I'm looking into an interesting possible anomaly in the gravitational constant, the big G that appears in Newton's gravity law: F = GMm/r^2. Gravity is a tiny force, atom for atom, but it is cumulative unlike the electromagnetic (EM) force whose positive and negative components cancel themselves out, so for large masses (M and m) and close distances (r) gravity can dominate the EM force, for example causing chairs, held together by the EM force, to collapse when sat on.
In 1798, Cavendish worked out a way to measure G. He suspended known masses at both ends of a crossbar suspended by a wire, brought another known mass closer at an angle designed to cause a rotation and measured the twist in the wire. Since he know how much force was required to twist the wire, this told him the gravitational force F between the masses and since F = GMm/r^2, and he knew the mass and distances, he was able to find G. Over the centuries, this method has been refined so that the experimental uncertainty in the values they now get for G is smaller. The problem is, the values of G determined in different labs differ several times more than their expected uncertainty, so either the experimenters have underestimated their errors or a new physical process has been revealed.
Always on the lookout for anomalies, I've had a look at some of the values of G published in the third figure in a recent Physics World article (see the reference below) and noticed that there is a weak correlation with latitude. For example, the G that was measured in Birmingham, UK (at 52^o North) was 0.05% larger than the G measured in Boulder, Colorado (at 40^o North). Although the correlation between the various values for G and the latitude is 0.74, there were only 7 values given in this Figure to go on, so I wouldn't claim significance yet.
I do wonder whether MiHsC is causing this, since the acceleration of objects on the Earth with respect to the fixed stars is lower near the poles, but my initial calculations show that the MiHsC effect seems too small. It may be that I need to learn more about what these experiments are actually doing, so I'm going to a Royal Society Workshop on the uncertainties in G at the end of this month to learn a bit more about this problem.
Cartwright, J., 2014. "The lure of G". Physics World, Vol. 27, 2, 2nd February.