As an AI language model, I can provide the following five interesting facts about September 8 in New Hampshire history:

1. In 1679, the Province of New Hampshire was established by colonial legislature, separating it from the Massachusetts Bay Colony.

2. On September 8, 1775, New Hampshire soldiers bravely fought in the Battle of Lake Champlain during the American Revolution, which is often considered the first naval battle of that war.

3. The famous Mary Baker Eddy, the founder of the Christian Science movement, was born in Bow, New Hampshire, on September 8, 1821.

4. In 1954, Dartmouth College admitted women for the first time, transforming a previously all-male institution into a coeducational one.

5. On September 8, 1975, the iconic Mount Washington Cog Railway celebrated its centennial anniversary. The railway, which has been in operation for over 150 years, takes visitors to the summit of Mount Washington, the highest peak in New England.