[quote name='gjones' timestamp='1398520663' post='2434931']
Handy to whack a sponge under the bridge ashtray, to damp the strings, like James Jamerson used to do. But originally, I think they were put there for purely aesthetic reasons.
[/quote]
According to Fender they were indeed something to mount the foam mute to so not entirely aesthetic...
http://www.fender.com/news/the-precision-bass-in-the-1950s/
"The first commercial unit of the Precision Bass was produced in October 1951. It had a “slab” (non-contoured) ash body with two “horns” (as opposed to the Telecaster’s one; this provided greater balance and was subsequently adapted for the Stratocaster), a one-piece 20-fret maple neck fixed to the body by four screws (despite use of the technically incorrect term “bolt-on”), a single pickup, black pickguard, Kluson tuners, treble-side thumb rest, [b]a string-through-body bridge with a cover (with a mute)[/b], and two pressed fiber bridge saddles."