by the preceding work, that the coefficient of uu' is zero; the coefficient of *vv',* 3σπ; and the coefficient of ww', 5σπ. Adding, we get the whole kinetic energy due to the vector-potential arising from *e* and the electric displacement arising from *e'*

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We can get that part of the kinetic energy due to the vector-potential arising from *e'* and the electric displacement from *e* by writing *e'* for *e,* and *u', v', w'* for *u, v, w* respectively. Hence, that part of the kinetic energy which is multiplied by *ee'*

or, substituting for σ its value,

Or if *q* and *q'* be the velocities of the spheres, and ε the angle between their directions of motion, this part of the kinetic energy

and the whole kinetic energy due to the electrification

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If *x, y, z* be the coordinates of the centre of one sphere, *x', y', z'* those of the other, we may write the last part of the kinetic energy in the form

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

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