1this Incile or Sluice or no, and what the Slope
is, certain Rules and Inſtruments have been
invented, which are of excellent Uſe. Ignorant
Workmen try their Slope by laying a Ball in
the Trench, and if this Ball rowls forwards
they think the Slope is right for their Water.
The Inſtruments of dexterous Artiſts are the
Square, Level, Plumb-line, and, in a Word, all
ſuch as are terminated with a right Angle.
This Art is a little more abſtruſe; but how
ever I ſhall open no more of it than is neceſ
ſary for the Purpoſe in Hand. The Practice
is performed by means of the Sight and of the
Object, which we ſhall call the Points. If the
Place through which we are to convey our
Water be an even Plain, there are two Ways of
directing our Sight: For we muſt ſet up cer
tain Marks or Objects, which we may place
either nearer or at a greater Diſtance from
each other. The nearer the Points of the Sight
and the Mark or Object are to each other, the
leſs the ſtraight Line of the Direction of the
Sight will depart from the Superficies of the
Globe; the further thoſe Points are from each
other, the lower the Superficies of the Globe
will fall from the Level of the Sight. In both
theſe you muſt obſerve to allow ten Inches
ſlope for every Mile of Diſtance. But if you
have not a clear Plain, and ſome Hill interferes,
then again you have two Ways of Proceeding:
One by taking the Height from the Incile or
Sluice, on the one Side, and the Height of the
Slope from the Head on the other. The Head
I call that appointed Place to which you would
bring the Water, in order to let it run from
thence free, or to appropriate it to ſome particular
Uſes. We find theſe Heights by taking different
Steps of Meaſurement. I call them Steps be
cauſe they are like thoſe Steps by which we
aſcend to a Temple. One Line of theſe Steps
is the Ray of Sight which goes from the Be
holder's Eye along the ſame Level with his Eye;
which is made by the Square, the Level and the
Plumb-line; and the other Line is that which
falls from the Beholder's Eye down to his Feet,
in a Perpendicular. By means of theſe Steps
you note how much one Line exceeds the
other, by caſting up the Amount of their Per
pendiculars, and ſo find which is the Higheſt,
that which riſes from the Sluice to the Top of
the Eminence, or that which riſes from the
Head. The other Method, is by drawing one
Line from the Sluice to the Top of the Hill
which interferes, and another Lime from thence
to the Head, and by computing the Proporti
ons of their Angles, according to the Rules of
Geometry. But this Method is diſſicult in
Practice, and not extremely ſure, becauſe in a
large Diſtance the leaſt Error occaſioned by
the Eye of the Meaſurer is of very great Conſe
quence. But there are ſome Things which
ſeem to bear ſome Relation to this Method, as
we ſhall ſhew by and by, which, if we have
occaſion to cut a Paſſage through a Hill to
bring Water to a Town, may be of great Uſe
for obtaining the right Directions. The Prac
tice is as follows: On the Summit of the Hill,
in a Place where you can have a View both of
the Sluice on one Side and of the Head on the
other, having laid the Ground exactly level, de
ſcribe a Circle ten Foot in Diameter. This
Circle we ſhall call the Horizon. In the Cen
ter of the Circle ſtick up a Pike exactly per
pendicular. Having made this Preparation, the
Artiſt goes round the Outſide of the Circle, in
order to find in what Part of its Circumference
his Eye being directed to one of the Points of
the Water which is to be conveyed, touches
the lower Part of the Pike which ſtands in the
Center. Having found out and marked this
exact Place in the Circumference of his Hori
zon, he draws a Line for this Direction from
that Mark quite to the oppoſite Side of his Cir
cle. Thus this Line will be the Diameter of
that Circle, as it will paſs through the Center,
and cut through both Sides of the Circumfe
rence. If this Line, upon taking oppoſite Views
leads the Eye on one Side directly to the
Sluice, and on the other directly to the Head
of our Water, it affords us a ſtraight Direction
for our Channel. But if the two Lines of Di
rection do not happen to meet in this Manner,
and the Diameter which leads to the Sluice,
falls on one Part of the Circumference, and
that which leads to the Head, on another;
then from the mutual Interſection of theſe
Lines at the Pike in the Center of the Circle,
we ſhall find the Difference between the two
Directions. I uſe the Help of ſuch a Circle to
make Platforms and draw Maps of Towns and
Provinces, as alſo for the digging ſubterraneous
Conduits, and that with very good Effect. But
of that in another Place. Whatever Canal we
make, whether for bringing only a ſmaller
Quantity of Water for Drinking, or a larger
for Navigation, we may follow the Directions
which we have here taught. But the Prepa
ration of our Canal muſt not be the ſame for
a large Quantity of Water, as for a ſmall. We
ſhall firſt go on with the Subject which we
is, certain Rules and Inſtruments have been
invented, which are of excellent Uſe. Ignorant
Workmen try their Slope by laying a Ball in
the Trench, and if this Ball rowls forwards
they think the Slope is right for their Water.
The Inſtruments of dexterous Artiſts are the
Square, Level, Plumb-line, and, in a Word, all
ſuch as are terminated with a right Angle.
This Art is a little more abſtruſe; but how
ever I ſhall open no more of it than is neceſ
ſary for the Purpoſe in Hand. The Practice
is performed by means of the Sight and of the
Object, which we ſhall call the Points. If the
Place through which we are to convey our
Water be an even Plain, there are two Ways of
directing our Sight: For we muſt ſet up cer
tain Marks or Objects, which we may place
either nearer or at a greater Diſtance from
each other. The nearer the Points of the Sight
and the Mark or Object are to each other, the
leſs the ſtraight Line of the Direction of the
Sight will depart from the Superficies of the
Globe; the further thoſe Points are from each
other, the lower the Superficies of the Globe
will fall from the Level of the Sight. In both
theſe you muſt obſerve to allow ten Inches
ſlope for every Mile of Diſtance. But if you
have not a clear Plain, and ſome Hill interferes,
then again you have two Ways of Proceeding:
One by taking the Height from the Incile or
Sluice, on the one Side, and the Height of the
Slope from the Head on the other. The Head
I call that appointed Place to which you would
bring the Water, in order to let it run from
thence free, or to appropriate it to ſome particular
Uſes. We find theſe Heights by taking different
Steps of Meaſurement. I call them Steps be
cauſe they are like thoſe Steps by which we
aſcend to a Temple. One Line of theſe Steps
is the Ray of Sight which goes from the Be
holder's Eye along the ſame Level with his Eye;
which is made by the Square, the Level and the
Plumb-line; and the other Line is that which
falls from the Beholder's Eye down to his Feet,
in a Perpendicular. By means of theſe Steps
you note how much one Line exceeds the
other, by caſting up the Amount of their Per
pendiculars, and ſo find which is the Higheſt,
that which riſes from the Sluice to the Top of
the Eminence, or that which riſes from the
Head. The other Method, is by drawing one
Line from the Sluice to the Top of the Hill
which interferes, and another Lime from thence
to the Head, and by computing the Proporti
ons of their Angles, according to the Rules of
Geometry. But this Method is diſſicult in
Practice, and not extremely ſure, becauſe in a
large Diſtance the leaſt Error occaſioned by
the Eye of the Meaſurer is of very great Conſe
quence. But there are ſome Things which
ſeem to bear ſome Relation to this Method, as
we ſhall ſhew by and by, which, if we have
occaſion to cut a Paſſage through a Hill to
bring Water to a Town, may be of great Uſe
for obtaining the right Directions. The Prac
tice is as follows: On the Summit of the Hill,
in a Place where you can have a View both of
the Sluice on one Side and of the Head on the
other, having laid the Ground exactly level, de
ſcribe a Circle ten Foot in Diameter. This
Circle we ſhall call the Horizon. In the Cen
ter of the Circle ſtick up a Pike exactly per
pendicular. Having made this Preparation, the
Artiſt goes round the Outſide of the Circle, in
order to find in what Part of its Circumference
his Eye being directed to one of the Points of
the Water which is to be conveyed, touches
the lower Part of the Pike which ſtands in the
Center. Having found out and marked this
exact Place in the Circumference of his Hori
zon, he draws a Line for this Direction from
that Mark quite to the oppoſite Side of his Cir
cle. Thus this Line will be the Diameter of
that Circle, as it will paſs through the Center,
and cut through both Sides of the Circumfe
rence. If this Line, upon taking oppoſite Views
leads the Eye on one Side directly to the
Sluice, and on the other directly to the Head
of our Water, it affords us a ſtraight Direction
for our Channel. But if the two Lines of Di
rection do not happen to meet in this Manner,
and the Diameter which leads to the Sluice,
falls on one Part of the Circumference, and
that which leads to the Head, on another;
then from the mutual Interſection of theſe
Lines at the Pike in the Center of the Circle,
we ſhall find the Difference between the two
Directions. I uſe the Help of ſuch a Circle to
make Platforms and draw Maps of Towns and
Provinces, as alſo for the digging ſubterraneous
Conduits, and that with very good Effect. But
of that in another Place. Whatever Canal we
make, whether for bringing only a ſmaller
Quantity of Water for Drinking, or a larger
for Navigation, we may follow the Directions
which we have here taught. But the Prepa
ration of our Canal muſt not be the ſame for
a large Quantity of Water, as for a ſmall. We
ſhall firſt go on with the Subject which we