Answer
The average rate of change of $\rho $ with respect to $S$ from $B$ to $C$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = 0.000625$ $kg/\left( {{m^3}\cdot ppt} \right)$
Work Step by Step
From Figure 27 we see that the contour interval is $m=0.0005$. From $B$ to $C$ it spans one level curve, so the change in altitude is $\Delta altitude = 0.0005$.
From $B$ to $C$, the horizontal change is the distance $\overline {BC} $. It can be read from Figure 27:
$\Delta horizontal = 0.8$
So, the average rate of change of $\rho $ with respect to $S$ from $B$ to $C$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = \frac{{0.0005}}{{0.8}} = 0.000625$ $kg/\left( {{m^3}\cdot ppt} \right)$
