We just bought a McPhail upright serial no. 46221. We understand it was made in 1910. It seems to be in very good condition. It has three foot pedals. I am wondering what the middle pedal is used for?

Well, that depends on the piano. Sometimes the middle pedal does nothing but look nice. Sometimes it duplicates the left (soft, half-blow) pedal. Sometimes it is connected to a piece of muffler felt that drops down between the hammers and the strings (a lot of old uprights that were originally so equipt have lost theirs over the years). And some vertical pianos have an honest-to-goodness sostinuto pedal (you will have to ask your piano teacher what that is, it's a special kind of sustain pedal). Very many American pianos of recent years have a sort of "fake sostinuto" that only raises the bass dampers.
Step on the pedal; if nothing happens don't worry about it, you are probably not missing anything. But ask your technician to take a look at it when you get it tuned.

Tom