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., - , , ., .. to see how there could lius therefore rejecbed Avogadro's auxiliary hypotheses which assert the existencc of polyatomic molecules of gaseous elements. Thus, because of his dualistic theory, hc rejected the correct form of A and assumed an incorrect hypothesis in its place. Since Berzelius was influential and the dualistic theoly was radher popular for a few decades, this n a s probably a major reason for the general ineffect,ive use of A for some time. Yet,, in spite of this, thcrc was considerablc interest in the hypothesis in some circles. We are not concerned wit,h its detailed history, but we should consider one more rather complicated and dramatic example of the Duhemian Pit,fall. This is the case of A. M. Ampbe, and some of his followers. .4mp&rc published A in 1814 (8) in an art,iclc concerned u-it11 the geometry of molecules. His geometrical theory was rather complex and its details need not concern us here. A good recent review of it is given by S. H. illauskopf (9). What is of interest here is the fact that AmpBre also had difficuhs with auxiliary hypotheses. Unlilic Dalton and Berzelius, lie assumed the existence of polyat,omic elemeut,al molecules, but he guessed the wrong formulas for them because of liis geometrical theory. For instance, he assumed that oxygen, nitrogen, and hydrogen were tetratomic, and that chlorine was octatomic (10). In spite of this, lie was able to explain some of Gay-Lussac's results. Thus, altliough he used incorrect auxiliary hypotheses, Ampere mas not completely trapped by the Duhemian Pit,fall. However, he inadvertently led other chemists into the trap. Most not,able among these was J . B. A. Dumas. Dumas tried to use A with vapor density measurements in order to determine atomic weights, but he encountered problems (11). Very briefly, they are as follows: I n 1826 Dumas began by stating A as applying to the "atoms" of gases. But be believed that the "atoms" of all elemental gases were composed of t v o "half-atoms" which could be separated in rcactions. These assumptions led to some satisfactory atomic weights. But also various discrepancies were obt,ained with elements such as mercury, sulfur, and phosphorus, when his results Tyere compared with results obtained by other methods. It is now accepted that the nlolecular formulas of the vapors of these elements are Hg, Se, and P n But Dumas mould not accept such auxiliary hypotheses. Inst,ead, he rejected A and, in the 1S301s, came to doubt the entire atomic t,heory. I t is especially sad that Dumas became a victim of the Pitfall, because in 1833 AmpBre's student M. A. A. Gaudin (12) showed h o v to avoid tho snare by liypothesizing different numbers of atoms in different polyatomic elemental molecules. However, Dumas was a distinguished chemist, ~ ~ h i Gaudin le mas littale known and liis theory mas not taken very scriously by most chemists. It is generally agreed that vide acceptance of A by chemists did not occur until the 1S60's after S. Cannizzaro published his extensive use of it in establishing a consistent system of atomic and molecular xeights (IS). The existence of the Duhemian Pitfall was one of several important reasons for the slov acceptance of A. 366
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One might expect physicists who were trying t o develop a general theory of gases to be less concerned t,han chemists ~ v i t hdetailed chemical data, and hence less concerned with the auxiliary hypotheses surrounding A. Therefore, one might conjecture that physicists considering A would have been less likely t,l~an the chemists t o become ensnared by the Duhemian Pitfall. At least in t,he case of the kinetic theorists, there is some evidence that this conjecture is correct. It is of interest to consider two important.cases. Apparentk the first kinedic theorist t,o consider A : was J. J. Waterston. I n 1845 he submitted to the Royal Society a paper on kinet,ic theory; unfortunately, he never succeeded in get,ting it published. This paper developed the kinetic theory far beyond previous work, and it presented results which later had to be indepen-: dently discovered by others. I n his article Waterston stated several gas laws, including A. He was aware of the Law of Combining Volumes, and he suggested that this law is true because of A and t,he existence of polyatomic element,al molecules. He maintained that such : molecules could split into parts in react,ions even though the parts were not known to exist in the free st>ate ( I / , ) . I t seems clear that Waterston was notf excessively bothered by the dualistic theory, or by other chemical problems with polyatomic elemental molecules. I t is extremely unfortunate that his ideas were not appreciated in liis own time. I n contrast to Waterston, 12. Clausins mas an early kinetic theorist. who was influential. His beautiful paper, "On the Nature of the Motion Which We Call Heat," was first published in German, and then in English in 1857 (15). Clausius' principal cont,ributions in this paper are his treatment of molecular energies other than just translationnl energy, and his treatment of specific heats. But he also mentioned the need to explain the Law of Combining Volumes, and proceeded t o argue for A. His rcasoning is quite interesting. Let e be the mean translational kinetic energy: (Clausius says "vis viva," which is just 2e) of a molecule. Then he sajrs t,liat, for a fixed temperature T, pressure P is proportiond to t,he number n of molecules per unit volume V and toe. I n other words
where K is a proportionality const,ant. Thus, if P and: T a r e fixed, and if A is assumed, then all molecules of all gases have the same e , or mean translational kinetic energy. Actually, Clausius first gives the above argument for atomic gases. Then he discusses its extension to polyatomic gases, and mentions some of the anomalies noticed by chemists, particularly the troubles with the vapor densities of sulfur and phosphorus. But he was not disturbed by such problems, and he concluded: "I a m of opinion, liowever, t,Iiat, under the present uncertainty v i t h respect t o the inner constitution of several bodies, and particularly of those which possess a: complicated chemical composition, too great weight ought not t o be laid upon individual anomalies; and I deem it probable, that, by means of the above hy-
[that they can be polyatomic], all relations of volume in gases may be referred hack t>othe theorem, that the seseral molecules of all gases possess equal vis viva in reference to their translatory motion" (16). It appears, t.herefore, that Clausius is recommending that t,he hypothesis of a constant e, a t a fixed tempera ture, he considered even more fundamental than A. Of course, if one assumes this hypothesis, then A follows from eqn. (2). It should also be noted that, Clausius' theory of specific heats indicated that there are probably polyato~nicelemental molecules. I,. I
