BRUMAIRE, the name of the second month in the repub lican calendar which was established in France by a decree of the National Convention on Oct. 5 in the year II. (1793), completed with regard to nomenclature by Fabre d'Eglantine, and promul gated in its new form on the 4th of Frimaire in the year II. (Nov. 24 1793). The month of Brumaire began on the day which corresponded, according to the year, to Oct. 22 or 23 of the old calendar, and ended on Nov. 20 or 21. Its name alludes to the fogs and mists frequent at that time of the year.