The  homeowners installation manual  (probably from the late teens or
into the 1920's) for my  Mills Violano calls it a "Tremolo Adjustment"
or a "Tremolo Tail Piece Shaker".  However, the 1984 book by Art Reblitz
and Mike Kitner says on page 38, as quoted, " ... producing a tremolo
(or more accurately, a vibrato)".

The strings are tuned with the vertical "tremolo" rod and weight
centered and hanging free, so that when the tremolo is activated, the
tail piece is pushed forward from the center and then back from the
center position, and so on.  It seems to me that this would raise the
pitch only, as it tightens the strings.

As well as sounding colorful, these continuing small changes in pitch
tend to mask any shortcomings of the tuning.  If you're lucky, the
speed attained won't cause the G-string weight to oscillate up and down.

Art Reblitz said it all in  991012 Digest.  I used to sell musical
instruments, and these two words were consistently incorrectly used.
Interesting!

Regards,

Dave Zeffertt