A study of the processes of Mack's brain at this time is not without interest. It shows the danger of intrusting the fate of an army to a man who cannot weigh evidence. Mack was not ignorant of the course of events, though his news generally came late. The mischief was that his brain warped the news. On October 6th he wrote to Vienna that the enemy seemed about to aim a blow at his communications: on October 7th, when he heard of the loss of Donauwörth, he described it as an unfortunate event, which no one thought to be possible. The Archduke now urged the need of an immediate retreat towards Munich, and marched in an easterly direction on Günzburg: another Austrian division of 8,000 men moved on Wertingen, where, on October 8th, it was furiously attacked by the troops of Murat and Lannes. At first the Imperialists firmly kept their ranks; but the unequal contest closed with a hasty flight, which left 2,000 men in the hands of the French Then Murat, pressing on through the woods, cut off Mack's retreat to Augsburg. Yet that general still took a cheerful view of his position. On that same day he wrote from Günzburg that, as soon as the enemy had passed over the Lech, he would cross the Danube and cut their communications at Nördlingen. He wrote thus when Ney's corps was striving to seize the Danube bridges below Ulm. If Mack were to march north-east against the French communications it was of the utmost importance for him to hold the chief of these bridges: but Ney speedily seized three of them, and on the 9th was able to draw closer the toils around Ulm.

From his position at Augsburg the French Emperor now directed the final operations; and, as before Marengo, he gave most heed to that side by which he judged his enemy would strive to break through, in this case towards Kempten and Tyrol. This would doubtless have been Mack's safest course; for he was strong enough to brush aside Soult, gain Tyrol, seal up its valleys against Napoleon, and carry reinforcements to the Archduke Charles. But he was still intent on his Nördlingen scheme, even after the loss of the Danube bridges exposed his march thither to flank attacks from the four French corps now south of the river. Nevertheless, Napoleon's miscalculation of Mack's plans, or, as Thiers has striven to prove, a misunderstanding of his orders by Murat, gave the Austrians a chance such as fortune rarely bestows.[30]

In spite of Ney's protests, one of his divisions, that led by Dupont, had been left alone to guard the northern bank of the Danube, a position where it might have been overwhelmed by an enterprising foe. What is more extraordinary, Dupont, with only 6,000 men, was charged to advance on Ulm, and carry it by storm. On the 11th he accordingly advanced against Mack's fortified camp north of that city. The Austrians met him in force, and, despite the utmost heroism of his troops, finally wrested the village of Hasslach from his grasp; later in the day a cloud of their horsemen, swooping round his right wing, cut up his tired troops, took 1,000 prisoners, and left 1,500 dead and wounded on the field. Among the booty was found a despatch of Napoleon ordering Dupont to carry Ulm by storm—which might have shown them that the French Emperor believed that city to be all but deserted.[31] In truth, Napoleon's miscalculation opened for Mack a path of safety; and had he at once marched away to the north, the whole aspect of affairs might have changed. The Russian vanguard was on the banks of the Inn: all the French, except the relics of Dupont's division, were south of the Danube, and a few vigorous blows at their communications might have greatly embarrassed troops that had little artillery, light stores of ammunition, and lived almost entirely on the produce of the country. We may picture to ourselves the fierce blows that, in such a case, Frederick the Great would have rained on his assailants as he wheeled round on their rear and turned their turning movements. With Frederick matched against Napoleon, the Lech and the Danube would have witnessed a very cyclone of war.

But Mack was not Frederick: and he had to do with a foe who speedily made good an error. On October 13th, when Mack seemed about to cut off the French from the Main, he received news through Napoleon's spies that the English had effected a landing at Boulogne, and a revolution had broken out in France. The tidings found easy entrance into a brain that had a strange bias towards pleasing falsities and rejected disagreeable facts. At once he leaped to the conclusion that the moves of Soult, Murat, Lannes, Marmont, and Ney round his rear were merely desperate efforts to cut back a way to Alsace. He therefore held fast to his lines, made only feeble efforts to clear the northern road, and despatched reinforcements to Memmingen. The next day brought other news; that Memmingen had been invested by Soult; that Ney by a brilliant dash across the Danube at Elchingen had routed an Austrian division there, and was threatening Ulm from the north-east; and that the other French columns were advancing from the south-east. Yet Mack, still viewing these facts in the twilight of his own fancies, pictured them as the efforts of despair, not as the drawing in of the hunter's toils.

He was now almost alone in his reading of events. The Archduke Ferdinand, though nominally in supreme command, had hitherto deferred to Mack's age and experience, as the Emperor Francis enjoined. But he now urged the need of instantly marching away to the north with all available forces. Still Mack clung to his notion that it was the French who were in sore straits; and he forbade the evacuation of Ulm; whereupon the Archduke, with Schwarzenberg, Kollowrath, Gyulai, and all whose instincts or rank prompted and enabled them to defy the madman's authority, assembled 1,500 horsemen and rode off by the northern road. It was high time; for Ney, firmly established at Elchingen, was pushing on his vanguard towards the doomed city: Murat and Lannes were charged to support him on the north bank, while across the river Marmont, and further south Soult, cut off the retreat on Tyrol.

At last the scales fell from Mack's eyes. Even now he protested against the mere mention of surrender. But again he was disappointed. Ney stormed the Michaelsberg north of Ulm, a position on which the Austrians had counted; and on October 17th the hapless commander agreed to terms of capitulation, whereby his troops were to march out and lay down their arms in six days' time, if an Austro-Russian army able to raise the siege did not come on the scene. These conditions were afterwards altered by the captor, who, wheedling his captive with a few bland words, persuaded him to surrender on the 20th on condition that Ney and his corps remained before Ulm until the 25th. This was Mack's last offence against his country and his profession; his assent to this wily compromise at once set free the other French corps for offensive operations; and that too when every day was precious to Austria, Russia, and Prussia.

On October 20th the French Emperor, with a brilliant staff, backed by the solid wall of his Guard and flanked by eight columns of his troops, received the homage of the vanquished. First came their commander, who, bowed down by grief, handed his sword to the victor with the words, "Here is the unfortunate Mack." Then there filed out to the foot of the Michaelsberg 20,000 foot and 3,000 horse, who laid down their arms before the Emperor, some with defiant rage, the most part in stolid dejection, while others flung them away with every sign of indecent joy.[32] As if the elements themselves conspired to enhance the brilliance of Napoleon's triumph, the sun, which had been obscured for days by storm-clouds and torrents of rain, now shone brightly forth, bathing the scene in the mild radiance of autumn, lighting up the French forces disposed on the slopes of that natural amphitheatre, while it cast deep shadows from the long trail of the vanquished beneath. The French were electrified by the sight: the fatigues of their forced marches through the dusty heats of September, and the slush, swamps, and torrents of the last few days were all forgotten, and they hailed with jubilant shouts the chief whose sagacity had planned and achieved a triumph hitherto unequalled in the annals of war. "Our Emperor," said they, "has found out a new way of making war: he no longer makes it with our arms, but with our legs."[33]

Meanwhile the other Austrian detachments were being hunted down. Only a few men escaped from Memmingen into Tyrol: the division, which, if properly supported, might have cut a way through to Nördlingen three days earlier, was now overwhelmed by the troops of Murat and Lannes; out of 13,000 foot-soldiers very few escaped. Most of the horsemen succeeded in joining the Archduke Ferdinand, on whose track Murat now flung himself with untiring energy. The beau sabreur swept through part of Ansbach in pursuit, came up with Ferdinand near Nuremberg, and defeated his squadrons, their chief, with about 1,700 horse and some 500 mounted artillerymen, finally reaching the shelter of the Bohemian Mountains. All the rest of Mack's great array had been engulfed.

Thus closed the first scene of the War of the Third Coalition. Hasty preparations, rash plans, and, above all, Mack's fatal ingenuity in reading his notions into facts—these were the causes of a disaster which ruined the chances of the allies. The Archduke Charles, who had been foiled by Masséna's stubborn defence, was at once recalled from Italy in order to cover Vienna; and, worst of all, the Court of Berlin now delayed drawing the sword.

Yet, even amidst the unstinted boons that she showered on Napoleon by land, Fortune rudely baffled him at sea. When he was hurrying from Ulm towards the River Inn, to carry the war into Austria, he heard that the French navy had been shattered. Trafalgar was fought the day after Mack's army filed out of Ulm. The greatest sea-fight of the century was the outcome of Napoleon's desire that his ships should carry succour to his troops in Italy. For this voyage the Emperor was about to substitute Admiral Rosily for Villeneuve: and the unfortunate admiral, divining that resolve, sought by a bold stroke to retrieve his fortunes. He put to sea, and Trafalgar was the result. It would be superfluous to describe this last and most splendid of Nelson's exploits; but a few words as to the bearing of this great victory on the events of that time may not be out of place. It is certain that Villeneuve at Trafalgar fought under more favourable conditions than in the conflict of July 22nd. He had landed his very numerous sick, his crews had been refreshed and reinforced, and, above all, the worst of the Spanish ships had been replaced by seaworthy and serviceable craft. Yet out of the thirty-three sail of the line, he lost eighteen to an enemy that numbered only twenty-seven sail; and that fact alone absolves him from the charge of cowardice in declining to face Cornwallis and Calder in July with ships that were cumbered with sick and badly needed refitting.