This operation was badly carried out by a leader who was at once relieved of his command. Our troops, after having carried Mulhouse, lost it and were thrown back on Belfort. The work had, therefore, to be recommenced afresh, and this was done from Aug. 14 under a new command. Mulhouse was taken on the 19th, after a brilliant fight at Dornach. Twenty-four guns were captured from the enemy. On the 20th we held the approaches to Colmar, both by the plain and by the Vosges. The enemy had undergone enormous losses and abandoned great stores of shells and forage, but from this moment what was happening in Lorraine and on our left prevented us from carrying our successes further, for our troops in Alsace were needed elsewhere. On Aug. 28 the Alsace army was broken up, only a small part remaining to hold the region of Thann and the Vosges. THE OPERATIONS IN LORRAINE. The purpose of the operations in Alsace was, namely, to retain a large part of the enemy's forces far from the northern theatre of operations. It was for our offensive in Lorraine to pursue still more directly by holding before it the German army corps operating to the south of Metz. This offensive began brilliantly on Aug. 14. On the 19th we had reached the region of Saarburg and that of the Etangs, (lakes,) and we held Dieuze, Morhange, Delme, and Château Salins. On the 20th our success was stopped. The cause is to be found in the strong organization of the region, in the power of the enemy's artillery, operating over ground which had been minutely surveyed, and, finally, in the default of certain units. On the 22d, in spite of the splendid behavior of several of our army corps, notably that of Nancy, our troops were brought back on to the Grand Couronne, while on the 23d and 24th the Germans concentrated reinforcements--three army corps, at least--in the region of Lunéville and forced us to retire to the south. This retreat, however, was only momentary. On the 25th, after two vigorous counter-attacks, one from south to north and the other from west to east, the enemy had to fall back. From that time a sort of balance was established on this terrain between the Germans and ourselves. Maintained for fifteen days, it was afterward, as will be seen, modified to our advantage. OPERATIONS IN BELGIAN LUXEMBOURG. There remained the principal business, the battle of the north--postponed owing to the necessity of waiting for the British Army. On Aug. 20 the concentration of our lines was finished and the General in Chief gave orders for our centre and our left to take the offensive. Our centre comprised two armies. Our left consisted of a third army, reinforced to the extent of two army corps, a corps of cavalry, the reserve divisions, the British Army, and the Belgian Army, which had already been engaged for the previous three weeks at Liège, Namur, and Louvain. [Illustration: [map]]