To test two hypotheses against seismology, the ¿rsted initial field model is used to estimate the radius of Earth's core by spectral methods. The model coefficients are used to compute the mean-square magnetic flux density in spherical harmonics of degree n on the reference sphere of radius a = 6371.2 km, which is an observational spectrum Rn. The theoretical spectrum tested, {Rnc} = K(n + 1/2)<(n(n + 1)>-1(c/a)2n+4, is obtained from the hypotheses of narrow-scale flow and a dynamically weak magnetic field near the top of Earth's core; it describes a low-degree, core source magnetic energy range. Core radius c and amplitude K are estimated by fitting log theoretical to log observational spectra at low degrees. Estimates of c from Rn of degrees 1 through N vary between 3441 and 3542 km as N increases from 4 to 12. None of these estimates differ significantly from the seismologic core radius of 3480 km. Significant differences do occur if N exceeds 12, which is consistent with appreciable noncore, crustal source fields at degrees 13 and above, or if other spectral forms are assumed. Similar results are obtained from the 1980 epoch Magsat model CM3. One way to deduce {Rnc} uses an expectation spectrum for low-degree secular variation (SV) induced by narrow-scale flow near the top of Earth's core, {Fnc} = Cn(n + 1/2)(n + 1)(c/a)2n+4. The value of c obtained by fitting this form to the mean observational SV spectrum from model GSFC 9/80 is 3470 ¿ 91 km, also in accord with seismologic estimates. This test of the narrow-scale flow hypothesis is independent of the weak field hypothesis. The agreement between SV, Magsat, ¿rsted, and seismologic estimates of core radius means the hypotheses pass these tests. Additional tests are described.