What kind of pine tree do we have?

We are trying to identify this pine tree. (without going to the library for identification books-gas prices)

I have not been able to find an easy identification site on-line.

The branches hang downward off a main branch.

Here are new little pinecones next to last years pinecones.
Teeny, tiny pinecones. The discovery of these has caused the search to begin for the name of this tree.
Different stages of the pinecones in our unknown tree.