following a log file over http

You can do this if the HTTP server accepts requests to return parts of a resource. For example, if an HTTP request contains the header:

Range: bytes=-500

the response will contain the last 500 bytes of the resource. You can fetch that and then parse it into lines, etc. I don't know of any ready-made clients which will do this for you - I'd write a script to do the job.

You can use Hurl to experiment with headers (from publicly available resources).