Le Bel-van't Hoff
1
This generalization is deplorable just as is the neglect of weighting factors. It is better to obtain the weight- ing 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 thermo- dynamic examples to illustrate (1) least squares with constraints, (2) simultaneous least squares detennina- tion of a sinrle set of uarameters from several tmes of 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 satu- rated carbon compounds (op. cit., [3],3,788 (1890)). For details see my paper in American Scientist, 43,97 (1955). -. property data, and ^(3) simultaneous least squares ,- ,,.- ,,..,-_. 1 V WLLi WU"", . determination of several sets of parameters from a single set of property data. These special techniques I am indebted to Dr. Sementsov for emphasizing the are widely applicable to thermodynamic data and point that LeBeldid not use the tetrahedron to account should find use in other fields when experimenters for the rotatory power of asymmetric molecules, as did learn of their utility. van't Hoff, and therefore would agree that the contri- butions of these two men should be considered sena- Le Bel-vant Hoff To the Editor: Dr. Larder in his interesting paper (J. CHEM. EDUC.,~~, 661 (1967) makes an error, which we meet in many books and papers. He assumes that Le Be1 together with van't Hoff introduced the tetrahedral concept. In another place he mentions the van't Hoff-Le Be1 theory. Le Be1 not only did not originate the tetra- hedron theory but tried to disprove it theoretically by emphasizing that substances of the formula CFL crystal- lize in other systems than cubic, e.g., CBr4and C14 give diaxial crystals [Bull. Sac. Chim. France, [3], 7 , 613 (1892)l. He also tried to disprove it experimentally by attempts to resolve ethylene derivatives, e.g., citraconic and mesaconic acids (op. cit., p. 164, and 131, 11, 292 L~ rately. 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 mole- cules 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. Into 1890 [Bull. Sac. Chim. Fr., [3], 3, 7884, (1890)], it seems to me that Le Be1 is not denying this but rather emphmizing that whereas van't Hoff con- sidered the tetrahedron as a premise, Le Be1 arrived at the tetrahedron as a conclusion from other premises. He notes that since that time (L'dds cette 4poque1'), which I take to mean 1874, he has had doubts about the tetrahedral arrangement of the atoms in bodies such as CR4 [op. cit., p. 7891, and he perhaps regretted his earlier statement. And he goes on to clearly state his dilemma [op. n't., pp. 789-901, and particularly tackles the deductions to be expected on the basis of tetrahedral arrangements, as indicated by Dr. Sement- SOT. (1894). DAVID F. LARDER He protested emphatically against crediting him with the tetrahedron theory [op. cit., 131, 3, 788 (1809) and DEPARTMENT OF TEE HI~TORY AND PEILOSOPHY OX. SCIENCE [3], 7,314 (1892). UNIVERSITY OF ABERDEEN The van't Hoff theory is very daring, because it as- A~ERDEEN, SCOTLAND 210 / lournal of Chemical Edumfion
Transcript of Le Bel-van't Hoff
This generalization is deplorable just as is the neglect of weighting factors. It is better to obtain the weight- ing 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 thermo- dynamic examples to illustrate (1) least squares with constraints, (2) simultaneous least squares detennina- tion of a sinrle set of uarameters from several tmes of
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 satu- rated carbon compounds (op. cit., [3] ,3 ,788 (1890)).
For details see my paper in American Scientist, 43,97 (1955).
-. property data, and ^(3) simultaneous least squares ,- ,,.- ,,..,-_.
1 V WLLi WU"", . determination of several sets of parameters from a single set of property data. These special techniques I am indebted to Dr. Sementsov for emphasizing the
are widely applicable to thermodynamic data and point that LeBeldid not use the tetrahedron to account should find use in other fields when experimenters for the rotatory power of asymmetric molecules, as did
learn of their utility. van't Hoff, and therefore would agree that the contri- butions of these two men should be considered sena-
Le Bel-vant Hoff To the Editor:
Dr. Larder in his interesting paper (J. CHEM. E D U C . , ~ ~ , 661 (1967) makes an error, which we meet in many books and papers. He assumes that Le Be1 together with van't Hoff introduced the tetrahedral concept. I n another place he mentions the van't Hoff-Le Be1 theory. Le Be1 not only did not originate the tetra- hedron theory but tried to disprove it theoretically by emphasizing that substances of the formula CFL crystal- lize in other systems than cubic, e.g., CBr4 and C14 give diaxial crystals [Bull. Sac. Chim. France, [3 ] , 7 , 613 (1892)l. He also tried to disprove it experimentally by attempts to resolve ethylene derivatives, e.g., citraconic and mesaconic acids (op. cit., p. 164, and 131, 11, 292
~ ~ ~ ~
L~ ~~
rately. 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 mole- cules 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.
Into 1890 [Bull. Sac. Chim. Fr., [3] , 3, 7 8 8 4 , (1890)], it seems to me that Le Be1 is not denying this but rather emphmizing that whereas van't Hoff con- sidered the tetrahedron as a premise, Le Be1 arrived at the tetrahedron as a conclusion from other premises. He notes that since that time (L'dds cette 4poque1'), which I take to mean 1874, he has had doubts about the tetrahedral arrangement of the atoms in bodies such as CR4 [op. cit., p. 7891, and he perhaps regretted his earlier statement. And he goes on to clearly state his dilemma [op. n't., pp. 789-901, and particularly tackles the deductions to be expected on the basis of tetrahedral arrangements, as indicated by Dr. Sement- SOT.
(1894). DAVID F. LARDER He protested emphatically against crediting him with
the tetrahedron theory [op. cit., 131, 3 , 788 (1809) and DEPARTMENT OF TEE HI~TORY AND PEILOSOPHY OX. SCIENCE
[ 3 ] , 7,314 (1892). UNIVERSITY OF ABERDEEN The van't Hoff theory is very daring, because it as- A ~ E R D E E N , SCOTLAND
210 / lournal of Chemical Edumfion
