NI being the demagnetizing force Hi. N may be called, after H. du Bois (Magnetic Circuit, p. 33), the demagnetizing factor, and the ratio of the length of the ellipsoid 2c to its equatorial diameter 2a (= c/a), the dimensional ratio, denoted by the symbol m.
Since
| e = √( 1 − | a² | ) = √( 1 − | 1 | ), |
| c² | m² |
the above expression for N may be written
| N = | 4π | ( | m | log | m + √(m² − 1) | − 1 ) |
| m² − 1 | 2√(m² − 1) | m − √(m² − 1) |
| = | 4π | { | m | log ( m+ √(m² − 1) ) − 1 }, |
| m² − 1 | √(m² − 1) |
from which the value of N for a given dimensional ratio can be calculated. When the ellipsoid is so much elongated that 1 is negligible in relation to m², the expression approximates to the simpler form
| N = | 4π | ( log 2m − 1 ) |
| m² |
(31)
In the case of a sphere, e = O and N = 4⁄3π; therefore from (29)