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We compared the small quantitative changes (range) in G over repeated measures (days) with recently improved methods of determinations and those recorded over 20 years ago. The range in the Newtonian constant of gravitation G is usually in the order of 400 ppm as reflected in experimentally-determined values. The moderate strength negative correlation between daily fluctuations in G, in the range of 3 × 10^{-3} of the average value, and an index of global geomagnetic activity reported by Vladimirsky and Bruns in 1998 was also found for the daily fluctuations in the angular deflection θ (in arcseconds) and geomagnetic activity within 24 hr for the Quinn et al. 2013 data. A temporal coupling between increases of geomagnetic activity in the order of 10^{-9} T with decreases in G in the order of 10^{-14}^{ }m^{3}·kg^{-1}·s^{-2} could suggest a recondite shared source of variance. The energy equivalence for this change in G and geomagnetic activity within 1 L of water is ~3 × 10^{-14} J.

We compared the small quantitative changes (range) in G over repeated measures (days) with recently improved methods of determinations and those recorded over 20 years ago. The range in the Newtonian constant of gravitation G is usually in the order of 400 ppm as reflected in experimentally-determined values. The moderate strength negative correlation between daily fluctuations in G, in the range of 3 × 10^{−3} of the average value, and an index of global geomagnetic activity reported by Vladimirsky and Bruns in 1998 was also found for the daily fluctuations in the angular deflection θ (in arcseconds) and geomagnetic activity within 24 hr for the Quinn et al. 2013 data. A temporal coupling between increases of geomagnetic activity in the order of 10^{−9} T with decreases in G in the order of 10^{−14 }m^{3}·kg^{−1}·s^{−2} could suggest a recondite shared source of variance. The energy equivalence for this change in G and geomagnetic activity within 1 L of water is ~3 × 10^{−14} J.

Gravitational Constant Variations, Geomagnetic Activity, Energy Convergence, Electromagnetic-Gravitational Interactions

The recent quantitative measurements by Quinn et al. [^{−11} m^{3}·kg^{−1}·s^{−2} and 6.67566 × 10^{−11} m^{3}·kg^{−1}·s^{−2}, respectively. The difference in G between the two methods was 4.6 × 10^{−15} m^{3}·kg^{−1}·s^{−2} or ~70 ppm. The difference is within the range of 10^{−4} which was considered by Vladimirskii [

This source involved heliophysical perturbations as inferred by inferences of geomagnetic activity. Subtle variations in G which are systematically and quantitatively related to alterations in geomagnetic activity could be secondary to direct influences upon instrumentation [

According to ^{−3} of an average for G. This value is within error measurement variability of 5.2 × 10^{−3} reported [_{p }values ranged between −8 and +8 nT. In those previous measurements [_{p }values were <15 nT and 6.6675 during the 48 measurements during which the A_{p} values were >30 nT.

The difference in G, 5.3 × 10^{−3}, is equivalent to 5.3 × 10^{−14} m^{3}·kg^{−1}·s^{−2}. The Pearson correlation was calculated from Vladimirsky and Bruns’ data [_{p} indices in their _{p} values.

For the Quinn et al. [^{−1}·s^{−1} per day (range = 31.542 to 31.549) and the Planetary A index (Sec) from http://www.dxlc.com/solar/indices.html (range 2 to 23) during the previous 24 hr for the 10 days measured from 31 August to 11 September 2007 was −0.70 (p < 0.05). The Spearman rho (−0.68, p < 0.05) was comparable indicating the effect was not due to outliers. Each of the 10 averages was based upon 34 values of angular deflection extracted from successive 30 minute (the limit where white noise dominated) data collections. Because G = τΓ^{−1} where τ = the measured torque and Γ is (70 Mmr^{4}·R^{−5}) fixed by the method, an increase in θ = τc^{−1} (c is the stiffness of the suspension) would imply an increase in G.

Lag/lead correlations for each day before and after the days in which these correlations were obtained were all <|0.20|, that is not significant statistically, which is similar to the results found for Vladimirsky and Bruns. The coefficient for the slope for the Quinn effect indicated that for every 0.001 θ a^{−1}·s^{−1} decrease there was a 1.6 unit increase in the Planetary A index. The quantitative proportion is similar to that obtained for [

The z-score differences for the correlation coefficients for the negative associations between the inferences of geomagnetic activity and G were not significant statistically for the Vladimirsky and Burns [^{−4}. However a recondite quantitative equivalence between some quality of gravity and electromagnetic phenomena [

Even a simplistic comparison of the energies associated with force suggests a shared convergence for 1 L (10^{−3} m^{3}) of water, perhaps the most relevant proportion of mass on the earth’s surface. The change of G of 3 × 10^{−15} m^{3}·kg^{−1}·s^{−2} multiplied by (1 kg^{2}/0.1m (10 cm)) is 3 × 10^{−14} J. On the other hand the energy represented (B^{2}/2μ) within this volume for a mean variation of ~8 nT from Vladimirsky and Burns’ [^{−14} J. Although there are insufficient data to conclude that they share the same source of variance at this time, the similarity of quantitative values suggests that further examination of this possible coupling is warranted.

Thanks to Dr. Blake T. Dotta and Viger Persinger for technical contributions.