Both the experimental and theoretical study on the Controlled excitation of the helical oscillation are made in a weakly ionized mercury discharge cylindrical plasma with a longitudinal magnetic field below the critical field value. The phase constant of the excited wave has almost linear relation With exciting frequency and is almost constant or becomes smaller as the applied uniform magnetic field increases. The attenuation : constant has a peak value near the critical frequency and becomes smaller with increasing magnetic field The relations are theoretically analysed as a kind of an eleCtrondriIt wave caused by the density gradient. The spacial attenuation of the wave is caused by the particle diffusion towards the direction across the magnetic field. The-cOMparison-of, the experimental values with the caliculated ones is in fairly good agreement.