The limits on θ are determined by finding the values of θ which make a and b both positive. For convenience, let the former be denoted by C$_{2}$$_{n}$ − 1 and the latter by C$_{2}$$_{n}$ . If we let θ$_{1}$ = (2 n − 2) π/ (2 n − 1), θ$_{2}$ = (2 n − 1) π/ 2 n and θ$_{3}$ = 2 nπ/ (2 n + 1), then it follows from the above discussion that C$_{2}$$_{n}$ − 1 lies beneath C$_{2}$$_{n}$ . By plugging θ = θ$_{1}$ into (51), we find that C$_{2}$$_{n}$ − 1 has an asymptote at a = tan $^{2}$( π/ (4 n − 2)) and by plugging θ = θ$_{3}$ into (53), we find that C$_{2}$$_{n}$ has an asymptote at a = tan $^{2}$( π/ (4 n + 2)). To test whether the process is allowed between these two or outside them, we study a test point. If b = 0 and a > 0, then θ exists and is given by Q − $^{1}$(1). Since (2 n − 3) π/ (2 n − 1) ≤ θ ≤ π , it follows that sin $^{2}$( θ/ 2) ≥ cos $^{2}$( π/ 2 n ) but from inequality (45) we need sin $^{2}$( θ/ 2) ≤ 0 at such a point. Thus the allowed region for the process is between the curves C$_{2}$$_{n}$ − 1 and C$_{2}$$_{n}$ . 18