Confused about push/pull of a branch

I can't get a second machine to pull in a branch that's in my remote repository. I'm confused.

The remote is a bare repository on machine_1.

In my working copy on machine_1:

machine_1$ git branch
   master
   search-controller
   use-tiles
* webservices
# The following should not be necessary, as gitk already
# identifies a remotes/origin/webservices, but just to be sporting:
machine_1$ git push origin webservices
Everything up-to-date

Branch webservices was created after the working copy on machine_2 was cloned.

In my working copy on machine_2:

machine_2$ git pull
Password:
# Progress messages, no protests.
machine_2$ git checkout webservices
error: pathspec 'webservices' did not match any file(s) known to git.
machine_2$ git branch
* master
machine_2$

git-config shows the two repository URLs are identical, net of machine_2 having to specify a user name and host. The machine_2 .git/ config shows a section for [branch "master"], but not for webservices. Is that the problem? What's the approved way of adding [branch "webservices"], and what do I put into it?

I've obviously forgotten something. Or never understood something (there's a lot in Git not to understand). How do I get the webservices branch onto machine_2, so I can check it out?

	— F