Galileo, Eotvos and the Fifth Force

Graphic - fifthforce
http://commons.wikimedia.org/wiki/File:Leaning_tower_of_pisa_4.png
Most people have heard the story about Galileo’s fun experiments at the Tower of Pisa, designed to show that, contrary to the prevailing Aristotlean view, all bodies have the same free-fall acceleration (if drag forces can be neglected) so that the graviational mass mG and the inertial mass mI of an object are equal. The story is probably untrue. But (with pendulum experiments) Galileo is generally credited with having shown that
\[ \frac{m_I}{m_G} = 1 \hspace*{1cm} \mbox{{to one part in }} \hspace*{0.5cm} 10^3 \]
This kind of experiment has subsequently been repeated, many times. Most famously in 1889 Eotvos showed that
\[ \frac{m_I}{m_G} = 1 \hspace*{1cm} \mbox{{to one part in }} \hspace*{0.5cm} 10^9 \]
In the last decade, however, Eotvos’ results have been reexamined. Some claim to have found evidence that the equality mI=mG is not (quite) correct...and thence evidence of a new ‘fundamental’ force, called (imaginatively) the ‘Fifth Force’. The ‘evidence’ does not appear to have withstood closer scrutiny.