giving the intrinsic equation.
41. The first problem of this kind, worked out by H. v. Helmholtz, of the efflux of a jet between two edges A and A1 in an infinite wall, is obtained by the symmetrical duplication of the above, with n = 1, b = 0, a′ = −∞, as in fig. 5,
| ch Ω = √ | u − a | , sh Ω = √ | − a | ; |
| u | u |
(1)
and along the jet APJ, ∞ > u = aeπs/c > a,
| sh Ω = i sin θ − i √ | a | = ie−1/2 πs/c, |
| u |
(2)
| PM = ∫∞s sinθ ds = ∫ e−½πs/c ds = | c | e−1/2 πs/c = | c | sin θ, |
| ½π | ½π |
(3)