43. When the barrier AA´ is held oblique to the current, the stream line xB is curved to the branch point B on AA´ (fig. 7), and so must be excluded from the boundary of u; the conformal representation is made now with d[Omega] [root](b - a·b - a´) -------- = - ---------------------------- (1) du (u - b) [root](u - a·u - a´) dw m 1 m´ 1 m + m´ u - b -- = - ---- ----- - ---- -----, = - ------ · -------------, du [pi] u - j [pi] u - j [pi] u - j·u - j´ mj´ + m´j b = ---------, (2) m + m´ taking u = [oo] at the source where [phi] = [oo], u = b at the branch point B, u = j, j´ at the end of the two diverging streams where [phi] = -[oo]; while [psi] = 0 along the stream line which divides at B and passes through A, A´; and [psi] = m, -m´ along the outside boundaries, so that m/Q, m´/Q is the final breadth of the jets, and (m + m´)/Q is the initial breadth, c1 of the impinging stream. Then /b - a´ /u - a /b - a /u - a´ ch ½[Omega] = / ------ / -----, sh ½[Omega] = / ------ / ------, (3) \/ a - a´ \/ u - b \/ a - a´ \/ u - b 2b - a - a´ N ch [Omega] = ----------- - -----, a - a´ u - b / [root](2·a - u·u - a´) sh [Omega] = / N----------------------, \/ u - b a - b·b - a´ N = 2------------. (4) a - a´ Along a jet surface, q = Q, and ch[Omega] = cos [theta] = cos [alpha] - ½sin² [alpha](a - a´)/(u - b), (5) if [theta] = [alpha] at the source x of the jet xB, where u = [oo]; and supposing [theta] = [beta], [beta]´ at the end of the streams where u = j, j´, u - b ½ sin² [alpha] u - j cos[theta] - cos[beta] ----- = -------------------------, ------ = ½ sin² [alpha]-----------------------------------------------------, a - a´ cos [alpha] - cos [theta] a - a´ (cos [alpha] - cos [beta])(cos [alpha] - cos [theta]) u - j´ cos [theta] - cos [beta]´ ----- = ½ sin² [alpha]------------------------------------------------------; (6) a - a´ (cos [alpha] - cos [beta]´)(cos [alpha] - cos [theta]) and [psi] being constant along a stream line d[phi] dw ds d[phi] dw du ------ = --, Q -------- = -------- = -- --------, du du d[theta] d[theta] du d[theta] [pi]Q ds [pi] ds (cos [alpha] - cos [beta])(cos [alpha] - cos [beta]´)sin[theta] ------ -------- = ---- -------- = ---------------------------------------------------------------------------------, m + m´ d[theta] c d[theta] (cos [alpha] - cos [theta])(cos [theta] - cos [beta])(cos [theta] - cos [alpha]´)