Then

KH2 = OH2 − OK2,

(10)

OK2 sin2 θ = CC′2 = G2 − 2GG′ cos θ + G′2,

(11)

A2 sin2 θ (dθ/dt)2 = 2A2n2 (F − cos θ) sin2 θ − G2 + 2GG′ cos θ − G′2;

(12)

and putting cos θ = z,

( dz) = 2n2 (F − z) (1 − z2) − (G2 − 2GG′z + G′2) /A2
dt

(13)