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Maxwell's multipoles are a natural geometric characterisation of realfunctions on the sphere (with fixed $\ell$). The correlations betweenmultipoles for gaussian random functions are calculated, by mapping thespherical functions to random polynomials. In the limit of high $\ell,$ the2-point function tends to a form previously derived by Hannay in the analogousproblem for the Majorana sphere. The application to the cosmic microwavebackground (CMB) is discussed.Comment: 6 pages, 2 figures (revised version

Correlations between Maxwell's multipoles for Gaussian random functions on the sphere