(1) In his “Recherches sur les déterminants,” published in the Bulletin of the Royal Academy of Belgium in 1846, Catalan gives a proposition in regard to circulants of the type

which deserves some special attention, as there can be little doubt that it is seriously misleading. Unfortunately, too, it has actually already misled to a considerable extent, the proposition having been reproduced by quite a number of writers without any care being taken to verify it. Even the very latest text-book, that written by Professor Pascal of Pavia and translated into German by H. Leitzmann, gives importance to the proposition, and by omitting the so-called proof diminishes the chance of detection of error.