1. The Battle of Hubbardton: On July 3, 1777, the Battle of Hubbardton was fought in Hubbardton, Vermont, which was then a part of New Hampshire. This battle was pivotal for the Revolutionary War as the American forces were able to slow down the British troops' advance towards Saratoga.

2. New Hampshire becomes a state: On July 3, 1776, New Hampshire became the first colony to declare its independence from Great Britain. It was also the ninth state to ratify the United States Constitution in 1788.

3. Mount Washington Auto Road opens: On July 3, 1861, the Mount Washington Auto Road officially opened, providing access to the summit of Mount Washington, which is the highest peak in the Northeastern United States. The road is still in use today and is a popular tourist destination.

4. The University of New Hampshire is founded: On July 3, 1866, the University of New Hampshire was founded in Durham, New Hampshire. It is a public research university and is the flagship university of the University System of New Hampshire.

5. Pinkham Notch Visitor Center opens: On July 3, 1953, the Pinkham Notch Visitor Center in the White Mountain National Forest was opened to the public. The center offers guided walks, exhibits on the natural history of the area, and scenic drives. It is also a popular starting point for hiking and skiing trips.