, from which a fragment of extremely white
colour was dislodged. So it is said that Pixodorus left his sheep in the
mountains and ran down to Ephesus carrying the fragment, since that very thing
was the question of the moment. Therefore they immediately decreed honours to
him and changed his name, so that instead of Pixodorus he should be called
Evangelus. And to this day the chief magistrate goes out to that very spot every
month and offers sacrifice to him, and if he does not, he is punished.
Chapter Three
The Elements of Motion
1. I have briefly set forth what I thought necessary about the principles of
hoisting machines. In them two different things, unlike each other, work
together, as elements of their motion and power, to produce these effects. One
of them is the right line, which the Greeks term εὑθεια; the other is the
circle, which the Greeks call κυκλωτἡ; but in point of fact, neither rectilinear
without circular motion, nor revolutions, without rectilinear motion, can
accomplish the raising of loads. I will explain this, so that it may be
understood.
2. As centres, axles are inserted into the sheaves, and these are fastened in
the blocks; a rope carried over the sheaves, drawn straight down, and fastened
to a windlass, causes the load to move upward from its place as the handspikes
are turned. The pivots of this windlass, lying as centres in right lines in its
socket-pieces, and the handspikes inserted in its holes, make the load rise when
the ends of the windlass revolve in a circle like a lathe. Just so, when an iron
lever is applied to a weight which a great many hands cannot move, with the
fulcrum, which the Greeks call ὑπομὁχλιον, lying as a centre in a right line
under the lever, and with the tongue of the lever placed under the weight, one
man's strength, bearing down upon the head of it, heaves up the weight.
3. For, as the shorter fore part of the lever goes under the weight from the
fulcrum that forms the centre, the head of it, which is farther away from that
centre, on being depressed, is made to describe a circular movement, and thus by
pressure brings to an equilibrium the weight of a very great load by means of a
few hands. Again, if the tongue of an iron lever is placed under a weight, and
its head is not pushed down, but, on the contrary, is heaved up, the tongue,
supported on the surface of the ground, will treat that as the weight, and the
edge of the weight itself as the fulcrum. Thus, not so easily as by pushing
down, but by motion in the opposite direction, the weight of the load will
nevertheless be raised. If, therefore, the tongue of a lever lying on a fulcrum
goes too far under the weight, and its head exerts its pressure too near the
centre, it will not be able to elevate the weight, nor can it do so unless, as
described above, the length of the lever is brought to equilibrium by the
depression of its head.
4. This may be seen from the balances that we call steelyards. When the
handle is set as a centre close to the end from which the scale hangs, and the
counterpoise is moved along towards the other arm of the beam, shifting from
point to point as it goes farther or even reaches the extremity, a small and
inferior weight becomes equal to a very heavy object that is being weighed, on
account of the equilibrium that is due to the levelling of the beam. Thus, as it
withdraws from the centre, a small and comparatively light counterpoise, slowly
turning the scale, makes a greater amount of weight rise gently upwards from
below.
5. So, too, the pilot of the biggest merchantman, grasping the steering oar
by its handle, which the Greeks call οἱαξ, and with one hand bringing it to the
turning point, according to the rules of his art, by pressure about a centre,
can turn the ship, although she may be laden with a very large or even enormous
burden of merchandise and provisions. And when her sails are set only halfway up
the mast, a ship cannot run quickly; but when the yard is hoisted to the top,
she makes much quicker progress, because then the sails get the wind, not when
they are[292] too
close to the heel of the mast, which represents the centre, but when they have
moved farther away from it to the top.
6. As a lever thrust under a weight is harder to manage, and does not put
forth its strength, if the pressure is exerted at the centre, but easily raises
the weight when the extreme end of it is pushed down, so sails that are only
halfway up have less effect, but when they get farther away from the centre, and
are hoisted to the very top of the mast, the pressure at the top forces the ship
to make greater progress, though the wind is no stronger but just the same.
Again, take the case of oars, which are fastened to the tholes by loops,—when
they are pushed forward and drawn back by the hand, if the ends of the blades
are at some distance from the centre, the oars foam with the waves of the sea
and drive the ship forward in a straight line with a mighty impulse, while her
prow cuts through the rare water.
7. And when the heaviest burdens are carried on poles by four or six porters
at a time, they find the centres of balance at the very middle of the poles, so
that, by distributing the dead weight of the burden according to a definitely
proportioned division, each labourer may have an equal share to carry on his
neck. For the poles, from which the straps for the burden of the four porters
hang, are marked off at their centres by nails, to prevent the straps from
slipping to one side. If they shift beyond the mark at the centre, they weigh
heavily upon the place to which they have come nearer, like the weight of a
steelyard when it moves from the point of equilibrium towards the end of the
weighing apparatus.
8. In the same way, oxen have an equal draught when their yoke is adjusted at
its middle by the yokestrap to the pole. But when their strength is not the
same, and the stronger outdoes the other, the strap is shifted so as to make one
side of the yoke longer, which helps the weaker ox. Thus, in the case of both
poles and yokes, when the straps are not fastened at the middle, but at one
side, the farther the strap moves from the middle, the shorter it makes one
side, and the longer the other. So, if both
ends are carried round in circles, using as a
centre the point to which the strap has been brought, the longer end will
describe a larger, and the shorter end a smaller circle.
9. Just as smaller wheels move harder and with greater difficulty than larger
ones, so, in the case of the poles and yokes, the parts where the interval from
centre to end is less, bear down hard upon the neck, but where the distance from
the same centre is greater, they ease the burden both for draught and carriage.
As in all these cases motion is obtained by means of right lines at the centre
and by circles, so also farm waggons, travelling carriages, drums, mills,
screws, scorpiones, ballistae, pressbeams, and all other machines, produce the
results intended, on the same principles, by turning about a rectilinear axis
and by the revolution of a circle.
Chapter Four
Engines for Raising Water
1. I shall now explain the making of the different kinds of engines which
have been invented for raising water, and will first speak of the tympanum.
Although it does not lift the water high, it raises a great quantity very
quickly. An axle is fashioned on a lathe or with the compasses, its ends are
shod with iron hoops, and it carries round its middle a tympanum made of boards
joined together. It rests on posts which have pieces of iron on them under the
ends of the axle. In the interior of this tympanum there are eight crosspieces
set at intervals, extending from the axle to the circumference of the tympanum,
and dividing the space in the tympanum into equal compartments.
2. Planks are nailed round the face of it, leaving six-inch apertures to
admit the water. At one side of it there are also holes, like those of a
dovecot, next to the axle, one for each compartment. After being smeared with
pitch like a ship, the thing is turned by the tread of men, and raising the
water by means of the apertures in the face of the tympanum, delivers it through
the holes next
to the axle into a wooden trough set underneath, with a conduit joined to it.
Thus, a large quantity of water is furnished for irrigation in gardens, or for
supplying the needs of saltworks.
3. But when it has to be raised higher, the same principle will be modified
as follows. A wheel on an axle is to be made, large enough to reach the
necessary height. All round the circumference of the wheel there will be cubical
boxes, made tight with pitch and wax. So, when the wheel is turned by treading,
the boxes, carried up full and again returning to the bottom, will of themselves
discharge into the reservoir what they have carried up.
4. But, if it has to be supplied to a place still more high, a double iron
chain, which will reach the surface when let down, is passed round the axle of
the same wheel, with bronze buckets attached to it, each holding about six
pints. The turning of the wheel, winding the chain round the axle, will carry
the buckets to the top, and as they pass above the axle they must tip over and
deliver into the reservoir what they have carried up.