Toroidal eigenfrequencies &ohgr;n/2&pgr; (with harmonic numbers n≥1) of dipolar magnetospheric B field lines are well approximated (within a few percent at most for L≥2) by the linear expression &ohgr;n≈(3&pgr;cA0/8La)csc&Lgr;+(n-3/4)Δ&ohgr;, if the plasma density &rgr; 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 Δ&ohgr;/2&pgr; between consecutive eigenfrequencies are nearly equal and well approximated by the reciprocal of ∮ (ds/cA), where cA is the local Alfv¿n speed and s is the coordinate that measures arc length along the field line. Poloidal eigenfrequencies &ohgr;n/2&pgr; with harmonic numbers n≥2 are equally well approximated by the same expression for &ohgr;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≥1 and/or poloidal with n≥2) would then yield a good estimate for the equatorial plasma density &rgr;0. The slope of this same linear fit would lead (when divided by &ohgr;0.75/2&pgr;) to a good estimate for the corresponding value of m, which is the exponent of La/r in the modeled plasma density distribution. ¿ American Geophysical Union 1996