Le Bel-van't Hoff (the author replies)

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This generalization is deplorable just as is the neglect of weighting factors. It is better to obtain the weighting factors from analysis of the errors inherent in the particular measurements being fitted (cf., the examples given by Maudel). The experimenter is in a unique position to perform this important analysis. A very general treatment of least squares fitting of a straight line, including several special cases, is given by D. York [Can. J . Phys., 44, 1079 (1966)l. The author concludes from examples that ". . .the best slope is not necessarily bounded by values found from the regressions of z on y and y on x." General formulations for more complex curvsfitting problems are given by J. G. Hust and R. D. McCarty [Clyogenics, 7, 200 (1967)l. The authors use thermodynamic examples to illustrate (1) least squares with constraints, (2) simultaneous least squares detennination of a sinrle set of uarameters from several t -. m e s of property data, and ^(3) simultaneous least squares determination of several sets of parameters from a single set of property data. These special techniques are widely applicable to thermodynamic data and should find use in other fields when experimenters learn of their utility.

sumes, a priori, attracting forces directed independently on the position of the attracted body, which was utter nonsense from the point of view of 19th century physics. To avoid this collision with physics Le Be1 created his own hypotheses-free theory of the equilibrium of saturated carbon compounds (op. cit., [3],3,788(1890)). For details see my paper in American Scientist, 43,97 (1955).

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I am indebted to Dr. Sementsov for emphasizing the point that LeBeldid not use the tetrahedron to account for the rotatory power of asymmetric molecules, as did van't Hoff, and therefore would agree that the contributions of these two men should be considered senarately. Le Bel's paper is more abstract and its title, unlike that of van't Hoff's paper, does not indicate an a prioripreoccupation with spatial arrangements. However, Le Be1 was "obliged to admit" for molecules of the type MAn, which furnish only one chemical isomer from one, two, or three substitutions, that the tetrahedral arrangement of the atoms accounted for the failure of these molecules to have rotatory power. He further indicates that this is the case with marsh gas which, we may conclude, therefore has a tetrahedral arrangement of its atoms, and this is the point that I should have made in my paper [p. 6641. This is the only reference to the tetrahedron in Le Bel's paper of 1874. Le Bel-vant Hoff Into 1890 [Bull. Sac. Chim. Fr., [3], 3, 7 8 8 4 , To the Editor: (1890)], it seems to me that Le Be1 is not denying this Dr. Larder in his interesting paper (J. CHEM.E D U C . , ~ ~ , but rather emphmizing that whereas van't Hoff con661 (1967) makes an error, which we meet in many sidered the tetrahedron as a premise, Le Be1 arrived at books and papers. He assumes that Le Be1 together the tetrahedron as a conclusion from other premises. with van't Hoff introduced the tetrahedral concept. I n He notes that since that time (L'dds cette 4poque1'), another place he mentions the van't Hoff-Le Be1 which I take to mean 1874, he has had doubts about theory. Le Be1 not only did not originate the tetrathe tetrahedral arrangement of the atoms in bodies hedron theory but tried to disprove it theoretically by such as CR4 [op. cit., p. 7891, and he perhaps regretted emphasizing that substances of the formula CFL crystalhis earlier statement. And he goes on to clearly state lize in other systems than cubic, e.g., CBr4and C14give [op. n't., pp. 789-901, and particularly his dilemma diaxial crystals [Bull. Sac. Chim. France, [ 3 ] , 7 , 613 tackles the deductions to be expected on the basis of (1892)l. He also tried to disprove it experimentally by tetrahedral arrangements, as indicated by Dr. Sementattempts to resolve ethylene derivatives, e.g., citraconic SOT. and mesaconic acids (op. cit., p. 164, and 131, 11, 292 (1894). DAVIDF. LARDER He protested emphatically against crediting him with DEPARTMENT OF TEE HI~TORY the tetrahedron theory [op. cit., 131, 3 , 788 (1809) and AND PEILOSOPHY OX.SCIENCE [ 3 ] ,7,314 (1892). UNIVERSITY OF ABERDEEN A ~ E R D E E N ,SCOTLAND The van't Hoff theory is very daring, because it as~

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