Ten Books on Architecture
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Vitruvius >> Ten Books on Architecture
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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 [Greek: epagon], 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 III
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 [Greek: eutheia]; the other is the circle, which the Greeks call
[Greek: kyklote]; 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 [Greek: hupomochlion], 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 [Greek: oiax], 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 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 IV
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.
CHAPTER V
WATER WHEELS AND WATER MILLS
1. Wheels on the principles that have been described above are also
constructed in rivers. Round their faces floatboards are fixed, which,
on being struck by the current of the river, make the wheel turn as they
move, and thus, by raising the water in the boxes and bringing it to the
top, they accomplish the necessary work through being turned by the mere
impulse of the river, without any treading on the part of workmen.
2. Water mills are turned on the same principle. Everything is the same
in them, except that a drum with teeth is fixed into one end of the
axle. It is set vertically on its edge, and turns in the same plane with
the wheel. Next to this larger drum there is a smaller one, also with
teeth, but set horizontally, and this is attached (to the millstone).
Thus the teeth of the drum which is fixed to the axle make the teeth of
the horizontal drum move, and cause the mill to turn. A hopper, hanging
over this contrivance, supplies the mill with corn, and meal is produced
by the same revolution.
CHAPTER VI
THE WATER SCREW
1. There is also the method of the screw, which raises a great quantity
of water, but does not carry it as high as does the wheel. The method of
constructing it is as follows. A beam is selected, the thickness of
which in digits is equivalent to its length in feet. This is made
perfectly round. The ends are to be divided off on their circumference
with the compass into eight parts, by quadrants and octants, and let the
lines be so placed that, if the beam is laid in a horizontal position,
the lines on the two ends may perfectly correspond with each other, and
intervals of the size of one eighth part of the circumference of the
beam may be laid off on the length of it. Then, placing the beam in a
horizontal position, let perfectly straight lines be drawn from one end
to the other. So the intervals will be equal in the directions both of
the periphery and of the length. Where the lines are drawn along the
length, the cutting circles will make intersections, and definite points
at the intersections.
[Illustration: CONSTRUCTION OF THE WATER SCREW]
[Illustration: THE WATER SCREW
(From the edition of Vitruvius by Fra Giocondo, Venice, 1511)]
2. When these lines have been correctly drawn, a slender withe of
willow, or a straight piece cut from the agnus castus tree, is taken,
smeared with liquid pitch, and fastened at the first point of
intersection. Then it is carried across obliquely to the succeeding
intersections of longitudinal lines and circles, and as it advances,
passing each of the points in due order and winding round, it is
fastened at each intersection; and so, withdrawing from the first to the
eighth point, it reaches and is fastened to the line to which its first
part was fastened. Thus, it makes as much progress in its longitudinal
advance to the eighth point as in its oblique advance over eight
points. In the same manner, withes for the eight divisions of the
diameter, fastened obliquely at the intersections on the entire
longitudinal and peripheral surface, make spiral channels which
naturally look just like those of a snail shell.
3. Other withes are fastened on the line of the first, and on these
still others, all smeared with liquid pitch, and built up until the
total diameter is equal to one eighth of the length. These are covered
and surrounded with boards, fastened on to protect the spiral. Then
these boards are soaked with pitch, and bound together with strips of
iron, so that they may not be separated by the pressure of the water.
The ends of the shaft are covered with iron. To the right and left of
the screw are beams, with crosspieces fastening them together at both
ends. In these crosspieces are holes sheathed with iron, and into them
pivots are introduced, and thus the screw is turned by the treading of
men.
4. It is to be set up at an inclination corresponding to that which is
produced in drawing the Pythagorean right-angled triangle: that is, let
its length be divided into five parts; let three of them denote the
height of the head of the screw; thus the distance from the base of the
perpendicular to the nozzle of the screw at the bottom will be equal to
four of those parts. A figure showing how this ought to be, has been
drawn at the end of the book, right on the back.
I have now described as clearly as I could, to make them better known,
the principles on which wooden engines for raising water are
constructed, and how they get their motion so that they may be of
unlimited usefulness through their revolutions.
CHAPTER VII
THE PUMP OF CTESIBIUS
1. Next I must tell about the machine of Ctesibius, which raises water
to a height. It is made of bronze, and has at the bottom a pair of
cylinders set a little way apart, and there is a pipe connected with
each, the two running up, like the prongs of a fork, side by side to a
vessel which is between the cylinders. In this vessel are valves,
accurately fitting over the upper vents of the pipes, which stop up the
ventholes, and keep what has been forced by pressure into the vessel
from going down again.
2. Over the vessel a cowl is adjusted, like an inverted funnel, and
fastened to the vessel by means of a wedge thrust through a staple, to
prevent it from being lifted off by the pressure of the water that is
forced in. On top of this a pipe is jointed, called the trumpet, which
stands up vertically. Valves are inserted in the cylinders, beneath the
lower vents of the pipes, and over the openings which are in the bottoms
of the cylinders.
3. Pistons smoothly turned, rubbed with oil, and inserted from above
into the cylinders, work with their rods and levers upon the air and
water in the cylinders, and, as the valves stop up the openings, force
and drive the water, by repeated pressure and expansion, through the
vents of the pipes into the vessel, from which the cowl receives the
inflated currents, and sends them up through the pipe at the top; and so
water can be supplied for a fountain from a reservoir at a lower level.
4. This, however, is not the only apparatus which Ctesibius is said to
have thought out, but many more of various kinds are shown by him to
produce effects, borrowed from nature, by means of water pressure and
compression of the air; as, for example, blackbirds singing by means of
waterworks, and "angobatae," and figures that drink and move, and other
things that are found to be pleasing to the eye and the ear.
5. Of these I have selected what I considered most useful and necessary,
and have thought it best to speak in the preceding book about
timepieces, and in this about the methods of raising water. The rest,
which are not subservient to our needs, but to pleasure and amusement,
may be found in the commentaries of Ctesibius himself by any who are
interested in such refinements.
CHAPTER VIII
THE WATER ORGAN
1. With regard to water organs, however, I shall not fail with all
possible brevity and precision to touch upon their principles, and to
give a sufficient description of them. A wooden base is constructed, and
on it is set an altar-shaped box made of bronze. Uprights, fastened
together like ladders, are set up on the base, to the right and to the
left (of the altar). They hold the bronze pump-cylinders, the moveable
bottoms of which, carefully turned on a lathe, have iron elbows fastened
to their centres and jointed to levers, and are wrapped in fleeces of
wool. In the tops of the cylinders are openings, each about three digits
in diameter. Close to these openings are bronze dolphins, mounted on
joints and holding chains in their mouths, from which hang cymbal-shaped
valves, let down under the openings in the cylinders.
2. Inside the altar, which holds the water, is a regulator shaped like
an inverted funnel, under which there are cubes, each about three digits
high, keeping a free space below between the lips of the regulator and
the bottom of the altar. Tightly fixed on the neck of the regulator is
the windchest, which supports the principal part of the contrivance,
called in Greek the [Greek: kanon mousikos]. Running longitudinally,
there are four channels in it if it is a tetrachord; six, if it is a
hexachord; eight, if it is an octachord.
3. Each of the channels has a cock in it, furnished with an iron handle.
These handles, when turned, open ventholes from the windchest into the
channels. From the channels to the canon there are vertical openings
corresponding to ventholes in a board above, which board is termed
[Greek: pinax] in Greek. Between this board and the canon are inserted
sliders, pierced with holes to correspond, and rubbed with oil so that
they can be easily moved and slid back into place again. They close the
above-mentioned openings, and are called the plinths. Their going and
coming now closes and now opens the holes.
4. These sliders have iron jacks fixed to them, and connected with the
keys, and the keys, when touched, make the sliders move regularly. To
the upper surface of the openings in the board, where the wind finds
egress from the channels, rings are soldered, and into them the reeds of
all the organ pipes are inserted. From the cylinders there are
connecting pipes attached to the neck of the regulator, and directed
towards the ventholes in the windchest. In the pipes are valves, turned
on a lathe, and set (where the pipes are connected with the cylinders).
When the windchest has received the air, these valves will stop up the
openings, and prevent the wind from coming back again.
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