In the deduction of divergence of orthogonal curvilinear coordinate in the textbook (P.C. Matthews. Vector Calculus. pp105), a rectangle box with length of $h_1\mathrm{d}u_1$, width of $h_2\mathrm{d}u_2$, and height of $h_3\mathrm{d}u_3$ was used to evaluate the total flux in the following formula: $$\nabla\cdot\boldsymbol{v}=\lim_{\delta V\rightarrow0}\frac{1}{\delta V}\oint_{\delta S}\boldsymbol{v}\cdot\boldsymbol{n}\mathrm{d}S$$ Here it first calculates the flux through the left and right surface. I have a question about this statement:"... where $v_1$, $h_2$ and $h_3$ are evaluated at $(u_1+\mathrm{d}u_1/2,u_2,u_3)$". It seems that the textbook holds that $(u_1+\mathrm{d}u_1/2,u_2,u_3)$ is the center of the right surface. But this is obviously wrong, for the length is $h_1\mathrm{d}u_1$ instead of $\mathrm{d}u_1$. I visualize my understanding as follows. my understanding $$\begin{align}\text{Let}~ f=v_1h_2h_3,\\ \iint_{S_1+S_2}\boldsymbol{v}\cdot\boldsymbol{n} \mathrm{d}S&=\left[f(u_1+\frac{h_1\mathrm{d}u_1}{2},u_2,u_3)-f(u_1-\frac{h_1\mathrm{d}u_1}{2},u_2,u_3) \right]\mathrm{d}u_2\mathrm{d}u_3\\ &=\frac{\partial f}{\partial u_1}h_1\mathrm{d}u_1\mathrm{d}u_2\mathrm{d}u_3 \end{align}$$ I could't find $h_1$ in the textbook or other resources. Is it missing or I made a mistake??? Thanks a lot!
