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By counting several thousand scattered protons at each angle and voltage with a linear amplifier, the numbers of protons scattered or projected by recoil through angles from 15\ifmmode^\circ\else\textdegree\fi{} to 45\ifmmode^\circ\else\textdegree\fi{} from a carefully defined mono-energetic proton beam in passing through 2 mm path length of pure hydrogen gas at a pressure of 12 mm have been measured for proton beam energies of 600, 700, 800, and 900 kv. The angular resolution for the slit systems was about 2\ifmmode^\circ\else\textdegree\fi{}. The high voltage was constant to within one percent and was measured directly to about two percent with a specially calibrated 10,000-megohm corona free voltmeter resistor. The spread in energy of the primary protons did not exceed one percent. At 600 kv the observed numbers at all angles are roughly two-thirds of the values predicted by Mott's formula. The curves for this observed "Mott ratio" versus angle change progressively as the voltage is increased and at 900 kv the observations show two-thirds of the Mott value at 15\ifmmode^\circ\else\textdegree\fi{}, 1.4 times Mott at 30\ifmmode^\circ\else\textdegree\fi{}, and 4.0 times Mott at 45\ifmmode^\circ\else\textdegree\fi{}. Measurements of the scattering of protons by deuterium, helium, and air, together with "vacuum-scattering" tests which eliminate slit scattering and unknown vapors, have led to the conclusion that the observed anomaly is not due to a contamination and must be ascribed to a proton-proton interaction at close distances (less than 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm) which involves a marked departure from the ordinary Coulomb forces. The observed curves lead quantitatively to a simple theoretical interpretation on the basis of wave mechanics, as shown in the accompanying paper by Breit, Condon and Present. A new scattering apparatus is under construction to eliminate possible small errors in the angular measurements and to permit observations (with Geiger point-counters) at lower voltages.