| = ½ρ ∫ φ | dφ | ds = ½ρ ∫ ψ | dψ | ds. |
| dν | dν |
(7)
For example, in the equilateral triangle of (8) § 28, referred to coordinate axes made by the base and height,
ψ′ = −2Rαβγ/h = −½ Ry [ (h − y)2 − 3x2 ] /h
(8)
| ψ = ψ′ − ½R [ ( 1⁄3 h − y)2 + x2 ] = −½R [ ½h3 + 1⁄3 h2y + h) (x2 − y2) − 3x2y + y3 ] /h |
(9)
and over the base y = 0,
dx/dν = −dx/dy = + ½R ( 1⁄3 h2 − 3x2) / h, ψ = −½R ( 1⁄9 h2 + x2).
(10)