Per cent humidity
=
e
1
e
2
′
=
D
2
D
2
′
{\displaystyle {\text{Per cent humidity}}={\frac {e_{1}}{e'_{2}}}={\frac {D_{2}}{D'_{2}}}}
71 In this formula
e
1
{\displaystyle e_{1}}
is the pressure of saturated vapor corresponding to the dew point
T
1
{\displaystyle T_{1}}
, and
e
2
′
{\displaystyle e'_{2}}
is the vapor pressure at saturation corresponding to temperature
T
2
{\displaystyle T_{2}}
. It also follows that
D
2
=
D
2
′
×
e
1
e
2
′
{\displaystyle D_{2}=D'_{2}\times {\frac {e_{1}}{e'_{2}}}}
At constant pressure
[30]
D
2
D
1
=
T
1
T
2
′
{\displaystyle {\frac {D_{2}}{D_{1}}}={\frac {T_{1}}{T'_{2}}}}
, or
D
2
=
D
1
T
1
T
2
{\displaystyle D_{2}={\frac {D_{1}T_{1}}{T_{2}}}}
Also if it is assumed
p
v
T
{\displaystyle {\frac {pv}{T}}}
is constant, i.e.,
e
D
T
{\displaystyle {\frac {e}{DT}}}
is constant for saturated water vapor (not exactly correct),
e
1
D
1
T
1
=
e
2
′
D
2
′
t
2
{\displaystyle {\frac {e_{1}}{D_{1}T_{1}}}={\frac {e'_{2}}{D'_{2}t_{2}}}}
Therefore
[31]
e
1
e
2
′
=
D
1
T
1
D
2
′
t
2
{\displaystyle {\frac {e_{1}}{e'_{2}}}={\frac {D_{1}T_{1}}{D'_{2}t_{2}}}}
But substituting
D
2
{\displaystyle D_{2}}
for its value in [30]
e
1
e
2
′
=
D
2
D
2
′
=
per cent of isothermal saturation
{\displaystyle {\frac {e_{1}}{e'_{2}}}={\frac {D_{2}}{D'_{2}}}={\text{per cent of isothermal saturation}}}