A 3rd bridge is created when a string is divided in such a manner that the division acts as a brake between its two segments and this brake is also able to be freely moved. This is typically done with a rigid slide such as a glass bottle, vial, or metal rod. Instruments that use this feature also typically have ways of amplifying both end of the strings sound. The sounds produced from the unexcited end of the string (the reciprocal end) are called ghost tones. When this division moves the two halves of the string move in pitch in reciprocal motion as one segment gets longer the other shorter and vice versa. This is a characteristic build of instruments made by Glenn Branca, Yuri Landman, Hans Reichel and Bart Hopkin and cal also be seen in the Kithara instruments by Harry Partch and the Pencilina made by Bradford Reed. Typically this is thought of as different then prepared guitar, slide guitar, or prepared piano because the inactive end of the string in 3rd bridge setups are also used for acoustic purposes, but cannot be typically heard on prepared instruments. The 3rd bridge principle is considered a specific example of Shared Resonance.
floating bridges and more complex setups that are about the way resonance travels to different harmonic structures has been moved to Shared Resonance. 1)
Wikipedia article on the third bridge- 2)
Used as a building technique by Yuri Landman and Glenn Branca.