so that § 34 (4) is satisfied, with
| ƒ′ (ψ′) = | 15 | Ua−2, ƒ (ψ′) = | 15 | Uψ′ a−2; |
| 2 | 2 |
(15)
and (10) reduces to
| p | + V − | 9 | U { ( | x2 | − 1 ) | 2 | − ( | y2 | − ½ ) | 2 | } = constant; |
| ρ | 8 | a2 | a2 |
(16)
this gives the state of motion in M. J. M. Hill’s spherical vortex, advancing through the surrounding liquid with uniform velocity.
39. As an application of moving axes, consider the motion of liquid filling the ellipsoidal case
| x2 | + | y2 | + | z2 | = 1; |
| a2 | b2 | c2 |
(1)