The question of the range of ejected liquid streams is connected with the relation of the stability of the jet motion to an initial infinitesimal disturbance. This is investigated as a theoretical problem for the planar and cylindrical cases neglecting any fluid viscosity. In addition, the stabilizing influence of either a surface or ``body tension'' is calculated. Comparison of the theory with some published data is found to yield qualitative and semiquantitative agreement. The possibility of applying this theory to the measurement of dynamic surface tensions is suggested.