ρ δx · ÿ = δ (P · ∂y/∂x).
(38)
Neglecting the vertical acceleration we have P = gρx, whence
| ∂2y | = g | ∂ | ( x | ∂y | ). |
| ∂t2 | ∂x | ∂x |
(39)
Assuming that y varies as eiσt we have
| ∂ | ( x | ∂y | ) + ky = 0. |
| ∂x | ∂x |
(40)
provided k = σ2/g. The solution of (40) which is finite for x = 0 is readily obtained in the form of a series, thus
| y = C ( 1 − | kx | + | k2x2 | − ... ) = CJ0(z), |
| 12 | 1222 |