In a previous paper, presented to the Royal Society of Edinburgh in December 1849, and read on the 5th of February 1850 (Trans. vol. xx.), the author deduced the principles of thermodynamics, and various properties of elastic fluids, from the hypothesis of molecular vortices, under certain special suppositions as to the figure and arrangement of the vortices, and as to the properties of the matter which moves in them. In subsequent papers, he showed how the hypothesis might be simplified, by dispensing with some of the special suppositions.