Cook Islands. Capt. Cook in 1773 discovered a number of islands between 8° and 23° south latitude and 157° and 170° west longitude. These number six principal and a number of smaller islands, which with several others were attached to New Zealand for administrative purposes in June, 1901. Rarotonga, the chief island, is 20 miles in circumference and has 2,060 inhabitants. The total population is 6,324.