(7)

yk+1 − yk = a (qk+1 + qk) + 2lsk+1.

(8)

Putting

x + yi = w, p + qi = ω, r + si = σ,

(9)

these three pairs of equations may be replaced by the three equations

Aῶk − Kῶki + 2Taῶk − Ta (σk+1 + σk) = 0,

(10)