or west–east direction. Notation: is the total centripetal acceleration when moving along the surface of the Earth. is the centripetal acceleration when stationary with respect to the Earth. is the angular velocity of the Earth: one revolution per Sidereal day. is the angular velocity of the airship relative to the angular velocity of the Earth. is the total angular velocity of the airship. is the airship's velocity (velocity relative to the Earth). is the Earth's radius. It can readily be seen that the formula above for motion along the equator follows from the more general equation below for any latitude where along the equator v = 0.0 and The second term represents the required centripetal acceleration for the airship to follow the curvature of the earth. It is independent of both the Earth's rotation and the direction of motion. For example, when an aeroplane carrying gravimetric reading instruments cruises over one of the poles at constant altitude, the aeroplane's trajectory follows the curvature of the earth. The first term in the formula is zero then, due to the cosine of the angle being zero, and the second term then represents the centripetal acceleration to follow the curvature of the Earth's surface. Explanation of the cosine in the first term The mathematical derivation for the Eötvös effect for motion along the Equator explains the factor 2 in the first term of the Eötvös correction formula. What remains to be explained is the cosine factor. Because of its rotation, the Earth is not spherical in shape, there is an Equatorial bulge. The force of gravity is directed towards the center of the Earth. The normal force is perpendicular to the local surface. On the poles and on the equator the force of gravity and the normal force are exactly in opposite direction. At every other latitude the two are not exactly opposite, so there is a resultant force, that acts towards the Earth's axis. At every latitude there is precisely the amount of centripetal force that is necessary to maintain an even thickness of the atmospheric layer. (The solid Earth is ductile. Whenever the shape of the solid Earth is not entirely in equilibrium with its rate of rotation, then the shear stress deforms the solid Earth over a period of millions of years until the shear stress is resolved.) Again the example of an airship is convenient for discussing the forces