The authorities, intensely disappointed at this almost ridiculous result, refused to furnish direct assistance to any farther attempts at arctic explorations.  The States-General however offered a reward of twenty-five thousand florins to any navigators who might succeed in discovering the northern passage, with a proportionate sum to those whose efforts in that direction might be deemed commendable, even if not crowned with success.

Stimulated by the spirit of adventure and the love of science far more than by the hope of gaining a pecuniary prize, the undaunted Barendz, who was firm in the faith that a pathway existed by the north of Nova Zembla and across the pole to farthest Ind, determined to renew the attempt the following summer.  The city of Amsterdam accordingly, early in the year 1596, fitted out two ships.  Select crews of entirely unmarried men volunteered for the enterprise.  John Cornelisz van der Ryp, an experienced sea-captain, was placed in charge of one of the vessels, William Barendz was upper pilot of the other, and Heemskerk, “the man who ever steered his way through ice or iron,” was skipper and supercargo.

The ships sailed from the Vlie on the 18th May.  The opinions of Peter Plancius prevailed in this expedition at last; the main object of both Ryp and Barendz being to avoid the fatal, narrow, ice-clogged Waigats.  Although identical in this determination, their views as to the configuration of the land and sea, and as to the proper course to be steered, were conflicting.  They however sailed in company mainly in a N.E. by N. direction, although Barendz would have steered much more to the east.

On the 5th June the watch on deck saw, as they supposed, immense flocks of white swans swimming towards the ships, and covering the sea as far as the eye could reach.  All hands came up to look at the amazing spectacle, but the more experienced soon perceived that the myriads of swans were simply infinite fields of ice, through which however they were able to steer their course without much impediment, getting into clear sea beyond about midnight, at which hour the sun was one degree above the horizon.

Proceeding northwards two days more they were again surrounded by ice, and, finding the “water green as grass, they believed themselves to be near Greenland.”  On the 9th June they discovered an island in latitude, according to their observation, 74 deg. 30’, which seemed about five miles long.  In this neighbourhood they remained four days, having on one occasion a “great fight which lasted four glasses” with a polar bear, and making a desperate attempt to capture him in order to bring him as a show to Holland.  The effort not being successful, they were obliged to take his life to save their own; but in what manner they intended, had they secured him alive, to provide for such a passenger in the long voyage across the North Pole to China, and thence back to Amsterdam, did not appear.  The attempt illustrated the calmness, however, of those hardy navigators.  They left the island on the 13th June, having baptised it Bear Island in memory of their vanquished foe, a name which was subsequently exchanged for the insipid appellation of Cherry Island, in honour of a comfortable London merchant who seven years afterwards sent a ship to those arctic regions.