| HP = | m | − | m | = m | 4dl | . |
| (d − l)² | (d + l)² | (d² − l²)² |
Therefore
| 2ml = M = | (d² − l²)² HP | = | (d² − l²)² HE tan θ | . |
| 2d | 2d |
(44)
And
| I = | M | = | (d² − l²)² HE | tan θ, |
| v | 2dv |
(45)
whence we can find the values of I which correspond to different angles of deflection.
(2) The rod may be placed horizontally east and west in such a position that the direction of the undeflected suspended needle bisects it at right angles. This is known as the “broadside-on” position, and is represented in fig. 7. Let the distance of each pole of the rod AB from the centre of the magnetometer needle = d. Then, since HP, the force at M due to m and −m, is the resultant of m/d² and −m/d², we have
| HP | = | 2l |
| m/d² | d |