We have used more than 14,000 three-component magnetic measurements from the database of Fairfield et al. [1994> in the magnetospheric domain with the inner boundary r=3 RE and outer boundary (x2+y2)1/2=10 RE, |z|=7 RE for studying statistical connection of the external magnetic field with Dst and Kp indices as well as with the solar wind dynamic pressure and the z component of the IMF. The components of the external magnetic field in the magnetosphere have been presented as fourth-order polynomials of the geocentric distance. The polynomials include 17 terms: six terms corresponding to the azimuthally symmetrical part of the field, six terms suggesting the day-night asymmetry and five terms accounting for the dipole tilt. Each coefficient of the series has been found as a linear combination of the four above mentioned parameters. The least squares technique allowed us to obtain 85 coefficients. The normalized residual sum of squares of the model equals 0.20, which is smaller than other models yield. The coefficients of all six terms of the azimuthally symmetrical part depend mostly on Dst. The asymmetrical and dipole tilt parts depend on the four above mentioned parameters to a nearly equal extent. The effect of each parameter on the cusp position has been examined. Dst appeared to be the strongest factor affecting the cusp latitude.¿ 1997 American Geophysical Union