Deep harmonic tremor originating at depths around 40 km under Kilauea was studied using records accumulated since 1962 at the Hawaii Volcano Observatory of the U. S. Geological Survey. The deep source of the tremor was determined by onset times and confirmed by the relative amplitude across the island-wide network of seismometers. The period of tremor was conclusively shown to be determined by the source effect and not by the path or station site effect because the period would change considerably in time but maintained uniformity across the seismic net during the tremor episode. The tremor appeared to be primarily composed of P waves. We interpret the observation period and amplitude in terms of the stationary crack model of Aki et al. (1977) and find that the seismic moment rates for deep tremors are considerably larger than those for shallow-tremors suggesting mor vigorous transport for the former. We propose a kinematic source model which may be more appropriate for deep tremor. According to this model, a measurable quantity called 'reduced displacement' is directly proportional to the rate of magma flow. A systematic search for deep tremor episodes was made for the period from 1962 through 1979, and the amplitude, period, and duration of the tremor were tabulated. We then constructed a cumulative reduced-displacement plot over the 18-year period. The result shows a generally steady process which does not seem to be significantly affected by major eruptions and large earthquakes near the surface. The total magma flow estimated from the reduced displacement is however, one order of magnitude smaller than that estimated by Swanson (1972). It may be that most channels transport magma aseismically, and only those with strong barriers generate tremor.