Accordingly he mustered his arms in double strength--eight army corps and the guard, a powerful cavalry force under Murat, and an auxiliary army from Bavaria. At once his officers began to study the possible roads from central to northern Germany, and the best appeared both to him and to them to be by the way of Bamberg. By September twenty-fifth the new levies of a hundred thousand well-drilled recruits were ready, and on that day the Emperor left Paris for Mainz with all possible secrecy. On the other hand, the Prussian king knew not whither to turn. The Bavarian agent in Paris recorded it as his opinion that Frederick William yielded to the war party in order that, having been defeated in one battle, his people would understand the impossibility of resistance and permit him to make the best terms possible. Whether this be true or not, the unhappy and unready King, unable any longer either to secure advantage from the misfortune of his neighbors, or to pursue a policy of weakness and indecision, with England still hostile and Russia not ardent, finally decided for war. On September twenty-fourth he arrived at his headquarters in Naumburg, and on October first the Prussian minister in Paris presented his sovereign's ultimatum to France. Germany must be evacuated, Wesel restored, and no obstacle be thrown in the way of a North German Confederation. The term set for a reply was October eighth. Napoleon received the paper on October seventh, in Bayreuth, and his columns were already marching. The answer was, of course, in the facts, which were a quite sufficient refusal.