so
that water for public use will not run short; for people will be unable
to divert it if they have only their own supplies from headquarters.
This is the reason why I have made these divisions, and also in order
that individuals who take water into their houses may by their taxes
help to maintain the conducting of the water by the contractors.

3. If, however, there are hills between the city and the source of
supply, subterranean channels must be dug, and brought to a level at the
gradient mentioned above. If the bed is of tufa or other stone, let the
channel be cut in it; but if it is of earth or sand, there must be
vaulted masonry walls for the channel, and the water should thus be
conducted, with shafts built at every two hundred and forty feet.

4. But if the water is to be conducted in lead pipes, first build a
reservoir at the source; then, let the pipes have an interior area
corresponding to the amount of water, and lay these pipes from this
reservoir to the reservoir which is inside the city walls. The pipes
should be cast in lengths of at least ten feet. If they are hundreds,
they should weigh 1200 pounds each length; if eighties, 960 pounds; if
fifties, 600 pounds; forties, 480 pounds; thirties, 360 pounds;
twenties, 240 pounds; fifteens, 180 pounds; tens, 120 pounds; eights,
100 pounds; fives, 60 pounds. The pipes get the names of their sizes
from the width of the plates, taken in digits, before they are rolled
into tubes. Thus, when a pipe is made from a plate fifty digits in
width, it will be called a "fifty," and so on with the rest.

5. The conducting of the water through lead pipes is to be managed as
follows. If there is a regular fall from the source to the city, without
any intervening hills that are high enough to interrupt it, but with
depressions in it, then we must build substructures to bring it up to
the level as in the case of channels and conduits. If the distance round
such depressions is not great, the water may be carried round
circuitously; but if the valleys are extensive, the course will be
directed down their slope. On reaching the bottom, a low substructure is
built so that the level there may continue as long as possible. This
will form the "venter," termed [Greek: Koilia] by the Greeks. Then, on
reaching the hill on the opposite side, the length of the venter makes
the water slow in swelling up to rise to the top of the hill.

6. But if there is no such venter made in the vall