Right
Honourable
,
and
Right
Worshipfull
.
I
Doubt
not
,
but
as
every
worthy
and
laudable
worke
is
subject
to
obliquie
and
ill
construction
:
So
this
my
good
intent
and
usefull
invention
,
which
I
here
present
unto
you
Right
Honourable
Lords
,
and
you
Right
Worshipfull
,
into
whose
clientlie
I
betake
both
my selfe
and
it
,
shall
meet
with
some
over-curious
and
supercilious
censurers
,
who
will
misse-judge
and
misse-say
the
same
:
though
not
for
the
art
(
against
which
I
perswade
my selfe
they
shall
find
little
cause
to
except
)
yet
in
respect
of
my
particular
calling
:
of
the
height
and
dignity
whereof
,
such
small
and
low
cogitations
may
seeme
to
be
unworthy
.
But
may
it
please
them
to
consider
,
that
Theologie
is
〈◊〉
〈◊〉
〈◊〉
〈◊〉
〈◊〉
,
the
chiefe
and
principall
Lady
and
Mistresse
of
all
other
faculties
;
unto
which
all
callings
in
this
life
,
for
their
just
,
faithfull
,
and
conscionable
execution
,
are
to
comply
,
and
bee
accountable
.
And
seeing
God
in
his
sacred
word
biddeth
not
onely
cease
to
doe
evill
,
but
also
learne
to
doe
well
,
and
seeke
judgement
;
that
Divine
may
bee
thought
best
to
performe
his
dutie
,
that
shall
not
onely
reprove
injustice
and
wrong
dealing
,
but
shall
also
even
in
particular
actions
informe
the
conscience
both
what
is
right
,
and
how
to
performe
it
.
This
I
have
herein
endeavoured
to
effect
.
The
holy
Scripture
is
frequent
in
shewing
the
abomination
of
false
and
deceitful
weights
,
and
in
forbidding
to
doe
unjustly
in
line
,
in
weight
,
or
in
measure
:
and
telleth
us
that
a
true
weight
,
and
a
just
balance
are
of
the
Lord
,
and
that
all
the
weights
in
the
bagge
are
his
worke
.
If
I
therefore
by
the
helpe
of
God
,
and
the
knowledge
hee
hath
beene
pleased
to
give
me
,
shall
exhibite
unto
this
renowned
Citie
,
a
line
and
rule
to
measure
vessels
with
according
to
true
art
,
and
shall
teach
how
to
reforme
an
errour
,
which
hath
for
some
time
(
through
ignorance
of
better
)
usurped
the
place
of
truth
;
and
that
with
much
more
facility
,
then
it
is
committed
:
I
hope
I
shall
not
justly
be
thought
to
wander
out
of
the
limits
of
my
profession
and
calling
.
Now
the
occasion
whereby
I
invented
it
was
this
.
Many
yeares
agoe
,
I
devised
for
my
private
use
an
instrument
,
which
I
the
Circles
of
proportion
:
which
is
nothing
else
but
the
Logarithmes
of
Numbers
,
Sines
,
and
Tangents
set
on
circles
.
And
I
writ
in
latine
the
manifold
uses
thereof
,
not
onely
in
Arithmetical
,
Geometrical
,
and
Astronomical
calculations
,
but
also
in
divers
other
accounts
,
practises
,
and
questions
,
which
are
occurrent
in
the
civill
societie
and
conversation
of
mankind
:
among
which
one
was
concerning
the
measuring
or
Gauging
of
vessels
:
wherein
taking
the
forme
of
them
to
be
spharoide
,
or
like
a
long
sphaere
,
with
the
two
ends
equally
cut
off
,
(
as
generally
both
by
the
ancienter
and
later
writers
is
supposed
,
and
in
the
fabric
of
such
vessels
is
still
aymed
at
by
the
Makers
)
I
delivered
out
of
the
grounds
and
inventions
of
that
most
admirable
Artist
Archimedes
,
the
true
and
artificiall
way
of
finding
their
severall
contents
:
and
applyed
it
unto
the
use
of
that
my
instrument
,
with
as
much
ease
and
expeditnesse
as
I
could
.
Neither
did
I
at
all
discourse
upon
the
Mechanicall
waves
practised
by
other
men
,
much
lesse
refute
any
of
their
errors
,
but
onely
barely
and
positively
delivered
the
truth
.
These
my
notes
,
and
that
my
instrument
(
after
many
yeares
)
at
the
perswasion
of
a
friend
of
mine
,
who
profered
to
translate
them
into
English
,
I
was
content
hee
should
set
out
and
make
common
,
my selfe
not
having
any
hand
in
that
publication
.
When
now
the
translation
was
ready
for
the
Printer
,
my
friend
having
perused
that
which
Master
Gunter
in
his
second
booke
of
the
Crosse
staffe
Chapt.
4.
writeth
very
obscurely
about
Gauging
of
vessels
,
asked
mee
what
he
meant
by
the
meane
Diameter
after
the
vsuall
manner
?
I
answered
him
that
in
the
vsuall
manner
of
art
there
was
no
medium
or
meane
,
but
the
meane
betweene
the
two
extreme
termes
in
some
kind
of
Proportion
:
and
that
all
proportion
being
either
Arithmetical
,
Geometrical
,
or
Musical
,
hee
being
a
Scholer
and
an
Artist
,
must
needs
(
as
I
thought
)
by
the
meane
understand
one
of
those
three
:
and
most
likely
the
meane
arithmetical
which
is
the
greatest
of
them
.
For
supposing
the
two
extreme
termes
to
bee
9
and
4
,
betweene
these
the
meane
arithmetical
is
61/●
,
which
is
halfe
the
summe
of
both
:
the
meane
geometrical
is
6
:
and
the
meane
in
musical
proportion
is
5●/13.
And
yet
said
I
,
the
meane
arithmetical
is
too
little
,
as
in
the
mensuration
of
tapering
timber
I
proved
:
much
more
either
of
the
two
rest
.
And
other
meane
diameter
,
which
may
give
the
true
content
of
a
sphaeroides
,
art
affordeth
none
.
My
friend
replyed
,
Master
Gunter
is
generally
acknowledged
to
have
bin
a
man
of
skill
,
and
you
utterly
unknowne
:
and
hee
that
shall
find
your
booke
disagreeing
from
his
documents
,
will
without
any
more
adoe
reject
it
;
you
shall
therefore
doe
well
to
write
in
a
few
lines
why
you
differ
from
Mr.
Gunter
,
and
to
shew
that
his
way
by
the
meane
diameter
cannot
stand
with
art
.
Which
his
counsell
I
seeing
not
to
be
unnecessary
,
especially
in
regard
of
the
great
paines
hee
had
taken
in
the
translation
of
my
notes
,
tooke
a
pen
,
and
presently
in
the
margine
of
his
translation
writ
that
short
advertisement
touching
Mr.
Gunters
meane
diameter
.
Not
long
after
that
translation
was
in
print
,
word
was
sent
me
into
the
countrey
,
that
an
old
man
(
that
said
he
was
)
the
Gauger
of
London
came
earnestly
inquiring
after
me
,
and
was
very
angry
;
professing
hee
would
vindicate
Mr.
Gunters
credit
,
and
speake
for
him
,
that
could
not
answer
for
himselfe
:
and
that
I
had
taught
a
false
way
of
Gauging
vessels
:
and
that
both
hee
and
many
others
,
had
bought
of
my
bookes
;
which
much
troubled
him
:
and
hee
was
very
solicitous
how
they
should
come
by
their
money
againe
:
and
that
hee
never
saw
such
a
booke
in
his
life
;
for
he
could
not
tell
what
to
make
of
it
.
The
translator
told
him
,
that
when
he
,
or
any
other
for
him
,
should
disprove
that
way
of
measuring
vessels
,
which
I
had
delivered
;
let
him
bring
his
booke
,
and
he
should
have
his
money
againe
for
it
.
At
my
next
comming
to
London
,
hee
hearing
of
my
being
in
towne
,
came
to
mee
,
and
expostulated
with
me
,
why
I
would
presume
to
question
any
thing
that
Mr.
Gunter
writ
?
I
answered
him
,
that
it
is
a
fault
incident
to
the
students
of
these
arts
,
to
be
very
incredulous
,
especially
if
they
see
demonstration
to
the
contrary
.
Hee
said
I
understood
not
what
Mr.
Gunter
meant
by
the
meane
diameter
after
the
vsuall
manner
:
For
Mr.
Gunter
(
though
hee
said
not
so
much
)
did
understand
the
manner
vsuall
in
London
;
and
that
hee
him selfe
followed
in
gauging
:
which
was
to
halfe
the
summe
of
the
diameters
at
the
head
and
bung
,
and
to
adde
one
quarter
of
their
difference
:
and
that
this
was
a
true
way
,
and
a
better
way
then
mine
:
and
that
if
hee
should
use
my
way
,
it
would
require
much
more
paines
,
and
longer
time
:
and
that
hee
had
a
man
,
whom
hee
had
taught
,
which
had
little
or
no
skill
in
Arithmetic
,
and
could
scarce
multiply
,
yet
in
his
way
hee
should
gauge
with
any
man
in
England
;
and
that
if
that
his
way
were
not
right
,
hee
might
doe
more
wrong
in
a
few
yeares
then
any
Aldermans
state
in
London
is
worth
;
and
that
hee
was
sworne
to
doe
justly
.
I
answered
,
that
the
greater
tye
lay
upon
him
to
doe
justly
,
and
the
more
hurt
hee
might
doe
by
misgauging
,
the
more
thankes
hee
owed
mee
,
for
shewing
him
the
right
;
and
with
the
more
gladnesse
hee
should
embrace
it
,
notwithstanding
it
might
have
some
more
difficultie
:
for
though
I
should
hold
my
peace
(
as
Mr.
Gunter
it
seemeth
did
)
yet
hee
were
never
the
more
justifiable
:
and
wished
him
to
looke
to
his
conscience
:
especially
seeing
now
hee
might
informe
himselfe
in
the
truth
.
Hee
said
hee
found
indeed
by
his
experience
,
that
the
adding
of
a
quarter
of
the
difference
was
somewhat
too
much
;
and
therefore
that
now
hee
began
to
take
one
fift
part
thereof
:
and
yet
both
wayes
were
better
then
mine
;
and
hee
would
not
learne
of
mee
to
gauge
vessels
.
And
so
went
his
way
in
great
choler
and
displeasure
.
I
did
indeed
wonder
at
that
his
assertion
;
that
whether
hee
tooke
the
quarter
,
or
the
fift
part
of
the
difference
,
yet
both
are
better
then
the
way
of
art
,
which
I
had
delivered
:
for
even
in
that
example
,
which
in
my
booke
is
set
downe
,
of
a
vessel
having
the
diameter
at
the
bung
32
inches
,
and
the
diameter
at
the
head
18
inches
,
and
the
length
40
inches
;
had
hee
but
made
triall
,
hee
should
have
found
the
content
computed
by
one
quarter
of
the
difference
,
to
have
beene
gallons
110
and
almost
an
halfe
;
and
by
one
fift
part
,
to
have
beene
gallons
1051/10
;
whereas
the
true
measure
by
art
is
gallons
107
▪
and
an
halfe
and
somewhat
better
;
which
is
almost
in
the
very
midst
betweene
both
:
so
that
if
any
man
will
suppose
one
of
his
wayes
,
bee
it
the
former
,
or
the
latter
,
to
bee
right
:
yet
the
other
must
of
necessitie
bee
further
from
the
truth
,
then
that
which
I
taught
;
because
it
falling
betweene
both
,
must
needs
bee
neerer
to
each
,
then
one
of
them
is
to
the
other
.
Not
long
after
Mr.
Elias
Allen
(
a
man
well
knowne
and
esteemed
by
all
men
of
art
for
his
skilfulnesse
in
making
instruments
in
metal
)
being
in
the
company
of
some
gentlemen
of
good
quality
and
worth
,
upon
occasion
related
these
former
words
of
the
Gauger
,
what
great
detriment
hee
might
doe
by
his
manner
of
Gauging
,
if
it
were
not
true
.
Which
his
speech
Mr.
George
Ethrege
,
then
Master
of
the
right
worshipfull
Company
of
Vinteners
,
hearing
and
observing
,
said
that
indeed
he
doubted
not
,
but
there
was
much
wrong
done
by
misgauging
wine
vessels
;
and
that
many
times
they
found
it
to
their
cost
;
but
they
could
not
easily
remedy
it
.
And
therefore
invited
Mr.
Allen
to
request
me
to
devise
a
Gauging
instrument
,
which
might
be
according
to
true
art
,
and
of
familiar
and
easie
performance
;
that
they
might
examine
and
try
their
vessels
themselves
:
and
said
it
would
bee
an
invention
very
acceptable
,
and
of
great
use
,
and
a
meanes
to
prevent
much
wrong
that
many
times
is
done
.
Which
inquisition
and
studie
,
to
find
out
a
true
and
perfect
instrument
for
measuring
of
vessels
(
though
at
first
without
any
hope
of
effecting
any
singular
thing
therin
after
such
a
number
of
learned
artists
,
and
writers
in
this
kind
,
with
the
meanest
of
which
I
am
not
to
bee
compared
)
I
undertooke
,
merely
our
of
my
love
to
the
society
of
mankind
,
and
my
desire
of
advancing
truth
and
justice
;
and
at
last
by
the
helpe
of
God
,
who
is
righteous
,
and
loveth
righteousnesse
,
have
brought
to
passe
:
And
herein
withall
humble
and
affectionate
serviceablenesse
,
both
unto
you
my
right
honourable
LL.
upon
whom
the
principall
care
of
all
such
admensurations
within
this
most
flourishing
and
illustrious
Citie
doth
rest
,
and
of
you
right
worshipfull
the
Masters
and
whole
Company
of
Vintners
,
and
to
as
many
of
this
most
renowned
Citie
as
shall
have
cause
to
use
the
same
,
I
present
this
my
new
gauging
instrument
.
Onely
desiring
thus
much
,
that
you
would
be
pleased
to
vouchsafe
it
your
acceptance
with
the
same
loving
and
benevolent
respect
,
as
I
my selfe
had
unto
you
,
and
the
truth
,
in
the
investigation
thereof
.
Neither
indeed
may
I
omit
to
report
the
noble
favour
that
the
right
worshipfull
Company
of
Vintners
did
afford
,
though
unknowne
,
unto
mee
.
For
when
Mr.
Elias
Allen
had
finished
up
one
of
those
my
instruments
or
gauging
rods
,
and
had
brought
it
to
their
Hall
,
they
presently
deputed
certaine
of
their
society
to
see
the
experience
and
performance
thereof
,
at
the
Taverne
by
Leaden-hall
under
the
signe
of
the
Kings-head
:
and
they
tooke
the
paines
to
examine
the
truth
of
it
in
many
and
sundry
kinds
of
wine
vessels
;
where
,
as
I
have
beene
told
(
for
I
was
not
there
present
my selfe
)
beyond
all
expectation
they
found
such
an
exact
agreement
with
the
measure
of
water
they
filled
in
by
gallons
,
after
the
sealed
Standard
for
wine
measure
,
that
in
most
the
difference
was
scarce
sensible
;
whereas
the
markes
set
thereupon
exceeded
the
same
measures
by
two
or
three
,
and
sometimes
more
then
foure
gallons
in
a
vessell
.
Whereupon
they
agreed
with
Mr.
Allen
for
a
price
,
and
bespake
of
him
threescore
of
the
same
my
rods
or
instruments
.
Which
so
noble
and
courteous
respect
unto
me
,
to
decree
the
examination
of
that
my
invention
(
though
other
benefit
or
recompense
for
the
same
I
demand
none
)
I
cannot
but
acknowledge
with
much
thankefulnesse
.
Neither
is
the
facilitie
of
working
For
therein
first
the
two
diameters
at
the
bung
,
and
at
the
head
measured
in
ynches
must
be
added
together
,
and
halfe
the
summe
of
them
taken
and
kept
.
Secondly
the
diameter
at
the
head
is
to
bee
subducted
out
of
the
diameter
at
the
bung
,
and
the
remaines
to
bee
divided
by
4
,
or
else
by
5
,
to
find
out
the
quarter
,
or
fift
part
of
their
difference
.
Thirdly
that
quarter
of
fift
part
of
the
difference
must
bee
added
to
the
halfe
summe
kept
;
to
make
up
a
meane
diameter
.
Lastly
there
remaineth
a
proportion
to
bee
wrought
by
multiplication
and
division
;
which
is
this
,
As
the
quadrate
of
17
⌊
15
(
which
Mr
Gunter
calleth
his
gauge
point
)
is
to
the
quadrate
of
the
meane
diameter
last
found
,
So
is
the
length
of
the
vessell
measured
in
inches
,
to
the
content
of
the
same
vessell
in
wine
gallons
.
Such
a
deale
of
paines
,
and
such
a
multiplicitie
of
worke
is
undergone
in
their
ordinary
gauging
:
and
yet
when
all
is
done
,
the
capacitie
or
content
of
the
vessell
so
found
is
merely
conjectural
,
sometimes
falser
and
sometimes
truer
,
according
as
the
diameters
of
the
vessell
are
more
or
lesse
unequall
.
But
this
way
of
art
,
which
I
propose
,
besides
that
it
is
constant
and
universall
in
all
kinds
of
wine
vessells
,
is
most
easily
performed
only
with
one
single
addition
&
multiplication
;
as
shall
anon
bee
declared
both
by
rule
,
and
examples
.
Soe
that
now
I
hope
I
have
made
Mr
Gauger
amends
for
the
too
much
difficultie
and
paines
hee
thought
my
booke
put
him
to
;
and
that
henceforth
hee
will
bee
as
earnest
to
vindicate
my
credit
also
,
as
hee
hath
egerly
traduced
it
before
he
rightly
knew
me
.
For
although
I
cannot
so
well
excuse
his
rashnesse
in
impertinent
interposing
himselfe
in
questions
hee
had
small
skill
in
:
yet
I
perswade
my selfe
he
had
no
malice
against
my
person
,
who
was
then
utterly
unknowne
to
him
.
And
for
my
part
(
for
ought
I
remember
)
I
had
not
so
much
as
heard
of
any
such
officer
about
the
Citie
.
But
I
wholly
impute
his
offence
at
me
partly
to
the
high
estimation
hee
had
of
Mr.
Gunter
,
from
whom
to
dissent
he
thought
to
be
a
hainous
matter
:
and
partly
to
his
dissidence
and
distrust
of
my
rule
,
how
it
might
hold
when
it
came
to
tryal
.
And
therefore
I
doe
willingly
returne
againe
into
favour
with
him
,
and
recommend
this
my
invention
and
my selfe
to
his
future
approbation
and
friendship
;
assuring
him
that
what
I
have
before
written
was
not
intented
against
him
:
but
onely
to
shew
the
true
occasion
how
I
fell
upon
this
search
and
disquisition
:
which
in
regard
of
my
profession
seemed
to
bee
very
necessary
.
The
principles
whereon
the
way
Secondly
,
that
a
sphaere
,
or
spharoide
containeth
two
third
parts
of
a
cylinder
hauing
the
same
length
and
thicknesse
;
and
consequently
that
the
solid
convexitie
betweene
two
cylinders
,
one
within
the
sphaeroide
,
and
the
other
without
touching
it
,
and
having
the
same
center
and
height
,
is
equall
to
two
third
parts
of
the
difference
of
those
two
cylinders
:
which
hath
long
since
beene
taught
by
the
ancient
Siracusan
Archimedes
in
his
first
booke
of
the
Sphaere
and
Cylinder
,
&
in
his
booke
of
Cone-like
and
sphaere-like
magnitudes
:
&
of
late
by
our
English
Archimedes
Mr
Henry
Briggs
,
in
his
Treatice
of
Arithmetica
logarith
mica
.
Out
of
the
consideration
of
these
two
principles
,
or
grounds
,
I
framed
my
rule
,
which
I
set
downe
in
my
booke
of
the
Circles
of
proportion
,
Chapt.
9.
in
these
words
.
Measure
the
two
diameters
of
the
vessell
,
in
ynches
,
or
else
in
tenth
parts
of
a
foot
,
the
one
at
the
bung
hole
,
the
other
at
the
head
,
and
also
the
length
within
.
And
by
the
diameters
found
,
find
out
the
circles
;
then
adde
together
two
third
parts
,
of
the
greater
circle
,
and
one
third
part
of
the
lesse
;
Lastly
,
multiply
the
aggregate
by
the
length
:
so
shall
you
have
the
content
of
the
vessell
,
either
in
cubic
ynches
,
or
cubic
tenth
parts
of
a
foot
.
Which
afterward
in
the
end
of
that
Chapter
(
having
first
inquired
the
quantity
of
a
gallon
both
Ale
,
and
Wine
measure
in
solid
ynches
,
the
one
to
bee
272¼
the
other
231
)
I
taught
how
to
reduce
into
gallons
and
hundreth
parts
,
by
dividing
the
whole
number
of
ynches
contained
in
the
vessell
by
either
of
those
two
numbers
respectively
.
And
this
is
that
very
rule
,
the
worke
and
practice
of
which
I
have
by
art
,
with
an
invention
not
yet
thought
upon
by
any
other
,
and
with
divisions
calculated
for
that
purpose
,
sitted
and
applyed
to
this
my
new
gauging
line
or
rod
.
It
consisteth
of
two
rulers
of
brasse
two
little
sockets
of
brasse
fastned
on
strongly
:
by
which
the
rulers
are
held
together
,
and
made
to
move
one
upon
another
,
and
to
bee
drawne
out
unto
any
length
,
as
occasion
shall
require
:
and
when
you
have
them
at
the
just
length
,
there
is
upon
one
of
the
sockets
a
long
Scrue-pin
to
serue
them
fast
.
These
two
little
sockets
encompasse
not
both
rulers
quite
round
:
but
have
each
of
them
a
slit
about
a
quarter
of
an
ynch
board
:
that
they
may
not
hinder
the
sight
of
the
divisions
,
which
are
upon
the
broad
or
flat
sides
of
the
rulers
.
Which
divisions
are
indeed
of
most
principall
use
:
being
properly
the
gauge-divisions
:
and
are
now
first
of
all
invented
,
and
accommodated
to
the
mensuration
of
vessels
.
The
gauge-divisions
are
in
all
two
hundred
and
thirtie
:
of
which
every
particular
division
standeth
for
one
hundreth
part
of
a
wine
gallon
:
so
that
they
are
in
all
a
wine
gallons
and
30
hundred
parts
.
And
for
the
more
perspicuous
distinguishing
of
them
they
are
figured
by
tens
thus
,
0
⌊
10
,
0
⌊
20
,
0
⌊
30
,
0
⌊
40
,
0
⌊
50
,
0
⌊
60
,
0
⌊
70
,
0
⌊
80
,
0
⌊
90
,
1
⌊
00
,
1
⌊
10
,
1
⌊
20
,
1
⌊
30
,
1
⌊
40
,
1
⌊
50
,
1
⌊
60
,
1
⌊
70
,
1
⌊
80
,
1
⌊
90
,
2
⌊
00
,
2
⌊
10
,
2
⌊
20
,
2
⌊
30
:
there
being
betweene
every
one
of
those
figures
ten
divisions
,
or
ten
hundreth
parts
.
At
the
other
end
of
both
the
rulers
is
a
hooke
framed
into
right
or
square
angles
to
be
scrued
on
:
the
one
with
a
Scrue-pin
,
the
other
with
a
matrix
or
Scrue-plate
.
And
above
these
hookes
the
edge
of
both
rulers
is
divided
into
ynches
,
beginning
exactly
equall
with
the
ends
of
the
hookes
:
and
figured
with
5
,
10
,
15
,
20
,
25
,
27
,
30
,
&c.
And
each
ynch
is
subdivided
into
ten
equall
parts
.
Which
division
of
ynches
,
together
with
the
hookes
,
serve
to
take
the
length
of
all
vessels
;
that
the
ends
of
the
barrell
boards
overreaching
the
bottoms
,
may
not
bee
an
impediment
to
the
measuring
thereof
.
Vpon
the
other
edge
of
each
ruler
is
set
the
the
line
of
Numbers
:
which
is
the
very
same
in
both
:
though
some
what
differently
figured
.
For
that
on
the
ruler
next
the
socket
with
the
long
Scrue-pin
,
is
noted
with
the
figures
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
,
20
,
which
I
therefore
call
the
line
of
digit
numbers
:
and
that
on
the
other
ruler
is
figured
with
tens
,
as
10
,
20
,
30
,
40
,
50
,
60
,
70
,
80
,
90
,
100
,
200
,
300
:
and
I
call
it
the
line
of
denarie
numbers
.
Wherein
you
are
to
remember
that
from
1
to
5
,
and
from
10
to
50
,
and
also
above
100
,
every
space
is
subdivided
into
one
hundred
parts
,
but
above
5
unto
10
,
and
above
50
unto
100
,
because
the
spaces
are
too
small
to
receive
an
hundred
parts
,
they
are
subdivided
but
into
fiftie
.
Thus
having
shewed
the
description
gauging
rod
:
I
now
come
to
the
use
thereof
in
measuring
any
kind
of
vessel
by
the
wine
gallon
.
For
which
I
will
set
downe
these
fower
rules
,
Rule
I.
How
to
take
the
length
of
a
Vessell
.
HAving
first
sitted
the
two
hookes
upon
the
ends
of
the
two
rulers
,
so
that
the
line
of
ynches
may
be
uppermost
,
draw
out
the
rulers
in
length
,
and
apply
them
to
the
vessell
long
wise
,
so
that
the
two
hookes
may
embrace
the
two
bottoms
thereof
:
at
that
length
scrue
them
fast
together
with
the
long
Scrue-pin
in
the
socket
:
then
take
off
the
hooke
,
which
hath
the
Scrue-pin
:
and
looke
how
many
ynches
the
socket
of
the
ruler
which
hath
the
hooke
on
doth
cut
in
the
ruler
without
the
hooke
:
for
that
shall
be
the
length
of
the
vessell
from
out
side
to
out
side
in
ynches
:
wherefore
if
out
of
that
measure
you
take
the
thicknes
of
the
two
bottoms
(
which
may
bee
easily
estimated
by
a
spigot
hole
)
you
shall
have
the
true
length
of
the
vessell
within
.
But
if
the
length
of
the
vessell
be
lesse
then
27
ynches
,
you
cannot
use
both
hookes
,
as
before
was
done
.
Wherefore
apply
the
ruler
which
hath
the
matrix
or
Scrue-plate
to
the
vessell
,
setting
that
hooke
against
one
of
the
bottoms
:
and
where
the
divisions
of
ynches
in
that
ruler
beginneth
,
stick
up
a
knife
:
then
remove
that
same
hooke
to
the
other
bottome
;
and
the
ynches
,
which
the
knife
cutteth
,
shall
give
the
length
of
the
vessell
from
out
side
to
outside
.
Rule
II.
How
to
take
the
Diameters
of
a
Vessell
at
the
Bunge
,
and
at
the
Head
.
and
how
to
adde
them
together
,
that
you
may
finde
the
summe
of
them
.
THe
Diameters
are
not
measured
by
ynches
,
as
the
length
is
,
but
by
Wine
gallons
,
and
hundreth
parts
:
in
this
maner
.
Take
off
the
hook
which
hath
the
scrue-pinne
,
and
dipp
that
end
of
the
Ruler
into
the
Vessell
at
the
bung
;
and
looke
how
many
parts
of
the
divisions
of
Gallons
the
inside
of
the
bung-hole
doth
cut
,
the
same
shall
bee
the
Diameter
at
the
bung
.
In
like
maner
apply
the
same
end
of
the
Ruler
to
the
head
of
the
Vessell
without
;
and
looke
how
many
parts
of
the
divisions
of
Gallons
it
is
broad
over
the
midd'st
or
center
thereof
;
the
same
shall
be
the
Diameter
at
the
head
.
But
if
the
Diameter
at
the
bung
be
greater
then
that
Ruler
is
long
:
draw
out
the
rulers
,
and
scrue
them
at
their
whole
length
:
and
so
measure
therewith
the
Diameters
,
as
was
before
shewed
.
The
two
Diameters
being
found
out
must
bee
added
together
,
thus
:
Write
downe
the
Diameter
at
the
bung
twice
,
and
under
it
the
Diameter
at
the
head
onely
once
,
setting
like
places
one
under
another
in
the
same
rowes
:
that
is
all
the
unites
in
one
rowe
;
all
the
tenth
parts
(
which
are
they
next
the
units
)
in
another
row
;
and
all
the
hundreth
parts
in
the
last
row
:
and
draw
a
long
line
betweene
the
unites
and
the
parts
,
then
adde
them
all
three
together
into
one
summe
by
the
way
of
ordinary
Addition
.
As
in
example
;
Suppose
a
Vessel
that
hath
the
diameter
at
the
bung
gallon
1
&
8
hundreth
parts
,
viz.
1
⌊
08
;
and
the
diameter
at
the
head
onely
96
hundreth
parts
of
a
Gallon
,
viz.
0
⌊
96.
you
shall
write
downe
the
Diameter
at
the
bung
twice
,
&
the
diameter
at
the
head
once
and
adde
them
altogether
,
as
you
see
done
in
the
side
:
and
the
summe
of
the
diameters
shall
bee
found
3
⌊
12
,
that
is
gallons
3
and
12
hundreth
parts
.
And
thus
shall
you
doe
in
all
Vessels
.
Rule
III.
How
to
multiply
the
summe
of
the
Diameters
of
a
Vessell
by
the
length
.
THe
length
of
a
Vessell
being
measured
in
ynches
and
tenth
parts
,
and
the
Diameters
being
found
out
in
Gallons
and
hundreth
parts
,
and
also
added
together
,
as
hath
beene
declared
:
The
summe
of
the
Diameters
is
to
bee
reconed
in
the
line
of
digit
numbers
,
which
is
noted
with
the
figures
1
,
2
,
3
,
4
,
5
,
&c.
and
the
length
,
in
the
other
line
of
denarie
numbers
,
which
is
noted
with
the
figures
10
,
20
,
30
,
40
,
50
,
&c.
In
both
which
lines
of
numbers
you
are
to
consider
,
that
in
the
spaces
betweene
the
figures
every
tenth
division
is
distinguished
with
a
long
line
:
and
every
single
division
with
a
short
line
:
and
every
fift
with
a
line
of
a
length
betweene
both
▪
and
in
the
line
of
digit
numbers
,
they
signifie
so
many
hundreth
parts
of
a
gallon
:
But
in
the
line
of
denarie
numbers
(
as
also
in
the
line
of
digit
numbers
beyond
10
)
every
tenth
division
is
for
unites
;
and
every
single
division
is
for
tenth
parts
.
and
beyond
100
every
tenth
division
is
for
ten
;
and
every
single
division
for
one
unite
.
Where
note
,
that
in
those
spaces
,
which
by
reason
of
their
smalnesse
have
but
50
,
yet
they
are
understood
to
bee
100
,
by
imagining
every
one
to
containe
two
.
The
nature
and
valuation
of
both
the
lines
of
numbers
,
the
digit
and
the
denarie
,
being
understood
,
multiplication
is
thus
to
be
wrought
.
Set
the
unite
place
of
the
line
of
digit
numbers
marked
with
1
,
to
the
place
of
the
length
of
the
Vessell
reconed
in
the
line
of
denary
numbers
:
there
scrue
the
Rulers
fast
▪
then
in
the
line
of
digit
numbers
recon
the
summe
of
the
Diameters
found
out
,
that
at
the
Bung
being
doubled
,
as
was
taught
before
:
and
looke
what
space
and
division
it
poynteth
out
in
the
line
of
denary
numbers
:
the
same
being
reasonably
aestimated
,
shall
bee
the
product
sought
for
.
By
aestimating
reasonably
I
understand
that
you
consider
whether
the
figure
of
that
space
is
to
bee
taken
for
tenns
or
for
hundreds
:
which
is
done
very
easily
:
for
no
man
is
so
simple
,
as
to
mistake
a
Vessell
of
ten
or
twenty
Gallons
,
for
one
or
two
hundred
;
or
of
one
or
two
hundred
gallons
,
for
one
of
ten
or
twenty
.
And
yet
this
short
rule
may
bee
given
.
That
the
product
is
to
bee
aestimated
according
to
that
former
valuation
of
the
line
of
denarie
numbers
:
unlesse
the
Vessell
be
so
small
,
that
the
summe
of
the
diameters
amount
not
to
one
gallon
:
for
then
the
figures
100
&
200
,
are
to
be
taken
for
10
and
twenty
.
And
if
at
any
time
it
chance
,
that
the
summe
of
the
diameters
falleth
not
betweene
the
unite
place
in
the
line
of
digit
numbers
,
and
the
socket
:
divide
the
same
summe
by
2
,
and
then
multiply
the
one
halfe
by
the
length
;
so
shall
you
have
halfe
the
product
sought
for
:
which
being
doubled
will
give
you
the
whole
.
Rule
IIII.
How
to
gauge
or
measure
the
content
of
any
Vessell
in
Wine
gallons
.
TAke
the
length
of
the
Vessell
proposed
in
ynch-measure
,
according
to
the
Rule
I
,
then
take
the
two
diameters
in
gallon
measure
,
and
adde
them
together
,
that
at
the
bung
being
doubled
,
according
to
the
Rule
II.
Lastly
multiply
the
summe
of
the
diameters
by
the
length
,
according
to
Rule
III
:
and
the
product
being
reasonably
aestimated
,
shall
give
the
number
of
Wine
gallons
contained
in
that
Vessell
.
The
performance
and
practice
of
this
Worke
by
Examples
.
Example
I.
ANd
first
I
will
take
the
Example
Circles
of
Proportion
,
Chap
9
,
of
a
Vessell
supposed
to
bee
in
length
40
ynches
;
and
the
diameter
at
the
bung
32
ynches
;
and
the
diameter
at
the
head
18
ynches
:
which
two
diameters
being
taken
with
my
gauging
rod
in
gallon
measure
,
would
have
beene
at
the
bung
gallons
1
and
16
hundreth
parts
,
and
at
the
head
almost
37
hundreth
parts
of
a
gallon
.
Set
downe
the
diameter
at
the
bung
twice
,
and
the
diameter
at
the
head
once
,
&
adde
them
:
the
summe
of
the
diameters
shall
be
gallons
2
&
almost
●9
hundreth
parts
,
by
Rule
II.
which
being
multiplyed
by
40
,
the
product
shal
be
gallons
107
,
and
better
then
an
halfe
;
which
is
the
true
content
sought
for
.
Example
II.
Suppose
a
small
Vessell
;
whose
length
is
ynches
45
and
3
tenth
parts
,
viz.
45
⌊
3
;
and
the
diameter
at
the
bung
38
hundreth
parts
of
a
gallon
;
and
the
diameter
at
the
head
30
hundreth
parts
.
what
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
,
the
summe
is
gallons
1
and
6
hundreth
parts
,
by
Rule
II.
Multiply
this
summe
by
the
length
45
⌊
3
:
and
the
product
shall
bee
48
⌊
12
▪
by
Rule
III
,
that
is
gallons
48
and
almost
12
hundreth
parts
:
which
is
the
true
content
sought
for
.
Exam.
III.
Suppose
another
small
vessel
,
whose
length
is
ynches
30
and
7
tenth
parts
,
viz.
30
⌊
7.
and
the
diameter
at
the
bung
34
hundreth
parts
of
a
gallon
:
and
the
diameter
at
the
head
28
hundreth
parts
,
what
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
:
the
summe
is
onely
96
hundreth
parts
of
a
gallon
,
by
Rule
II.
Multiply
this
summe
by
the
length
30
⌊
7
:
and
the
product
shall
be
29
⌊
47
,
by
Rule
III
,
that
is
gallons
29
,
and
47
hundreth
parts
,
which
is
almost
an
halfe
.
which
is
the
true
content
.
For
the
first
figure
2
signifyeth
not
200
(
though
it
be
so
marked
on
the
line
of
denarie
numbers
)
but
only
20
;
as
both
plaine
reason
,
&
also
the
short
rule
,
at
the
end
of
Rule
III
,
wil
shew
.
Exam.
IIII.
Suppose
a
great
vessell
:
whose
length
is
ynches
70
and
an
halfe
,
viz.
70
⌊
5
;
and
the
diameter
at
the
bung
gallons
2
and
3
hundreth
parts
,
viz
,
2
⌊
03
;
and
the
diameter
at
the
head
gallons
1
and
10
hundreth
parts
,
viz.
1
⌊
10.
what
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
;
the
summe
is
gallons
5
and
16
hundreth
parts
,
by
Rule
II.
Multiply
this
summe
by
the
length
70
⌊
5
:
but
because
the
unit●
place
of
the
line
of
digit
numbers
,
being
set
to
70
⌊
5
in
the
line
of
denarie
numbers
,
the
summe
of
the
diameters
5
⌊
16
will
over-reach
beyond
the
socket
:
therefore
to
helpe
this
,
take
halfe
the
summe
of
the
diameters
,
viz.
gallons
2
⌊
58
:
and
multiply
that
halfe
summe
by
the
length
70
⌊
5
:
and
the
product
shall
bee
181
⌊
8●
,
by
Rule
III
,
that
is
gallons
181
and
almost
9
tenth
parts
:
which
is
halfe
the
true
content
.
And
being
doubled
shall
give
gallons
363
⌊
78
for
the
whole
content
of
that
great
vessell
.
The
Examples
following
are
of
some
vessels
measured
in
the
presence
of
them
,
which
were
deputed
by
the
Company
of
Vinteners
to
see
the
tryall
of
this
Gauging
line
or
rod
.
Exam.
V.
A
Canarie
pipe
whose
length
was
ynches
48
and
an
halfe
,
viz.
48
⌊
5
;
and
the
diameter
at
the
bung
93
hundreth
parts
of
a
gallon
,
viz.
0
⌊
93
:
and
the
diameter
at
the
head
54
hundreth
parts
,
viz.
0
⌊
54.
what
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
,
the
summe
is
gallons
2
and
4
tenth
parts
,
by
Rule
II.
Multiply
this
summe
by
the
length
48
⌊
5
:
and
the
product
shall
bee
116
⌊
4
by
Rule
III
,
that
is
gallons
116
&
4
tenth
parts
:
which
is
the
content
sought
for
.
Examp.
VI.
A
Graves-hogshead
whose
length
was
ynches
31
and
2
tenth
parts
,
viz.
31
⌊
2
:
And
the
diameter
at
the
bung
73
hundreth
part●
of
a
gallon
,
viz.
0
⌊
73
;
and
the
diameter
at
the
head
57
hundreth
parts
,
viz.
0
⌊
●7
.
What
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
,
the
Summe
is
gallon
●
and
3
hundreth
parts
,
by
Rule
II.
Multiply
this
summe
by
the
length
31
⌊
2
:
and
the
product
shall
bee
63
⌊
34
by
Rule
III
,
that
is
gallons
63
and
34
hundreth
parts
:
which
is
the
content
sought
for
.
Example
VII
.
A
High-countrey
hogshead
whose
length
was
ynches
30
,
and
82
hundreth
parts
,
viz.
30
⌊
82
:
And
the
diameter
at
the
bung
63
hundreth
parts
of
a
gallon
:
viz.
0
⌊
63
and
the
diameter
at
the
head
51
hundreth
parts
,
viz.
0
⌊
51.
What
is
the
content
?
Adde
the
two
diameters
together
,
that
at
the
bung
being
doubled
,
the
summe
is
gallons
1
and
77
hundreth
parts
,
by
Rule
II.
Multiply
this
summe
by
the
length
30
⌊
82
:
and
the
product
shall
bee
54
⌊
55
,
by
Rule
III
,
that
is
gallons
54
and
55
hundreth
parts
:
which
is
the
true
content
sought
for
.
Although
this
Gauging
instrument
is
properly
framed
for
measuring
(
w
)
;
and
the
other
at
231
,
noted
with
the
letter
(
a
)
.
The
use
of
which
I
deliver
in
this
Rule
following
.
Seeke
out
the
content
of
the
vessell
proposed
in
wine
gallons
,
upon
the
ruler
figured
with
denarie
numbers
,
as
hath
before
beene
taught
:
and
thereto
set
the
marke
(
w
)
:
and
so
shall
the
other
marke
(
a
)
point
to
the
number
of
beere
gallons
contained
in
the
same
vessell
.
I
will
shew
the
practice
of
this
Rule
by
the
vessells
measured
in
the
three
last
examples
.
First
The
Canarie
pipe
,
whose
length
was
ynches
48
⌊
5
:
and
the
diameter
at
the
bung
gallon
0
⌊
93
:
and
the
diameter
at
the
head
gallon
0
⌊
54
:
the
measure
whereof
was
by
Example
V
found
to
be
gallons
116
⌊
4
:
how
many
beere
gallons
will
it
containe
?
Set
the
marke
(
w
)
unto
the
wine
measure
116
⌊
4
reconed
upon
the
ruler
figured
with
denarie
numbers
,
scruing
it
there
fast
,
and
the
marke
(
a
)
shall
in
the
same
ruler
point
out
98
⌊
76
that
is
gallons
98
and
76
hundreth
parts
,
the
content
thereof
in
beere
measure
.
Againe
,
The
Graves
hogshead
,
whose
length
was
ynches
31
⌊
2
:
and
the
diameter
at
the
bung
gallon
0
⌊
73
:
and
the
diameter
at
the
head
gallon
0
⌊
57
:
the
measure
whereof
was
by
Example
VI
found
to
bee
gallons
63
⌊
●4
:
how
many
beere
gallons
will
it
containe
?
Set
the
marke
(
w
)
unto
the
wine
measure
63
⌊
34
reconed
upon
the
ruler
figured
with
denarie
numbers
,
scruing
it
there
fast
:
and
the
marke
(
a
)
shall
in
the
same
Ruler
point
out
53
⌊
74
,
that
is
gallons
53
,
and
74
hundreth
parts
,
the
content
thereof
in
beere
measure
.
Lastly
the
High
countrey
hogges-head
,
whose
length
was
ynches
30
⌊
82
:
and
the
diameter
at
the
bung
gallon
0
⌊
63
:
and
the
diameter
at
the
head
gallon
0
⌊
51
:
the
measure
whereof
was
by
Example
VII
found
to
bee
gallons
54
⌊
55
:
how
many
beere
gallons
will
it
containe
?
Set
the
marke
(
w
)
unto
the
wine
measure
54
⌊
●5
reconed
upon
the
ruler
figured
with
denarie
numbers
,
scruing
it
there
fast
:
and
the
marke
(
a
)
shall
in
the
same
ruler
point
out
46
⌊
28
,
that
is
gallons
46
,
and
●8
hundreth
parts
,
the
content
thereof
in
beere
measure
.
And
now
I
have
finished
what
I
determined
to
write
concerning
the
use
of
this
my
new
Gauging
line
or
rod
:
and
have
made
it
so
plaine
and
easie
that
I
doubt
not
but
every
meane
capacitie
will
bee
able
with
a
little
care
to
apprehend
the
meaning
and
practice
:
I
have
also
delivered
the
Rule
which
I
follow
,
and
whereupon
I
ground
this
worke
:
only
the
maner
of
computing
the
Gauge-divisions
I
have
concealed
:
both
because
that
speculation
is
impertinent
to
the
managing
and
hand-working
therewith
:
and
also
that
because
unto
men
of
art
by
comparing
the
rule
with
the
performance
,
it
will
not
bee
difficult
to
find
out
the
reason
:
but
especially
because
I
intend
and
wish
the
benefit
of
making
and
fabricating
this
Instrument
,
unto
Mr.
Elias
Allen
,
who
gave
the
occasion
of
it
,
and
at
whose
request
I
invented
it
.
And
if
it
shall
bee
serviceable
to
this
most
illustrious
Citie
,
as
a
meanes
of
keeping
truth
and
equitie
in
that
kind
,
and
acceptable
to
you
Right
Honourable
LL
,
and
to
you
Right
Worshipfull
to
whom
I
present
it
,
and
conducing
unto
the
glory
of
Almighty
God
,
the
author
of
every
good
abilitie
,
it
hath
obtayned
the
desired
END
.