Did the inventor of basketball, James Naismith, also invent the football helmet?

By Brian Cronin
The Los Angeles Times

One of the most famous sports innovators is Dr. James Naismith, the McGill grad who invented basketball in 1891 at Springfield, Mass. Obviously, though, if Naismith was an instructor before  he invented basketball, he must have been involved in other sports.

One such sport that Naismith was heavily involved in was football, which itself was still in the early years of making its transition from rugby to its own unique sport.

This leads to a great story about the early days of football and Naismith, which is specifically; did James Naismith also invent the football helmet?