The experiments on the changes Of temperature which gases experience when they are allowed to expand under such conditions as to do no external work are of great importance from two standpoints: 1. Owing to the minuteness of the change of temperature, it may be assumed that the intrinsic energy of a gas is almost entirely kinetic; and so conclusions may be drawn between the mechanical work done in compress ing a gas and the rise of temperature produced 2. Measure ments Of the minute changes lead to a method of comparing temperatures as registered on a gas-thermometer and those which are given on Thomson's Absolute Scale. Robert Mayer assumed that there was no internal work done in compressing a gas, and so made a calculation for what is now called the mechanical equivalent of heat. The question as to whether Mayer was acquainted with the experiments of gay-lussac at the time he made his calculation or not has long been an open one but it is generally acknowledged now that he was familiar with the results obtained by gay-lussac. And so was justified in his theoretical work. Gay-lussac per formed his experiments ou the free expansion of gases in the year 1807; and a translation of his memoir is given in this volume.