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'
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
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