The possibility that there is a lunar modulation of geomagnetic activity around the time of total lunar eclipses is investigated. The modulation of acitivity, as seen in the Ap indices for the years 1932--1980, consists of a 4-day increase starting 3 days before the eclipse day. This characteristic of the modulation suggests that it may be caused by entry of the moon into the magnetospheric tail and by the subsequent motion of the moon within the tail; it is not observed in conjunction with partial lunar eclipses. By using the aa indices, which are avaiable back to 1868, it is possilbe to study the long-term temporal characteristics of the modulation. It is found that the increase in acitivity after 1932 is not replicated in the data prior to 1932 (during the years 1870--1931), and it is concluded that the increase is most probably a statistical anomaly and that it would be inappropriate to conclude from it that the moon's entry into the geomagentic tail enchances geomagnetic activity.