The Scalar Potential Field

Abstract

Let S be a scalar point-function which may be mapped out in space by a series of level surfaces, upon each of which the scalar has a definite but different constant value. These surfaces divide up the region of space into a series of layers or laminae. Associated therewith is a vector field Vs directed everywhere normal to the level surfaces, i.e. in the direction of the greatest rate of increase of S at any point and having a magnitude equal to that rate of increase. This is expressed by 4.3, namely,

$$ {V_s} = gradS = \nabla S. $$