<s>
A	O
nomogram	B-Application
(	O
from	O
Greek	O
,	O
"	O
law	O
"	O
and	O
,	O
"	O
line	O
"	O
)	O
,	O
also	O
called	O
a	O
nomograph	B-Application
,	O
alignment	O
chart	O
,	O
or	O
abac	O
,	O
is	O
a	O
graphical	O
calculating	O
device	O
,	O
a	O
two-dimensional	O
diagram	O
designed	O
to	O
allow	O
the	O
approximate	O
graphical	O
computation	O
of	O
a	O
mathematical	O
function	O
.	O
</s>
<s>
The	O
field	O
of	O
nomography	B-Application
was	O
invented	O
in	O
1884	O
by	O
the	O
French	O
engineer	O
Philbert	O
Maurice	O
d'Ocagne	O
(	O
1862	O
–	O
1938	O
)	O
and	O
used	O
extensively	O
for	O
many	O
years	O
to	O
provide	O
engineers	O
with	O
fast	O
graphical	O
calculations	O
of	O
complicated	O
formulas	O
to	O
a	O
practical	O
precision	O
.	O
</s>
<s>
Nomograms	B-Application
use	O
a	O
parallel	O
coordinate	O
system	O
invented	O
by	O
d'Ocagne	O
rather	O
than	O
standard	O
Cartesian	O
coordinates	O
.	O
</s>
<s>
A	O
nomogram	B-Application
consists	O
of	O
a	O
set	O
of	O
n	O
scales	O
,	O
one	O
for	O
each	O
variable	O
in	O
an	O
equation	O
.	O
</s>
<s>
Nomograms	B-Application
flourished	O
in	O
many	O
different	O
contexts	O
for	O
roughly	O
75	O
years	O
because	O
they	O
allowed	O
quick	O
and	O
accurate	O
computations	O
before	O
the	O
age	O
of	O
pocket	O
calculators	O
.	O
</s>
<s>
Results	O
from	O
a	O
nomogram	B-Application
are	O
obtained	O
very	O
quickly	O
and	O
reliably	O
by	O
simply	O
drawing	O
one	O
or	O
more	O
lines	O
.	O
</s>
<s>
The	O
user	O
does	O
not	O
even	O
need	O
to	O
know	O
the	O
underlying	O
equation	O
the	O
nomogram	B-Application
represents	O
.	O
</s>
<s>
In	O
addition	O
,	O
nomograms	B-Application
naturally	O
incorporate	O
implicit	O
or	O
explicit	O
domain	O
knowledge	O
into	O
their	O
design	O
.	O
</s>
<s>
For	O
example	O
,	O
to	O
create	O
larger	O
nomograms	B-Application
for	O
greater	O
accuracy	O
the	O
nomographer	O
usually	O
includes	O
only	O
scale	O
ranges	O
that	O
are	O
reasonable	O
and	O
of	O
interest	O
to	O
the	O
problem	O
.	O
</s>
<s>
Many	O
nomograms	B-Application
include	O
other	O
useful	O
markings	O
such	O
as	O
reference	O
labels	O
and	O
colored	O
regions	O
.	O
</s>
<s>
Like	O
a	O
slide	O
rule	O
,	O
a	O
nomogram	B-Application
is	O
a	O
graphical	O
analog	O
computation	O
device	O
.	O
</s>
<s>
Unlike	O
the	O
slide	O
rule	O
,	O
which	O
is	O
a	O
general-purpose	O
computation	O
device	O
,	O
a	O
nomogram	B-Application
is	O
designed	O
to	O
perform	O
a	O
specific	O
calculation	O
with	O
tables	O
of	O
values	O
built	O
into	O
the	O
device	O
's	O
scales	O
.	O
</s>
<s>
Nomograms	B-Application
are	O
typically	O
used	O
in	O
applications	O
for	O
which	O
the	O
level	O
of	O
accuracy	O
they	O
provide	O
is	O
sufficient	O
and	O
useful	O
.	O
</s>
<s>
Alternatively	O
,	O
a	O
nomogram	B-Application
can	O
be	O
used	O
to	O
check	O
an	O
answer	O
obtained	O
by	O
a	O
more	O
exact	O
but	O
error-prone	O
calculation	O
.	O
</s>
<s>
Other	O
types	O
of	O
graphical	O
calculators	O
—	O
such	O
as	O
intercept	O
charts	O
,	O
trilinear	O
diagrams	O
,	O
and	O
hexagonal	O
charts	O
—	O
are	O
sometimes	O
called	O
nomograms	B-Application
.	O
</s>
<s>
These	O
devices	O
do	O
not	O
meet	O
the	O
definition	O
of	O
a	O
nomogram	B-Application
as	O
a	O
graphical	O
calculator	O
whose	O
solution	O
is	O
found	O
by	O
the	O
use	O
of	O
one	O
or	O
more	O
linear	O
isopleths	O
.	O
</s>
<s>
A	O
nomogram	B-Application
for	O
a	O
three-variable	O
equation	O
typically	O
has	O
three	O
scales	O
,	O
although	O
there	O
exist	O
nomograms	B-Application
in	O
which	O
two	O
or	O
even	O
all	O
three	O
scales	O
are	O
common	O
.	O
</s>
<s>
An	O
example	O
of	O
this	O
type	O
of	O
nomogram	B-Application
is	O
shown	O
on	O
the	O
right	O
,	O
annotated	O
with	O
terms	O
used	O
to	O
describe	O
the	O
parts	O
of	O
a	O
nomogram	B-Application
.	O
</s>
<s>
For	O
example	O
,	O
the	O
nomogram	B-Application
at	O
the	O
top	O
of	O
this	O
article	O
could	O
be	O
constructed	O
as	O
a	O
parallel-scale	O
nomogram	B-Application
because	O
it	O
can	O
be	O
expressed	O
as	O
such	O
a	O
sum	O
after	O
taking	O
logarithms	O
of	O
both	O
sides	O
of	O
the	O
equation	O
.	O
</s>
<s>
The	O
sample	O
isopleth	O
shown	O
in	O
red	O
on	O
the	O
nomogram	B-Application
at	O
the	O
top	O
of	O
this	O
article	O
calculates	O
the	O
value	O
of	O
T	O
when	O
S=	O
7.30	O
and	O
R	O
=	O
1.17	O
.	O
</s>
<s>
Note	O
that	O
any	O
variable	O
can	O
be	O
calculated	O
from	O
values	O
of	O
the	O
other	O
two	O
,	O
a	O
feature	O
of	O
nomograms	B-Application
that	O
is	O
particularly	O
useful	O
for	O
equations	O
in	O
which	O
a	O
variable	O
cannot	O
be	O
algebraically	O
isolated	O
from	O
the	O
other	O
variables	O
.	O
</s>
<s>
Nomograms	B-Application
for	O
more	O
than	O
three	O
variables	O
can	O
be	O
constructed	O
by	O
incorporating	O
a	O
grid	O
of	O
scales	O
for	O
two	O
of	O
the	O
variables	O
,	O
or	O
by	O
concatenating	O
individual	O
nomograms	B-Application
of	O
fewer	O
numbers	O
of	O
variables	O
into	O
a	O
compound	O
nomogram	B-Application
.	O
</s>
<s>
Nomograms	B-Application
have	O
been	O
used	O
in	O
an	O
extensive	O
array	O
of	O
applications	O
.	O
</s>
<s>
The	O
work	O
of	O
Lawrence	O
Henderson	O
,	O
in	O
which	O
nomograms	B-Application
were	O
used	O
to	O
correlate	O
many	O
different	O
aspects	O
of	O
blood	O
physiology	O
.	O
</s>
<s>
It	O
was	O
the	O
first	O
major	O
use	O
of	O
nomograms	B-Application
in	O
the	O
United	O
States	O
and	O
also	O
the	O
first	O
medical	O
nomograms	B-Application
anywhere	O
.	O
</s>
<s>
These	O
nomograms	B-Application
often	O
included	O
markings	O
for	O
standard	O
dimensions	O
and	O
for	O
available	O
manufactured	O
parts	O
.	O
</s>
<s>
Aeronautics	O
,	O
in	O
which	O
nomograms	B-Application
were	O
used	O
for	O
decades	O
in	O
the	O
cockpits	O
of	O
aircraft	O
of	O
all	O
descriptions	O
.	O
</s>
<s>
As	O
a	O
navigation	O
and	O
flight	O
control	O
aid	O
,	O
nomograms	B-Application
were	O
fast	O
,	O
compact	O
and	O
easy-to-use	O
calculators	O
.	O
</s>
<s>
The	O
nomogram	B-Application
below	O
performs	O
the	O
computation	O
:	O
</s>
<s>
This	O
nomogram	B-Application
is	O
interesting	O
because	O
it	O
performs	O
a	O
useful	O
nonlinear	O
calculation	O
using	O
only	O
straight-line	O
,	O
equally	O
graduated	O
scales	O
.	O
</s>
<s>
For	O
example	O
,	O
it	O
is	O
the	O
parallel-resistance	O
formula	O
in	O
electronics	O
,	O
and	O
the	O
thin-lens	O
equation	O
in	O
optics	B-Algorithm
.	O
</s>
<s>
It	O
also	O
demonstrates	O
that	O
an	O
object	O
at	O
a	O
distance	O
of	O
56cm	O
from	O
a	O
lens	O
whose	O
focal	B-Algorithm
length	I-Algorithm
is	O
24cm	O
forms	O
a	O
real	O
image	O
at	O
a	O
distance	O
of	O
42cm	O
.	O
</s>
<s>
The	O
nomogram	B-Application
below	O
can	O
be	O
used	O
to	O
perform	O
an	O
approximate	O
computation	O
of	O
some	O
values	O
needed	O
when	O
performing	O
a	O
familiar	O
statistical	O
test	O
,	O
Pearson	B-General_Concept
's	I-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
This	O
nomogram	B-Application
demonstrates	O
the	O
use	O
of	O
curved	O
scales	O
with	O
unevenly	O
spaced	O
graduations	O
.	O
</s>
<s>
This	O
allows	O
five	O
different	O
nomograms	B-Application
to	O
be	O
incorporated	O
into	O
a	O
single	O
diagram	O
.	O
</s>
<s>
In	O
performing	O
the	O
test	O
,	O
Yates	B-General_Concept
's	I-General_Concept
correction	I-General_Concept
for	I-General_Concept
continuity	I-General_Concept
is	O
often	O
applied	O
,	O
and	O
simply	O
involves	O
subtracting	O
0.5	O
from	O
the	O
observed	O
values	O
.	O
</s>
<s>
A	O
nomogram	B-Application
for	O
performing	O
the	O
test	O
with	O
Yates	O
's	O
correction	O
could	O
be	O
constructed	O
simply	O
by	O
shifting	O
each	O
"	O
observed	O
"	O
scale	O
half	O
a	O
unit	O
to	O
the	O
left	O
,	O
so	O
that	O
the	O
1.0	O
,	O
2.0	O
,	O
3.0	O
,	O
...	O
graduations	O
are	O
placed	O
where	O
the	O
values	O
0.5	O
,	O
1.5	O
,	O
2.5	O
,	O
...	O
appear	O
on	O
the	O
present	O
chart	O
.	O
</s>
<s>
Although	O
nomograms	B-Application
represent	O
mathematical	O
relationships	O
,	O
not	O
all	O
are	O
mathematically	O
derived	O
.	O
</s>
<s>
The	O
pair	O
of	O
nomograms	B-Application
at	O
the	O
top	O
of	O
the	O
image	O
determine	O
the	O
probability	O
of	O
occurrence	O
and	O
the	O
availability	O
,	O
which	O
are	O
then	O
incorporated	O
into	O
the	O
bottom	O
multistage	O
nomogram	B-Application
.	O
</s>
<s>
Lines	O
8	O
and	O
10	O
are	O
'	O
tie	O
lines	O
 '	O
or	O
'	O
pivot	O
lines	O
 '	O
and	O
are	O
used	O
for	O
the	O
transition	O
between	O
the	O
stages	O
of	O
the	O
compound	O
nomogram	B-Application
.	O
</s>
<s>
The	O
final	O
pair	O
of	O
parallel	O
logarithmic	O
scales	O
(	O
12	O
)	O
are	O
not	O
nomograms	B-Application
as	O
such	O
,	O
but	O
reading-off	O
scales	O
to	O
translate	O
the	O
risk	O
score	O
(	O
11	O
,	O
remote	O
to	O
extremely	O
high	O
)	O
into	O
a	O
sampling	O
frequency	O
to	O
address	O
safety	O
aspects	O
and	O
other	O
'	O
consumer	O
protection	O
 '	O
aspects	O
respectively	O
.	O
</s>
<s>
This	O
risk	O
assessment	O
nomogram	B-Application
was	O
developed	O
by	O
the	O
UK	O
Public	O
Analyst	O
Service	O
with	O
funding	O
from	O
the	O
UK	O
Food	O
Standards	O
Agency	O
for	O
use	O
as	O
a	O
tool	O
to	O
guide	O
the	O
appropriate	O
frequency	O
of	O
sampling	O
and	O
analysis	O
of	O
food	O
for	O
official	O
food	O
control	O
purposes	O
,	O
intended	O
to	O
be	O
used	O
to	O
assess	O
all	O
potential	O
problems	O
with	O
all	O
foods	O
,	O
although	O
not	O
yet	O
adopted	O
.	O
</s>
