The part depending on *p* in the second integral

or (see Maxwell's 'Electricity and Magnetism,' § 405)

Adding this to the term already obtained, we get as the part of the kinetic energy depending on *p*. We have evidently similar expressions for the parts of the kinetic energy depending on *q* and *r*. Hence the part of the kinetic energy with which we are concerned will

By Lagrange's equations, the force on the sphere parallel to the axis of *x*

. |

Similarly, the force parallel to the axis of *y*

, | (5) |

the force parallel to the axis of *z*

where *a _{1}, b_{1}, c_{1}* are the components of magnetic induction at the centre of the sphere due to the external magnet. These forces are the same as would act on unit length of a conductor at the centre of the sphere carrying a current whose components are , , . The resultant force is perpendicular