The Austrian scientist Ernst Mach (1838-1916) carried out work of importance in several fields of enquiry, including physics, physiology and psychology. In this short work, first published in German in 1872 and translated here into English in 1911 by Philip E. B. Jourdain (1879-1919) from the 1909 second edition, Mach discusses the formulation of one of science's most fundamental theories. He provides his interpretation of the principle of the conservation of energy, claiming its foundations are not in mechanical physics. Mach's 1868 work on the definition of mass - one of his most significant contributions to mechanics - has been incorporated here. His perspective on the topic as a whole remains relevant to those interested in the history of science and the theory of knowledge. Also reissued in this series in English translation are Mach's The Science of Mechanics (1893) and Popular Scientific Lectures (1895).