The kinetic energy
with similar expressions for G and H.
with similar expressions for and . Since the particles are supposed to be very small, we shall neglect those terms in F which depend on a² and a'².
The part of the kinetic energy we are concerned with involves the product ee': let us first calculate that part of it arising from the product of that part of F due to e with that part of due to e'. We shall take the line joining the particle as the axis of x; and for brevity we shall denote by σ.
The coefficient of uu' in the part of the kinetic energy we are considering
Now, for values of r > R,
where Qn is a zonal harmonic of the nth order; and since the product of two harmonics of different degrees integrated over