pipe stem

From a site dating back to at least the 1850's.

Howdy All! I have what looks like a pipe stem to me, but I?d like some input. I am not saying it is from the following era, but for context I found this on a property with a house from about 1860 in central New Jersey. (Permission was of course obtained for searching and retrieval.) The land...

These were all found at the same spot. The small pieces are regular clay pipe stem pieces but what is the larger one? It appears to be clay and somewhat crudely made but has the letter "C" on the larger end as seen in the picture.