On the 4th of May Moreau directed his own corps and that of Lecourbe on Mosskirch; St. Cyr arrived at Geisingen; and Ste. Suzanne, who had been forcing his way through the Black Forest, was at Donaueschingen.

On the following day Kray, having been joined by the remnants of his reserve, beaten at Stokach, took position at Mosskirch with forty thousand men. His right was at Tuttlingen, about twelve miles distant; but Kienmayer and Starray were beyond supporting distance on the north side of the Danube. On this day Moreau attacked Kray with fifty thousand men, and, after hard fighting, succeeded in forcing the Austrians back towards Sigmaringen. But Kray did not retire far. Being anxious for the safety of the Austrian troops at Tuttlingen, he halted, formed line of battle, and with the right of his line strongly re-enforced, attacked the French and drove them from the Tuttlingen-Mosskirch road. This success opened his communications with the Austrians at Tuttlingen, and enabled them to join him. Being thus re-enforced, he again attacked the left flank of Moreau, and attempted to seize the Stokach-Mosskirch road. But in his attempt to outflank the French, he was in turn outflanked by them, and was again compelled to retire.

In the battle of Mosskirch the Austrians lost in killed, wounded, and prisoners, about five thousand men; the French, about three thousand. In this battle both sides fought fiercely, but neither gained a decided success. Nevertheless, Kray saw the necessity of retreating; for St. Cyr, who had taken no part in the battle, was now about to join Moreau; and Ste. Suzanne was pushing rapidly forward towards Mosskirch by way of Tuttlingen. In other words, Kray, with less than fifty thousand men, could not expect to hold his own in a second battle at Mosskirch against the united French corps.

Kray crossed the Danube at Sigmaringen, and, being joined by the two corps of his right wing, retired towards Ulm by way of Rietlingen and Biberach. He was followed by Moreau. Lecourbe marched by way of Memmingen, St. Cyr by way of Biberach, and Ste. Suzanne descended the Danube towards Ulm. At Biberach Kray attempted to make a stand, in order to save the Austrian magazines there, but was defeated with considerable loss. Lecourbe also defeated an Austrian garrison occupying Memmingen, and captured the place.

On the 11th of May Kray continued his retreat on Ulm, which, through the foresight of the Archduke Charles in the preceding year, had been converted into a strongly intrenched camp. At Ulm Kray sought and found safety for his army. Here he collected the shattered remains of his defeated forces, and for several weeks made a successful stand against Moreau. Here, eyeing each other with suspicion, these two armies remained for a time, each ready to take advantage of any false movement of the other, while more stirring operations and greater deeds were happening in the valley of the Po.

It is difficult to estimate accurately the losses sustained by the contending armies in these operations. Probably the loss of the Austrians was about twenty thousand men; that of the French, about fifteen thousand. At the opening of hostilities, Kray's forces, not counting the left wing under the Prince de Reuss, since it took no part in the active operations, numbered ninety-five thousand men. At Ulm Kray had seventy-five thousand. On the other hand, Moreau had crossed the Rhine with one hundred and four thousand soldiers, and had reached Ulm with nearly ninety thousand; but he was about to send fifteen thousand men into Italy, which would leave the opposing armies about equal in numbers.

The time had arrived for the commander of the Army of the Rhine to carry out the agreement entered into between himself and the First Consul. In fact, since the battle of Engen, Bonaparte had awaited anxiously for Moreau to start the promised re-enforcements towards Italy. Fearing that Moreau might still delay in the matter, the First Consul had sent Carnot, the French minister of war, to Moreau's headquarters, in order to make the necessary arrangements, and to insist that the troops should be detached and ordered forward at the earliest possible moment.

Moreau did not comply fully with the agreement entered into with the First Consul, but on the 11th and 12th of May he selected fifteen thousand men from the different French corps, united these troops into a single corps and ordered it to proceed into Italy.

Though Moreau had not succeeded in severing the communications of Kray, and in capturing or destroying his army, he had been generally successful in his manœuvres; he had pushed the Austrians back from Lake Constance, defeated them at Stokach and Engen, forced them to retreat after the battle of Mosskirch, and compelled them to seek security in the intrenched camp of Ulm. Though he had retained General Lecourbe and his corps in the valley of the Danube, and had failed to send into Italy the full number agreed upon in the stipulation with the First Consul, nevertheless, he had weakened his army by fifteen thousand men, and, by so doing, had given Bonaparte the opportunity of bringing to a successful issue one of the most striking and dramatic campaigns of his career.

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