That term, in a formula for the value of gravity, explicitly containing the geodetic longitude ë and geodetic latitude ö as arguments and implying that the geoid is represented by an ellipsoid having three unequal axes. With this additional term (longitude term), the gravity formula would be written as τ_o = τ_e ((1 + β ₁ sin²φ + β ₂ sin²2φ + β ₃ cos²φ cos 2(λ - λ _o)), in which τ_e is the average value of gravity at the equator and β ₃, like β ₁ and β ₂, is a dimensionless number. As always the gravity formula implies a surface of definite shape; when the surface is an ellipsoid having three axes of different lengths, the shortest axis is the polar axis, corresponding to the Earth's rotational axis, while the two longer axes lie in the equatorial plane. The longest axis lies in the plane at longitudes λ _o and λ _o ± 180^o. The two equatorial axes differ in length by 4aβ ₃, in which a is the length of the longer semi-major axis. The idea of representing the Earth by an ellipsoidal body having axes of three unequal lengths is by no means new. There was, however, no continuing interest in the idea until Helmert and his assistant, Berroth, each published in 1915 his calculations on which were based gravity formulae containing a longitude term of the type given above. Since 1915, various discussions of the accumulating amount of data on gravity have tended to confirm the belief that the geoid is closely approximated by an ellipsoid having a size and character like that proposed by Helmert. Studies of the deflection of the vertical have likewise tended to confirm that belief. But such a surface is not likely to be used as a reference surface for geodetic networks, maps or deflections of the vertical. The mathematical complications are two great. Also, it is convenient to use the same reference surface for both gravity and deflections of the vertical and therefore to omit the longitude term from the gravity formula. Besides Helmert's formula, a number of other gravity formulae have contained a longitude term. The values are given, in the table below, for the constants in some of these formulae.