The present third edition of this work has been enlarged by the addition of a new lecture, "On Some Phenomena Attending the Flight of Projectiles." The additions to the second consisted of the following four lectures and articles: Professor Mach's Vienna Inaugural Lecture, "The Part Played by Accident in Invention and Discovery," the lecture on "Sensations of Orientation," recently delivered and summing up the results of an important psychological investigation, and two historical articles (see Appendix) on Acoustics and Sight.

The lectures extend over a long period, from 1864 to 1898, and differ greatly in style, contents, and purpose. They were first published in collected form in English; afterwards two German editions were called for.

As the dates of the first five lectures are not given in the footnotes they are here appended. The first lecture, "On the Forms of Liquids," was delivered in 1868 and published with that "On Symmetry" in 1872 (Prague). The second and third lectures, on acoustics, were first published in 1865 (Graz); the fourth and fifth, on optics, in 1867 (Graz). They belong to the earliest period of Professor Mach's scientific activity, and with the lectures on electrostatics and education will more than realise the hope expressed in the author's Preface.

The eighth, ninth, tenth, eleventh, and twelfth lectures are of a more philosophical character and deal principally with the methods and nature of scientific inquiry. In the ideas summarised in them will be found one of the most important contributions to the theory of knowledge made in the last quarter of a century. Significant hints in psychological method, and exemplary specimen-researches in psychology and physics, are also presented; while in physics many ideas find their first discussion that afterwards, under other names and other authorship, became rallying-cries in this department of inquiry.

All the proofs of this translation have been read by Professor Mach himself.

T. J. McCormack.

La Salle, Ill., May, 1898.