A note on Maxwellʹs theory of poles

We prove that l successive directional differentiations in Maxwellʹs theory of poles can be equivalently expressed as a summation of 2 l - 1 degree-l zonal harmonics oriented along 2 l - 1 axes. These axes are the Maxwell axes and their combinations. This expression suggests a new method of computing the Maxwell axes and the moment without explicit evaluation of differential forms.