By Steven J. Grisafi, PhD.
The demonstration of a differential gauge presented in the research article Conic Yields: Empirical Yield Transmission is not limited to either conic section curve-fittings nor use only of the diffusivity ratio, Ξ/Γ. One may also use the money potential itself, Ψ, either in conjunction with the gradient’s ratio or the diffusivity ratio. Preferably, we seek linear curve-fits to empirical data whenever possible. But the most important attribute of any curve-fitting is the stability of its well defined structure through the passage of time. An example of the use of the money potential itself, used in a differential gauge with its gradient’s ratio, can to be found in the USA Federal Reserve Bank money supply analysis.
The figure presented below has been added to the Federal Reserve Bank money supply analysis. The graph in the figure displays reasonable linearity worthy of a curve-fit. A linear least squares regression applied to the data points within the figure yields the numerical values for the slope, m, and the intercept, b, shown in the table below.
The proportional constant, K, appears as before in the conic sections analysis. Using μ and η to designate the first and second coordinates of a right-hand rectangular coordinate system, respectively, the differential gauge relationship is:
dμ = K dη
However, now in the linear case, while using the money potential instead of the diffusivity ratio, it is defined as:
K = (Ψ – b)/m