The constants a ₁, a ₂ , a ₃, A ₀ and A ₁ in Section 5.6.2 are related by (5.213) with ? = - ? _m, = ? _m( m = 1, 2), and, since there are only four equations, it is clear that one constant is undetermined.

When ? = - ? ₁, (5.200) becomes

(E.1)

and for ? = - ? ₁ we have

(E.2)

The addition of these gives

(E.3)

where

(E.4)

and there is an equation similar to (E.3) with ? ₁ replaced by ? ₂. These are sufficient to specify ? ₁ and ? ₃ in terms of C. By expanding (sin ? _m) ^-1 sin 3 ? _m etc. in powers of cos ² ? _m and using the fact that

(E.5)

it can be shown that

(E.6)

(E.7)

(E.8)

for any ?.

To complete the specification we need another equation connecting C and ?. Subtraction of (E.2) from (E.1) gives

and there is again a similar equation with ? ₁, ? ₁ and ? ₂ replaced by ? ₂ , ? ₂ and ? ₁, respectively. On eliminating a ₂ from the two equations, we obtain

(E.9)

where we have used the fact that

cos 3 ? _m = - cos 2 ? _m

and by a...