(7.142) |

where is real and positive. It follows that

(7.143) | ||

(7.144) |

Let

(7.145) | ||

(7.146) |

Thus, in the meridian plane, the curve corresponds to the ellipse

(7.147) |

We conclude that the surface is an

respectively. Setting , and substituting into the governing equation, (7.86), we obtain

(7.150) |

The solution that satisfied the constraint (7.148) is

(7.151) |

Let be the eccentricity of the spheroid. Thus, , , , and . The constraint (7.149) yields

(7.152) |

Hence,

(7.153) |

Finally, from Equation (7.84),

(7.154) |

which can be integrated to give

(7.155) |

It is easily demonstrated that

(7.156) |

and

(7.157) |

Thus,

(7.158) |

It follows that the added mass of the spheroid is

(7.159) |

where

(7.160) |

is a monotonic function that takes the value when , and asymptotes to as .