Thomson suggested that the gas to be examined should be forced through a pipe ending in a fine nozzle, or, preferably, through a plug of porous material placed in a pipe along which the gas was forced by a pump, and observations made of the temperature in the steady stream on both sides of the plug. The experiments were carried out with a plug of compressed cotton-wool held between two metal disks pierced with holes, in a tube of boxwood surrounded also by cotton-wool, and placed in a bath of water closely surrounding the supply pipe. This was of metal, and formed the end of a long spiral all immersed in the bath. Thus the temperature of the gas approaching the plug was kept at a uniform temperature determined by a delicate thermometer; another thermometer gave the temperature in the steady stream beyond the plug. In the case of hydrogen the experiments showed a slight heating effect of passage through the plug; air, oxygen, nitrogen and carbonic acid were cooled by the passage. The theory of the matter is set forth in the original papers, and in a very elegant manner in the article on Heat. The result of the analysis shows that if ∂w be the positive or negative work-value of the heat which will convert one gramme of the gas after passage to its original temperature; and T be absolute temperature, and v volume of a gramme of the gas at pressure p, and the difference of pressure on the two sides of the plug be dp, the equation which holds is (1⧸T) (∂T⧸∂v) = 1⧸{v + (∂w⧸dp)} ... (E)[18] It was found by Joule and Thomson that ∂w was proportional to dp for values of dp up to five or six atmospheres. At different temperatures, however, in the case of hydrogen the heating effect was found to diminish with rise of temperature, being .100 of a degree centigrade at 4° or 5° centigrade, and .155 at temperatures of from 89° to 93° centigrade for a difference of pressure due to 100 inches of mercury. If there is neither heating nor cooling ∂w = 0, and we obtain by integration T = Cv, where C is a constant. Elaborate discussions of the theory of this experiment will be found in modern treatises on thermodynamics, and in various recent memoirs, and the differential equation has been modified in various ways, and integrated on various suppositions, which it would be out of place to discuss here.