| σ = | Q | 1 | . | |
| 4πabc | √(x² / a4 + y² / b4 + z² / c4) |
and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression,
| V = ∫ | σdS | = | Q | ∫ | dS |
| r | 4πabc | r √(x² / a4 + y² / b4 + z² / c4) |
(4).
Accordingly the capacity C of the ellipsoid is given by the equation
| 1 | = | 1 | ∫ | dS |
| C | 4πabc | √(x² + y² + z²) √(x² / a4 + y² / b4 + z² / c4) |
(5).
It has been shown by Professor Chrystal that the above integral may also be presented in the form,[7]
| 1 | = ½ ∫∞0 | dλ |
| C | √{(a² + λ) (b² + λ) (c² + λ)} |
(6).