In this study we consider the influence of the Earth's free core nutation (FCN) on diurnal tidal admittance estimates for 11 stations of the globally distributed International Deployment of Acclerometers network. The FCN causes a resonant enhancement of the diurnal admittances which can be used to estimate some properties of the FCN. Estimations of the parameters describing the FCN (period, Q, and resonance strength) are made using data from individual stations and many stations simultaneously. These yield a result for the period of 423--452 sidereal days, which is shorter than theory predicts but is in agreement with many previous studies and suggests that the dynamical ellipticity of the core may be greater than its hydrostatic value. The estimate of 3035--49,689 for the Q falls in between the incompatible results of previous estimates based on tidal gravity and very long baseline interferometry observations, but the formal uncertainties are large enough for this result to be compatible with all of the previous studies. More careful consideration of the four-dimensional confidence interval, however, indicates that one reason for our relatively large error bars is a strong trade-off between the real and imaginary parts of the eigenfrequency and the real and imaginary parts of the resonance strength, respectively. This trade-off should probably be considered in future work in order to facilitate comparisons between different studies. Finally, we point out that observation of the freely excited wobble in the diurnal surface gravity spectrum does not seem likely based on the most recent estimates of its nutation amplitude. ¿American Geophysical Union 1993