| 1 | dp | + 4πρBy + hx + βy + fz = 0, | |
| ρ | dy |
(12)
| 1 | dp | + 4πρCz + gx + fy + γz = 0, | |
| ρ | dz |
(13)
and integrating
pρ−1 + 2πρ (Ax2 + By2 + Cz2)
+ ½ (αx2 + βy2 + γz2 + 2fyz + 2gzx + 2hxy) = const.,
(14)
so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and dynamical considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and
| α = | 4c2(c2 − a2) | Ω22 − ( | c2 − a2 | Ω2 − η ) | 2 |
| (c2 + a2)2 | c2 + a2 |
| − | 4b2(a2 − b2) | Ω32 − ( | a2 − b2 | Ω3 − ζ ) | 2 | , |
| (a2 + b2)2 | a2 + b2 |