Observations of sea level at Port Arthur, Tasmania, southeastern Australia, based on a two-year record made in 1841--1842, a three-year record made in 1999--2002, and intermediate observations made in 1875--1905, 1888 and 1972, indicate an average rate of sea level rise, relative to the land, of 0.8 ¿ 0.2 mm/year over the period 1841 to 2002. When combined with estimates of land uplift, this yields an estimate of average sea level rise due to an increase in the volume of the oceans of 1.0 ¿ 0.3 mm/year, over the same period. These results are at the lower end of the recent estimate by the Intergovernmental Panel on Climate Change of global average rise for the 20th century. They provide an important contribution to our knowledge of past sea level rise in a region (the Southern Hemisphere) where there is a dearth of other such data.