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The recent claim by Smylie [1992] to have detected the Slichter modes of the Earth's inner core rests on what appears to be a remarkable agreement between theory and observation. However the theoretical eigenperiods which are used by Smylie conflict significantly with all previously published periods for the Slichter modes, both for non-rotating and rotating Earth models. A closer examination of the theory used in these calculations reveals the use of static Love numbers to represent the response of the inner core and mantle to dynamics in the liquid core. We here show that the use of dynamic Love numbers restores the eigenperiods to those obtained using standard seismological theory and consequently destroys agreement between these periods and the claimed observations.