Toroidal eigenfrequencies omega(n)/2 pi, (with harmonic numbers n greater than or equal to 1) of dipolar magnetospheric B field lines are well approximated (within a few percent at most for L greater than or equal to 2) by the linear expression omega(n) approximate to (3 pi c(A0)/8La) csc Lambda + (n-3/4)Delta omega, if the plasma density rho is proportional to (La/r)(m) along the magnetic field line of interest (r being the geocentric distance, a being the planetary radius, and subscript 0 signifying evaluation at the magnetic equator). The spacings Delta omega/2 pi between consecutive eigenfrequencies are nearly equal and well approximated by the reciprocal of closed integral(ds/c(A)), where c(A) is the local Alfven speed and s is the coordinate that measures are length along the field line. Poloidal eigenfrequencies omega(n)/2 pi with harmonic numbers n greater than or equal to 2 are equally well approximated by the same expression for omega(n). This means that observed pulsation periodicities can be identified with their respective harmonic numbers by plotting the corresponding frequencies on a rectangular grid against possible harmonic numbers to see which reasonable identifications produce the best straight line. (Identification. could alternatively be achieved, without plotting, through a modified form of linear regression.) Extrapolated to n = 3/4, the linear fit to an observed eigenfrequency spectrum (toroidal with n greater than or equal to 1. and/or poloidal with n greater than or equal to 2) would then yield a good estimate for the equatorial plasma density rho(0). The slope of this same linear fit would lead (when divided by omega(0.75)/2 pi) to a good estimate for the corresponding value of m, which is the exponent of La/r in the modeled plasma density distribution.
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