1. On October 13, 1778, British explorer Captain James Cook arrived in Hawaii for the first time. He named the island group the Sandwich Islands and his arrival marked the beginning of major Western involvement in Hawaiian affairs.

2. On October 13, 1819, King Kamehameha I of Hawaii died after a long reign of over 30 years. He is credited with unifying the Hawaiian Islands under one kingdom and establishing a stable government and economy.

3. In 1843, on October 13, British Admiral Richard Thomas and French Rear Admiral Louis Tromelin arrived in Hawaii aboard their respective warships to demand compensation for damages done to their nationals' property during a recent coup. This event is known as the Paulet Affair and marked a significant challenge to Hawaiian sovereignty during a time of political instability.

4. On October 13, 1900, the first territorial legislature of Hawaii opened its first session in Honolulu. This marked a significant turning point for the islands as they transitioned from a monarchy to a US territory.

5. In 1970, on October 13, the Kilauea Iki volcanic eruption began on the island of Hawaii. It lasted for over 2 years and resulted in the formation of a new vent and lava lake within the Kilauea caldera. The eruption also served as a significant research opportunity for geologists and volcanologists from around the world.