Members of the Society are called Fellows and are permitted to use the 'FCPS' post-nominal title.
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The Society has a reciprocity relationship with American Mathematical Society and Cambridge Philosophical Society, whereby a member of one of the societies can become a member of the other by paying just half the subscription.
The first modern descriptions of these celts were published in the 1890s when Gilbert Walker wrote his "On a curious dynamical property of celts" for the Proceedings of the Cambridge Philosophical Society in Cambridge, England, and "On a dynamical top" for the Quarterly Journal of Pure and Applied Mathematics in Somerville, Mass.