Solar eclipses occur with periodicities of 29.53 days, 6 months, 8.85 years, and 18.6 years. Since these are nearly commensurate with known solar-terrestrial event repetition cycles (27.3 days, semiannual, and 11 years), searches for possible solar eclipse effects in daily geophysical data using standard autocorrelation techniques are likely to have serious side-band interference problems. Therefore a survey of the geomagnetic Ci index for the years 1906--1976 (164 eclipses) was performed by using a modified version of the well-known t test for the difference of two means to define eclipse departure probability Pd). Eclipse epoch Ci changes are shown to satisfy a simple probabilistic model composed of two events-one due to the eclipse E and another due to a 'background' of zero ecliptic latitude Ci fluctuations ZL such that the mean values of the departure probabilities are ⟨Pd(E‖ZL) ⟩=0.5¿0.1,⟨Pd(E) ⟩=0.3¿0.1, and ⟨Pd(ZL‖E) ⟩ (1.8¿0.2) ⟨Pd(ZL) ⟩. It is also shown that the derived ⟨Pd(E) ⟩ value is consistent with a simple statistical occulation model and the Pd derived from geomagnetic effects observed during one total solar eclipse. The large and persistent conditional probabilities, however, appear to require some sort of geomagnetic reverberation effect between the earth and moon.