On Tue, 28 Oct 2008 21:03:43 -0500, Ignoramus20172
wrote:

The application is to make a turning handle for a vise, of a mild
steel rod 9/16 in diameter, and two hard bearing balls 1" in
diameter. Obviously, this is not a critical weld and strength
requirements are minimal. The most strain on it would be when it falls
vertically through the vise screw and is stopped by the screw, the
worst outcome is that it will hurt my foot.

So. Is there some way to weld it that would not crack and would hold up?

If the rod end is planar, I'd TIG it. Easy weld. If the rod end can
be made concave on the lathe, cone would do, then I'd silver-braze it.
The silver-brazed joint would be about invisible and have more than
ample strength.