Principal
Formulas
in
Part

Notation
(Chapter
2)
(Measured
value
of
x)
=
x,.,
=
Ox,
(p
13)
where
Xpesy
=
Dest
estimate
for
x,
ox
=
uncertainty
or
error
in
the
measurement.
:
:
Ox
Fractional
uncertainty
=
:
(p.
28)
xbest
Propagation
of
Uncertainties
(Chapter
3)
If
various
quantities
x,
...,
w
are
measured
with
small
uncertainties
ox,
...,
ow,
and
the
measured
values
are
used
to
calculate
some
quantity
g,
then
the
uncertainties
in
x,
...,
w
cause
an
uncertainty
in
g
as
follows:
If
g
is
the
sum
and
difference,
g
=
x
+
+
+
z
—
(u
+

+
w),
then
=
B2+
+
(82)%
+
(Bu)®
+


+
(8w)?
5q
for
independent
random
errors;
<=
&b
++86+06u+
+
ow
always.
(p
60)
If
g
is
th
duct
and
tient,
g
=
,
th
q
is
the
product
and
quotient,
g
=
~—————"—,
then
(
Ox\2
0z\2
ou\2
ow\2
B
(_)
+
o
+
(—)
+
(———)
+
o
+
(——)
X
Z
U
w
oq
J
for
independent
random
errors;
"1'
Ox
0z
Oou
ow
<
—
4
o4
=
=
44+
—
x]
o]
y
W]
)
always.
(p.
61)
If
g
=
Bx,
where
B
i1s
known
exactly, then
8¢
=
Béx.
(p
54)
If
g
is
a
function
of
one
variable,
g(x),
then
d
5g
=
fi
5x.
(p.
65)
If
g
is
a
power,
g
=
X",
then
o
o
1
=

=,
(p.
66)