(1)

dw= − m 1 m′ 1,
du πu − j πu − j
= − m + m′· u − b,
π u − j·u − j′
b = mj′ + m′j,
m + m′

(2)

taking u = ∞ at the source where φ = ∞, u = b at the branch point B, u = j, j′ at the end of the two diverging streams where φ = −∞; while ψ = 0 along the stream line which divides at B and passes through A, A′; and ψ = 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

ch ½Ω = √ b − a′ u − b, sh ½Ω = √ b − a u − a′,
a − a′ u − ba − a′ u − b

(3)

ch Ω = 2b − a − a′ N,
a − a′ u − b
sh Ω = √ N √ (2·a − u·u − a′),
u − b