Reo

I found this photo here Tampa's Oldest Automobile - Sticks of Fire

This is a 1908 Reo, which is probably very similar to the one Matthew Nelson had. I imagine his had more seats, because I can't see how half a dozen or more people could fit in that seat.

Here's some fun trivia from the article. Reo was actually an accronym that stood for Ransom Eli Olds. He founded Oldsmobile and lived in Oldsmar. Something tells me he was part of the founding family. The cars were built in Lansing, MI.