Figure 26.1 The same argument as the last chapter, one dimension up, and deliberately the
same motion: every patch walked counterclockwise and held apart, then closed so
that each interior pair annihilates, leaving the boundary and nothing else.Figure 26.2 The curl is a vector, and a surface can only feel the part of it pointing along
the surface's own normal. That is the whole reason Stokes' theorem dots one
against the other.Figure 26.3 Stokes' theorem needs a normal on the surface and a direction round the
boundary, and it needs them married: choose the normal, and the right hand
decides the other.Figure 26.4
26.2The Divergence Theorem
Figure 26.5 Chapter 23 measured flux across a surface with a boundary — a net in a stream.
Close the surface up and one word changes: outward. There is no longer a
choice about which side counts as positive, because a closed surface has an
inside.Figure 26.6 The cancellation a third time, and for the last: cells shared an edge, patches
shared an edge on a surface, boxes share a face. What leaves one box through
a face enters its neighbour through the very same face, so the two readings are
equal and opposite — one red, one blue — and they annihilate as the boxes close.Figure 26.7