g armies, in a marshy forest region, intersected in every
direction by well-guarded rivers, was one of his most brilliant
achievements. But his necessities were overwhelming. On the 21st of June
Warsaw was retaken by the Poles, and four days later Charles was obliged
to purchase the assistance of Frederick William by the treaty of
Marienburg. On July 18-20 the combined Swedes and Brandenburgers, 18,000
strong, after a three days' battle, defeated John Casimir's army of
100,000 at Warsaw and reoccupied the Polish capital; but this brilliant
feat of arms was altogether useless, and when the suspicious attitude of
Frederick William compelled the Swedish king at last to open
negotiations with the Poles, they refused the terms offered, the war was
resumed, and Charles concluded an offensive and defensive alliance with
the elector of Brandenburg (treaty of Labiau, Nov. 20) whereby it was
agreed that Frederick William and his heirs should henceforth possess
the full sovereignty of East Prussia.

This was an essential modification of Charles's Baltic policy; but the
alliance of the elector had now become indispensable on almost any
terms. So serious, indeed, were the difficulties of Charles X. in Poland
that it was with extreme satisfaction that he received the tidings of
the Danish declaration of war (June 1, 1657). The hostile action of
Denmark enabled him honourably to emerge from the inglorious Polish
imbroglio, and he was certain of the zealous support of his own people.
He had learnt from Torstensson that Denmark was most vulnerable if
attacked from the south, and, imitating the strategy of his master, he
fell upon her with a velocity which paralysed resistance. At the end of
June 1657, at the head of 8000 seasoned veterans, he broke up from
Bromberg in Prussia and reached the borders of Holstein on the 18th of
July. The Danish army at once dispersed and the duchy of Bremen was
recovered by the Swedes, who in the early autumn swarmed over Jutland
and firmly established themselves in the duchies. But the fortress of
Fredriksodde (Fredericia) held Charles's little army at bay from
mid-August to mid-October, while the fleet of Denmark, after a stubborn
two days' battle, compelled the Swedish fleet to abandon its projected
attack on the Danish islands. The position of the Swedish king had now
become critical. In July an offensive and defensive alliance was
concluded between Denmark and Poland. Still more ominously, the elector