It is evident that there is a decided need for a correct formula for the longitudinal shearing stress in a beam of variable cross section. The formulas which will be derived in this paper apply only to the longitudinal shearing stress at the neutral axis of a cross section, at which location, however, the maximum value of the longitudinal stress always occurs. Furthermore, only that case will be considered in which the longitudinal neutral axis of the beam is a straight line. The formulas will be derived on the assumption that all the external loads are perpendicular to the neutral axis. However, it will be shown later that these same formulas are also valid when the loads have an axial component.