English: Diagram showing a volume ${\displaystyle V}$ split into two parts, ${\displaystyle V_{1}}$ and ${\displaystyle V_{2}}$, illustrating that the flux ${\displaystyle \Phi }$ of a vector field out of the original volume is equal to the sum of the fluxes out of each component volume. This is because flux out of ${\displaystyle V_{1}}$ through surface ${\displaystyle S_{3}}$ is flux into ${\displaystyle V_{2}}$, so the flux through ${\displaystyle S_{3}}$ cancels out. This is part of a series of diagrams illustrating the proof of the divergence theorem.