went on the assumption that the molecules behave like centres of forces. He demonstrated anew the law of distribution of velocities; but the proof had a flaw in argument, pointed out by Boltzmann, and recognised by Maxwell, who adopted
a somewhat different form of the distributive function in a paper of 1879, intended to explain mathematically the effects observed in Crookes' radiometer. Boltzmann gave a rigorous
general proof of Maxwell's law of the distribution of velocities.
None of the fundamental assumptions in the kinetic theory of gases leads by the laws of probability to results in very close agreement with observation. Boltzmann tried to establish kinetic theories of gases by assuming the forces between molecules to act according to different laws from those previously assumed. Clausius, Maxwell, and their predecessors took the mutual action of molecules in collision as repulsive, but Boltzmann assumed that they may be attractive. Experiments of Joule and Lord Kelvin seem to support the latter
assumption.
Among the latest researches on the kinetic theory is Lord
Kelvin's disproof of a general theorem of Maxwell and Boltzmann, asserting that the average kinetic energy of two given portions of a system must be in the ratio of the number of degrees of freedom of those portions.
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[1]Addenda
[addend:14]Page addend:14. The new Akhmim papyrus, written in Greek, is probably the copy of an older papyrus, antedating Heron's works, and is the oldest extant text-book on practical Greek arithmetic. It contains, besides arithmetical examples, a table for finding "unit-fractions," identical in scope with that of Ahmes, and, like Ahmes's, without a clue as to its mode of construction. See Biblioth. Math., 1893, p. 79–89. The papyrus is edited by J. Baillet (Mémoires publiés par les membres de la mission archéologique française au Caire, T. IX., 1r fascicule, Paris, 1892, p. 1–88).
[addend:39]Page addend:39. Chasles's or Simson's definition of a Porism is preferable to Proclus's, given in the text. See Gow, p. 217–221.
[addend:114]Page addend:114. Nasir Eddin for the first time elaborated trigonometry independently of astronomy and to such great perfection that, had his work been known, Europeans of the 15th century might have spared their labours. See Biblioth. Math., 1893, p. 6.
[addend:116]Page addend:116. This law of sines was probably known before Gabir ben Aflah to Tabit ben Korra and others. See Biblioth. Math., 1893, p. 7.
[addend:125]Page addend:125. Athelard was probably not the first to translate Euclid's Elements from the Arabic. See M. Cantor's Vorlesungen, Vol. II., p. 91, 92.