The
compleat
Cannoniere
.
And
first
of
principalls
of
Philosophy
fit
to
be
knowne
.
ALl
motions
or
things
moveable
endeth
in
their
rest
or
repose
.
So
all
motions
are
made
upon
some
quantity
continually
.
Every
simple
bodies
is
either
bright
and
light
,
or
else
grosse
,
darke
,
and
ponderous
:
and
according
to
the
variety
and
differences
,
it
is
alwayes
naturally
carried
towards
some
one
or
other
part
.
The
World
hath
height
as
upwards
,
or
depth
as
downewards
;
and
the
depth
dependeth
upon
the
influence
of
the
height
.
All
pure
and
rare
Bodies
ascend
as
the
fire
,
more
than
the
aire
;
but
the
thicke
and
grosse
bodies
descend
,
as
the
Eearth
more
than
the
Water
.
Nothing
worketh
naturally
in
that
which
is
wholly
like
,
or
wholly
dislike
,
but
in
that
which
is
contrary
to
it
,
and
more
feeble
.
The
forme
working
is
aided
by
the
quallities
as
the
matter
suffering
,
which
suffereth
by
the
quantity
.
Nature
is
extreamely
curious
as
well
of
her
perfection
,
as
of
her
conservation
?
and
then
when
all
things
conspire
.
Aswell
the
action
that
commeth
from
the
Agent
,
as
the
passion
from
the
patient
hath
proportion
.
Accident
taketh
his
unity
from
the
subject
,
and
goetli
not
from
one
thing
to
another
.
Every
Corporall
thing
reposeth
in
its
naturall
place
,
motion
may
be
made
any
where
within
the
Moones
Orbe
,
nature
admitteth
no
Empresse
.
A
body
rarifying
its
selfe
,
the
place
thereof
increaseth
as
the
body
increaseth
.
The
resistance
of
the
moved
,
proportioned
to
the
mover
furthereth
the
motion
.
The
longer
the
chase
of
a
peece
,
the
louder
the
report
.
Also
the
force
of
the
stroke
dependeth
on
the
swiftnesse
of
the
course
.
A
Table
of
the
Square
.
|
A
Table
of
Cubes
.
|
1
|
1
|
1
|
1
|
2
|
4
|
2
|
8
|
3
|
9
|
3
|
27
|
4
|
16
|
4
|
64
|
5
|
25
|
5
|
125
|
6
|
36
|
6
|
216
|
7
|
49
|
7
|
343
|
8
|
64
|
8
|
512
|
9
|
81
|
9
|
729
|
How
to
extract
the
square
roote
.
SEt
downe
any
number
as
comes
into
your
minde
,
as
thus
,
2̇
1
6̇
0
9˙
.
Then
begin
at
your
right
hand
,
and
put
a
pricke
over
the
first
figure
,
and
then
over
the
third
,
as
you
see
above
done
;
&
aske
what
is
the
square
root
of
2.
which
is
as
many
figures
as
you
have
under
your
first
pricke
,
&
you
shal
find
but
1.
then
put
that
figure
in
the
quotient
,
and
substract
that
1.
out
of
2.
so
remaineth
1.
then
double
your
quotient
,
&
set
that
double
under
your
second
figure
,
dividing
the
number
over
by
that
double
.
But
take
heede
you
leave
enough
to
take
the
square
of
that
figure
last
set
in
the
quotient
out
of
the
remainder
.
Lastly
,
double
all
your
quotient
,
and
divide
as
afore
;
then
square
your
third
figure
in
the
quotient
againe
,
and
substract
it
out
of
the
remainder
,
so
have
you
done
this
summe
.
Looke
how
often
you
have
prickes
,
so
often
must
you
double
and
multiply
squarely
,
and
substract
also
,
so
many
figures
also
will
there
bee
in
the
quotient
,
as
there
are
pricks
.
And
consequently
of
any
number
whatsoever
.
To
know
the
neerest
root
of
a
number
not
square
.
IF
any
fraction
remaine
,
by
diligent
observation
of
this
,
you
may
come
as
neere
you
would
desire
in
any
practicke
,
to
guesse
within
lesse
than
ordinary
is
knowne
.
Set
next
your
right
hand
after
your
summe
,
either
two
,
foure
,
or
sixe
cyphers
,
the
more
,
the
lesser
your
errour
;
and
the
nearer
by
much
shall
you
come
unto
the
roote
,
observing
the
same
manner
in
working
as
you
did
before
.
And
now
I
will
shew
you
by
particular
questions
in
the
art
Military
,
how
necessary
it
is
for
any
one
intending
to
be
a
compleat
martiall
man
,
to
have
good
judgement
in
the
extraction
of
the
square
and
cubicke
rootes
,
and
also
in
the
depth
of
Arithmeticke
,
and
what
excellencie
of
knowledge
is
attained
unto
thereby
,
and
how
farre
they
are
from
being
Souldiers
,
as
are
ignorant
thereof
.
The
first
Question
.
A
Generall
having
3
great
Armies
,
would
cast
them
into
three
square
battailes
,
but
he
knowes
not
how
many
men
he
shall
set
in
the
front
of
each
battaile
.
The
number
of
the
3
Armies
are
these
,
in
the
first
there
are
5625.
in
the
second
9216.
and
in
the
third
15129.
To
doe
this
,
you
must
extract
the
root
of
every
Armie
severally
,
so
have
you
your
desire
.
In
the
first
you
have
75.
men
square
,
in
the
second
96.
men
,
and
in
the
third
123.
If
you
were
commanded
to
make
a
square
battaile
of
all
three
Armies
,
adde
them
first
together
,
then
extract
the
square
roote
;
and
if
any
remainder
be
,
you
may
imploy
them
where
you
please
.
The
second
Question
.
A
King
hath
a
great
Armie
in
a
valley
that
in
marching
,
the
front
can
be
but
18.
men
,
&
the
flank
44352
which
he
is
desirous
to
cast
into
a
square
battaile
.
Multiply
the
flanke
by
the
front
,
so
have
you
the
full
number
of
the
men
:
then
extract
the
square
root
thereof
,
so
have
you
what
can
be
desired
.
The
third
question
.
A
Generall
hath
3
Armies
in
the
Field
,
to
the
number
of
28289.
men
,
and
none
of
these
three
apt
to
make
a
square
battaile
;
the
Serjant
Major
is
commanded
by
his
Generall
to
set
them
in
three
square
battailes
.
These
are
the
3
numbers
of
the
three
severall
Armies
:
In
the
first
there
are
10296.
men
:
in
the
second
9493
,
and
in
the
thire
8500
men
.
Marke
this
seriously
for
it
is
not
ordinary
;
you
shall
finde
more
exquisite
worke
than
you
imagine
,
because
the
question
is
more
difficult
.
First
,
extract
the
severall
roots
of
the
3
Armies
.
Then
take
the
greatest
squares
of
all
3
numbers
,
as
10201.
and
his
excesse
95.
together
with
his
root
,
which
is
101.
In
the
second
the
greatest
square
is
9409
,
and
〈◊〉
●…cesse
84
,
and
his
roote
97.
In
the
third
,
the
greatest
square
is
8464
,
his
excesse
36
,
and
his
roote
92.
And
thus
have
I
found
the
3
excesses
.
Now
for
to
end
the
3
defaults
or
wants
,
I
adde
one
to
each
roote
,
and
multiply
them
squarely
,
and
so
of
1●…2
.
I
find
the
square
to
be
10404
,
and
if
I
substract
the
first
number
,
which
is
10296
,
out
of
it
there
will
remaine
108
for
the
first
want
,
and
thus
doe
by
the
other
two
,
so
your
excesses
and
wants
will
be
as
are
here
set
downe
in
particular
.
|
A
|
B
|
C
|
Excesses
|
95
|
84
|
36
|
Wants
|
108
|
111
|
149
|
Here
I
compare
the
excesses
with
the
wants
,
to
see
if
any
two
excesses
will
make
up
the
others
want
,
and
I
see
by
a
light
proofe
it
will
not
justly
serve
.
As
for
the
wants
,
I
doe
not
compare
them
to
the
excesses
,
for
every
want
is
greater
than
the
excesse
:
therefore
two
wants
farre
too
great
for
one
excesse
.
Wherefore
when
this
rule
faileth
,
take
the
two
wants
of
any
two
numbers
,
and
adde
them
first
together
,
then
abate
them
from
the
third
number
,
and
if
the
remainder
be
a
square
number
,
you
have
gotten
your
desire
.
As
for
example
,
take
the
wants
of
the
first
and
second
,
which
makes
219
,
and
that
doe
I
abate
from
the
third
number
8500
,
and
there
remaines
8281
,
which
I
see
may
be
a
square
number
,
and
91
the
roote
thereof
.
Wherefore
I
say
,
that
these
three
numbers
following
shall
be
the
rootes
of
the
square
battailes
,
as
here
I
have
set
them
.
-
The
first
battaile
10404
,
and
his
Front
102.
-
The
second
battaile
9604
,
and
his
Front
98.
-
The
third
battaile
8281
,
and
his
Front
91.
The
summe
totall
of
all
the
3
battailes
28289
men
.
The
fourth
Question
.
A
Generall
having
3.
Armies
in
three
severall
battailes
,
in
the
first
4900.
men
in
the
second
2401
,
and
in
the
third
2500.
so
that
the
greatest
is
as
much
as
both
the
other
,
except
one
man
,
and
hee
is
enforced
to
joyne
all
three
battailes
into
one
:
but
is
in
doubt
whether
he
may
have
good
and
convenient
ground
to
encampe
them
in
for●…
of
battaile
.
Wherefore
considering
that
all
three
battailes
together
are
but
double
to
the
greatest
of
the
three
alone
:
The
Serjeant
Major
desiring
a
meere
ground
for
his
Army
,
so
joyned
in
one
square
battaile
,
is
in
doubt
what
square
of
ground
will
serve
his
purpose
;
but
sure
hee
is
,
that
it
must
be
double
to
the
ground
,
that
the
greatest
Army
of
the
three
did
use
,
and
that
was
every
way
21●…
.
foot
:
wherefore
his
demand
is
how
many
foote
square
shall
the
side
of
that
ground
be
,
that
is
,
double
to
the
former
square
,
whose
roote
was
210.
foote
.
First
multiply
210.
by
it selfe
,
and
so
have
I
the
just
〈…〉
.
plat
of
ground
of
44100
foot
;
that
must
I
double
,
and
it
will
be
88200.
and
out
of
this
number
shall
I
seeke
(
as
before
is
taught
,
)
the
nyest
square
root
.
For
just
square
I
see
it
is
not
,
by
reason
that
after
the
even
cyphers
,
there
followeth
the
figure
2.
which
is
one
of
those
figures
that
cannot
begin
any
square
number
,
therefore
(
as
I
said
above
)
you
must
seeke
the
neerest
square
root
,
which
for
brevities
sake
,
and
because
I
have
sufficiently
already
treated
of
,
doe
leave
it
to
your
best
leasure
to
practise
.
Infinite
more
questions
tending
to
this
purpose
,
could
I
set
downe
,
but
that
time
will
not
permit
,
or
my
intended
little
volume
containe
,
therefore
I
will
proceed
to
shew
you
the
extraction
of
the
Cubicke
roote
,
which
will
bee
much
to
the
purpose
and
subject
I
am
now
to
treat
of
.
How
to
extract
the
Cubicke
root
.
FIrst
,
begin
at
your
right
hand
,
and
set
a
prick
over
the
first
figure
,
then
another
over
the
fourth
,
so
leave
two
figures
unprickt
,
and
pricke
the
third
still
untill
you
have
done
thus
,
79864345
As
many
pricks
as
are
over
the
number
,
just
so
many
figures
will
there
be
in
the
quotient
.
1
Then
aske
what
is
the
Cubick
root
of
the
first
pricke
,
and
set
downe
that
in
the
quotient
:
and
if
it
bee
so
that
root
doth
not
take
all
away
of
the
number
from
the
first
prick
,
substract
as
much
as
the
roote
containeth
,
and
set
the
remander
over
head
the
figures
which
stood
there
before
,
being
cancelled
.
2
Then
triple
your
quotient
,
and
that
triple
you
shal
set
under
the
next
number
towards
your
right
hand
,
before
that
pricke
which
you
did
last
end
.
3.
Next
,
multiply
that
triple
by
the
same
quotient
,
and
set
it
downe
under
the
first
triple
,
and
that
number
shall
be
your
Devisor
.
4.
Now
must
you
look
out
a
quotient
that
may
declare
how
often
the
devisor
is
in
the
number
over
it
.
5.
This
being
done
,
you
must
multiply
the
last
figure
in
the
quotient
by
your
devisor
,
and
set
it
under
your
devisor
,
with
a
line
betweene
.
6.
Then
multiply
the
last
figure
in
the
quotient
by
it selfe
,
and
then
in
the
triple
,
and
set
that
product
below
the
former
one
figure
more
towards
your
right
hand
.
7.
Lastly
,
multiply
the
last
figure
cubically
,
&
set
that
sum
also
one
figure
nearer
the
right
hand
:
then
adde
all
these
three
multiplications
together
,
and
substract
it
out
of
the
first
&
second
pricks
;
I
meane
out
of
al
those
figures
unto
the
second
prick
:
this
done
,
triple
all
your
quotient
,
and
divide
as
before
,
and
as
you
did
by
the
first
and
second
pricks
after
your
division
,
so
doe
by
the
rest
,
and
you
have
obtained
your
desire
.
Looke
upon
this
following
example
.
To
finde
the
nearest
Cubicke
root
not
cubical
.
You
must
doe
it
by
addition
of
cyphers
(
as
is
spoken
of
before
in
the
square
root
)
in
such
sort
that
they
must
be
alwayes
ternaries
,
as
3
or
6
,
or
9
or
12
,
and
then
proceed
forward
with
the
like
order
of
worke
,
as
before
.
A
question
of
doubling
a
Cube
.
IF
the
side
of
a
Cube
be
3
foote
,
how
many
foote
shall
the
side
of
that
Cube
be
,
which
must
be
double
unto
it
?
First
finde
the
quantity
of
that
Cube
that
is
propounded
,
and
then
double
that
quantity
;
lastly
,
extract
the
cubick
root
of
that
double
number
.
As
for
example
,
the
cube
is
3
,
and
therefore
the
whole
Cube
is
27
,
whose
double
is
54
,
and
the
Cubick
roote
is
3
foot
,
and
●…/100
and
1/7
of
1/100.
Cube
of
2.
Cube
of
5.
A
question
of
two
Cubes
.
A
Cube
of
brasse
of
foure
inches
square
,
doth
weigh
7.
pound
weight
,
what
shall
a
cube
of
brasse
of
nine
inches
weigh
?
The
proportion
of
their
sides
are
as
9/4
,
which
I
must
set
downe
twice
,
and
multiply
them
together
as
fractions
should
be
,
and
so
will
it
be
thus
999/444
that
maketh
●…/●…
.
Wherefore
I
multiply
the
weight
of
the
lesser
Cube
,
being
7.
by
729.
and
it
maketh
5103.
and
that
doe
I
divide
by
64.
and
so
find
I
79.
●…/●…
,
whereby
I
may
know
,
that
the
weight
of
the
greater
cube
is
79.
pound
,
and
neare
¼
of
a
pound
.
A
question
of
a
Gunne
.
A
Gunne
of
sixe
inches
diameter
,
doth
shoot
a
bullet
of
twenty
pound
weight
,
what
weight
shall
that
bullet
be
,
that
serves
for
a
Gun
of
14.
inches
in
diameter
.
All
Globes
beare
triple
that
proportion
,
that
their
diameter
does
.
So
in
this
example
,
the
proportion
of
their
diameters
〈◊〉
being
as
14.
to
6.
or
as
7.
to
3.
I
shall
triple
it
,
and
Some●…ake
more
,
as
now
is
sound
.
then
have
I
the
proportion
of
their
globes
.
Wherefore
I
set
the
3.
fractions
thus
,
●…/●…
and
they
make
●…/●…
,
that
is
12
.
●…/●…
when
you
have
divided
the
Numerator
by
the
Denominator
.
And
so
is
the
proportion
of
the
globes
as
well
in
weight
as
in
bignesse
.
Therefore
I
multiply
20.
that
is
the
weight
of
the
lesser
by
the
numerator
of
the
proportion
,
&
divide
it
by
the
denominator
.
And
so
shall
I
have
254.
●…/●…
for
the
weight
of
the
greater
bullet
.
Another
question
of
a
bullet
.
A
Bullet
of
Iron
of
seven
inches
diameter
,
weighed
27
pound
,
what
shall
be
the
diameter
of
that
bullet
,
that
shall
weigh
125.
pound
?
I
set
downe
●…/●…
and
I
see
the
cubicke
root
of
125.
is
5
,
and
the
like
root
of
27
is
3
;
which
numbers
I
set
in
the
roome
of
the
other
thus
⅓
which
declare
the
proportion
between
the
diamiters
of
the
two
bullets
.
The
diameter
of
the
lesser
is
knowne
to
be
7.
Therefore
I
multiply
that
7
by
5
,
whereof
commeth
35
:
that
divided
by
3
,
yeeldeth
in
the
quotient
11.
The
proofe
hereof
.
Multiply
both
roots
cubically
,
if
their
roots
be
in
proportion
as
their
weights
,
then
is
your
work
true
,
else
not
.
As
for
example
,
7
multiplied
cubically
,
make
343
,
and
11
⅓
multiplied
also
cubically
,
makes
428
●…/●…
.
To
multiply
a
fraction
cubically
,
as
11
⅔
first
reduce
it
,
and
make
it
35
:
that
35.
multiply
cubically
,
you
have
your
desire
.
How
to
turne
a
whole
number
into
a
fraction
of
the
like
denomination
.
SVppose
7
is
the
number
you
desire
to
turne
into
the
like
denomination
,
that
is
●…/●…
(
as
above
)
is
of
,
Multiply
7.
by
3.
the
denominater
of
the
other
fraction
,
and
it
maketh
21.
that
21
multiply
cubically
,
and
it
will
be
●…/●…
:
These
few
rules
diligently
observed
,
will
much
enable
an
Artest
to
perform
many
things
belonging
to
this
subject
,
also
much
benefit
,
experience
,
and
delight
,
shall
any
man
reape
,
that
hath
judgement
to
try
and
practise
the
secrets
thereof
.
A
question
of
whole
numbers
and
fractions
.
A
Faulcon
of
2.
inches
in
the
diameter
shoots
a
bullet
of
3.
pound
,
what
shall
the
Culvering
shot
weigh
,
whose
diameter
is
5.
inches
¼
.
To
answer
this
and
all
such
questions
that
must
be
cubically
multiplied
,
you
must
reduce
each
bullet
into
his
proper
fraction
.
As
for
example
,
2
¼
maketh
●…/●…
and
also
5
¼
maketh
●…/●…
then
I
multiply
each
numerator
cubically
,
and
I
find
the
Cube
of
the
lesser
to
bee
●…/●…
and
the
Cube
of
the
greater
to
bee
●…/●…
.
Then
I
set
downe
3
,
the
Diameter
of
the
lesser
fraction
like
as
before
thus
●…/●…
which
being
wrought
punctually
by
the
rule
of
three
in
fractions
,
you
shall
have
for
the
weight
of
the
bigger
bullet
20.
pound
,
and
almost
¼
.
How
you
Geometrically
finde
out
the
Diameter
of
any
bullet
that
weigheth
twice
so
much
as
a
knowne
bullet
.
TAke
the
true
weight
or
diameter
of
the
lesser
bullet
,
whose
weight
you
know
,
and
square
the
same
as
in
the
figure
following
:
Then
draw
a
line
that
may
divide
the
said
square
into
two
equall
parts
,
in
the
2.
opposite
angles
,
and
that
line
shall
be
the
diameter
of
a
bullet
,
twice
the
weight
of
the
other
;
then
divide
that
diametriall
line
in
2.
equall
parts
,
setting
on
foote
of
your
compasse
in
the
Center
,
and
with
the
other
foote
draw
a
circle
.
and
that
circumference
will
represent
a
bullet
twice
as
much
in
weight
as
the
lesser
.
To
prove
it
Arithmetically
.
THe
diameter
of
the
lesser
bullet
is
5.
inches
,
the
square
25.
that
sum
double
is
50.
the
square
roote
of
50.
is
7.
and
somewhat
more
,
and
so
much
is
the
diameter
of
the
greater
bullet
.
By
one
bullet
to
know
the
weight
of
another
,
the
Diameter
given
.
A
Canon
of
7.
inches
,
shootes
a
bullet
of
32.
pound
:
I
demand
what
weight
that
bullet
shall
be
of
,
that
is
9
inches
in
the
Diameter
.
Multiply
the
Diameter
of
each
Bullet
cubically
,
as
7.
times
7.
is
49.
and
seven
times
49.
is
343
,
then
9.
times
9.
is
81.
and
9.
times
81.
is
729.
then
by
the
rule
of
3.
say
,
if
343.
give
32.
pound
,
what
shall
729.
give
?
Multiply
and
divide
,
and
your
quotient
will
be
68.
●…/●…
.
How
by
the
weight
of
one
Peece
,
to
know
the
weight
of
the
other
.
IF
a
Minion
of
three
inches
Bullet
,
weigh
500.
pound
,
I
demand
how
much
a
Cannon
of
8.
inches
bullet
will
weigh
,
that
is
able
to
receive
his
proportionall
charge
to
the
Minion
.
The
Cube
of
3.
is
27.
the
Cube
of
8.
is
512
:
now
by
the
rule
of
proportion
say
,
if
27.
give
512
,
what
shall
500.
give
?
multiply
512.
by
500.
and
divide
that
product
by
27
,
and
you
will
have
in
the
quotient
9481.
●…/●…
the
true
answer
to
the
question
.
The
Cannon
therefore
that
shall
be
able
to
carry
a
proportionall
charge
to
the
Minion
,
must
have
9481
●…/●…
pounds
of
mettall
:
but
because
commonly
those
greater
sorts
of
Ordnance
are
not
so
massie
of
mettall
as
indeede
they
ought
to
be
.
The
Gunners
observe
this
for
a
generall
rule
,
that
in
all
peeces
of
above
6.
inches
in
bore
,
they
abate
●…/●…
of
their
ordinary
charge
.
To
know
how
many
shots
of
Pouder
will
be
in
a
grand
Barrell
of
Pouder
,
for
any
Peece
.
SVppose
a
Culvering
shoot
10.
pound
at
one
shoot
,
how
many
times
will
a
grand
Barrell
of
Pouder
serve
the
Barrell
holding
three
hundred
weight
?
Example
.
Divide
300.
by
10.
the
quotient
is
30.
your
desire
.
The
proofe
.
Multiply
30.
by
30.
or
30.
by
10.
gives
300.
so
may
you
know
for
all
other
sorts
of
Ordnance
whatsoever
.
By
knowing
what
pouder
a
Piece
must
have
,
to
know
how
much
a
piece
of
another
bore
will
require
;
but
,
Cave
.
IF
a
Minion
of
3.
inches
the
Bullet
,
requires
3.
pound
of
pouder
for
his
charge
,
what
pouder
will
a
Cannon
of
8.
inches
bullet
require
?
Multiply
512.
the
Cube
of
8.
by
3.
the
charge
of
the
Minion
,
and
it
maketh
1536.
which
divide
by
27.
the
Cube
of
3.
the
Diameter
of
the
said
Minions
Bullet
,
so
have
you
in
the
quotient
59
●…/●…
,
so
many
pound
of
powder
is
the
due
charge
of
your
Cannon
,
but
by
the
rule
aforesaid
you
find
the
Cannon
hath
not
his
proportionall
mettall
,
therefore
you
ought
to
abate
¼
of
the
powder
,
so
will
there
remaine
44.
pounds
,
or
neare
for
your
Cannons
charge
.
To
finde
the
superficies
of
a
Bullet
.
FIrst
,
by
a
paire
of
Callibres
finde
out
the
Diameter
,
which
suppose
it
be
7.
then
must
the
circumference
be
neare
22.
but
for
speedy
worke
,
and
to
avoyd
a
tedious
discourse
thereof
,
being
that
no
great
errour
ensueth
thereby
,
take
22.
now
multiply
that
number
by
7.
it
produceth
the
superficiall
content
of
that
Globe
,
ball
,
bowle
,
or
bullet
.
A
Table
shewing
the
weight
of
all
Iron
Bullets
,
in
Haberdepoize
weight
.
Height
of
the
Shot
,
in
inches
and
parts
.
|
Weight
of
the
Shot
in
pound
&
parts
.
|
Height
of
Shot
incircles
&
.
parts
|
Weight
of
Shot
in
pounds
and
parts
.
|
Height
.
|
Weight
.
|
Height
.
|
Weight
.
|
2
|
1●…/●…
|
5½
|
19●…/●…
|
2¼
|
1½
|
5●…/●…
|
22●…/●…
|
2½
|
2⅓
|
5¼
|
25⅙
|
2¼
|
3●…/●…
|
6
|
29½
|
3
|
4½
|
6¼
|
32⅛
|
3¼
|
5
|
6¼
|
40¼
|
3½
|
6●…/●…
|
7
|
46
|
3¼
|
7●…/●…
|
7¼
|
52●…/●…
|
4
|
9
|
7½
|
56⅝
|
4●…/●…
|
10¼
|
7¼
|
64½
|
4●…/●…
|
12⅔
|
8
|
70
|
4¼
|
14⅛
|
8¼
|
76⅔
|
5
|
16¼
|
|
|
To
find
out
how
many
square
inches
are
contained
in
a
solid
content
of
a
bullet
,
and
consequently
,
how
many
pound
weight
.
THere
is
a
bullet
whose
diameter
is
nine
inches
,
how
many
square
inches
are
there
in
the
solid
content
?
Multiply
the
diameter
9.
cubically
,
ariseth
729.
which
multiply
againe
by
11.
maketh
8919
:
that
divide
by
21.
yeeldeth
381
inches
and
●…/●…
:
so
many
inches
are
in
a
bullet
of
9.
inches
diameter
.
Now
to
know
how
many
pound
weight
is
contained
in
that
globall
body
,
multiply
that
quotient
381
●…/●…
by
4.
and
divide
by
16.
it
will
shew
how
many
pounds
of
Iron
that
bullet
weigheth
:
for
an
inch
square
of
cast
Iron
,
weigheth
foure
ounces
ferè
.
To
finde
the
true
content
of
a
circle
.
TAke
the
one
halfe
of
his
diameter
,
and
multiply
it
in
one
halfe
of
the
circumference
,
and
it
produceth
the
Area
,
or
square
the
diameter
,
and
multiply
the
product
by
11.
and
divide
the
result
by
14.
and
it
also
sheweth
the
content
.
Arithmetically
to
finde
out
the
meane
proportion
betweene
two
numbers
.
MUltiply
both
numbers
one
in
another
,
and
then
extract
the
square
root
,
so
have
you
the
meane
proportionall
.
Suppose
the
line
given
is
12.
and
the
perpendicular
9.
now
you
must
multiply
12.
in
it selfe
,
and
it
maketh
144.
then
multiply
9.
in
it selfe
,
and
it
maketh
in
product
●…
.
then
adde
both
the
multiplications
together
,
and
it
maketh
225.
Lastly
extract
the
square
root
,
and
it
leaveth
15.
the
justlength
of
the
hypothenusall
sought
.
Geometrically
to
finde
the
meane
proportiou
betweene
two
lines
.
EXtend
one
of
the
lines
to
the
number
of
inches
he
is
in
length
,
upon
the
end
whereof
erect
a
perpendicular
to
the
just
length
of
your
other
supposed
line
:
then
that
line
which
is
the
hypothenusall
to
them
both
,
is
the
meane
proportionall
.
The
hypothenusall
and
one
side
given
,
finde
the
other
.
MUltiply
each
number
in
it selfe
:
then
substract
the
lesser
out
of
the
greater
:
the
square
roote
of
the
remainder
is
the
true
length
of
the
third
side
.
Arithmetically
to
know
how
much
of
every
sort
of
mettal
is
in
a
peece
of
Ordnance
.
FOr
every
hundred
pound
weight
of
Copper
,
to
p●…
in
ten
pound
of
Lattin
,
and
eight
pound
of
Tin
.
I
d●…mand
the
quantity
of
each
sort
of
metall
is
in
a
Culvering
of
5600.
pound
weight
?
Note
that
I
joyne
all
the
severall
mixtures
together
,
and
they
make
118.
pound
,
which
is
my
Devisor
:
then
I
multiply
the
weight
of
the
peece
by
each
mixture
severally
,
and
there
ariseth
of
100.
of
Copper
560000
:
the
which
summe
is
to
be
divided
by
the
Devisor
118.
and
the
quotient
is
4745.
and
●…/●…
parts
,
so
much
Copper
is
there
in
that
Ordnance
,
and
thus
must
you
doe
to
know
how
much
you
have
of
the
other
two
sorts
of
mettall
.
To
prove
this
,
adde
all
three
quotients
together
,
if
they
make
the
summe
before
mentioned
,
it
is
right
.
The
Lattin
doth
incorporate
,
and
causeth
the
peece
to
be
of
a
good
colour
,
and
the
Tin
doth
strengthen
and
binde
the
other
mixtures
together
.
To
finde
the
superficiall
content
of
the
hollow
concavity
of
a
peece
of
Ordnance
.
SUppose
the
diameter
be
7.
inches
,
and
the
cilinder
12.
foot
,
what
is
the
content
superficiall
?
Reduce
the
Cilinder
12.
foot
into
inches
,
maketh
144.
which
multiplied
by
22.
the
circumference
of
the
muzell
ariseth
3168.
the
superficiall
content
of
the
metall
compassing
the
hollow
cilinder
.
To
finde
the
crassitude
,
or
solid
content
of
the
Cilinder
of
any
peece
.
FIrst
multiply
one
halfe
of
the
diameter
,
in
one
halfe
the
circumference
,
or
else
square
the
diameter
,
and
multiply
that
product
by
11.
and
divide
the
result
by
14
,
the
quotient
will
shew
you
the
content
:
the
which
multiply
in
the
length
of
the
Cilinder
,
the
product
is
your
desire
.
If
you
desire
how
many
foot
in
square
measure
it
containes
,
divide
the
number
of
inches
in
the
solid
content
,
by
the
number
of
inches
in
a
foot
square
,
which
are
1728.
your
question
is
resolved
.
To
measure
any
sort
of
Timber
.
SUppose
your
timber
be
8.
inches
one
way
,
and
6.
inches
another
way
,
and
you
are
desirous
to
know
how
many
inches
in
length
will
make
a
foot
square
.
Multiply
8.
by
6.
and
it
maketh
48.
which
number
divide
1728.
(
because
there
are
so
many
inches
in
a
foote
square
)
and
you
shall
have
36.
inches
in
the
quotient
,
so
many
inches
long
will
make
a
foot
square
of
Timber
.
Thus
of
all
other
cubically
.
A
Table
how
to
weigh
a
great
deale
with
few
weights
.
You
may
weigh
any
number
of
pounds
from
-
One
to
40.
with
these
4.
weights
.
-
1
-
3
-
9
-
27
-
One
to
121.
with
these
5.
weights
.
-
1
-
3
-
9
-
27
-
81
-
One
to
364.
with
these
6.
weights
.
-
1
-
3
-
9
-
27
-
81
-
243
The
pounds
to
be
weighed
,
are
weighed
with
as
many
namelike
weights
,
to
be
done
either
double
or
threefold
:
sometimes
by
adding
one
weight
to
another
,
and
sometimes
by
taking
away
and
adding
to
the
contrary
ballance
.
To
measure
any
sort
of
board
,
glasse
,
pavement
,
&c.
FIrst
multiply
the
breadth
by
the
length
,
as
a
board
is
17.
inches
one
way
,
and
139.
inches
another
way
,
multiply
139.
by
17.
and
it
maketh
2363
,
which
divided
by
144.
leaveth
in
the
quotient
16.
foot
and
●…/●…
parts
of
a
foot
.
Note
that
in
flat
measure
there
is
but
144.
inches
in
a
foot
,
but
in
square
measure
1728.
To
measure
Land
.
MUltiply
the
breadth
by
the
length
(
if
square
or
long
square
)
and
divide
the
product
by
160.
because
there
is
160.
square
perches
in
an
acre
,
so
shall
you
come
to
the
Area
,
but
if
your
ground
be
irregular
,
you
must
cast
it
into
triangles
;
&
if
it
be
a
right
angled
triangle
,
multiply
halfe
the
perpendicular
by
the
whole
base
,
and
divide
it
by
160
:
but
if
it
be
an
obtuse
triangle
,
let
fall
a
perpendicular
from
the
obtruse
angle
to
the
base
,
and
multiply
halfe
the
length
of
that
perpendicular
by
the
whole
base
,
and
divide
by
160.
as
before
,
you
have
the
content
.
Also
if
you
have
a
peece
of
Land
to
set
out
,
as
to
know
if
it
be
12.
Perches
in
bredth
,
how
many
perches
it
should
be
in
length
,
say
by
the
back
ward
rule
of
3.
if
4.
gives
40.
what
shall
12.
give
?
multiply
,
4.
by
40.
makes
160.
which
divided
by
12.
and
it
giveth
13
,
perches
,
and
⅓
so
of
all
such
like
.
To
measure
any
irregular
substance
whatsoever
,
as
a
crowne
,
Horse-head
,
or
any
Image
,
or
concaved
peece
.
TAke
a
vessell
that
is
very
stanch
,
and
4.
square
,
and
put
water
into
it
,
&
when
the
water
is
setted
,
marke
with
your
knife
how
high
it
riseth
in
the
Vessell
,
and
then
put
in
your
irregular
forme
whatsoever
it
be
,
&
marke
with
a
knife
againe
how
high
the
water
then
beares
,
or
riseth
;
then
take
out
the
irregular
forme
againe
,
and
measure
exactly
the
space
betweene
the
markes
,
and
multiply
the
breadth
by
the
thicknesse
,
and
observe
the
length
,
and
you
have
your
desire
.
●…ow
by
knowing
the
weight
of
one
Fathome
of
Rope
,
to
know
the
weight
of
another
.
A
Cable
of
10.
inches
compasse
weighing
16.
pound
every
Fathome
,
how
much
will
a
Fathome
of
that
Rope
weigh
that
is
15.
inches
in
the
Diameter
,
and
made
of
the
same
stuffe
▪
Multiply
15.
the
greater
in
it selfe
maketh
225
,
and
that
multiplyed
by
16.
the
weight
of
a
Fathome
of
the
lesser
Rope
,
maketh
3600.
which
divided
by
100.
being
the
square
of
the
lesser
rope
,
leaveth
in
the
quotient
36.
pound
,
the
true
content
.
By
the
compasse
of
any
small
rope
,
to
find
the
Diameter
and
weight
of
one
,
foure
,
five
,
or
sixe
times
as
bigge
.
SUppose
the
small
rope
is
3.
inches
compasse
,
and
that
it
is
required
to
know
the
height
of
another
5.
times
that
compasse
,
multiply
the
number
3.
squarely
ariseth
9.
which
multiply
againe
by
5.
maketh
45.
then
extract
the
square
roote
thereof
,
and
you
shall
have
6.
½
so
much
in
Diameter
is
the
greater
,
that
done
,
you
may
as
before
finde
his
weight
and
circumference
.
How
to
know
what
empty
Caske
will
carry
any
sort
of
Ordnance
over
a
river
.
IT
is
thought
sufficient
,
5.
Tun
of
Caske
will
sw●…
a
Cannon
of
8.
or
.
9000.
weight
,
4.
Tun
a
〈◊〉
,
3.
Tun
a
Culvering
,
and
two
Tun
a
Saker
,
accounting
all
provisions
to
be
made
fast
the
reunto
,
as
plankes
&
ropes
.
How
,
by
knowing
what
powder
a
few
peeces
spend
,
being
seldome
discharged
,
to
know
how
much
many
of
the
same
will
spend
being
often
discharged
:
IF
4
Cannons
bee
twice
discharged
,
and
shoot
24●…
pound
of
powder
,
how
much
powder
will
serve
5.
Cannons
,
to
shoote
every
one
6.
shoot
,
worke
by
the
double
rule
of
3.
and
say
,
if
foure
Cannons
shoote
240.
pound
,
what
shall
5.
doe
?
and
you
shall
finde
300.
then
say
againe
,
if
2.
give
300.
what
shall
6.
give
?
multiply
and
divide
,
and
you
shall
have
in
the
quotient
9●…
.
To
know
how
much
powder
each
Cannon
spent
in
the
former
conclusion
at
a
shot
.
MUltiply
4.
the
number
of
Gunnes
first
propounded
,
by
2.
the
number
of
times
they
were
discharged
,
ariseth
8.
by
which
divide
240.
the
quotient
will
be
30
which
they
spent
at
a
time
.
The
proportions
betweene
Bullets
of
Iron
,
Stone
,
and
Lead
.
A
Bullet
of
Iron
to
the
like
bullet
of
Marble
,
is
in
proportion
as
15.
is
to
34.
A
Bullet
of
Lead
to
the
like
of
Iron
,
is
in
proportion
as
28.
to
19.
A
Bullet
of
Lead
to
the
like
of
Marble
,
is
in
proportion
as
4.
to
1.
By
knowing
the
Diameter
and
weight
of
an
Iron
Bullet
,
to
finde
the
weight
of
a
Bullet
of
Marble
.
ADmit
an
Iron
Bullet
weigh
9.
pound
,
of
4.
inches
high
,
what
shall
a
Bullet
of
Marble
weigh
of
like
Diameter
?
He
shall
have
such
proportion
as
34.
to
15
;
therefore
multiply
9
by
15.
the
proportion
of
the
Stone
bullet
beareth
,
and
there
ariseth
135.
which
divided
by
34.
the
quotient
is
3.
pound
,
and
●…/●…
parts
of
a
pound
.
How
to
know
Arithmetically
where
to
place
the
Trunnions
of
any
peece
of
Ordnance
.
MEasure
the
length
of
the
bore
of
the
peece
from
the
muzle
to
the
breech
;
divide
that
measure
by
7.
and
multiply
that
summe
that
commeth
of
the
quotient
by
●…
.
the
product
will
shew
you
how
many
inches
the
trunnions
must
stand
from
the
lowest
part
of
the
concavity
of
the
peece
.
And
farther
note
,
that
the
trunions
ought
to
be
placed
as
●…/●…
of
the
circumference
of
the
peece
may
be
seene
in
that
place
where
the
trunnions
are
set
.
How
much
rope
will
make
breechings
and
tacklings
for
any
peece
.
IT
is
a
rule
,
though
not
observed
by
the
vulgar
,
yet
by
the
most
experienced
Sea
Gunners
,
that
looke
how
many
foot
your
peece
is
in
length
,
so
many
fathome
of
rope
must
there
be
in
one
tackle
for
ordinary
or
extraordinary
peeces
,
and
their
breechings
to
be
foure
times
the
length
of
the
●…eece
,
with
some
overplus
for
fastning
at
both
ends
.
I
have
against
stormy
foule
weather
caused
divers
quoyners
to
bee
bored
twice
through
with
an
angor
,
and
nailed
down
upon
the
deck
,
the
thickest
ends
close
as
could
be
to
the
fore
trucks
,
of
purpose
to
hinder
(
what
might
be
)
the
stretching
or
straining
of
the
breechings
&
tackle
,
that
the
peece
should
not
any
way
swerve
.
But
if
your
peece
accidentally
breake
her
tacklings
and
breechings
,
you
have
no
better
way
for
the
present
to
prevent
danger
,
but
with
expedition
to
dismount
her
.
Also
I
could
wish
the
rammers
and
spunges
made
of
small
haser
,
should
(
for
lasting
and
for
better
service
also
)
be
armed
close
and
hard
with
strong
twisted
yarne
from
the
rammers
end
quite
to
the
spunge
,
which
would
much
stiffen
,
and
make
it
more
usefull
and
lasting
to
ram
both
wad
and
bullet
close
to
the
powder
,
especially
being
done
in
time
.
I
doe
advise
all
his
Majesties
Gunners
of
the
Navie
,
to
take
an
especiall
heed
,
and
diligent
care
in
the
election
and
choosing
of
the
Yeoman
of
the
powder-roome
,
by
reason
he
is
upon
all
occasions
to
be
amongst
the
amunition
:
for
by
his
negligence
or
dishonesty
,
infinite
losse
and
danger
may
accrew
;
therefore
it
is
fit
such
a
man
should
be
first
knowne
to
be
a
loyall
subject
,
and
one
that
would
performe
the
office
with
both
care
and
diligence
before
he
be
admitted
the
charge
thereof
.
The
names
of
the
principall
members
of
a
peece
of
Ordnance
.
FIrst
,
the
uppermost
part
round
about
the
peece
,
may
be
called
the
Superficies
of
her
metall
;
the
substance
or
whole
masse
of
mettall
,
the
Body
;
the
hollownesse
thereof
,
the
Concave
,
Cillinder
,
or
Soule
:
the
whole
length
,
the
Chase
:
So
much
of
her
Bore
as
containeth
her
powder
and
shot
,
is
the
Chamber
,
or
charged
Cillinder
;
the
remainder
her
vacant
Cillinder
;
the
Spindals
or
Eares
are
called
her
Trunnions
;
and
the
space
between
them
,
the
gravity
of
her
Center
;
the
pumell
at
her
coyle
,
the
Casacabell
,
or
her
Decke
:
the
little
hole
,
the
Touch-hole
;
all
the
metall
behind
the
touch-hole
,
her
breech
,
or
Coyle
,
the
greatest
Ring
at
her
touch-hole
,
her
Base
Ring
;
the
next
Ring
,
or
Circle
,
is
the
reinforst
Ring
;
the
next
to
that
,
the
Trunnion
ring
;
and
the
circle
foremost
,
her
Muzzle
Ring
.
Lastly
,
the
Ring
betweene
the
Trunons
and
Muzzle
ring
,
is
called
the
Cornish
ring
;
and
all
the
Rings
,
Circles
,
and
emenencies
at
her
Muzzle
,
are
called
the
Frieze
,
as
you
may
see
in
the
figure
just
against
this
matter
.
What
instruments
are
most
fit
for
a
Gunner
.
THe
Callabre
Compasses
,
height
board
,
inch
sight-rule
,
Gunners
scale
,
Gunners
quadrant
divided
into
90.
degrees
,
and
into
12.
poynts
,
&
their
minutes
,
with
a
Geometricall
square
to
take
mountures
,
levels
,
heights
,
breadths
,
and
distancies
:
a
paire
of
streight
pointed
Compasses
,
with
a
little
brasse
levell
,
scales
and
weights
,
Priming
Irons
,
moulds
to
make
crosse-barre
shot
for
Muskets
,
a
faire
Booke
for
your
accompts
,
and
an
Iron
with
a
Spring
and
a
Transome
to
dispart
a
Peece
of
Ordnance
;
let
the
Transome
bee
to
goe
up
and
downe
,
●…ccording
to
the
diameter
and
thicknesse
of
any
peece
;
let
the
Transome
be
long
enough
to
reach
the
Base-ring
from
the
Touch-hole
.
This
Instrument
is
very
necessary
,
though
not
commonly
knowne
.
How
to
loade
and
fire
a
Peece
of
Ordnance
like
an
Artist
.
HAving
all
things
fitted
,
and
in
readinesse
prepar'd
for
●…vice
,
first
,
marke
the
winde
,
and
be
sure
to
lay
●…ur
budge-barrell
,
and
the
rest
of
your
powder
to
wea●…r
your
Peece
,
then
place
your
Lindstocke
to
leawards
,
having
clear'd
the
Touch-hole
,
spunge
her
well
,
standing
by
the
right
side
of
the
Gunne
,
and
when
he
drawes
out
the
spunge
,
strike
two
or
three
blowes
upon
the
muzzle
,
to
beate
off
the
foulenesse
of
the
spunge
;
then
his
assistant
declining
the
Budge-barrell
aside
,
hee
shall
thrust
●…n
the
Ladle
to
fill
it
,
striking
off
the
heaped
powdes
,
and
giving
a
little
shogge
,
the
better
to
settle
the
rest
in
in
the
Ladle
;
so
being
filled
and
striked
,
stand
by
the
right
side
of
the
Peece
,
(
as
cleare
as
hee
can
from
the
muzzle
)
and
put
in
the
Ladle
to
the
bottome
of
the
concave
very
steddy
quite
home
to
the
touch-hole
,
and
when
it
is
arived
to
the
bottome
of
the
bore
,
laying
your
right
thumbe
upon
the
upper
part
of
the
Ladle-staffe
,
turn●…
the
staffe
,
untill
your
thumbe
be
quite
under
it
,
and
give
a
shake
or
two
to
free
the
powder
from
the
Ladle
,
bearing
him
up
,
that
non●…
may
come
out
againe
:
Then
put
the
powder
home
softly
with
the
〈◊〉
a●…ter
which
put
in
a
good
wadde
,
and
thrus●…●…hom
〈◊〉
powder
giving
three
or
foure
hard
str●…kes
,
which
will
gathe●…
the
scatter'd
powder
together
,
that
it
ma●…
fire
the
better
the
●…ssistant
having
a
thumbe
upon
the
Touch-hole
all
the
while
,
then
put
in
the
shot
,
which
with
a
Rammer
h●…
must
put
softly
home
,
and
afterwards
another
wadde
and
then
give
two
or
three
good
strokes
with
the
Rammer
more
,
to
settle
all
close
together
,
that
there
may
be
no
vacuity
betweene
powder
,
first
wadde
,
bullet
,
or
las●…
wadde
:
This
done
,
place
your
Budge-barrell
againe
to
wind-wards
,
and
be
sure
to
weather
your
Peece
in
the
fiering
,
to
prevent
all
danger
.
Lastly
,
have
speciall
care
in
directing
her
to
the
marke
,
and
in
priming
her
,
let
the
powder
come
from
the
Touch-hole
to
the
base
ring
,
so
may
you
fire
there
safely
,
without
danger
of
the
fire
of
the
Touch-hole
to
force
your
Lintstocke
out
of
your
hand
,
provided
you
draw
backe
your
hand
in
the
fiering
,
your
leg
standing
forwards
,
and
so
doing
,
the
Peece
will
be
loaden
,
and
fier'd
Gunner
like
.
Some
use
to
prime
before
the
Touch-hole
forwards
two
or
three
inches
,
and
fire
there
;
for
the
bigger
the
Touch-hole
is
,
the
more
care
must
bee
taken
in
priming
,
and
especially
in
fiering
.
What
powder
is
allowed
for
proofe
,
and
what
for
action
of
each
Peece
.
FIrst
,
I
will
begin
with
the
biggest
Peeces
,
as
with
all
sorts
of
Cannons
,
for
proofe
⅘
and
for
service
½
,
o●…
the
weight
of
her
Iron
shot
.
For
the
Culverings
,
the
whole
weight
of
their
shot
for
proofe
,
and
foraction
,
●…/●…
and
for
the
Saker
and
Faulcon
●…/●…
,
and
for
lesser
Peeces
,
the
whole
weight
in
action
,
untill
they
grow
hot
;
for
then
must
abatement
bee
made
with
discretion
:
But
in
proofe
the
lesser
Peeces
should
have
once
,
and
●…/●…
of
the
powder
that
the
Bulletweigheth
.
If
Weights
,
Scales
,
and
Ladles
be
wanting
,
how
many
Diameters
of
a
bullet
will
make
a
reasouable
charge
in
powder
for
any
peece
named
.
FOR
the
Cannons
2.
½
for
Culverings
3.
and
for
the
Saker
3.
½
for
the
lesser
peeces
,
4.
Diameters
of
the
Cillinder
.
For
3.
Diameters
makes
●…/●…
and
3.
●…/●…
makes
●…/●…
and
foure
diameters
and
a
halfe
makes
the
whole
weight
of
a
cast
Iron
shot
,
it
being
corne
powder
,
which
length
will
also
serve
for
Cartredges
for
the
like
peeces
.
How
Moulds
,
Formes
,
and
Cartredges
are
to
be
made
for
any
sort
of
Ordnance
.
CArtredges
are
made
of
Canvas
,
or
paper
Royall
;
which
prepared
,
take
the
height
of
the
bore
of
the
peece
,
without
the
vent
of
the
shot
,
and
cut
the
cloth
or
paper
of
the
bredth
of
three
such
heights
,
and
for
the
Cannon
in
length
three
diameters
,
for
the
Culvering
foure
diameters
,
for
the
Saker
,
Faulcon
,
&c.
½
of
the
height
of
their
proper
bores
,
and
leaving
in
the
middest
,
at
the
top
or
bottom
,
one
other
such
height
,
to
make
a
bottome
for
the
Cartredge
,
cutting
each
side
somewhat
larger
for
the
sowing
and
glewing
them
together
,
having
a
due
respect
for
the
augmenting
or
diminishing
of
your
powder
,
according
to
the
goodnesse
or
badnesse
of
the
powder
,
and
to
the
extraordinary
over-heating
of
your
peece
.
Having
resolved
for
what
sort
of
Ordnance
your
Cartredges
are
to
serve
,
you
are
accordingly
to
have
a
former
of
wood
,
turned
to
the
height
of
the
shot
,
and
a
convenient
length
longer
than
the
Cartredge
is
to
bee
:
and
before
you
paste
your
paper
on
the
former
,
first
tallow
him
,
so
will
the
paper
slip
off
without
staying
or
tearing
.
If
you
deale
with
taper-bored
Gunnes
,
your
formers
must
be
made
accordingly
tapred
.
If
you
make
your
Cartredges
of
Canvas
,
halfe
a
diameter
more
is
allowed
for
the
seames
;
but
if
of
paper
½
or
●…/●…
of
an
inch
over-plus
for
the
pasting
,
will
serve
,
being
lapt
once
about
the
former
,
having
a
bottome
first
fitted
upon
the
end
of
the
former
,
which
must
bee
hard
and
close
pasted
to
the
lower
sides
of
the
Cartredge
;
and
then
the
bottome
pasted
also
down
hard
round
about
:
then
dry
them
well
before
you
fill
them
,
and
marke
every
one
with
inke
or
blacke
lead
,
how
high
they
ought
to
be
filled
,
and
let
some
want
of
their
weight
against
times
they
are
over-hot
,
otherwise
great
danger
may
ensue
.
To
make
Ladles
,
Rammers
,
and
Spunges
of
all
sorts
of
Ordnance
.
IT
is
fit
every
Gunner
should
know
how
to
trace
,
cut
out
,
and
also
make
up
and
finish
all
manner
of
Ladles
,
Spunges
and
Rammers
,
and
to
direct
others
how
they
should
and
ought
to
be
severally
fortified
,
made
and
distinguished
,
as
followeth
.
For
double
fortified
Cannons
to
charge
them
with
two
Ladle
fulls
,
they
are
to
be
two
diameters
and
a
halfe
of
their
shot
in
length
from
the
head
of
the
Ladle
staffe
,
which
shall
be
one
diameter
more
of
plate
,
which
must
goe
about
the
said
head
.
The
brasse
plate
must
bee
in
bredth
two
diameters
unto
the
said
head
,
where
each
side
must
have
halfe
a
diameter
more
to
inclose
the
head
of
the
Ladle
staffe
within
the
plate
.
The
Button
or
head
of
the
Ladle
staffe
must
bee
one
diameter
,
and
of
such
height
or
thicknesse
,
that
it
together
with
the
brasse
plate
,
may
be
equall
to
the
height
of
the
shot
(
due
vent
abated
.
)
For
Spunges
their
bottomes
or
heads
are
to
be
made
of
soft
fast
wood
,
as
Aspe
,
Birch
,
Willow
,
or
such
like
,
and
to
be
one
diameter
,
and
●…/●…
in
l●…ngth
,
and
not
above
●…/●…
of
the
shots
height
.
The
rest
being
covered
with
raw
sheeps
skinnes
wooll
,
and
nailed
on
with
copper
nailes
,
so
that
together
they
may
fill
the
concave
of
the
peece
.
The
Button
or
head
of
the
Rammer
must
be
turned
of
hard
wood
,
in
length
one
diameter
,
and
⅓
of
such
height
&
thicknesse
,
that
it
may
fitly
enter
into
the
peece
,
the
shots
vent
allowed
:
it
were
the
better
for
fashion
and
strength
,
if
that
⅓
next
the
staffe
were
handsomely
turned
with
abatement
,
and
a
Ferrill
or
circle
of
brasse
fitted
thereon
to
save
the
head
from
cleaving
,
when
as
with
force
wee
shall
ram
the
shot
home
.
All
these
heads
and
buttons
must
be
pierced
●…/●…
with
a
hole
for
the
staffe
,
an
inch
or
more
,
whereinto
the
staffe
must
be
fastened
,
let
the
staffe
be
one
foot
longer
then
the
concave
of
the
Gunne
.
For
the
ordinary
Cannons
the
Ladles
must
bee
of
the
same
breadth
,
but
must
not
surpasse
2.
diameters
of
the
shot
in
length
.
And
for
the
lessened
Cannons
,
two
diameters
onely
to
loade
at
twice
,
all
according
to
the
fashion
and
breadth
as
before
.
The
Ladles
for
Culverings
and
Demi-culverings
,
have
foure
Diameters
of
their
proper
shot
in
length
,
and
two
in
breadth
.
The
Sakers
,
Faulcons
,
and
Faulconets
,
which
may
at
one
Ladle
full
be
loaden
,
may
have
their
Diameters
of
seven
diameters
and
a
halfe
of
their
shot
in
length
,
besides
that
coverture
of
the
head
of
the
staffe
,
and
of
breadth
two
;
as
all
the
rest
have
.
For
Periors
,
which
usually
have
Chambers
with
Orloes
½
and
⅓
lesse
in
bore
then
their
Chase
containeth
,
to
them
three
times
the
diameters
of
their
Chambers
may
be
allowed
for
the
length
of
their
Ladles
.
How
to
make
a
Ladle
for
a
chambred
bored
peece
.
YOur
Compasses
opened
to
the
just
diameter
of
your
chamber
within
⅛
part
of
an
inch
thereof
,
divide
that
measure
just
in
two
equall
parts
,
then
set
your
compasses
to
one
of
them
,
and
with
the
one
foote
fixed
on
a
paper
or
smooth
boord
,
draw
with
the
other
foote
a
circle
,
the
diameter
whereof
will
be
a
just
quarter
of
an
inch
shorter
than
the
diameter
of
the
Chamber
bore
,
by
the
Circumference
whereof
you
may
find
out
the
bredth
of
the
plate
of
a
Ladle
that
is
fit
for
such
a
Chamber
bored
Cannon
,
by
the
rule
afore
set
downe
how
to
finde
the
true
breadth
of
the
plate
of
any
Ladle
for
any
other
peece
in
taking
the
three
fifts
parts
of
the
circumference
thereof
,
the
length
ought
to
be
twice
the
diameter
,
and
●…/●…
parts
to
hold
at
two
times
the
just
quantity
of
corne
pouder
.
Example
.
The
diameter
of
the
circle
drawne
for
any
Cannon
whose
chamber
bore
is
7.
inches
,
containeth
6.
●…/●…
the
Circumference
whereof
is
neere
21.
inches
●…/●…
and
⅕
parts
thereof
is
12.
●…/●…
and
so
much
ought
that
Ladle
to
be
in
breadth
,
and
in
length
18.
in
the
●…/●…
parts
.
By
this
rule
you
may
make
a
Ladle
for
any
tapred
peece
.
Take
this
for
a
generall
observation
,
that
a
Ladle
9.
bales
in
length
,
and
2.
bales
in
breadth
,
will
neare
containe
the
just
weight
in
powder
that
the
Iron
shot
for
any
peece
weigheth
.
How
to
finde
the
height
of
the
Chamber
,
and
how
to
find
the
the
thicknesse
of
Metall
round
about
the
Chamber
of
any
tapred
peece
.
TAke
a
streight
peece
of
wyre
,
and
bow
the
end
thereof
in
the
bottome
so
as
it
may
goe
through
the
touch-hole
,
then
put
it
to
the
bottome
of
the
bore
in
at
the
touch-hole
,
and
with
any
thing
marke
the
wyre
upon
the
upper
part
of
the
Metall
,
then
measure
by
your
rule
how
long
the
wyre
is
from
the
stroke
to
the
end
;
Then
put
in
the
same
wyre
againe
,
and
put
it
up
so
as
the
bowed
end
may
rest
within
the
Cillinder
,
and
make
another
marke
on
the
said
wyre
hard
by
the
upper
part
of
the
metall
,
round
about
the
Chamber
,
the
which
abated
from
the
first
stroke
to
the
lowest
end
,
the
remainder
is
the
Diameter
of
the
Chamber
bore
in
that
place
.
This
needeth
no
example
.
To
know
whether
the
carriage
of
your
peece
be
truely
bord
,
and
how
to
make
them
for
any
peece
.
MEasure
the
length
of
the
Cillinder
of
your
Gunne
,
the
plankes
of
your
carriage
ought
to
be
once
and
a
halfe
that
length
.
Also
measure
the
Diameter
,
and
the
plankes
at
the
fore
end
should
bee
in
depth
4.
times
the
Diameter
,
and
at
the
end
next
the
ground
two
times
½
the
Diameter
,
and
in
thicknes
once
the
Diameter
.
How
you
may
finde
whether
a
peece
have
any
flawes
,
cracks
,
or
honey-combes
.
AFter
you
have
clear'd
her
,
put
a
usuall
searcher
made
of
two
or
three
springs
,
with
points
,
like
great
pin-heads
bending
outwards
,
which
being
bended
together
with
your
hand
,
untill
it
will
enter
into
the
Peece
,
and
put
up
to
the
touch-hole
,
or
bottom
of
the
Cilinder
,
turning
it
round
in
putting
it
in
,
and
pulling
it
out
of
the
Chace
,
and
if
any
honey-combes
be
therein
,
it
will
sticke
with
the
poynts
therein
.
Also
in
a
Sun-shine
day
with
a
Looking-glasse
,
the
Sun-beames
may
be
reflected
into
the
Chace
,
as
that
the
flawes
,
cracks
,
and
honey-combes
may
be
discerned
.
But
if
the
Sun
shine
not
,
a
waxe-candle
put
upon
a
halfe
pike
will
also
shew
them
:
If
no
flawes
be
found
,
proceede
to
her
proofe
,
but
if
any
be
therein
,
the
Peece
is
indeed
very
dangerous
both
in
fiering
,
and
loading
;
and
if
it
can
possibly
be
prevented
,
not
to
be
used
at
all
,
but
with
great
care
and
good
respect
first
had
in
her
proofe
.
The
allowance
for
vent
,
comparing
the
height
of
the
shot
with
the
height
of
the
bore
of
the
Peece
assigned
.
MAny
Gunners
hold
,
that
a
quarter
of
an
inch
space
betweene
the
Bore
and
the
Bullet
is
vent
sutable
for
all
Ordnance
,
and
not
too
much
,
nor
too
little
.
But
others
maintaine
●…/●…
part
of
the
Diameter
of
the
Peeces
Cilinder
is
more
proper
and
correspondent
for
al
sorts
of
Peeces
whatsoever
;
take
which
you
please
.
To
dispart
a
Peece
of
Ordnance
.
TO
dispart
a
Peece
,
is
to
bring
the
mettall
at
muzle
equall
with
the
mettall
at
the
base
ring
:
In
true
founded
Ordnance
,
the
halfe
of
the
Diamiter
of
the
Cilinder
is
her
dispart
:
also
you
may
put
a
priming
Iron
(
such
a
one
as
I
spake
of
before
,
with
a
Spring
and
Transome
)
into
the
Touch-hole
,
to
the
bottome
of
the
concave
there
,
and
putting
downe
the
Transome
hard
upon
the
superficies
of
the
mettall
of
the
base
ring
,
which
resting
there
,
apply
the
instrument
to
the
muzle
,
and
place
him
upon
the
lower
most
edge
of
the
concave
perpendicular
,
and
raise
your
dispart
from
the
Muzle-ring
as
high
as
the
Transome
,
so
you
have
laid
the
mettall
at
the
Muzle
in
a
Horizontall
line
with
the
mettall
at
the
base
ring
.
But
for
nicenesse
I
would
make
another
dispart
upon
the
Trunnions
,
which
may
be
thus
done
,
Lay
a
peece
of
soft
waxe
upon
the
Trunnions
,
and
let
one
raise
it
in
height
,
I
meane
,
make
it
longer
or
shorter
,
untill
that
the
mettall
at
the
top
of
the
base
ring
,
the
waxe
betweene
the
Trunnions
and
the
dispart
on
the
muzle
ring
,
be
all
three
of
a
precise
height
,
and
in
an
equall
straight
line
direct
.
If
I
were
to
fire
a
Peece
of
Ordnance
at
a
marke
,
to
gaine
credit
indeed
thereby
,
I
would
have
a
twine
silke
thread
that
should
touch
both
the
tops
of
the
Disparts
,
&
come
to
the
upper
part
of
the
base
ring
upon
the
midst
thereof
,
by
which
thread
I
would
direct
my
Ordnance
to
the
marke
many
degrees
better
.
I
could
wish
that
the
Disparts
should
be
skrew'd
into
the
muzle
ring
of
the
Peeces
,
that
it
might
bee
used
to
that
purpose
,
and
had
alwayes
in
readinesse
belonging
to
the
same
Gunne
,
and
upon
any
occasion
taken
out
at
pleasure
.
Also
I
could
advise
the
Sea-gunners
upon
some
occasions
to
use
disparts
betweene
the
Trunnions
of
their
Peeces
,
made
of
a
just
heights
of
purpose
to
serve
there
:
〈…〉
let
them
be
tyed
about
the
Peece
with
a
twine
,
because
else
at
every
shot
they
will
bee
to
seeke
,
when
upon
the
suddaine
they
should
use
them
;
which
I
can
by
good
experience
speake
,
they
will
much
availe
,
and
stand
you
in
great
stead
.
I
could
expresse
divers
other
wayes
to
dispart
a
Peece
,
but
these
being
sufficient
,
I
hold
it
needlesse
to
spend
time
,
and
fill
this
little
treatise
with
unnecessary
Instructions
.
The
Geometricall
finding
the
Diameter
for
the
weight
of
any
shot
assigned
.
SUppose
your
shot
bee
one
,
two
,
or
three
pound
weight
of
metall
or
stone
assigned
,
if
of
one
pound
divide
the
Diameter
into
4.
parts
,
and
five
such
parts
will
make
the
Diameter
of
a
shot
of
the
said
metall
or
stone
,
that
shall
weigh
just
two
pound
.
Divide
the
Diameter
of
a
shot
weigheth
just
2.
pound
in
7.
equall
parts
,
and
8.
such
parts
will
make
a
Diameter
of
a
shot
of
3.
pound
.
And
divide
the
Diameter
of
a
shot
of
3.
pound
into
10.
equall
parts
,
and
11.
such
parts
maketh
a
shot
of
4.
pound
Divide
the
Diameter
of
a
shot
of
4.
pound
into
13.
parts
,
14.
such
parts
will
make
a
Diameter
for
a
shot
of
5.
pound
.
And
so
dividing
each
next
Diameter
into
3.
parts
,
equall
more
than
the
next
lesser
was
divided
into
;
and
it
will
with
one
part
added
from
a
Diameter
of
a
shot
,
that
will
weigh
just
one
pound
more
:
So
you
may
proceed
infinitely
increasing
,
or
decreasing
by
taking
one
part
lesse
then
it
is
appointed
to
be
divided
into
.
To
tertiate
a
Peece
of
Ordnance
.
THere
are
three
differences
in
fortification
of
each
sort
of
Ordnance
,
be
they
of
Cannons
,
or
Culverings
;
for
they
are
either
ordinary
fortified
,
lessened
,
or
double
fortified
,
as
legitimate
Peeces
,
bastard
Peeces
,
or
extraordinary
Peeces
.
For
the
Cannon
double
fortified
,
hath
fully
one
diameter
in
thicknesse
of
metall
at
her
Touch
hole
,
and
●…/●…
at
her
Trunnions
,
and
●…/●…
at
her
muzzle
.
And
the
lessened
Cannons
have
at
their
Touch-hole
but
●…/●…
and
at
the
Trunnions
●…/●…
and
at
the
muzzle
●…/●…
whereas
the
ordinary
fortified
Cannons
have
⅞
at
the
Touch-hole
,
and
⅝
at
the
Trunnions
,
and
⅛
at
the
muzle
.
Now
all
the
double
fortified
Culverings
,
and
all
lesser
Peeces
of
that
kind
,
have
one
Diameter
,
and
⅛
at
the
Touch-hole
,
and
●…/●…
at
the
Trunnions
,
and
●…/●…
at
the
muzle
.
And
the
ordinary
forified
Culverings
are
fortified
every
way
like
the
double
fortified
Cannons
.
And
the
lessened
Culverings
like
the
ordinary
fortified
Cannons
in
all
points
.
The
difference
betweene
the
common
legitimate
Peeces
,
and
the
bastard
peeces
,
and
extraordinary
.
COmmon
or
legitimate
Peeces
are
such
Ordnance
,
as
have
a
due
length
of
their
Chases
,
proportioned
according
to
this
height
of
their
proper
bores
.
Bastard
peeces
are
such
as
have
shorter
Chases
than
the
proportion
of
their
bore
doth
require
.
And
extraordinary
peeces
are
such
Ordnance
,
as
have
longer
chases
than
the
proportion
of
the
bore
alloweth
:
And
these
are
called
Bastard
Culverings
,
and
extraordinary
Culverings
,
so
likewise
of
Saker
and
Faulcon
.
To
coole
a
Peece
of
Ordnance
,
when
she
is
growne
hot
with
overmuch
fiering
.
IF
you
cannot
have
time
to
rest
her
,
because
the
Service
is
hot
,
as
it
was
with
us
at
Bargen
,
in
that
case
she
must
be
coold
with
spunges
wet
in
lee
and
water
,
or
water
and
vinegar
,
or
with
the
coolest
fresh
or
salt
water
,
bathing
and
washing
her
both
within
and
without
,
untill
shee
come
unto
her
due
temper
;
but
if
time
would
permit
,
rest
her
one
or
two
houres
in
twelve
,
and
coole
her
as
before
every
eighth
or
tenth
shot
.
Reasons
that
cause
a
Shot
,
though
well
directed
,
to
erre
in
her
charge
,
and
to
be
either
wide
,
short
.
or
over
at
the
marke
.
MAny
accidents
may
make
a
shot
to
deviate
from
the
expected
course
,
though
well
directed
.
As
if
the
soule
of
the
peece
lyeth
awry
in
the
body
of
her
metall
And
if
the
Trunnions
also
be
not
duely
placed
directly
in
a
Diagonal
line
with
the
Axis
of
the
peece
.
If
the
platforme
be
unequall
.
Also
if
the
Gunner
shoot
without
a
just
dispart
.
If
one
wheele
bee
higher
than
another
.
If
the
naves
be
one
longer
and
wider
than
the
other
.
When
one
wheele
meetes
with
a
stone
to
stay
it
:
or
that
one
wheele
reverseth
in
soft
ground
,
and
the
other
in
hard
.
The
Carriage
or
Trunnion
eares
are
higher
one
than
another
.
If
the
cariage
be
too
wide
,
so
that
the
peece
lyeth
not
fast
therein
,
but
starteth
in
her
discharge
.
If
the
shot
be
not
equally
round
,
the
winde
,
if
vehement
,
may
somewhat
hurt
.
The
slight
ramming
,
leaving
space
betweene
powder
,
wad
,
and
bullet
,
may
alter
her
course
.
These
and
many
more
,
are
true
and
infallible
causes
of
the
failing
of
a
shot
at
an
assigned
marke
,
yet
the
peece
well
directed
.
The
difference
betweene
shooting
by
the
met
all
of
the
peece
,
and
the
dispart
.
THeir
differences
are
uncertaine
,
by
reason
there
are
seldom
any
constant
proportion
held
in
the
founding
especially
concerning
the
eminencies
of
their
muzle
and
base-ring
:
for
laying
the
peece
directly
to
the
mark
,
with
her
due
dispart
,
and
then
take
of
that
dispart
,
and
lay
her
by
the
metall
,
observe
the
difference
with
a
squadrant
,
and
you
shall
sometimes
finde
that
the
peece
will
bee
elevated
more
by
the
mettall
than
by
the
dispart
,
foure
,
five
,
yea
sometimes
sixe
or
seven
degrees
.
And
so
consequently
will
the
randons
of
the
metall
bee
more
than
the
randons
of
the
dispart
,
(
which
by
the
table
of
Ranges
)
may
for
every
elevation
be
made
certainly
knowne
;
but
this
take
for
an
example
,
on
the
levell
the
metall
rangeth
neare
double
the
distance
of
the
dispart
in
most
peeces
.
To
know
at
how
many
degrees
of
mounture
a
Peece
will
convey
her
bullet
far
thest
,
called
her
best
Randon
.
THe
approved
best
Artists
of
late
times
,
maintaine
with
good
reason
,
that
the
utmost
degree
of
Randon
is
at
or
about
24.
degrees
of
the
quadrant
,
neverthelesse
most
ancient
authors
hold
45.
being
the
middle
or
meane
between
the
levell
and
the
perpendicular
;
namely
,
the
halfe
of
90.
degrees
.
But
because
the
peece
rangeth
a
bullet
but
one
tenth
part
of
the
utmost
randon
as
it
doth
also
at
84.
degrees
of
the
elevation
,
therefore
it
stands
with
more
reason
,
and
experience
also
hath
found
,
that
the
utmost
randon
of
any
peece
should
be
(
being
duely
charged
&
discharged
)
at
42.
degrees
,
the
halfe
of
84
the
elevation
.
A
necessary
Table
of
Periors
and
Drakes
proportioned
.
Names
of
Peeces
.
|
Height
of
the
bore
in
inches
▪
|
Length
in
Diameter
.
|
Weight
in
●…et
.
pound
|
Weight
of
Powder
.
|
Length
of
the
Ladle
.
|
Canon
Pe●…ior
.
|
9.
10.
12.
|
8
|
3500
|
3
,
3⅓
4.
|
3
|
D.
Canon
Drake
|
6½
|
16
|
3000
|
9
pound
.
|
4½
|
Culvering
Drake
|
5½
|
16
|
2000
|
5
|
4½
|
D.
Cul.
Drake
.
|
4
●…/●…
|
16
|
1500
|
3½
|
4½
|
Sa●…er
Drake
.
|
3½
|
18
|
1200
|
2
|
4
●…/●…
|
A
Table
truely
proportioned
for
our
English
Ordnance
.
Bore
.
|
Height
●…f
Shot
.
|
Weight
of
Shot
.
|
Ladles
length
.
|
Ladles
breadth
.
|
Length
of
the
peece
.
|
Weight
of
the
peece
.
|
Weight
of
Corne
P●…wder
.
|
Inches
.
|
Inches
.
|
Lib.
|
Inches
.
|
Inches
.
|
Foote
.
|
Lib.
|
Li●…
.
|
8
|
7¼
|
63
|
24
|
14
|
12
|
8000
|
27
〈…〉
|
7
|
6¼
|
39
|
22
|
12¼
|
11
|
7000
|
18
〈…〉
|
6½
|
6¼
|
30
|
21
|
11½
|
10
|
6000
|
14
|
5¼
|
4¼
|
15
|
19
|
9
|
12
|
4300
|
10
〈…〉
|
5
|
5
|
15½
|
20
|
10
|
4400
|
12
|
5½
|
5¼
|
20
|
21
|
11
|
4600
|
15
|
4¼
|
4
|
9
|
17
|
7
|
11
|
2200
|
6
〈…〉
|
4½
|
4¼
|
10½
|
18
|
8
|
2400
|
7¼
|
4¼
|
4½
|
12½
|
19
|
9
|
2500
|
8
|
3¼
|
3
|
5
|
30
|
9
|
9
|
2400
|
4
〈◊〉
▪
|
3¼
|
3½
|
5¼
|
31
|
9
|
1500
|
4¼
|
4
|
3¼
|
5½
|
32
|
10
|
1600
|
5½
|
3
|
2½
|
3
|
25
|
5½
|
7½
|
1200
|
3
〈…〉
|
2¼
|
2⅓
|
2
|
22
|
5
|
7
|
700
|
2
〈…〉
|
2¼
|
2
|
1●…/●…
|
18
|
3●…/●…
|
6
|
500
|
1
〈…〉
|
1½
|
1¼
|
¾
|
11½
|
2●…/●…
|
4
|
300
|
⅓
〈…〉
|
¼
|
1
|
●…/●…
|
9
|
2
|
3●…/●…
|
202
|
½
〈…〉
|
A
Table
of
Randous
for
the
sixe
first
poyntr
of
the
Quadrant
.
|
1
|
2
|
3
|
4
|
5
|
6
|
●…once
|
375
|
637
|
795
|
885
|
892
|
900
|
●…aulcon
.
|
550
|
935
|
1166
|
1254
|
1309
|
1320
|
Minion
.
|
450
|
765
|
954
|
1026
|
1071
|
1080
|
●…ake
|
625
|
1062
|
1325
|
1425
|
1487
|
1500
|
D.
Culvering
.
|
725
|
1232
|
1537
|
1653
|
1725
|
1740
|
Culvering
.
|
750
|
1275
|
159●…
|
1710
|
1785
|
1800
|
De●…-canon
.
|
625
|
1062
|
1●…25
|
1425
|
1487
|
1500
|
Canon
of
7.
|
675
|
1147.
|
1431
|
1489
|
1606
|
1020
|
Double
Cau●…n
.
|
750
|
1275
|
1660
|
1710
|
1785
|
1800
|
The
use
of
this
Table
.
FIrst
,
by
this
Table
,
having
resolved
upon
the
poynt
of
mounture
,
looke
against
the
name
of
the
Peece
,
and
right
under
that
poynt
in
the
common
angle
,
you
shall
find
the
number
of
paces
of
her
Randon
sought
.
A
Table
of
the
proportion
of
right
ranges
and
first
what
a
Range
is
.
A
Right
Range
in
any
peece
is
indeed
so
farre
as
the
Bullet
is
carried
violently
in
a
straight
line
,
which
by
some
Gunners
of
these
our
moderne
times
,
is
by
them
properly
called
the
Right
Range
.
This
kind
of
shooting
is
so
farre
as
a
marke
is
within
the
straight
line
of
a
Peece
,
which
for
some
elevations
and
mountures
is
much
more
than
for
others
:
for
that
the
more
a
peece
is
mounted
,
the
farther
she
conveyeth
her
shot
in
a
right
Range
.
A
Table
of
right
Ranges
.
0
|
192
|
1
|
209
|
2
|
226
|
3
|
243
|
4
|
260
|
5
|
277
|
6
|
294
|
7
|
311
|
8
|
328
|
9
|
345
|
10
|
362
|
20
|
532
|
30
|
702
|
40
|
872
|
50
|
1042
|
60
|
1212
|
70
|
1382
|
80
|
1552
|
90
|
1722
|
The
use
of
this
Table
,
with
a
plaine
Example
.
HAving
found
by
experience
,
that
at
60
degrees
of
mounture
the
peece
assigned
shot
200
paces
in
a
right
line
,
and
would
know
how
far
the
same
Peece
would
shoote
in
a
straight
line
being
mounted
to
10
degrees
,
say
by
the
Table
,
if
285
,
the
number
against
6
degrees
,
giveth
200
paces
,
what
will
354
,
the
number
therein
against
10
degrees
give
?
Multiply
354
by
200
,
the
product
will
be
70800
,
which
divided
by
285
,
produceth
in
the
quotient
283
paces
,
and
●…/●…
parts
.
Of
〈…〉
at
a
Marke
beyond
the
right
line
of
the
〈◊〉
〈◊〉
,
or
right
range
of
the
sh●…t
,
and
of
the
dead
〈◊〉
of
any
Peece
at
every
degree
.
THe
dead
range
consisteth
of
the
addition
of
the
right
and
crooked
ranges
together
into
one
,
and
that
called
the
dead
Range
,
which
is
the
whole
distance
from
the
plat-forme
unto
the
first
graze
of
the
Bullets
,
whereby
for
the
first
sixe
points
of
the
Gunners
quadrant
,
you
having
the
dead
range
of
one
shot
made
out
of
any
Peece
;
whether
it
be
of
a
Culvering
,
(
which
is
betweene
30.
and
4●…
.
Diameters
of
her
bore
in
length
)
by
the
range
of
numbers
set
against
the
letter
S.
in
the
Table
here
underneath
;
or
whether
it
be
of
the
quality
of
a
Cannon
,
(
that
is
betweene
18.
and
24.
Diameters
of
her
bore
in
length
by
the
ranke
of
Numbers
set
against
the
letter
C.
in
the
said
Table
)
you
may
,
having
one
shot
,
by
that
shot
,
and
by
the
rule
of
proportion
,
know
the
dead
range
of
any
other
point
of
mounting
sought
.
Example
.
SUppose
a
Culvering
that
shooteth
levell
260.
paces
,
I
would
know
how
farre
she
would
convey
her
shot
upon
an
Horizontall
plaine
,
she
being
mounted
to
the
third
point
of
the
quadrant
.
Say
by
the
rule
3.
if
192.
(
the
number
against
S.
)
for
the
levell
range
in
the
Table
giveth
2032
,
the
number
under
the
third
point
,
what
will
260.
give
?
Multiply
2032
by
60
,
and
divide
that
product
by
192
,
and
you
shall
have
in
your
quotient
2751
●…/●…
for
the
number
of
paces
shee
will
convey
her
shot
,
being
so
mounted
.
The
Table
of
dead
Ranges
.
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
Points
|
S
|
192
|
985
|
1623
|
2032
|
2185
|
2281
|
2300
|
Paces
.
|
C
|
201
|
958
|
1600
|
1983
|
2135
|
2232
|
2250
|
Paces
.
|
To
know
how
the
range
of
his
Peece
increaseth
,
or
decreaseth
from
degree
to
degree
.
FIrst
,
you
must
finde
by
the
table
of
right
Ranges
how
much
your
levell
right
Range
of
your
Peece
is
,
which
number
of
paces
divide
by
25
,
and
multiply
the
quotient
by
11
,
and
the
product
will
be
the
first
and
greatest
digression
,
which
is
betweene
the
first
and
second
degrees
,
which
divided
by
40
,
the
degrees
contained
betweene
the
first
degree
,
and
42
the
utmost
Randon
,
and
the
quotient
sheweth
the
number
of
paces
that
the
shot
shall
loose
at
every
digression
,
from
degree
to
degree
,
to
the
last
Randon
,
and
contrariwise
for
the
increasing
digression
from
42
degrees
,
the
utmost
Randon
downe
to
the
first
degree
.
How
to
finde
the
right
Line
,
or
right
Range
of
any
Bullet
for
every
elevation
by
any
one
right
or
dead
Range
given
for
the
Peece
assigned
.
AS
for
example
,
you
are
to
seeke
the
right
Range
of
30
degrees
for
that
peece
,
whose
dead
Range
for
30
degrees
is
knowne
to
be
2200
paces
,
by
it
multiply
the
tabular
number
of
right
Ranges
for
30
degrees
,
which
are
695
,
and
divide
the
product
by
2150
,
the
tabular
number
for
30
degrees
in
the
Table
of
dead
Ranges
,
and
the
quotient
will
bee
711
paces
for
the
right
Range
of
that
peece
mounted
and
discharged
at
30
degrees
elevation
.
Another
Example
.
SUppose
the
levell
right
Range
is
given
,
and
the
right
Range
of
30
degrees
sought
,
say
,
if
192
the
first
number
in
the
Table
of
right
Ranges
,
give
695
,
the
tabular
number
therof
for
30
degrees
,
what
shal
197
paces
give
,
the
levell
right
Range
given
be
,
multiply
and
divide
,
and
the
quotient
will
bee
713
paces
,
for
the
right
Range
sought
.
To
finde
how
much
of
the
Horizontall
line
is
contained
directly
under
the
right
range
of
any
shot
.
TO
finde
what
partlyeth
under
the
right
Range
at
30
degrees
elevation
,
the
right
Range
at
30
degrees
by
the
precedent
example
being
found
to
be
713
paces
,
and
the
right
signe
of
sixty
grades
,
the
complement
of
30
being
866
,
which
multiplyed
together
,
and
the
product
divided
by
1000
,
the
whole
signe
leaveth
in
the
quotient
621
●…/●…
for
the
number
of
paces
lying
directly
under
the
●…ight
Range
.
To
finde
how
much
of
the
Horizontall
line
lyeth
under
the
crooked
Range
of
a
shot
made
out
of
any
peece
of
Ordnance
at
any
elevation
assigned
.
THe
crooked
Range
is
so
much
of
the
course
or
way
as
the
shot
maketh
as
it
goeth
Helically
between
the
right
Range
and
the
natural
motion
,
or
before
it
maketh
the
first
graze
;
And
may
be
thus
found
by
deducting
of
the
levell
distance
contained
directly
under
the
right
line
,
or
right
Range
of
any
shot
made
(
found
by
the
precedent
Chapter
)
out
of
the
dead
Range
thereof
,
found
by
the
Chapter
before
going
.
For
the
remainder
will
be
the
paces
,
or
other
measures
lying
directly
under
the
crooked
Range
.
To
make
a
good
shot
in
a
peece
not
truly
boared
,
and
to
know
how
much
any
peece
will
shoot
amisse
,
the
metal
thicker
of
one
side
than
another
.
SVppose
a
Cannon
is
said
to
bee
two
inches
thicker
of
one
side
in
her
mettall
,
than
another
,
the
distance
to
the
mark
suppose
to
be
500
paces
.
that
is
2500
foot
,
the
which
divided
by
9
foote
,
the
just
length
of
the
Cillinder
of
the
peece
,
yeeldeth
in
the
quotient
277
foote
●…/●…
that
againe
being
multiplyed
by
½
the
superfluity
of
the
mettall
being
1
inch
,
makes
still
277
●…/●…
,
which
is
the
true
demand
sought
.
To
remedy
a
Peece
not
truely
bored
.
SEarch
the
peece
with
an
instrument
to
know
which
is
the
thicker
side
;
then
divide
the
over
plus
of
the
metall
in
two
parts
,
as
before
,
suppose
2
inches
,
setting
the
dispart
of
your
peece
on
that
part
to
wards
the
thickest
side
of
the
peeces
muzle
,
and
bringing
the
middle
part
of
the
metall
at
the
base
ring
to
that
dispart
and
the
upper
part
of
the
marke
all
in
one
line
,
fire
her
,
and
without
question
you
make
a
very
good
shot
,
care
being
taken
in
loading
.
If
the
thicker
part
of
her
metall
be
above
,
then
you
ought
to
make
your
dispart
one
inch
more
:
if
under
,
one
inch
lesse
.
To
choose
a
Peece
to
shoot
at
single
marke
,
the
course
also
to
be
observed
therein
.
BY
my
will
I
would
choose
a
peece
as
I
had
formerly
practised
in
,
and
well
examined
her
qualities
;
and
when
I
came
to
load
her
,
I
would
not
ramme
home
her
powder
any
thing
hard
,
but
very
easie
,
least
in
taking
fire
,
it
should
lye
blowing
first
,
and
cause
the
peece
to
start
from
her
position
,
but
let
her
be
duely
directed
by
a
true
disparture
,
that
the
axes
of
her
bore
may
precisely
respect
the
marke
.
And
lastly
,
endeavour
heedfully
to
prevent
all
impedimentall
accidents
which
otherwise
may
happen
,
and
give
fire
.
Having
found
the
first
Shot
faulty
to
the
right
or
left
hand
,
over
or
under
,
to
amend
the
next
time
,
and
make
an
effectuall
shot
.
IF
it
were
wide
towards
the
right
or
left
hand
,
I
would
place
my
eye
on
the
base
ring
at
the
next
time
,
a
little
more
to
the
same
side
accordingly
more
or
lesse
;
if
it
were
too
high
,
direct
the
dispart
under
the
marke
as
much
:
if
two
low
,
lay
some
small
stone
,
or
other
thing
,
on
the
highest
of
the
base
ring
,
and
by
that
bring
the
dispart
and
the
marke
into
one
with
discretion
.
How
to
plant
Ordnance
in
secret
and
double
Batteryes
,
so
they
may
not
easily
be
dismounted
.
THey
must
be
planted
upon
a
platforme
that
discendeth
behind
,
that
in
their
reverse
they
may
go
under
the
vamure
of
the
Tronier
,
the
Tronier
being
vaulted
,
they
must
by
tackles
bee
brought
up
above
the
vamure
,
and
opened
,
and
fire
given
immediately
at
the
opening
,
so
in
their
reverse
will
they
be
againe
under
the
vamure
,
and
be
free
from
dismounting
,
so
long
as
the
furnemouth
and
vamure
is
able
to
keepe
from
the
ruine
of
Counter-batteries
.
Take
this
by
the
way
for
a
note
,
that
a
Cannon
at
120
Paces
,
will
pierce
a
wall
or
rampart
,
meanely
settled
,
onely
10
or
12
foot
,
but
in
close
sandy
ground
,
20
,
or
24
foote
deep
:
And
that
a
Cannon
may
being
well
fortified
and
discreetly
managed
,
be
discharged
100
times
in
one
day
.
Note
that
a
Cannon
with
one
shot
will
ruine
more
than
a
100
hods
of
earth
can
repaire
.
Further
note
,
that
1000
shot
made
out
of
10
Cannons
will
ruine
more
than
1500
shot
can
do
out
of
made
out
of
5
Cannons
:
And
lesse
can
the
enemy
repaire
the
first
than
the
last
;
for
a
Cannon
shot
made
every
eighth
part
of
an
houre
,
at
100
paces
distant
,
will
make
as
much
ruine
as
twelve
men
can
keepe
in
repaire
.
To
make
a
shot
in
the
night
at
a
marke
shewed
you
in
the
day
,
how
to
prepare
for
it
.
I
Would
first
lay
the
Peece
precisely
to
the
marke
in
the
the
day
,
then
with
a
chalke
line
,
dipt
in
Gum-water
,
I
would
strike
a
right
line
on
the
upper
part
of
the
metall
,
from
the
breech
to
the
muzle
,
upon
which
I
would
apply
a
good
Magneticall
needle
,
or
flye
with
a
chart
exactly
divided
,
and
note
the
intersection
;
then
from
the
end
of
the
line
that
was
mark't
,
or
stricken
upon
the
mettall
,
I
let
fall
plumbe
lines
upon
the
platforme
,
and
at
the
places
where
they
touch
,
I
knocke
in
at
each
a
small
nayle
.
Lastly
,
with
a
Quadrant
I
observe
the
elevation
of
the
concave
,
or
else
with
some
staffe
take
the
perpendicular
height
of
some
marke
made
in
the
mettall
as
well
at
the
breech
,
as
at
the
muzle
above
the
said
two
nayles
:
and
so
you
may
againe
lay
the
peece
thereby
,
alwayes
to
have
the
selfe-same
position
,
and
so
shoote
as
certaine
at
the
marke
by
night
,
as
by
day
.
To
make
a
goodshot
at
an
Enemies
light
in
a
darke
Night
,
not
having
any
Candle
,
or
other
light
by
.
I
Would
light
two
peeces
of
match
,
the
one
as
much
longer
as
the
other
,
as
the
quantity
of
the
dispart
of
the
peece
,
and
set
the
longer
upon
the
upper
part
of
the
Muzle-ring
,
and
the
shorter
upon
the
base
ring
,
still
traversing
and
quoyning
the
peece
,
untill
I
have
brought
the
light
of
the
Enemies
,
and
the
lights
of
the
two
matches
all
three
into
one
line
,
and
so
give
sire
.
To
order
a
Peece
,
to
make
a
goodshot
at
a
moveable
Marke
,
as
at
a
ship
under
sayle
,
Boate
rowing
,
or
Horsman
riding
.
TAke
a
peece
that
will
reach
the
Marke
in
a
streight
line
,
then
observe
how
the
Marke
moveth
:
Next
,
note
the
winde
if
it
blowes
much
,
whether
side-wayes
,
with
,
or
against
you
,
and
accordingly
take
advantage
:
Then
with
the
dispart
considered
,
observe
some
cloud
,
or
marke
,
or
point
of
land
that
lyeth
in
the
course
of
his
motion
,
and
when
according
to
the
swiftnesse
thereof
he
is
come
so
neare
it
,
as
I
guesse
the
shot
and
hee
may
meete
at
the
Marke
,
I
give
fire
:
wherein
remember
this
secret
of
Nature
,
that
any
Peece
will
shoote
farther
from
Sea
to
Land-ward
,
than
from
Land
to
Sea-ward
.
To
shoote
at
a
Squadron
of
men
,
and
what
Peece
to
choose
.
ACcording
to
the
distance
,
I
would
choose
a
Peece
that
in
a
streight
line
can
reach
the
marke
,
be
it
with
Demi-culvering
,
Saker
,
or
Faulcon
,
and
plant
my
peece
if
I
could
paralell
to
the
Champion
plaine
,
that
the
shot
may
range
to
shoote
at
girdle-height
,
unlesse
the
ground
be
stony
;
for
then
would
I
place
my
shot
short
of
them
,
that
grazing
amongst
the
stones
,
the
stones
may
spoile
them
more
than
the
shot
of
it selfe
can
doe
by
much
;
but
in
no
case
would
I
shoote
wide
,
or
over
them
;
for
that
were
both
losse
,
and
foule
shame
for
the
Gunner
.
To
shoote
farther
than
ordinary
in
one
and
the
selfe-same
Peece
with
like
quantity
of
pouder
and
shot
.
I
Will
gently
put
home
the
powder
,
and
wad
the
same
accordingly
,
then
the
shot
being
involved
with
paper
,
leather
,
okam
,
or
such
like
,
to
fill
close
the
concave
of
the
bore
,
I
would
drive
the
shot
close
to
the
powder
with
a
good
wad
,
putting
after
it
a
Tampion
of
Cork
,
and
with
a
spunge
moistned
with
oyle
,
I
would
annoint
the
vacant
Cilinder
,
and
so
barricadoe
the
peece
,
that
it
should
not
reverse
in
the
discharge
.