The latitude and longitude of Jupiter's Red Spot were measured from photographic plates obtained between June 1962 and May 1965 at the New Mexico State University Observatory. The longitudes measured from photographs have been found to be an order of magnitude more accurate than the longitudes obtained from visual estimates of central meridian transit times. The Red Spot was observed to increase irregularly in System II longitude from 10° in June 1962 to 24° in May 1965. The significantly improved accuracy of photographic observations made possible the detection of rapid, short-term changes in longitude. The Red Spot slowly oscillated in latitude, remaining within 1°.4 of its mean latitude of -22°.4 for the reported interval.