Answer
The average rate of change of $\rho $ with respect to $T$ from $B$ to $A$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = - 0.000167$ $kg/\left( {{m^3}^\circ C} \right)$
Work Step by Step
From Figure 27 we see that the contour interval is $m = 0.0005$. From $B$ to $A$ it spans five level curves, so the change in altitude is $\Delta altitude = - 0.0025$.
From $B$ to $A$, the horizontal change is the distance $\overline {BA} $. It can be read from Figure 27:
$\Delta horizontal = 15$
So, the average rate of change of $\rho $ with respect to $T$ from $B$ to $A$ is
$\frac{{\Delta altitude}}{{\Delta horizontal}} = \frac{{ - 0.0025}}{{15}} = - 0.000167$ $kg/\left( {{m^3}{\ }^\circ C} \right)$
