the surface of a sphere vanishes, we may substitute in the integral for ; then, transforming to polars, the integral

:
; |

for values of r < R,

Now is a solid harmonic of the nth order; hence is a solid harmonic of the (n-2)th order; and in particular is a solid harmonic of the second order; and, by the same reasoning as before, we may substitute in the integral for . Now

;
. |

So for values of *r* < R the integral becomes

. |

Adding this to the part of the integral for *r* > R, we get for the coefficient of *uu'* ,. The coefficients of *uv'* and *uw'* vanish by inspection.

The coefficient of *vv'*

Now when *r* > R we may, by the same reasoning as before, substitute for , in the integral, and it becomes