Horses in one of the many ranches near Waimea. Big Island. AMERICAN INVASION. Many things have happened in the streets of Hawaii since it landed in January 1778 the first westerner, Captain James Cook, who named his discovery with the name of the Sandwich Islands. After a trip to the north Pacific, Cook returned to Hawaii for the winter, but the previously friendly relations with the Hawaiians had deteriorated and was killed during a punitive expedition against them in 1779. About 1790, the West had settled on the island and contagious diseases and alcoholism decimated the number of native inhabitants. Between 1790 and 1910, the islands were united under King Kamehameha the Great, whom still revere some voices against the U.S. occupation placing flowers at the statue erected in his honor in the town of Kapaau on the Big Island, and there is a second Hale Ali'iolani replica front Honolulu.