Summary: The report is separated into two parts. In the first part the theoretical basis for calculating the lateral motions of an airplane flying through continuous random atmospheric turbulence is presented. The lateral motions are derived in terms of (1) the transfer functions relating the motion in the various degrees of freedom to the yawing moment, rolling moment, and side force, (2) the statistical forces and moments at the center of gravity due to gust velocities acting on the lifting surfaces of the airplane, and (3) the power spectra of the three orthogonal components of gust velocity acting on the airplane along the flight path. The method takes into account the random variations of gust velocity across the span and along the fuselage. Solutions are given in the form of equations relating the power spectra of the angular motions of the airplane to the power spectra of the gust velocities.