Of Parameters and Principles: Producing Theory in Twentieth Century Physics and Chemistry

*Department of Philosophy, Smith College, Northampton, MA 01063, U.S.A. (e-mail : [email protected]).

Stud. Hist. Phil. Mod. Phys., Vol. 31, No. 4, pp. 549}567, 2000( 2000 Elsevier Science Ltd. All rights reserved.

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Of Parameters and Principles:Producing Theory in Twentieth Century

Physics and Chemistry

Jeffry Ramsey*

1. Introduction

Are there limits to modifying an established theory for use in other theoreticaland experimental contexts? Since the alterations often produce qualitativelynew theories, are there &right' and &wrong' ways to produce theory in thismanner? Scientists often hold strong views about the appropriateness of ways tomodify theory. Among chemists, for instance, it is quite common to hear thatsemi-empirical techniques &represent no more than methods of interpolation'(Dewar, 1992, p. 133. Cf. LoK wdin, 1957; Freed, 1995). This is because semi-empirical modellers replace &some of the integrals required to solve the equa-tions by parameters' (Suckling et al., 1978, p. 135). That is, instead of using puretheoretical principles to calculate values for variables, the variables are "lledin*crossword-puzzle style*with values determined by experiment. As a result,many &assume that the result of ab initio calculations are inherently `bettera and`nearer to realitya' (Dewar, 1973, p. 243) and question &whether the semiempiri-cal approaches are [2] bereft of any true theoretical foundations' (Freed, 1995,p. 26). In short, the debate between the &principle' and &parameter' approacheshas been cast as a &right' vs a &wrong' way to produce theory.

For at least two reasons, however, this division is rather curious. Froma theoretical point of view, &In distinguishing between `semi-empiricala and`purea theories, one should always remember that all theories in physics andchemistry are basically semi-empirical in the sense that they correlate someexperimental data with other experimental data [2]' (LoK wdin, 1957, p. 58. Cf.

PII: S 1 3 5 5 - 2 1 9 8 ( 0 0 ) 0 0 0 2 4 - 1

549

1As outlined by Galison and Warwick (1998), a &cultures of theory' approach addresses thepedagogical training of theorists, how experimentalists and theorists interact, and di!ering attitudestoward the appropriate degree of mathematical rigour. This paper examines issues independent ofbut related to the issue of rigour, viz. how theorists appropriate and then modify existing theories,how they legitimate certain styles of theory production in this process, and how the styles are relatedto historically given conceptions of prediction and explanation.2By &style', I do not mean simply mere di!erences of approach, as when two musicians play the samewritten notes but interpret them di!erently. I have in mind more thorough-going di!erences, aswhen the English National Opera produces &The Marriage of Figaro' and the Royal Opera Houseproduces &Il Nozze di Figaro'. Since the two houses have very di!erent traditions, the same operalooks very di!erent in the two places. Many thanks to Nalini Bhushan for calling my attention to theconnotation of the word &style' and to Joe Early for the example.

Berry, 1960; Dewar et al., 1993; Freed, 1995; LoK wdin, 1989). Second, even thoughscientists in other disciplines employ these two approaches, they have seldominterpreted the di!erence in such stark terms. Moreover, chemists as a grouphave not agreed on the character of theory or on the appropriate means ofconstructing a theory. Perhaps the chemists' dependence on rules has led themto be more at ease with theoretical schemata that do not necessarily have thestatus of theories (Nye, 1993; Gavroglu, 1997).

But if this is the case, why has this group of chemists interpreted the debate asa di!erence in kind rather than degree? I believe a signi"cant part of the answerto that question lies in history. At a broad level, the stage for con#ict was set bythe presence of the two approaches to theory production and the rise of new,principle-based theories in physics. During the 1930s, many chemical theoristswere attempting to translate the new theories of physics into the pre-existingtheoretical and laboratory language of chemistry. Some interpreted this asa chance to move chemical theorising from parameters to principles; othersthought there were good reasons to retain the parametric approach. Upon thisstage, the play performed by local actors was important. When semi-empiricaltechniques were introduced, defenders of the two traditions clashed andcemented the dichotomous interpretation.

Gavroglu (1997), Nye (1993) and Bensaude-Vincent and Stengers (1996) haveargued that, in order to locate and understand the theoretical particularity ofchemistry, one must know the historically-constituted peculiarities and com-monalities of chemistry vis a vis its neighbouring sciences. In this paper, I com-pare the story in chemistry with similar episodes in the history of turbulencetheory to argue that the disciplinary and individual di!erences noted above didmake a di!erence. The comparative history thus provides me with a glance intothe &cultures of theory' (Galison and Warwick, 1998, p. 288)1 of physics andchemistry in the twentieth century. Moreover, this &contextualised treatment ofthe manifold practices of theory' (Galison and Warwick, 1998, p. 288) allows meto address the questions with which I began the paper. Theories must often be&articulated' (Hacking, 1983) with other theories and with laboratory practice(Gavroglu, 1997). Di!erent processes of articulation or modi"cation producedi!erent kinds of explanations. And when there are many di!erent projects ofexplanation in a science, multiple styles2 of theory production and articulation

550 Studies in History and Philosophy of Modern Physics

3Lorentz's theory could explain the dependence of mass on velocity, the contraction of movingobjects, and the isotropy of the velocity of light in inertial reference systems. All were explained tohave been caused by the interaction between the electrons constituting matter and the ether.

are needed. All this implies that the debate in chemistry should not be presentedas a debate between the &right' vs the &wrong' approaches to theory production.More generally, it shows that the appropriateness of modi"cations to existingtheory is conditional. Among other factors, an alteration's acceptability must bejudged by considering the kinds of problems theorists confront and the tradi-tions of theory structure and problem solving within a given discipline.

I begin by characterising the traditions of &principles' and &parameters'. I thenmove to the local context of the introduction and reception of semi-empiricaltechniques into chemical theorising. Finally, I expand more fully on the remarksabove.

2. The Broad Historical Context

2.1. Physics

Many twentieth century theoretical physicists have been strongly attracted toa style of theory production that emphasises principles rather than parameters.Thus, one might expect to hear physicists condemning semi-empirical ap-proaches as strongly as the chemists do. However, the history of turbulencetheory shows that physicists have been quite accepting of alternative styles whenthe situation has demanded it.

It is well known that Einstein preferred what he called &principle' theories,which involved &"nding a restrictive principle which made no assertions regard-ing the constitution of matter' (Miller, 1980, p. 14). Importantly for the purposesof this paper, &as examples of such principles Einstein saw before himself the lawsof thermodynamics which assert the impossibility of a perpetuum mobile, regard-less of the system's material constitution' (ibid.). Einstein was trying to avoidwhat he called &constructive theories', which do make such assertions. Examplesof constructive theories included mechanics and electromagnetism.

What led Einstein to this preference? At the turn of the twentieth century,physics was faced with two primary contradictions between mechanics andelectromagnetism. First, the success of Lorentz's electromagnetic theory, whichrequired the ether, contrasted with the failure of the mechanical world picture tosimulate the ether's action.3 Second, Planck's radiation law, derived from hiswork on cavity radiation, violated both mechanics and electromagnetic theory.It restricted the states of motion of radiation, thereby violating mechanics. Inaddition, the law violated electromagnetic theory by postulating discontinuousexchanges of electromagnetic energy between the constituent electrons and theradiation within the cavity.

551Of Parameters and Principles

4This quali"cation is already a hint that &principle' theories are not just a matter of content-lessprinciples. They also involve commitments to particular kinds of entities or structures. Thus, thedi!erence between the two approaches is a di!erence in degree rather than kind. I return to thispoint later in the paper.5The literature documenting these di!erences is very large. For a quick, introductory sketch, seeBarrow (1991, pp. 90! ). Barrow notes that Planck saw physical science as an essentially inductiveenterprise. For Planck, &there could be no attainable all-encompassing theory that explained thevalues of all the constants of nature' (ibid., p. 90). Likewise, the instrumentalists Duhem andBridgman had great skepticism about the power of fundamental theory to explain (ibid., p. 91; cf.Cartwright, 1983). Gavroglu (1995) has called attention to a third tradition in physics, the phenom-enological approach favoured by Fritz London and others.

For my purposes here, three characteristics of a principle theory are mostimportant. First, as already noted, principle theories make few or no assump-tions about the constitution of matter. Einstein's theories do make assertionsabout the structure of the spacetime continuum (Friedman, 1983, p. 29), but theyare relatively if not entirely silent on the kinds of entities that "ll that structure.4Second, no theoretical value is to be parametrised by experiment. This isbecause parameters are seen as endorsing a particular ontological framework.For example, if the mass of the electron is taken from experiment, one is usuallycommitted to the assumption that the electron has those properties. The use ofexperimentally-determined values had led to the contradictions noted above byEinstein. Third, a commitment to those properties eliminates the ability toprovide an explanation why those were the appropriate values. As one theoret-ician has noted recently:

In his search for a uni"ed theory, Einstein re#ected on whether God could havemade the universe in a di!erent way; that is, whether the necessity of logicalsimplicity leaves any freedom at all. With this remark, Einstein articulated thenascent form of a view currently shared by many physicists: If there is a "nal theoryof nature, one of the most convincing arguments in support of its particular formwould be that the theory couldn't be otherwise [2]. Such a theory would declarethat things are the way they are because they have to be that way (Greene, 1999,p. 283).

In short, explanations are to be explanations why something must be the case.Commentators agree that this mode of theorising has continued to have

a profound in#uence on theorists over the course of the century (see Cushing,1990; Davies, 1995, p. 16; Greene, 1999, p. 296). Even so, physicists havecontinued to use a number of styles of theorising.5 During the twentieth century,physicists have employed the constructive approach, particularly when theyhave been confronted with computational di$culties and experimental uncer-tainties. As a case study, I examine e!orts by Werner Heisenberg and CarlFriedrich von Weiszaecker to produce a theory of turbulence in the 1940s.

In 1948, Heisenberg (1948) and von Weizsaecker (1948) produced a theory ofturbulence by employing a semi-empirical technique. Essentially, the problem of


6The eddy viscosity is a measure of how long a &blob' will stay together as it travels along in theoverall motion of the liquid or gas.7Liquids and gases are waves; you can shine a light on the wave and, depending on the size of thewave, you will get a characteristic re#ectance.

turbulence is to predict the process of energy transfer between di!erent elementsof a turbulent liquid or gas. This is usually visualised as understanding howenergy is lost within the eddies and also how it is transferred between the eddiesand the laminar elements of the #ow. If one knows this, one can calculate howmuch energy is lost overall in the moving liquid or gas. Presumably, all this isdeducible from the equations of motion. However, at the time, no-one had anyidea how such a deduction would proceed.

Using the kinetic theory of gases, Heisenberg and von Weiszaecker produceda solution to the question of energy transfer by deriving, among other things,expressions for the eddy viscosity6 and the mean free path of elements within aneddy. Values for these expressions could be identi"ed with spectroscopicmeasurements,7 and Heisenberg and von Weiszaecker inserted the spectro-scopic values into the equations they had derived. This is the semi-empiricalmove: the use of evidence*the spectra*to supply values for theoretical vari-ables that were mathematically derivable in principle. While Heisenberg typic-ally did not insert experimental values into equations directly, such a move isconsonant with his overall approach to theorising. Both his original quantummechanical matrix and his later attempts at producing an S-matrix relied uponexperimental data to constrain the theories (Cushing, 1990). In this case, theevidence is being "tted into a theoretical or conceptual framework (of the kinetictheory of gases) which is itself only loosely tied to the &fundamental' representa-tion of the equations of motion. For instance, the equations of motion do notcontain expressions for &blobs' or &eddies'. In addition, the kinetic theory in-volved explicit assumptions about the constitution of matter that were notderivable from the expressions for the motion. However, the constructive movewas necessary at the time. Without the use of the experimentally determinedvalues, calculations and thus predictions were impossible.

How was this method of constructing a theory received? Apparently, physi-cists were quite happy with it. Using the Science Citation Index from 1948 to1960 to locate the papers citing Heisenberg and von Weiszaecker, I discoveredno harsh criticisms and few if any mild ones. Most authors cite the methodapprovingly throughout the 1950s, even after Chandrasekhar's (1955, 1956)striking advances that moved the theory much closer to the &principle' ideal.Even though Chandrasekhar carefully noted his own theory was more deductiveand, in virtue of this, more easily calculable than Heisenberg's, other authors didnot then heap scorn on the semi-empirical method. More typically, they explicit-ly recognised the limitations of all theories and then opportunistically used theone that was closest to their own experimental evidence. The one exceptionI have been able to "nd (Kraichnan, 1957) makes a point of criticising both theHeisenberg}von Weiszaecker and Chandrasekhar versions of the theory.


8Chandrasekhar's theory included only a very simpli"ed description of the exchange of energyamong the various Fourier components of the velocity "eld. Kraichnan (1957), the critic mentionedearlier, attacks Chandrasekhar's theory on the basis that it lacks the detailed account of the energyexchange. Since it turns out that both the semi-empirical theory of Heisenberg and Chandrasekhar'stheory share this particular simpli"cation, Kraichnan is able to criticise both types of theories at thesame time even though they have very di!erent conceptual bases.9Many thanks to Sharon Crasnow for calling this to my attention.10Nye argues that, at least since Lavoisier, theoretical chemists have struggled to de"ne the meaningof theoretical chemistry within two methodological traditions. In one tradition, which she calls&positivist' or &exact', theoreticians have attempted to provide an &algebraic formulation' of chemistry&on mechanical principles' (Nye, 1993, p. 276). The alternative tradition, which she terms the&philosophical' or &realist' tradition, aimed, &in the words of Humphry Davy, to `ascertain the causesof all [chemical changes], and to discover the laws by which they are discovereda and that,according to Dumas, studies `the material particles chemists call atoms and the forces to which theseparticles are submitteda' (Nye, 1993, p. 274).

Chandrasekhar's own remarks are perhaps important. Despite being more&principled' and less &parametrised', Chandrasekhar did not claim his methodwas &closer to reality' or that Heisenberg's was &bereft of theoretical foundation'.Rather, he modestly distinguishes his approach from Heisenberg's. He callsHeisenberg's theory a &heuristic' theory in that it attempts &to describe turbu-lence in terms of certain a priori concepts derived from the kinetic theory ofgases but which are not deducible from the equations of motion' (1955, p. 1). Henotes further that it is clear that &heuristic' theories have their place even if theydo not measure up to the deductive ideal. He simply notes the limitations of suchtheories without deriding them in any way. Further, he is also quite straightfor-ward that his own, more deductive theory is nonetheless approximate (ibid., p. 4)and therefore limited in its own way.8

In summary, physicists have aimed for &principle' theories, but they haveaccepted other forms of theories when conditions demand them. For instance,even today, many turbulence theorists continue to use the parametric approachwhen developing solutions to computationally di$cult problems (cf. Sahu,Kumar and Joshi, 1998; Wratt, 1987). Only the simplest turbulence problemshave proven to be amenable to Chandrasekhar's analysis.9

2.2. Chemistry

What of chemists and their approaches to theory production? Speakingbroadly, historians and philosophers of science agree that chemistry has beenless dominated by theory than physics (cf. Bensaude-Vincent and Stengers,1996). Additionally, historians and philosophers of chemistry have noted that,even though both the principle and parameter traditions have been present inchemistry at least since Lavoisier,10 chemical theorists have been less willing tosee the principle approach as a holy grail of theorising. The majority oftheoretical chemists have noted the need to construct theories that are appropri-ate to chemical problems, and chemists have been more willing than physicists


to live with multiple representations (Nye, 1993; Brush, 1999; Weininger, forth-coming; Ho!mann, 1995).

Given this, one would expect theoretical chemists to employ constructivetheories more freely and thus for the semi-empirical techniques to be receivedrather more warmly than they were. It is in fact easy to cite fully developedexamples of the constructive approach in chemistry. Two twentieth centuryexamples are relevant here. Einstein looked to the principles of thermodynamicsas inspiration for his principle approach to theorising. Importantly for my storyhere, chemical thermodynamicists found it largely impossible to use only theprinciples. They employed constructive theories in order to tie the theory ofchemical thermodynamics to experimentally measurable quantities. Gavroglu(1997) has examined G. N. Lewis' introduction of activity and Van der Waals'construction of free energy surfaces for binary mixtures from this perspective.

The other salient story involves quantum mechanics. Since the advent ofquantum mechanics, the computational intractability of the wave equation hascaused theoretical chemists to continue to rely heavily on semi-empirical pro-cedures. Nonetheless, perhaps inspired by Born's remark that physics waspositioned to &impose her laws upon her sister science' of chemistry (Born, 1923,p. 78) and Dirac's oft-quoted remark that quantum wave mechanics reveals that&the underlying part of physics and the whole of chemistry are thus completelyknown' (Dirac, 1929, p. 714), some quantum mechanists and chemists embracedthe &principle', deductive approach to chemical problems shortly after theintroduction of the quantum theory. It was in this twin context of thermo-dynamics and quantum mechanics that perspectives on semi-empirical ap-proaches were cemented into modern chemical theorising. I turn now to thiscontext.

3. The Local Context

While Henry Eyring was in Berlin as a National Research Council Fellowduring 1929 and 1930, he and Michael Polanyi set themselves the task ofcalculating rates for chemical reactions. Just as Heisenberg and von Weis-zaecker were to do later in the 1940s, Eyring and Polanyi turned to a construct-ive approach when faced with insoluble theoretical equations.

To calculate the rates, Eyring and Polanyi needed to know how much energythe molecules possessed at the beginning, middle and end of the reaction. Themiddle, the point at which the reactant molecules are just transforming them-selves into the product molecules, is termed the &activated state'. They used thenew quantum mechanics to construct potential energy surfaces, which givea measure of how much energy molecules are gaining or losing as they reachthe activated state. They used thermodynamics to calculate the concentrationof activated molecules; this allowed them to calculate the passage of theactivated molecules over the energy barrier separating reactant and productmolecules.


11The coulombic energy results from the attraction of oppositely charged particles, i.e. protons andelectrons. The resonance energy is due to such quantum mechanical considerations as the delocalisa-tion of electrons and their indistinguishability.12The theoretical calculations were done by Sugiura (1927). Sugiura's calculations underestimatedthe overall force in the atom without indicating how much of an error was involved. In addition, thesolution contained no resources to assess the direction of the errors in the individual calculations.13The principal investigators of other reactions were candid that the available experimental valueswere too unreliable for any serious comparison with theoretical values (Boehm and Bonhoe!er,1926; Bodenstein and Jung, 1926). Even if the experimental values had been good, theoretical valuesfor other reactions simply did not exist. No one was able to evaluate the complex wave functions forsystems more complex than hydrogen.

They were not unaware of the approach via "rst principles. In fact, in their"rst attempt in the paper, they tried to use only the fundamental theory. In orderto calculate the energy of the activated state, they needed to know the relativecontributions of the coulombic and exchange energies.11 That the total energy isdecomposable into discrete contributions from each was an assumption, andEyring and Polanyi knew it was only an approximation (cf. their 1931, p. 300).However, since calculations from "rst principles only were simply impossible in1931, they employed this constructive move. Even then, they were faced witha problem. They judged that &unfortunately, we have only a sorry knowledge' ofthe coulombic and exchange energy functions (Eyring and Polanyi, 1931, p. 284)due to the &amassed uncertainties which come in with the introduced approxi-mations' in the theoretical calculation (Eyring and Polanyi, 1931, p. 299).12 Tofurther complicate the situation, the experimentally determined value for thetotal energy could not be separated into its components. So, faced with anexperimentally determined value that was not decomposable and a total theor-etical value that was not very accurate, Eyring and Polanyi advocated theirsemi-empirical method. Essentially, the method subtracts the theoretical valuefor the coulombic energy from the empirical value for the total binding energy.The exchange, or resonance, energy remains. Here, I call attention to theconstructive element in the method: the value for the coulombic charge para-meter, a value which was in principle calculable from theory, was being set byexperiment.

Next, Eyring and Polanyi generalised the method to other reactions. In sodoing, they employed further elements of the constructive style. Eyring andPolanyi had constructed their surface for the reaction of hydrogen atoms withhydrogen molecules, and they had calculated a value of about 10 kcal for thecoulombic contribution. For other reactions, both theoretical and experimentalvalues were too uncertain to be of any help.13 As a result, Eyring and Polanyisimply postulated that the coulombic contribution to other reactions was alsoaround 10 kcal. They gave no justi"cation for such an approximation; theysimply assumed that the value was valid. However, the assumption made thepotential energy surfaces of the other reactions partially accessible to boththeoretical and experimental investigation. By assuming a value for the coulombicenergy contribution, researchers could explore the variation in the strength


of the bond arising from quantum e!ects. They did this by assuming a distancebetween the reactant molecules, calculating the energies that resulted, thenmoving the molecules slightly closer together or farther apart and then calculat-ing again. Eventually, a surface could be constructed.

Reaction to Eyring and Polanyi's solution was mixed. On the one hand,chemists used it immediately to begin calculating the previously inaccessibleenergy surfaces. On the other hand, some criticised the method because itviolated the canons and characteristics of the &principle' approach to theorising.

A. S. Coolidge and H. James (1934) criticised the method because it generateda model that did not faithfully represent the physical situation. Eyring andPolanyi had used London's method for solving the wave equation, and Lon-don's method required unwarranted assumptions of bond orthogonality andunmodi"ed atomic orbitals. In addition, it did not provide a theoretical ration-ale for why the Coulombic energy should be only a small percentage of theoverall binding energy. Given these problems, Coolidge and James argued that&the relation of quantum mechanics to the socalled `semi-empiricala method ismerely suggestive, rather than justi"catory. There can of course be no logicalobjection to the application of this method as a purely empirical one; as such itsjusti"cation can arise from its e!ectiveness in dealing with a large number ofspecial problems' (Coolidge and James, 1934, p. 817). For Coolidge and James,a justi"catory connection*and thus a method that is other than &purely empir-ical'*had to describe why the errors involved in the assumption of bondorthogonality cancelled each other. They were not able to produce such anargument, but they did produce a theoretical argument (based on screening byinner shell electrons) for the low percentage of the coulombic contribution to theoverall binding energy. The search for the why is, as Greene noted, characteristicof the principle approach.

Interestingly, Coolidge and James' theoretical calculation produced approxi-mately the same percentage for the coulombic energy as that assumed by Eyringand Polanyi. In addition, the problem of bond orthogonality plagued a number ofattempts to apply quantum mechanics to physical systems during and after the1930s. Notably, this was the case with the simpli"ed version of Hueckel's schemefor treating mobile electrons in conjugated systems. Yet, the assumption did notalways lead to absurd results. Thus, there was pragmatic justi"cation for such anassumption even if the theoretical justi"cation was lacking or incomplete.

At the Faraday Society meeting of 13 to 15 September 1937, proponents of theconstructive and principle traditions faced o!. Many scientists were present, butI will focus on Henry Eyring and Michael Polanyi as representatives of theconstructive tradition and E. A. Guggenheim as the representative of theprinciple tradition.

Throughout his career, Guggenheim endorsed the principle style of theor-ising. He repeatedly stressed that thermodynamics was an exact science(Tompkins and Goodeve, 1971, p. 306), and he had a profound dislike ofarbitrary parameters (ibid., pp. 314, 316). Additional support for this character-isation can be found in his published works, speci"cally in his comments about


G. N. Lewis' concepts of fugacity and activity. In his in#uential text Thermo-dynamics, "rst published in 1949, Guggenheim does employ fugacities and activ-ities. However, he nearly always quali"es his use with a claim that these have littleor no theoretical basis. He notes Lewis introduced a &device' employing a &"cti-tious pressure' (Guggenheim, 1949, p. 118). Likewise, he notes that Lewis employsa &physical assumption' (ibid., p. 221) to derive an expression for the partialpressures of gaseous mixtures. Since the physical assumption is not based intheory, the expression has &no theoretical or experimental basis in general' (ibid., p.221). This leads to an &empirical relation' that is &often assumed for calculation. Itis equivalent to the assumption [that the partial pressures of gaseous mixtures willbe a simple relation derivable from the pressures of single gases], which we repeathas in general neither theoretical nor experimental basis' (ibid., p. 222).

At the Faraday Society meeting, Guggenheim objected strongly to Eyring andPolanyi's method. As he and his co-author Weiss noted, they wished to &com-pletely dissociate' themselves from Polanyi and Evans' point of view (Guggen-heim and Weiss, 1938, p. 66). Evans and Polanyi endorsed an assumption thatthe concentrations of activated molecules in reactions were maintained at theirequilibrium concentrations relative to the unactivated molecules. Guggenheimand Weiss remarked that the strongest evidence that this is the case was the

success of the crude collision theory, but this is a posteriori evidence. To establishthe validity of the assumption on theoretical grounds would require a detailedconsideration of the e!ectiveness of collisions in producing energetic molecules.Up to the present such a calculation has proved intractable [2]. Calculationswhich ignore this phenomenon [of the production of the activated species] seem tous too crude to be useful, and none have as yet been made which take adequateaccount of it (ibid., 66}67; italics in the original).

Clearly, Guggenheim required a rigorous derivation of assumptions from "rstprinciples. Any assumptions not so derivable render theoretical schemes useless.

Guggenheim's objections to Eyring's paper also show him holding "rmly tothe &principle' tradition. He levelled the charge that &the formulae for activationenergies used by Eyring were at "rst described as derived from quantum theory,[but] they are now admitted to be semi-empirical. I hope [2] it will be realisedthat they are entirely empirical' (Guggenheim, 1938, p. 27; cf. also Guggenheimand Weiss, 1938). Guggenheim advanced three lines of criticism, all of whichlocate his style of theorising in the alternate camp. First, he argued that it wasnot evident that the reaction rate could be &calculated without using dataobtained from the reaction itself ' (ibid., p. 27). Again, he regarded parametrisa-tion as unacceptable. Second, echoing Greene's remark quoted earlier about therequirement of necessity in theorising, Guggenheim objected because the semi-empirical model did not provide unique solutions to the theoretical equations. Ifthe fraction of coulombic binding energy &is to be adjusted for each reaction soas to give the right answer, the method is useless' (ibid.). The values wereadjusted so frequently, he charged, the &model' consisted of only a singlereaction. In other words, the method was only interpolative. Third, he argued


14Some applications of the semi-empirical technique involve fundamental equations with three ormore independent parameters (cf. Bruenger and Karplus, 1991; Dewar, 1973).15This is not an exhaustive survey of their responses. I highlight here only those that seem mostclearly to reveal the constructive elements. For a more complete discussion, see Ramsey (1997).16Zener (1930) and Slater (1930, 1931) provided greatly improved approximate analytic wavefunctions for atoms and molecules. These calculations weakened the rationale for the 10% solution.In 1933, Rosen and Ikehara used the improved functions to calculate coulombic values of 23%, 32%and 38% for Li

2, Na

2and K

2respectively (Hirschfelder, 1983, p. 13). Even so, for many reacting

molecules, a value of 10% appeared not unreasonable. Also, experimental values were changingconstantly (cf. Kassel, 1928, 1932a, 1932b, 1933; Rice, 1930, 1931, 1934).

the method had no inferential content. Since the total energy is composed ofonly two terms, assuming a value for one automatically gives the value for theother.14 Experiment is su$cient to provide the interpretation.

How did Eyring and Polanyi and their fellow travellers respond?15 Beforeanswering this, let me sketch Eyring and Polanyi's styles in order to locate themwithin the constructive tradition. Eyring loved to throw out di!erent modelsand did not care about consistency or rigour. &As I look back over my e!orts,I would characterize my contributions as being largely in the realm of modelbuilding [2] I perceive myself as rather uninhibited, with a certain mathemat-ical facility and more interest in the broad aspect of a problem than the delicatenuances' (Eyring, 1977, p. 1). One of his students remarked that a &judiciouscombination of theory and empirical results became a characteristic of much ofHenry's work' (Henderson, 1983, p. 2639).

Polanyi was also a model builder. His philosophy of &tacit knowledge' is wellknown, but his scienti"c work and the roots of his philosophy in his scienti"cpractice are less well known. In an unpublished essay, Mary Jo Nye (1996)argues that Polanyi most often employed*in the terms I am using here*aconstructive approach in his theorising. In his work on the theory of gasadsorption, x-ray crystallography, and reaction kinetics, Polanyi emphasisedthe deductive ordering from assumed principles rather than precise calculationfrom "rst principles. He freely used constructs only loosely related to thetheories of statistical mechanics and thermodynamics.

Given their approaches, Eyring, Polanyi and theoreticians of like mind notunexpectedly responded by emphasising the characteristics of the constructivetradition. Let me sketch out those characteristics while detailing the speci"cresponses to the charges.

With respect to the charge that the value of the coulombic energy wasadjusted for each reaction, Eyring and Polanyi did not respond. I can onlysurmise that they knew this was an exaggeration on Guggenheim's part. Soonafter the joint paper of 1931, Eyring (1931) assumed values of 10% for somereactions and 3% for others. A few years later, Eyring was assuming 14% for allreactions (cf. Hirschfelder, 1983, p. 13). Generally speaking however, the strategywas to assume as few values as necessary. Further, the change in values was notcapricious. New theoretical derivations and experimental determinations ofreaction rates constantly altered the values of the parameters.16


17 It was eventually realised that, although explosions do often occur, they do not result from theinherent reactivity of #uorine. Rather, catalytic in#uences leading to local heating are responsible.

First, defenders of the method invoked a di!erent concept of explanation. Ratherthan focusing on explanations from "rst principles, they stressed the patterns thatemerged upon the assumption of the value for the coulombic energy. As Coulsonwas to stress later, &con"dence was warranted that the model was essentially theright one if choosing one parameter resulted in a "rst right answer, followed bya succession of good "ts in the series' (Nye, 1992, p. 216). Joe Hirschfelder, a studentof Eyring's and Eugene Wigner's, noted that because molecular quantum mechan-ics was simply not mature enough to provide any answers, &We must be contentwith determining the functional relationships from a rough theoretical treatment'(Hirschfelder, 1941, p. 645). The one available rough treatment, the semi-empiricalmethod, had to pass muster &based on the accuracy of its predictions' (ibid., p. 645).Nearly one hundred activation energies had been calculated in the last decade, andthe agreement with experiment was respectable (within ten kilocalories) in nearly allcases. The attempt to argue that the method has inferential content is noticeable.Note that this strategy of pattern discovery is outlawed on the principle approachbecause that approach forbids the use of experimentally derived parameters.

Support for the claim that the method provided a &good "t' also came fromtheoretical quarters. Pelzer and Wigner (1932) corrected Eyring and Polanyi'ssolution to include the quantum mechanical leakage through the energy barrier.The correction moved the calculated activation energy closer to the acceptedexperimental value. Thus, it appeared that the approximations in the methodwere not too far from the correct quantum mechanical point of view eventhough, as Coolidge and James had argued, the method apparently misrepresent-ed the actual physical situation. Not surprisingly, supporters of the method tookthis correction to indicate that the method did have some inferential contentindependent of experiment.

Second, defenders of the method emphasised a di!erent role for prediction thanthat given by the principle approach. Rather than theoretically-based predictionsabout experimental values, they focused on predictions that translated the theoryinto the language of the laboratory. Eyring in particular stressed the utility of themethod in bridging the previously cavernous gap between theory and evidence.While making assumptions which were &not strictly correct', he argued he couldperform calculations which &will make possible a comparison of the theory withexperiment and lead to some striking qualitative predictions [2]' (Eyring, 1931, p.2530). The comparisons did allow him to make some striking predictions. In 1931,conventional theoretical wisdom held that the hydrogen}#uorine reaction pro-ceeded very quickly. Experiment bore out this opinion. Eyring used the semi-empirical method to claim that the two gases should actually be fairly inert towardseach other at room temperature. This suggestion was derided when Eyring an-nounced it at the 1931 spring meeting of the American Association for theAdvancement of Science. Shortly thereafter, however, independent experimentscon"rmed Eyring's calculations.17


18They are used even today for the same purpose. &Perhaps the main thing to realize aboutpotential energy surfaces for chemical reactions, is that we know very little about them'. Calculationsfrom theoretical principles &play a vital complementary role to experimental results in aiding thechoice of [the] potential energy surface used to interpret speci"c reactions' (Balint-Kurti, 1975,p. 174).19For a similar point about the importance of models in biology, see Rheinberger (1997), Bechteland Richardson (1993), and Wimsatt (1987).

Finally, defenders noted that di!erent facts were being explained. That is, themethods emphasised di!erent explananda. The thing to be explained was thecourse of a reaction and not the values for theoretical variables. Polanyi featuredthis in his remarks. For example, in response to a remark by Guggenheim,Polanyi noted

I ask: what can we say about the mechanism of any reaction if we refuse to considerthese energy surfaces? Take the reaction H#D

2PHD#D. The only prediction

that can be made on such lines is that the reaction can proceed by a preliminarydissociation of D

2into atoms, i.e. with an activation energy of 101 Kcals. Since,

however, the true activation energy is much lower, the dissociation mechanismmust be wrong, and we are left without any explanation of the reaction (Polanyi,1938, p. 28).

The semi-empirical method was the only way to get past the lack of information.Although the approximations involved in the method caused it to be unfaithfulto the underlying mechanisms of bonding, its use was justi"ed because it gavea &reasonable picture of the mechanisms of chemical reactions which wouldotherwise remain in the dark' (ibid.). Some method was better than no methodwhen fundamental theory gave you no handle on the thing you wanted toexplain.

A "nal characteristic feature of many constructive theories is the presence ofentities not given by the fundamental theory. Critics can defend the use ofconstructive theories because they give information about these explanatoryentities. The potential energy surface is such an entity. The surface was (and is)inaccessible to experiment. In the 1930s and 1940s, it was accessible by notheoretical means other than the semi-empirical method. Since very little wasknown about the surfaces, precise predictions about experimental data were notterribly important. Eyring claimed he wanted &to illustrate the principles in-volved [in the semi-empirical method] and to xnd what information regarding thepotential surface can be obtained by a comparison with experiment. In this waysuggestive results are obtained which should be helpful in guiding furtherinvestigations by both experiment and theory' (Wheeler, Topley and Eyring,1936, p. 179; emphasis added).18 Thus, it is important to realise that the site ofinterpretation is the model and not the theory. Consistency with the funda-mental theory can be less important than having a partially explanatory and/orpredictive model.19


20 Ab initio methods have a number of calculational and conceptual problems of their own. Forinstance, like semi-empirical methods, they involve some aspects of trial and error in the choice ofthe calculational base. For a good introduction to the issues, see Freed (1995).

4. Re6ection on the Narrative

The historically-based, contextualised treatment of theory given above showsthat scientists need to be able to have recourse to multiple styles of theoreticalreasoning within a science. Longino (1990) and others have argued that*amongother things*a diversity of theories is needed if a science is to have integrity.The same goes for a diversity of styles of reasoning. Theory construction andproblem solution must be sensitive to the obstacles theoreticians face and thepurposes to which they employ theoretical explanation. Einstein wanted toformulate laws of motion that were valid in all reference frames or coordinatesystems, and this involved unifying two disparate theories. In contrast, Heisen-berg, von Weiszaecker, Eyring and Polanyi were all trying to adapt a giventheory to problems that were theoretically and computationally intractable.When trying to apply one theory to a given problem, one should not be forced toemploy a mode of theorising that scientists have used to successfully resolvecontradictions between two theories. Endorsing only one ideal of theoreticalexplanation forces both evidence and theory into idealised, unrealisable roles(Ramsey, 1997). Just as with water, the need for purity in one's theoreticalexplanation depends on the situation.

A contextualised treatment of theory also provides critical distance on the abinitio, or fundamental, approach to theoretical explanation. Each style must bejudged according to its own criteria of assessment and how well it solves its owncalculational and conceptual problems. Ab initio approaches do have their ownproblems.20 One of those problems is that ab initio theoreticians typicallychoose an arbitrary set of molecules and them optimise the values for thetheoretical variables to those speci"c molecules. For other molecules, otheroptimisations must be performed (Dewar et al., 1993 p. 5036). This criticalperspective shows clearly that*as noted in the introduction*the di!erencebetween the approaches is one of degree rather than kind.

By recovering the di!erent ways in which a theory can be applied to a set ofproblems, we can also more readily appreciate the fact that the two styles oftheorising often lead to complementary results. It is an oft-repeated sentiment inthe literature that ab initio calculations can be corrected by sensitive semi-empirical calculations. Often, &chemistry could be said to be solving the math-ematicians' problems and not the other way around' (Coulson, 1948, quoted inNye, 1992, p. 216). This continues to be true even today, when*in contrast tothe time period in my historical narrative*we have fairly powerful ab initiomethods available (cf. Freed, 1995).

An attention to the culture of theory also recovers the fact that theorists areinvolved in di!erent projects of explanations. Sometimes the explanation is an


21Perhaps such sentiments have been expressed in letters and conversations. I have not yet exploredthe archival material.

explanation of theory; at other times it is an explanation using a given theory.Recognition of these multiple projects of explanations provides one way torecover the essential role of models in the theoretical process. For instance,potential energy surfaces and not laws or even the wave equation carry much ofthe interpretation in studies of reactions. The interpretation involves informa-tion that is connected to, but partially independent of the underlying theory.Semi-empirical methods allow one to get at that information and to ex-plain*using the theory*other problems of interest. If constructive approachesare outlawed, explanations with those models becomes impossible. Since thosemodels often uncover and provide a rationale for interesting patterns in thedata, this is to be resisted.

Finally, I hope to have provided some ground for endorsing the historical andcomparative approach to philosophical issues. One gets a critical distance onthe di!erent styles only by examining the history of the disciplines. Additionally,such an approach hints at a number of interesting di!erences between thetheoretical cultures of chemistry and physics. For instance, it is striking thatchemists have long been more tied to experiment than physicists, yet it is thechemists who agonised over the use of evidence in equations. Second, chemistscite the computer as one of the primary means of rapprochement between theapproaches. &With the development of modern electronic computers, [...] chem-ists in general have become much more accustomed to the use of high-browmathematics and large-scale computations. Today many chemists undertakeboth experimental and theoretical work, and many computational programsbased on quantum theory are now used both the interpret the experimentalresults obtained and to predict new ones' (LoK wdin, 1991a, p. 1; cf. LoK wdin,1991b, pp. 10}11; Dewar et al., 1993, pp. 5007, 5009, 5031; Schaefer, 1991; andnumerous other sources). However, as the history of turbulence theory shows,the computer need not have been an essential element of the increasing cordial-ity. All of the turbulence theoreticians of the 1940s and 1950s relied on hand andpaper calculations to produce better predictions. Thus, a historical and com-parative approach allows us to begin to ask questions about why chemists haveresponded to the computer in the ways they have. Third, in contrast to chemists,physicists*at least those involved in turbulence theory*did not publicly re-mark that, on the basis of the mistakes that were involved in previous calcu-lations, they could now build a better theory.21 Certainly, there wasa recognition that the heuristic theories lacked some qualities of the principle-oriented, deductive theories, but there was no attempt to use a ladder and thenthrow it away. Why is this? Something in the respective cultures of the physicistsand chemists is surely conditioning such a response, but I do not have a moredetailed answer. In any case, an historical and comparative approach opens upinteresting questions about the theoretical cultures of di!erent disciplines.


5. Conclusion

I have not fully answered the questions with which I began. I do not know ifthere are absolute limits on the modi"cation of theories. However, I have arguedthat &doing theory' is a broad category of activities. Comparative history showsthat it is not a simple matter to judge that there are not &right' vs &wrong'ways todo theory. Among other things, the &right' way depends on the nature of theproblem chosen, the theoretical techniques available at the time, the kind ofexplanation sought, and the adeptness of the theoretician. In short, theoryemerges as a heterogeneous and situationally speci"c way of treating problems.In chemistry at least, I believe this perspective is needed. As Joe Hirschfelder(1982, p. 350) once remarked, &Although nature might be simple and elegant,molecular problems [are] de"nitely complicated'. Woody Allen had a similarinsight in Husbands and Wives. He said, &God does not play dice with theuniverse. He plays hide and seek'. For complicated games of hide and seek,multiple styles of theorising are needed.

Acknowledgements*Research and much of the writing for this paper was completed while I wasa fellow at the Oregon State University's Center for the Humanities during the fall quarter of 1997.Many thanks to the Center for providing a very conducive atmosphere for research. A version of thispaper was read at the Center in November 1997. A version was also read in July 1999 at the meetingof the International Society for the Philosophy of Chemistry in Columbia, SC. Questions from theaudience and conversations with the conference participants contributed greatly to the paper.I would also like to thank Kostas Gavroglu and Mary Jo Nye for their valuable conversations andsuggestions.

References

Balint-Kurti, G. G. (1975) &Potential Energy Surfaces for Chemical Reactions', Advancesin Chemical Physics 30, 137}179.

Barrow, J. (1991) Theories of Everything (Oxford: Clarendon Press).Bechtel, W. and Richardson, R. (1993) Discovering Complexity: Decomposition and Local-

ization as Stategies in Scientixc Research (Princeton, NJ: Princeton University Press).Bensaude-Vincent, B. and Stengers, I. (1996) A History of Chemistry, transl. by D. van

Dam (Cambridge, MA: Harvard University Press).Berry, R. S. (1960) &Time-Dependent Measurements and Molecular Structure: Ozone',

Reviews of Modern Physics 32, 447}454.Bodenstein, M. and Jung, G. (1926) &Die Dissoziation des Wassersto!molekuels', Zeit-

schrift fu( r physikalische Chemie 121, 127}135.Boehm, E. and Bonhoe!er, K. F. (1926) &Ueber die Gasreaktionen des activen Wasser-

sto!s', Zeitschrift fu( r physikalische Chemie 119, 385}399.Born, M. (1923) The Constitution of Matter, Modern Atomic and Electron Theories, transl.

from 2nd German edn by E. W. Blair and T. S. Wheeler (London: Methuen).Bruenger, A. T. and Karplus, M. (1991) &Molecular Dynamics Simulations with Experi-

mental Restraints', Accounts of Chemical Research 24, 54}61.Brush, S. (1999) &Dynamics of Theory Change in Chemistry: Part 2. Benzene and

Molecular Orbitals, 1945}1980', Studies in History and Philosophy of Science 30A,263}302.


Cartwright, N. (1983) How the Laws of Physics Lie (New York: Oxford University Press).Chandrasekhar, S. (1955) &A Theory of Turbulence', Proceedings of the Royal Society of

London 229A, 1}19.Chandrasekhar, S. (1956) &Theory of Turbulence', Physical Review 102, 941}952.Coolidge, A. S. and James, H. M. (1934) &The Approximations Involved in Calculations

of Atomic Interaction and Activation Energies', Journal of Chemical Physics 2,811}817.

Coulson, C. (1948) &Inaugural Lecture' for the Chair of theoretical physics, King'sCollege, London. Coulson papers, d21, Oxford University.

Cushing, J. (1990) Theory Construction and Selection in Modern Physics: The S-Matrix(New York: Cambridge University Press).

Davies, P. (1995) About Time (New York: Simon and Schuster).Dewar, M. J. S. (1973) &The Role of Semi-empirical SCF MO Methods', in W. Price, S.

Chissick, T. Ravensdale (eds), Wave Mechanics: The First Fifty Years (New York: JohnWiley and Sons), pp. 239}254.

Dewar, M. J. S. (1992) A Semi-Empirical Life (Washington, DC: American ChemicalSociety).

Dewar, M. J. S., Jie, C. and Yu, J. (1993) &SAM1: The First of a New Series of GeneralPurpose Quantum Mechanical Molecular Models', Tetrahedron 49, 5003}5038.

Dirac, P. A. M. (1929) &Quantum Mechanics of Many-Electron Systems', Proceedings ofthe Royal Society of London A123, 714}733.

Eyring, H. (1931) &The Energy of Activation for Bimolecular Reactions Involving Hydro-gen and the Halogens, According to the Quantum Mechanics', Journal of the AmericanChemical Society 53, 2537}2549.

Eyring, H. (1977) &Men, Mines and Molecules', Annual Reviews of Physical Chemistry 27,1}13.

Eyring, H. and Polanyi, M. (1931) &Ueber einfache Gasreaktionen', Zeitschrift fu( rPhysikalische Chemie B12, 279}311.

Freed, K. (1995) &Building a Bridge Between Ab Initio and Semiempirical Theoriesof Molecular Electronic Structure', in J. L. Calais, E. S. Kryachko (eds), Structureand Dynamics of Atoms and Molecules: Conceptual Trends (Dordrecht: Kluwer),pp. 25}67.

Friedman, M. (1983) Foundations of Space-Time Theories (Princeton, NJ: PrincetonUniversity Press).

Galison, P. and Warwick, A. (1998) &Introduction: Cultures of Theory', Studies in Historyand Philosophy of Modern Physics 29B, 287}294.

Gavroglu, K. (1995) Fritz London: A Scientixc Biography (New York: Cambridge Univer-sity Press).

Gavroglu, K. (1997) &Philosophical Issues in the History of Chemistry', Synthese 111,283}304.

Greene, B. (1999) The Elegant Universe (New York: W. W. Norton).Guggenheim, E. A. and Weiss, J. (1938) &The Application of Equilibrium Theory to

Reaction Kinetics', Transactions of the Faraday Society 34, 57}70.Guggenheim, E. A. (1938) &Untitled Remarks in Discussion', Transactions of the Faraday

Society 34, 27.Guggenheim, E. A. (1949) Thermodynamics: An Advanced Treatment for Chemists and

Physicists (4th edn 1959, Amsterdam: North Holland Publishing Company). Pagereferences are to the 1959 edition.

Hacking, I. (1983) Representing and Intervening (New York: Cambridge University Press).Heisenberg, W. (1948) &Zur statistischen Theorie der Turbulenz', Zeitschrift fu( r Physik 124,

628}657.Henderson, D. (1983) &Henry Eyring, My Friend', Journal of Physical Chemistry 87,

2637}2640.


Hirschfelder, J. (1941) &Semi-Empirical Calculations of Activation Energies', Journal ofChemical Physics 9, 645}653.

Hirschfelder, J. (1982) &My Fifty Years of Theoretical Chemistry, I: Chemical Kinetics',Berichte der Bunsengesellschaft fu( r Physikalische Chemie 86, 349}355.

Hirschfelder, J. (1983) &My Adventures in Theoretical Chemistry', Annual Reviews inPhysical Chemistry 34, 1}29.

Ho!mann, R. (1995) The Same and Not the Same (New York: Columbia UniversityPress).

Kassel, L. (1928) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 4 (Washington: National Research Council),pp. 30}41.

Kassel, L. (1932a) The Kinetics of Homogeneous Gas Reactions (New York: AmericanChemical Society).

Kassel, L. (1932b) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 7 (Washington: National Research Council), pp.26}37.

Kassel, L. (1933) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 8 (Washington: National Research Council),pp. 26}38.

Kraichnan, L. (1957) &Relation of Fourth-Order to Second-Order Moments in StationaryIsotropic Turbulence', Physical Review 107, 1485}1490.

Longino, H. (1990) Science as Social Knowledge (Princeton, NJ: Princeton UniversityPress).

LoK wdin, P.-O. (1957) &Present Situation of Quantum Chemistry', Journal of PhysicalChemistry 61, 55}68.

LoK wdin, P.-O. (1989) &Some Aspects on the Structure and Present Situation of QuantumChemistry as Expressed at the Girona Workshop', in R. CarboH (ed.), Quantum Chem-istry: Basic Aspects, Actual Trends (Amsterdam: Elsevier), pp. 605}622.

LoK wdin, P.-O. (1991a) &On the Historical Development of the Valence Bond Methodand the Non-orthogonality Problem', Journal of Molecular Structure (Theochem) 229,1}14.

LoK wdin, P.-O. (1991b) &On the Importance of Theory in the Future Development ofChemistry', Journal of Molecular Structure (Theochem) 230, 1}3.

Miller, A. I. (1980) &Forward: The Historical Context', in I. Rosenthal-Schneider (ed.),Reality and Scientixc Truth (Detroit: Wayne State University Press), pp. 9}21.

Nye, M. J. (1992) &Physics and Chemistry: Commensurate or Incommensurate Sciences?',in M. J. Nye et al. (eds), The Invention of Physical Science (Dordrecht: Kluwer),pp. 205}224.

Nye, M. J. (1993) From Chemical Philosophy to Theoretical Chemistry (Berkeley: Univer-sity of California Press).

Nye, M. J. (1996) &Laboratory Practice and the Physical Chemistry of Michael Polanyi',unpublished manuscript.

Pelzer, H. and Wigner, E. (1932) &Ueber die Geschwindigskeitkonstante von Austausch-reaktionen', Zeitschrift fu( r Physikalische Chemie B15, 445}471.

Polanyi, M. (1938) &Untitled remarks in discussion', Transactions of the Faraday Society34, 28.

Ramsey, J. (1997) &Between the Fundamental and the Phenomenological: The challengeof `Semi-Empiricala Methods', Philosophy of Science 64, 627}653.

Rheinberger, H. -J. (1997) Toward a History of Epistemic Things (Stanford, CA: StanfordUniversity Press).

Rice, O. K. (1930) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 5 (Washington: National Research Council),pp. 21}35.


Rice, O. K. (1931) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 6 (Washington: National Research Council),pp. 23}36.

Rice, O. K. (1934) &Kinetics of Homogeneous Gas Reactions', in C. J. West (ed.), AnnualSurvey of American Chemistry, Vol. 6 (Washington: National Research Council), pp.35}48.

Sahu, A., Kumar, P. and Joshi, J. (1998) &Simulation of Flow in Stirred Vessel with AxialFlow Impeller: Zonal Modeling and Optimization of Parameters', Industrial andEngineering Research 37, 2116}2130.

Schaefer, L. (1991) &The Mutation of Chemistry: The Rising Importance of Ab InitioComputational Techniques in Chemical Research', Journal of Molecular Structure(Theochem) 230, 5}11.

Slater, J. (1930) &Atomic Shielding Constants', Physical Review 36, 57}64.Slater, J. (1931) &Molecular Energy Levels and Valence Bonds', Physical Review 38,

1109}1144.Suckling, C. J., Suckling, K. and Suckling, C. W. (1978) Chemistry through Models:

Concepts and Applications of Modelling Chemical Science, Technology and Industry(Cambridge: Cambridge University Press).

Sugiura, Y. (1927) &Ueber die Eigenschaften des Wassersto!molekuK ls um Grundzu-staende', Zeitschrift fu( r Physik 45, 484}492.

Tompkins, F. C. and Goodeve, C. F. (1971) &Edward Armand Guggenheim', BiographicalMemoirs of Fellows of the Royal Society 17, 303}326.

Weininger, S. (forthcoming) &Butlerov's Vision: The Timeless, the Transient, and theRepresentation of Chemical Structure', to appear in N. Bhushan and S. Rosenfeld (eds),Of Minds and Molecules: Philosophical Perspectives on Chemistry (New York: OxfordUniversity Press).

Weizsaecker, C. F. V. (1948) &Das Spektrum der Turbulenz bei grossen ReynoldsschenZahlen', Zeitschrift fu( r Physik 124, 614}627.

Wheeler, A., Topley, B. and Eyring, H. (1936) &The Absolute Rates of Reaction ofHydrogen with the Halogens', Journal of Chemical Physics 4, 178}187.

Wimsatt, W. (1987) &False Models as Means to Truer Theories', in M. Nitecki and A.Ho!man (eds), Neutral Models in Biology (New York: Oxford University Press), pp.23}55.

Wratt, D. (1987) &An Experimental Investigation of Some Methods of Estimating Turbu-lence Parameters for Use in Dispersion Models', Atmospheric Environment 21,2599}2608.

Zener, C. (1930) &Analytic Atomic Wave Functions', Physical Review 36, 51}56.


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