In conclusion, allow me to remark that the results of my investigation, of which but a succinct account has been given here, negative certain derivations, which have been believed in, though they have never been proved; such as that of the form I have last discussed from the Assyrian palmetta, or from a cypress bent down by the wind.  To say the least the laws of formation here laid down have a more intimate connection with the forms as they have come down to us, and give us a better handle for future use and development.  The object of the investigation was, in general words, to prepare for an explanation of the questions raised; and even if the results had turned out other than they have, it would have sufficed me to have given an impulse to labors which will testify to the truth of the dead master’s words: 

    “Was Du ererbt von deinen Vaetern hast,
    Erwirb es, um es zu besitzen.”

* * * * *

STEPS TOWARD A KINETIC THEORY OF MATTER.

[Footnote:  Meeting of the British Association, Montreal. 1884.  Section A. Mathematical and Physical science.  Opening Address by Prof.  Sir William Thomson, M.A., LL.D., D.C.L., F.R.SS.L. and E., F.R.A.S., President of the Section.]

By Sir WILLIAM THOMSON.

The now well known kinetic theory of gases is a step so important in the way of explaining seemingly static properties of matter by motion, that it is scarcely possible to help anticipating in idea the arrival at a complete theory of matter, in which all its properties will be seen to be merely attributes of motion.  If we are to look for the origin of this idea we must go back to Democritus, Epicurus, and Lucretius.  We may then, I believe, without missing a single step, skip 1800 years.  Early last century we find in Malebranche’s “Recherche de la Verite,” the statement that “la durete de corps” depends on “petits tourbillons.” [1] These words, embedded in a hopeless mass of unintelligible statements of the physical, metaphysical, and theological philosophies of the day, and unsupported by any explanation, elucidation, or illustration throughout the rest of the three volumes, and only marred by any other single sentence or word to be found in the great book, still do express a distinct conception which forms a most remarkable step toward the kinetic theory of matter.  A little later we have Daniel Bernoulli’s promulgation of what we now accept as a surest article of scientific faith—­the kinetic theory of gases.  He, so far as I know, thought only of Boyle’s and Mariotte’s law of the “spring of air,” as Boyle called it, without reference to change of temperature or the augmentation of its pressure if not allowed to expand for elevation of temperature, a phenomenon which perhaps he scarcely knew, still less the elevation of temperature produced by compression, and the lowering of temperature by dilatation, and