I've used MANY of those clamps reptilezs linked from Amazon on orphaned seatposts. Here's how you use it with the OP's partial seatpost:

1. order Amazon seat-clamp, or scavenge it from bike-shop's junk pile. Or local college student self-serv bike-shop.

2. unscrew two nuts from both sides

3. remove two cupped washers from each side (4 total)

4. slide out clamp part in middle and toss (keep the bolt).

5. slide square bolt through seatpost top

6. slide on larger of cupped clamp washers on each side

7. install seat, rotate clamp washer to hold rails

8. slide on smaller clamp washers, rotate so clamp goes over seat-rails

9. install nuts on each side, rotate/slide seat to proper position

10. tighten nuts.