We present further results of our Hercules X-1 balloon observation on 1976 May 3 which confirm the existence of a strong line feature at approx.58 keV in the pulsed (1.24s) X-ray spectrum we reported earlier. The spectral excess in the line region over the extrapolated continuum is 5-6 sigma. Our best estimates of the line flux and line width are 3 x 10/sup -3/ photons cm/sup -2/ s/sup -1/ and less than approx.12 keV, respectively. The most likely interpretation of this line is electron cyclotron emission at the basic frequency from the hot polar plasma of the rotating neutron star. The corresponding magnetic field strength is 5.3 x 10/sup 12/ gauss. We have searched for the second-harmonic cyclotron emission line in that part of our data showing the highest signal-to-noise ratio and find a 3.3 sigma spectral enhancement near the predicted energy (110 keV). We discuss implications of the line width and the line intensity ratio for the physical conditions of the emitting plasma and the beaming geometry.