As is well known, the usual form of the Addition-Theorem for Elliptic Functions of several arguments expresses these functions as the quotient of two determinants. When two or more arguments become equal, both numerator and denominator of this quotient vanish, and in seeking to remove the common vanishing factor, Cayley, in his paper “Note sur l'addition des fonctions elliptiques,” in connection with the cases of three and four arguments, brought to light some identities connecting certain alternants. Cayley gave these identities without proof, saying, “Je n'ai pas encore trouvé la loi générale de ces équations.”