In the Italian campaign of 1796-97, when the Austrians advanced against Bonaparte on both sides of Lake Garda, he united his forces at the foot of the lake; and, by throwing a strong force against one and then against the other of the advancing armies, defeated both in succession before they could unite. In these manœuvres, with a total force of forty-five thousand soldiers, he defeated seventy-two thousand Austrians.

In the campaigns of Arcole and Rivoli, the Austrians likewise advanced with divided forces. In the former, forty thousand Frenchmen opposed seventy thousand Austrians; in the latter, forty-four thousand Frenchmen opposed sixty-five thousand Austrians. By skilful combinations, similar to those just described, Bonaparte defeated the Austrian armies in both campaigns.

In 1814, when the Prussians, under Blucher, and the Austrians, under Schwarzenberg, were advancing from different points of the French frontier upon Paris, the results obtained by Napoleon's leaving a retarding force before one army, and by massing his remaining forces against the other, were still more remarkable. With a force numerically inferior to either army opposed to him, he succeeded in winning battle after battle. Though in the campaign of 1814 we find strategical problems with which we are not now concerned, yet Napoleon's victories there in the face of such odds show what he might have accomplished had Kray and Melas crossed the French frontiers and advanced on Paris.

But the combination that offered Bonaparte the greatest chance of success yet remains to be considered. Should Masséna be able single-handed to hold in check the Austrians in Italy, Bonaparte could unite the Army of Reserve, forty thousand strong, to Moreau's army of one hundred and thirty thousand. This junction would give Bonaparte one hundred and seventy thousand soldiers with whom to attack the one hundred and twenty thousand Austrians under Kray. With such a superiority in numbers, Bonaparte would probably have annihilated the Austrian forces in the valley of the Danube.

But the mere superiority in numbers, which, by this combination, might have been obtained in Germany, is not the only advantage which Bonaparte could have derived from the positions of the opposing armies. In order to understand the subject better and see, perhaps, in a measure, the whole strategical situation as it appeared to Bonaparte himself, it will be necessary to examine somewhat carefully the positions of the opposing forces, and point out the advantages which the possession of Switzerland gave to the French.

Since Moreau's army was in position in France along the west bank of the Rhine from Strasburg to Bâle, and extended into Switzerland along the south bank of the Rhine from Bâle to Lake Constance, Bonaparte could use either France or Switzerland as a base of operations from which to attack the Austrians in the Black Forest. This angular base gave to Bonaparte a great advantage. His adversary could not know on which side to expect him. By making demonstrations on one side, Bonaparte might deceive Kray as to the real point of attack; then, by massing his forces on the other, he might surprise and overwhelm him. Moreover, by crossing the Rhine in force between Lake Constance and Schaffhausen, he could strike the left flank of the Austrian divisions in the Black Forest, and might be able to defeat them in detail before they could unite. Even should Kray succeed in concentrating his divisions, he would be compelled to face south in order to give battle. In this position, his line of battle being parallel to his line of retreat, he must, if defeated, lose his communications. In this position, defeat meant ruin to his army; for with the loss of his communications he could not escape capture or annihilation.

On the other hand, Bonaparte's line of battle would face the north, and be perpendicular to his line of retreat. If defeated, he could fall back and cross the Rhine with little danger of losing his communications.

By uniting the Army of Reserve to Moreau's army, and by crossing the Rhine in force near Schaffhausen, Bonaparte could not only greatly outnumber Kray upon the battle-field, but could force him to fight in a position where an Austrian defeat would be fatal to the Austrian cause. By this manœuvre Bonaparte would threaten the communications of the enemy without exposing his own, and would, if victorious, decide in a single battle the fate of the Austrians in the valley of the Danube. He could then march rapidly upon the Austrian capital, and could seize the Brenner and Pontebba passes, the possession of which would sever the communications of the Austrians in the valley of the Po. Such a manœuvre would paralyze the operations of Melas in Italy, and compel the Austrian Emperor to sue for peace.

Though this plan offered Bonaparte great results, yet in several respects it was somewhat difficult to execute. In order to gain a favorable position for attacking Kray in the Black Forest, Bonaparte would have to make a flank march from Bâle to Lake Constance; and consequently would have to expose his own flank to the attacks of the enemy. But in this case the French flank would be protected by the Rhine; and as Bonaparte would march rapidly, he would in all probability succeed in crossing the river in force near Lake Constance before his adversary should discover his plan. Nevertheless, this flank march would be attended with considerable danger. In fact, every flank march in the vicinity of an active enemy is dangerous; for a commander who gains a position on the enemy's flank must necessarily expose his own flank to the attacks of the enemy. Even when his flank is protected by a river, he cannot cross it without taking some risks. Had Kray's army been assembled in force near Schaffhausen, where it could have attacked the French divisions in detail as they crossed the Rhine, Bonaparte would have had much difficulty in carrying out successfully this plan of campaign. "Of all the operations of war," says Jomini, "there is none more hazardous and difficult than the passage of a large river in the presence of an enemy."

Had Bonaparte adopted this plan, he would undoubtedly have attempted to deceive Kray as to the real point of attack. If we form a judgment of what he would have done by what he afterwards did in the Ulm campaign, we can safely assume that he would have ordered at least one division to cross the Rhine from France, and to advance directly eastward upon Kray's army in the Black Forest. The march of this division would have deceived Kray, and would probably have led him to expect the entire French army from that direction. Bonaparte could then have made his flank march in safety, and could have crossed the river with little danger of having his divisions defeated in detail.