It was not, in fact, to gain a position on interior lines--with respect to _two_ opponents--that Napoleon pushed his army to Carcare. Before the campaign began he hoped by using the "cannon-road" to destroy the Piedmontese _before the Austrians were in existence at all_ as an army. But on the news from Voltri and Monte Legino he swiftly "concentrated fire, made the breach, and broke the equilibrium" at the spot where the interests and forces of the two Allies converged and diverged. The hypothesis in the first case was that the Austrians were practically non-existent, and the whole object in the second was to breach the now connected front of the Allies ("strategic penetration") and to cause them to break up into two separate systems. More, having made the breach, he had the choice (which he had not before) of attacking _either_ the Austrians or the Sardinians, as every critic has pointed out. Indeed the Austrians offered by far the better target. But he neither wanted nor used the new alternative. His purpose was to crush Piedmont. "My enemies saw too much at once," said Napoleon. Singleness of aim and of purpose, the product of clear thinking and of "personality," was the foundation-stone of the new form of strategy. Relative superiority. In the course of subduing the Sardinians, Napoleon found himself placed on interior lines between two hostile masses, and another new idea, that of "relative superiority." reveals itself. Whereas Souham had been in superior force (90,000 against 70,000), Napoleon (40,000 against 50,000) was not, and yet the Army of Italy was always placed in a position of relative superiority (at first about 3 to 2 and ultimately 2 to 1) to the immediate antagonist. "The essence of strategy," said Napoleon in 1797, "is, with a weaker army, always to have more force at the crucial point than the enemy. But this art is taught neither by books nor by practice; it is a matter of tact." In this he expressed the result of his victories on his own mind rather than a preconceived formula which produced those victories. But the idea, though undefined, and the method of practice, though imperfectly worked out, were in his mind from the first. As soon as he had made the breach, he widened it by pushing out Massena and Laharpe on the one hand and Augereau on the other. This is mere common sense. But immediately afterwards, though preparing to throw all available forces against Colli, he posted Massena and Laharpe at Dego to guard, not like Vandamme on the Lys against a real and pressing enemy, but against a _possibility_, and he only diminished the strength and altered the position of this containing detachment in proportion as the Austrian danger dwindled. Later in his career he defined this offensive-defensive system as "having all possible strength at the decisive point," and "being nowhere vulnerable," and the art of