In the first and second Symposia of this series von Weizsäcker and von Hoerner discussed the problem of turbulence in the Orion Nebula, while in the second Symposium Courtès has further treated the problem. Von Hoerner has presented a detailed discussion of the methodologies of the treatment. It was suggested that the observed variations in radial velocity in the nebula are consistent with the predictions of the Kolmogoroff equilibrium theory of turbulence, which is valid at sufficiently high Reynolds numbers. However, their results to some extent were inconclusive, mainly because the observations which they analyzed were not sufficiently numerous and accurate. With the purpose of reanalyzing the whole problem, Dr. O. C. Wilson and I undertook the task of determining radial velocities and profiles of selected emission lines in the spectrum of the nebula, using the largest practical resolving power in angle and frequency available with the 200-in. telescope. In order to use advantageously the efficiency of the instrument, we have photographed the brighter parts of the nebula (roughly subtending a solid angle of about 6′ aperture) with the Coudé spectrograph fitted with 31 parallel entrance slits, which are separated from each other by a distance of 1 mm in the focal plane or 1″.3 in the sky. In this manner we obtain in one exposure the spectrum of an area about 40″X40″ with a dispersion such that 1 μ = 0.27 km/sec. In each of these plates about 600 Doppler shifts of the lines [OII] λ3726, Hγ, and [OII] λ5007 have been measured, each of which represents some average value (not necessarily the same for the three lines) of the velocities of nebular matter along the line of sight. Altogether we have about 50 000 radial velocities measured. The accuracy with which a radial velocity may be determined is set by the intrinsic shape of the lines, which reflects the distribution of velocities along the line of sight. To give an idea of the orders of magnitude of the quantities involved, I may mention here that typical values of the mean widths h at half-intensity of the hydrogen, [OIII], and Fe—comparison lines are h(H) = 28.6 km/sec, h(OIII) = 20.0 km/sec, h(Fe) = 8.3 km/sec. The bisection of a line with a cross wire to an accuracy around 0.5 km/sec is thus feasible; repeated measurements have, indeed, shown such precision. On the assumption that the profiles to which the above widths correspond are Gaussian, we may easily disentangle the thermal and turbulent components of the mean square radial velocities, through the dependence on atomic weight of the former. We find from the representative values given aboveThe corresponding kinetic temperature is 9700°K, in close agreement with the value of the electron temperature determined by other methods.