For a presentation and discussion of Smith's concept of

An Investigation into the Smithian System of Sympathy:

from Cognition to Emotion, Laurie Bréban * Published in The Adam Smith Review,10,.

Introduction

In the first part of the Theory of Moral Sentiments (1759, 1790) -"Of the Propriety of Action" -Smith seeks to explain the origin of moral approbation. It is well-known that the solution to this problem lies in his famous concept of sympathy. 1

Of course, the question of the precise nature of Smithian sympathy gave rise to an abundant literature from as early as the nineteenth century with the emergence of the Adam Smith

Problem. 2 This famous Problem, which suggests that there is an inconsistency between Smith's two major works -The Theory of Moral Sentiments and The Wealth of Nations( 1776) -led Smith scholars to question whether or not sympathy, in the Theory of Moral Sentiments, was a specific sentiment ("the sentiment of sympathy") or a specific virtue (like altruism or benevolence) as it was interpreted to be by the advocates of the Adam Smith Problem (with authors from the Older German Historical School such as Carl Knies and Wiltold von Skarzynskiat the top of the list). 3 But this was challenged, albeit much later, by contributions following the scientific publication of the complete works of Adam Smith in the late 1970s. 4 Since the publication of the Glasgow edition, it has generally been agreed that Smithian sympathy does not refer to a specific sentiment or a specific virtue. 5 This does not mean, however, that there is a consensus among commentators about what Smith meant by sympathy, so that the question of its precise nature remains open.

For some commentators, Smith used the term sympathy to refer to a concordance of sentiments between two persons (a spectator and an actor) rather than a specific sentiment felt by the spectator. 6 They claimed that such a concordance was brought about by the spectator undergoing an imaginary change of situation in order to conceive of what he would feel in the actor's situation. At the end of the process, if he feels something which concords with the actor's feeling, then there is sympathy. On this interpretation, Smith's concept denotes something in the emotional realm (a specific configuration of both persons' emotions). For other commentators, Smith's sympathy refers to the imaginary change of situation itself. Thus, sympathy is held to be rather a cognitive process, prior to the emotional realm, which would enable us to conceive of the sentiments of others. It purportedly gives rise to an emotion related to the other but not necessarily concordant with the other's actual emotion (see [START_REF] Cropsey | Adam Smith and Political Philosophy[END_REF][START_REF] Macfie | The Individual in Society: Papers on Adam Smith[END_REF][START_REF] Biziou | Introduction, in Adam Smith, Théorie des sentiments moraux[END_REF][START_REF] Peil | Adam Smith and Economic Science: a Methodological Reinterpretation[END_REF][START_REF] Nanay | Adam Smith's concept of sympathy and its contemporary interpretations, in The Philosophy of Adam Smith: Essays Commemorating the 250th Anniversary of The Theory of Moral Sentiments[END_REF]Urquhart, 2010and Dellemotte, 2011).

Between these two interpretations, there are contributions which indistinctly use the word sympathy to refer to both the concordance of sentiments and to the imaginary change of situation in the Theory of Moral Sentiments (see, for instance, Fleischacker, 2012 7 and Frazer, 2012). Even commentators who claim to adhere to one of the two interpretations above maintain some confusion about the precise content of Smithian sympathy. This is typically the case of [START_REF] Campbell | Adam Smith's Science of Morals[END_REF] who, after having stated that "'sympathy' is Smith's word for agreement, coincidence or harmony of sentiments" (1971, p. 94), suggests "that Smith has a general meaning for 'sympathy', namely the perception of the coincidence of sentiments, and a specific meaning, the capacity to achieve such a coincidence through the imaginary change of one's point of view" (1971, p. 94).

The same kind of confusion is at work in [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF] and [START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF]. For instance, [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF], who insists on the emotional dimension of sympathy, states that part of what Smith says could correspond to the modern concept of empathy, in the sense that the spectator, 5 However, [START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF], prompts us to give a more nuanced picture of this consensus.

6 See, for instance, [START_REF] Campbell | Adam Smith's Science of Morals[END_REF], [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF] and [START_REF] Raphael | The Impartial Spectator: Adam Smith's Moral Philosophy[END_REF].

7

For instance, [START_REF] Fleischacker | Sympathy in Hume and Smith: a Contrast, Critique, and Reconstruction, inIntersubjectivity and Objectivity in Adam Smith and Edmund Husserl[END_REF], right from the beginning of his article, makes it clear that "for Hume and Smith, sympathy is not compassion. Ratherthey use the word for any case, in which one person participates in another's feelings". But at the same time, Fleischacker claims that "we might identify Humean and Smithian sympathy with what today we call 'empathy', except that that word is generally employed for a thinking of oneself into other people's shoes that fits Smith's but not Hume's account of shared feelings" (2012, p. 273).

identifying with the person he observes, could imagine the emotional experience of this person (R. Sugden, 2002, p. 71). 8 As for [START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF], he maintains that sympathy, as the faculty which enables one to perceive and then feel another's sentiments, is prior to any sentiments. But at the same time, he cannot help underscoring what he considers to be the polysemous character of Smith's concept. Dellemotte claims that Smith uses the word sympathy to refer to an explanatory principle (the system of sympathy), to a cognitive process and to an emotional result. 9 Finally, other scholars go so far as to attribute this confusion to Smith himself (Binmore, 1998 10 and Frazer, 2012 11 ).

Such confusion prompts us to pay more attention to the exact terminology used by Smith, in the Theory of Moral Sentiments. As shall be seen, when Smith uses the term "sympathy" in isolation (or synonymously "fellow-feeling" (TMS, I, i, 1, p. 10)), he is not designating a cognitive process but rather a particular result of it that would seem to be in the realm of emotion. Smith never uses the word "sympathy" to refer to this cognitive process. He uses instead the expression "imaginary change of situation" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 19,p. 21;VII,iii,1,p. 317). Of course, this imaginary change of situation plays an important part in his system of sympathy. But Smith does not leave any ambiguity about this part: a few times in the text, sympathy is said "to be founded" or "to arise from" an imaginary change of situation. 12 Thus, as [START_REF] Raphael | The Impartial Spectator: Adam Smith's Moral Philosophy[END_REF] remarked, it constitutes a 8 For an opposing interpretation, see Nanay (2010).

9 "[S]ympathy designates […] in Smith's work both an explanatory principle (as in the expression "system of sympathy"), an operator, or the main cog of a "mechanism" by which an individual, identifying with another and conceiving what he would feel in his situation, is likely to share his feelings, and lastly the result of this operation when it succeeds (the actual concordance of sentiments between the actor and the spectator)" [START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF](Dellemotte, , p. 2248)).

10 Some recent contributions on Smithian sympathy still refer to the Adam Smith Problem. This is the case of Binmore's second volume of Game Theory and the Social Contract (1998). According to Binmore, the Adam Smith Problem stems from Smith's ambiguous understanding of sympathy. On the one hand, Smith allegedly defines sympathy as empathy in its modern sense, but on the other hand, he often uses it in the sense of today's sympathetic preferences (1998, pp. 368-9). In order to reconcile Smith's two major works, Binmore proposes to free Smithian sympathy from its supposed initial confusion by reinterpreting it in terms of modern empathy (1998, p. 12, pp. 368-9).

11 "Smith confusingly speaks of sympathy and compassion (as do we all) in many different senses. Smith sometimes uses the term sympathy to refer to stage one alone [the imaginary change of situation; L.B.] or to stage two alone [the spectator feels some reaction herself in response to this imagined situation]; when it is used in these senses sympathy need not imply any approval at all. Yet Smith also calls moral approval itself 'sympathy' […] and the same name is given to the whole process to the extent that approval is the result" (Frazer, 2012, p. 101).

12 My italics in all the quotations hereafter: "and we have no occasion for sympathy, or for that imaginary change of situations from which it arises" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 19); "He must […] strive to render as perfect as possible, that imaginary change of situation upon which his sympathy is founded" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 21); "That imaginary change of situation, upon which their sympathy is founded, is but momentary" (TMS, I, i, 4, p. 21); "When I sympathize with your sorrow or your indignation, it may be pretended, indeed, that my emotion is founded in self-love, because it arises from bringing your case home to myself, from putting myself in your situation, and thence conceiving what I should feel in the like circumstances. But though sympathy is very properly said to arise from an imaginary change of situations with the prerequisite for sympathy, not sympathy itself. Finally, to designate the entire system (both the "imaginary change of situation" and "sympathy"), Smith broadly speaks of "the system of sympathy" (TMS, VII, iii, 1, p. 317). In the rest of the paper, I will strive to remain faithful to Smith's terminology.

Beyond the clarification that it brings, this terminological detour allows us to emphasize that Smith's system of sympathy, as a whole, contains both a cognitive and an emotional dimension. Now, there remains a point barely addressed by commentators, that is, how does Smith connect both dimensions or, in others words, how can this cognitive process give rise to something in the emotional realm?

The literature often claims that Smith's conception of sympathy is superior to Hume's because Smith's supposedly includes a further cognitive dimension that is missing from Hume's (see, for instance, [START_REF] Macfie | The Individual in Society: Papers on Adam Smith[END_REF][START_REF] Campbell | Adam Smith's Science of Morals[END_REF][START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF]. [START_REF] Fleischacker | Sympathy in Hume and Smith: a Contrast, Critique, and Reconstruction, inIntersubjectivity and Objectivity in Adam Smith and Edmund Husserl[END_REF] goes so far as to write that Smith, in his opening chapter on sympathy, "uses technical terms borrowed from Hume to make an anti-Humean point" (2012, p. 279). In this paper, I take the opposite view. Of course, there are differences between Smith's and Hume's system of sympathy. 13 However, the fact remains that the Smithian system uses elements from the Humean philosophy of knowledge. This is especially the case for the way Smith views the connection between the cognitive and the emotional dimensions within his system. As shall be seen, such a connection relies on a neglected concept of the Theory of Moral Sentiment, inherited from Hume's theory of beliefs and that Smith calls "the force of conception".

Far from being a concept of secondary importance, the force of conception provides a key to answering a question raised by some commentators and which concerns the possibility of moral evaluation based on Smith's system of sympathy (see, for instance, [START_REF] Macfie | The Individual in Society: Papers on Adam Smith[END_REF][START_REF] Campbell | Adam Smith's Science of Morals[END_REF][START_REF] Gordon | Sympathy, Simulation, and the Impartial Spectator[END_REF][START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF][START_REF] Nanay | Adam Smith's concept of sympathy and its contemporary interpretations, in The Philosophy of Adam Smith: Essays Commemorating the 250th Anniversary of The Theory of Moral Sentiments[END_REF][START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF]. The issue generally arises as to whether the imaginary change of situation allows for the spectator's emotion to be distinct from the emotion of the person with whom he identifies (the original emotion). Commentators agree person principally concerned […]" (TMS, VII, iii, 1, p. 317). Smith even writes "that this is the source of our fellowfeeling for the misery of others, that it is by changing places in fancy with the sufferer, that we come either to conceive or to be affected by what he feels" (TMS, I, i, 1, p. 10;On the synonymy between sympathy and fellowfeeling, see above, §1.1).

that it cannot be otherwise -if only because, as [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF] rightly observed, there would be no room for moral evaluation in the Theory of Moral Sentiments.

For some, the mere existence of an imaginary change of situation ensures the possibility of moral evaluation, because they understand the word "situation" in the strict sense of the term (see, for instance, [START_REF] Macfie | The Individual in Society: Papers on Adam Smith[END_REF][START_REF] Campbell | Adam Smith's Science of Morals[END_REF]. They claim that, by imaginary change of situation, Smith meant the process by which a spectator imagines what he would feel in another's situation.

It would then be possible that Smith's imaginary change of situation would lead him to feel an emotion distinct from the one felt by the person with whom he identifies. Now, Smith does not understand the word "situation" in the strict sense of the term. For Smith, the imaginary change of situation implies that the spectator imagines being the other in his situation (see TMS, VII,iii,1,p. 317). This has made some scholars quite skeptical about the possibility of moral evaluation in the Theory of Moral sentiments (see, for instance, [START_REF] Gordon | Sympathy, Simulation, and the Impartial Spectator[END_REF][START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF]. Their skepticism stems from their interpretation of Smith's imaginary change of situation which they consider to involve the spectator's loss of identity. Contrary to them, I will show that this is not the case. 14 After having made it explicit that Smithian sympathy, strictly speaking, possesses an emotional content, I show, in the first section of the paper, that it relies on a complex cognitive process (the "imaginary change of situation") which enables one to conceive of others' sentiments. Of course, Smith's aim, with his system of sympathy, was not to explain how we manage to conceive of others' feelings but rather how we come to be affected by them. This cognitive process constitutes, therefore, just one step, the next step being to highlight how we move from the cognitive to the emotional realm. I argue that such a movement relies on the concept of "force of conception" which allows for our conception of others' feelings to give rise to an emotion being experienced that is related to others' situations ( §1).

In the second section, we offer a characterization of the emotional result that arises from Smith's imaginary change of situation. We do so by highlighting the influence of the cognitive realm on the emotional realm, through the role of the force of conception. After having highlighted two 14 [START_REF] Nanay | Adam Smith's concept of sympathy and its contemporary interpretations, in The Philosophy of Adam Smith: Essays Commemorating the 250th Anniversary of The Theory of Moral Sentiments[END_REF] and Frazer (2012) also share the position according to which Smith's imaginary change of situation does not entail the spectator's loss of identity. However, [START_REF] Nanay | Adam Smith's concept of sympathy and its contemporary interpretations, in The Philosophy of Adam Smith: Essays Commemorating the 250th Anniversary of The Theory of Moral Sentiments[END_REF] does not set out Smith's reasons for such an eventuality. As for [START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF], he identifies one of the reasons put forward by Smith (the fact that the imaginary change is momentary). But Frazer fails to explain how, for Smith, this reason ensures that the spectator will retain his own identity during the imaginary change.

properties of Smith's imaginary change of situation [(i) the conception bias and (ii) the weakness of conception], we show that it is not only possible but that it is also taken for granted that this imaginary change of situation leads the spectator to feel an emotion distinct from the one felt by the person with whom he identifies ( §2).

To conclude, I highlight the conditions under which the emotional result of Smith's imaginary change of situation can properly be called "sympathy". Unlike [START_REF] Nanay | Adam Smith's concept of sympathy and its contemporary interpretations, in The Philosophy of Adam Smith: Essays Commemorating the 250th Anniversary of The Theory of Moral Sentiments[END_REF], I come to the conclusion that Smithian sympathy does consist in a correspondence of sentiments between the sympathizer and the person he is sympathizing with. It shall be argued that the question of the content of sympathy does not lie so much in knowing whether it is a correspondence of sentiments but rather in knowing what Smith means by correspondence?

Moving from the cognitive to the emotional realm

The emotional content of sympathy

According to some commentators, in order to restore the consistency between The Theory of Moral Sentiments and The Wealth of Nations, Smith's sympathy has to be interpreted as a cognitive process, prior to the emotional realm. Thus, while recognizing the necessity to link the concept of sympathy with the emotional realm (see, for instance, Biziou, Gautier and Pradeau, 1999, p. 6), these commentators neglect one of its fundamental aspects: its emotional content.

Yet, asserting that sympathy possesses an emotional content is not to say that it refers to a specific sentiment, such as supported by the advocates of the Adam Smith Problem. This is why we would like to emphasize the emotional content of Smithian sympathy, without, for the time being, going into the details of this content.

The emotional content of sympathy can be emphasized through Smith's use of two words:

1) It concerns, of course, the word "sympathy" itself, which the author describes as something that we feel or express (my italics in the following quotations, L.B.): "The sympathy, which my friends express with my joy, might, indeed, give me pleasure by enlivening that joy: but that which they express with my grief could give me none, if it served only to enliven that grief." (TMS, I, i, 2, p. 14) "But though we feel no proper sympathy with an attachment of this kind" (TMS, I, ii, 2, p. 32) "The sympathy which we feel with them, renders the passion which they accompany less disagreeable" (TMS, I, ii, 2, p. 33)

2) But, it also concerns the word "fellow-feeling":

Pity and compassion are words appropriated to signify our fellow-feeling with the sorrow of others. Sympathy, though its meaning was, perhaps, originally the same, may now, however, without much impropriety, be made use of to denote our fellow-feeling with any passion whatever. (TMS,I,i,1,p. 10) This last excerpt from the Theory of Moral Sentiments, in which Smith acknowledges a synonymy between "sympathy" and "fellow-feeling", is very explicit about the fact that sympathy refers to something located in the emotional realm: it is obviously what is signified by the words "fellowfeeling". 15 However, despite textual evidence, the synonymy between "sympathy" and "fellow-feeling" is not supported by all commentators. For instance, [START_REF] Montes | Adam Smith in Context: A Critical Reassessment of Some Central Components of His Thought[END_REF] asserts that "sympathy" should not be confused with "fellow-feeling". He claims that the difference between them turns on the fact that sympathy arises from our knowledge of the cause of the other's passion whereas fellowfeeling refers only to a real (and not fictitious) sharing of sentiments. Though appealing, this interpretation is debatable. On the one hand, textual evidence shows that information on the cause of the other's passion is necessary for the emergence of "fellow-feeling":

Even our sympathy with the grief […] before we are informed of the cause of either, is always extremely imperfect […] The first question which we ask is, What has befallen you? Till this be answered, though we are uneasy both from the vague idea of his misfortune, and still more from torturing ourselves with conjectures about what it may be, yet our fellow-feeling is not very considerable. (TMS, I, i, 1, p. 12) On the other hand, just like sympathy, "fellow-feeling" does not always refer to a real sharing of sentiments. The case that best illustrates this point is the one of our sympathy with the dead with whom no sharing of sentiment is possible at all:

We sympathize even with the dead, and overlooking what is of real importance in their situation, that awful futurity which awaits them, we are chiefly affected by those circumstances which strike our senses, but can have no influence upon their happiness […] Surely, we imagine, we can never feel too much for those who have suffered so dreadful a calamity. The tribute of our fellow-feeling seems doubly due to them now, when they are in danger of being forgot by every body. (TMS, I, i, 1, p. 13) 15 Sugden also insists on this synonymy between "sympathy" and "fellow-feeling" in order to show the emotional content of Smithian sympathy (2002, p. 71). This leads him to reject both the modern concepts of sympathy and empathy as used in what he calls "rational choice theory" as possible candidates for expressing Smithian sympathy, since they would be deprived of any emotional content which, he argues, characterizes Smith's conception (on the more general question of the emotional content of rational choice theory, see the debate between Diaye and Lapidus (2005a;2005b) and Sugden (2005)).

The result is that fictitious "fellow-feelings" are possible. They correspond to cases that Smith calls "illusive sympathy" (TMS, II, i, 2, p. 71). 16 In this context, it remains difficult to deny the synonymy that Smith establishes between "sympathy" and "fellow-feeling". And this synonymy together with the foregoing textual evidence strongly suggests that Smithian sympathy belongs to the emotional realm. Now that the reasons which prompt us to think that Smithian sympathy belongs to the emotional realm have been stated, let us turn to what could be considered its foundation.

Smith's imaginary change of situation: a complex cognitive process

The secondary literature has widely acknowledged the cognitive dimension within Smith's system of sympathy. But, as we saw in the introduction, part of this literature assigns it to sympathy strictly speaking. However, the Theory of Moral Sentiments leaves no doubt about the fact that the cognitive process that Smith describes -the "imaginary change of situation"-and "sympathy" are separate concepts, serving different purposes.

Let us now focus on the specific purpose served by the imaginary change of situation. Actually, Smith dedicates a whole paragraph to it, in the opening chapter of the Theory of Moral Sentiments entitled "Of sympathy" (TMS, I, i, 1, §2). In this paragraph, he tries to deal with a fundamental philosophical issue which is well known today as the attribution problem. As he observes, we cannot have an "immediate experience" of others' feelings. But all the same, we are able to perceive "the manner in which [they] are affected" (TSM, I, i, 1, §2).17 This leads him to conclude that It is by the imagination only that we can form any conception of what are [others'; L.B] sensations. Neither can that faculty help us to this any other way, than by representing to us what would be our own, if we were in [their] case. (TSM, I, i, 1, §2, p. 9) 16 Smith defines illusive sympathy as follows: "But as we put ourselves in [the deceased's situation] we feel upon this, as upon many other occasions, an emotion which the person principally concerned is incapable of feeling, and which yet we feel by an illusive sympathy with him" (TMS, II, i, 2, p. 71). It may be noticed that illusive sympathy refers not only to our sympathy with the dead. Smith also gives other typical illustrations such as the case of our sympathy with a man who has lost his reason or a mother nursing a sick child (see TMS, I, i, 1, pp. 12-13). Now, the cognitive process that Smith describes is more complex than it appears. Such complexity arises from the twofold operation of the imagination. 18 On the one hand, as already observed, imagination allows for a change -an imaginary change -of situation. This operation constitutes, for Smith, the only way by which we can bypass a fundamental limitation of our senses. Our senses, he says, "never did, and never can, carry us beyond our own person". But it is not the same for the imagination. Thanks to the imagination, we are able to go "beyond our own person" and to "place ourselves" in the other's situation (TMS, I, i, 1, §2, p. 9). 19 On the other hand, though the limitation of our senses has been overcome, they remain decisive in the process which leads us to conceive of others' sentiments. In that we can say that Smith endorses the Humean opposition to innatism. 20 According to Smith, when putting ourselves in the situation of others, we do not give up what we have learnt from our senses. On the contrary, it is only on the basis of what we felt in the past that we manage to conceive of what others feel. Now, such a transition from the past experiences of our senses to our conception of others' feelings also rests on the operation of imagination. Indeed, using the same vocabulary as his mentor and friend David Hume, Smith asserts that once we are in the situation of others, "[i]t is the impressions of our own senses only, not those of [theirs], which our imaginations copy" (TMS, I, i, 1, §2, p. 9), so that our conception of others' feelings is none other than our representation of what our own would be if we were in the same situation.21 18 Indeed, for Smith, imagination is a cognitive faculty. This specific role that Smith grants to imagination is even more salient in his History of Astronomy (1795). For a discussion of the role of imagination in Smith's work, see, among others, [START_REF] Harrison | Imagination and Aesthetics in Adam Smith's Epistemology and Moral Philosophy[END_REF], [START_REF] Campbell | Adam Smith's Science of Morals[END_REF][START_REF] Skinner | Adam Smith, Science and the Role of the Imagination[END_REF]1979, pp. 14-41) and [START_REF] Raphael | The Impartial Spectator: Adam Smith's Moral Philosophy[END_REF]. For a more specific discussion of the central role of imagination in Smith's moral philosophy and, especially, in sympathy, see Evensky (2005, I, 1, pp. 3-9).

19 Consequently, identification requires information about the situation which gives rise to the other's emotion (see TMS, I, i, 1, p. 11). This latter, per se, does not constitute sufficient information for the spectator to identify with the other. This is why Smith asserts that "Sympathy […] does not arise so much from the view of the passion, as from that of the situation which excites it" (TMS, I, i, 1, p. 12). According to some commentators, the importance Smith accords to information for the emergence of sympathy introduces an objective element on which a spectator can rely in order to accompany, or not, the other's emotions (Biziou, Gautier, Pradeau, 1999, p. 8;Griswold, 1999, pp. 83-96;Rick, 2007, pp. 138-9).

Thus, according to Smith, imagination -and not sympathy, as it is sometimes argued (see [START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF]) -is the faculty that enables us to conceive of others' feelings. 22 This faculty is the foundation of a complex cognitive process which, as has been shown, allows us both to put ourselves in others' situations and, from there, call on the past experiences of our own senses in order to conceive of what they feel, namely, what we would feel in their situation.

The force of conception: a bridge between the cognitive and the emotional realms

Now, the aim of the first chapter of the Theory of Moral Sentiments is not to explain how we manage to conceive of others' feelings. In the opening lines of the chapter, Smith observes:

That we often derive sorrow from the sorrow of others, is a matter of fact too obvious to require any instances to prove it; for this sentiment, like all the other original passions of human nature, is by no means confined to the virtuous and humane, though they perhaps may feel it with the most exquisite sensibility. (TMS, I, i, 1, §1, p. 9)

The issue then becomes for him to explain how we come to be affected by others' feelings. In this perspective, the cognitive process described above is just one step in the author's reasoning; the following step is to show how we move from the cognitive to the emotional realm. Such a movement relies on a neglected concept of the Theory of Moral Sentiments which is somewhat reminiscent of the Humean theory of "belief" and that Smith sometimes calls "the force of conception" (see, for instance, TMS, I, i, 1, p. 10). It is well known that, for Hume, the difference between an idea and the original impression from which it derives depends on their respective emotional contents. For Hume, unlike an impression, an idea does not per se have any emotional content. But it may give rise to an impression thanks to belief, the specificity of which is to endow an idea with "the force and the vivacity" of the original impression (Hume, 1739-40, I, iii, 7). 23 Now, this is the same kind of influence that Smith ascribes to the force of conception while explaining how our conception of others' feelings comes to give rise to an emotion related to others. In terms similar to Hume's, Smith argues: For as to be in pain or distress of any kind excites the most excessive sorrow, so to Conceive or to imagine that we are in it, excites some degree of the same emotion, in proportion to the vivacity or dullness of the conception. (TMS, I, i, 1, p. 9; my italics, L. B.)

Beyond the terminological similarities, it is obvious that Smith uses here the general conception of belief built by his elder. The very basis of his argument constitutes the outcome of the prior cognitive process: our conception of others' feelings. As has been observed, this actually corresponds to our conception of what our emotion would be if we were in the others' situation. But this conception does not have any emotional content so long as we do not really believe that we are experiencing this situation. It is because, during our imaginary change of situation, we believe ourselves in some measure to be in the other's situation that it is endowed with an emotional content -the emotional content of the emotion that we imagine we would feel in the other's situation. This is how, for Smith, we come to be affected by others' feelings. Our belief about being in the others' situation, or in Smith's words, the force of our conception allows for our conception of others' feelings, which arises from our imaginary change of situation, to give rise to an emotion being experienced that is related to the other's situation.

We began this first section by emphasizing that Smithian sympathy, strictly speaking, belongs to the emotional realm. Now, with regard to what has just been shown, it becomes legitimate to ask whether the emotional result which arises from Smith's imaginary change of situation, thanks to the force of conception, corresponds to what the author properly calls sympathy. It will be shown that, under certain circumstances, this is indeed the case.

The influence of the cognitive realm on the emotional realm

Smith's imaginary change and the spectator's identity

Some commentators complain that Smith's account of his imaginary change of situation is equivocal since it is unclear how it could allow for the spectator's emotion to be distinct from the original emotion (see, for instance, [START_REF] Gordon | Sympathy, Simulation, and the Impartial Spectator[END_REF][START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF]. Their doubts arise from a passage of the Theory of Moral Sentiments in which Smith reviews "those Systems which deduce the Principle of Approbation from Self-love" (TMS, VII, iii, 1, p. 315). On this occasion, Smith argues that the other's situation to which he refers while speaking of an imaginary change of situation is a matter of both "circumstances" and "person": though sympathy is very properly said to arise from an imaginary change of situations with the person principally concerned, yet this imaginary change is not supposed to happen to me in my own person and character, but in that of the person with whom I sympathize. (TMS,VII,iii,1,p. 317) Consequently, through identification, Smith says, "I not only change circumstances with you, but I change persons and characters" (TMS,VII,iii,1,p. 317). This passage gave rise to various and sometimes conflicting interpretations of Smith's imaginary change, the question then being whether such an imaginary change of position, which involves becoming the other person, could leave room for the emergence of an emotion distinct from the original one.

For instance, [START_REF] Fontaine | Identification and Economic Behavior _ Sympathy and Empathy in Historical Perspective[END_REF] considers that Smith's identification process corresponds to what he calls "empathetic identification", as opposed to "partial empathetic identification" which would only imply a change of circumstances. But Fontaine does not make explicit the consequences of such an identification process for the resulting emotion, as if it were obvious that it would allow for the spectator's emotion to be distinct from the original one. This is, however, a point raised by [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF] who remains skeptical about such a possibility. Endorsing Fontaine's categories, Sugden argues that "given the central role that Smith's account of approval plays in the Theory of Moral Sentiments, […] we must assume that Smith intended identification to be only partial" (Sugden, 2002, p. 75). Thus, despite textual evidence, Sugden considers "empathetic identification" as inconsistent with Smith's moral philosophy.

In substance, Sugden's skepticism stems from the fact that he associates empathetic identification with the spectator's loss of identity. Of course, for the sake of the consistency of the Theory of Moral Sentiments, I agree with Sugden that Smith's identification process should not involve such a phenomenon. However, I do not share his interpretation of Smith's intentions. Unlike Sugden, I take Smith at his word arguing that he intended identification to involve an imaginary change both of circumstances and persons. Moreover, I maintain that Smith is clear about the fact that this does not suppose the spectator's loss of identity. As a result, it is not only possible but it is assumed that, for him, identification leads the spectator to feel an emotion distinct from the one felt by the person with whom he identifies. 24 24 Several commentators have remarked that Smith's imaginary change systematically leads the spectator to feel a distinct emotion from the original one (see, for instance, [START_REF] Campbell | Adam Smith's Science of Morals[END_REF]Griswold, 1999, pp. 86-7;Dellemotte, 2002, 147-9;Broadie, 2006, pp. 168-9;Nurock, 2009, pp. 66-7). Nonetheless, the question will be addressed differently hereafter.

Actually, the issue of the spectator's loss of identity lies not so much in the elements that he changes with others while identifying with them (circumstances or both circumstances and persons) as in the specificities of Smith's imaginary change evoked in the previous section, namely: 1) in the way the spectator comes to conceive of the others' circumstances and persons;

2) in the degree to which he believes himself to be the other person, in his circumstances.

It is from this perspective that we are now going to show that identification, for Smith, does not involve the spectator's loss of identity. So as not to be too ponderous, in what follows, we remain faithful to Smith's terminology and refer to the other's circumstances and person as "the other's situation".

The properties of Smith's imaginary change: conception bias and weakness of conception

From what has been shown in the first section, it can be argued that Smith's imaginary change involves the spectator's loss of identity if:

1) He has no conception bias: his conception of the other's situation is strictly identical to the latter's conception of his own situation;

2) The force of his conception is maximal: his belief about being in the other's situation is such that he is no longer able to differentiate himself from the other. Now, it will be shown that Smith's imaginary change, does not possess either of these two properties and so there is no ground for claiming that it is consistent with the spectator's loss of identity.

First of all, the spectator's conception of the other's situation cannot be identical to the latter's conception of his own situation. As seen before, by means of the imagination, the Smithian spectator is able to go beyond his own person and to put himself in the other's situation.

However, the fact remains that this spectator cannot have any direct experience of the other's situation. Consequently, it is only on the basis of his own experiences that the spectator can form a conception of this situation (see above, §1.2). Now, experiences of the one are irreducible to experiences of the other. This gives rise to a conception bias that Smith illustrates through several extreme cases of illusive sympathy. 25 Here, we focus on the case of the man who has lost his reason: Of all the calamities to which the condition of mortality exposes mankind the loss of reason appears, to those who have the least spark of humanity, by far the most dreadful, and they behold that last stage of human wretchedness with deeper commiseration than any other. But the poor wretch, who is in it, laughs and sings perhaps, and is altogether insensible of his own misery. The anguish which humanity feels, therefore, at the sight of such an object, cannot be the reflection of any sentiment of the sufferer. The compassion of the spectator must arise altogether from the consideration of what he himself would feel if he was reduced to the same unhappy situation, and, what perhaps is impossible, was at the same time able to regard it with his present reason and judgment. (TMS,I,i,1,pp. 12) In this case, it is clear that the spectator's conception of the other's situation is not identical to the other's conception of his own situation. This difference arises from the respective states of their reasons and judgments. The man who has lost his reason does not seem to be aware of his situation. However, the spectator is fully aware of it, because to his observations about the other's situation, he adds elements of his own experience: elements coming from "his present reason and judgment". This leads him to conceive of the loss of reason in a very distinct way from the man who has really lost his reason. Whereas the spectator considers it to be an "unhappy situation" or the "last stage of human wretchedness ", the latter "is altogether insensible of his own misery". 26 Of course, an immediate consequence of such a bias regarding our conception of the other's situation is that our conception of the other's emotion cannot be identical to the original emotion either. Typically, in the foregoing case, Smith claims that the imaginary change of situation leads the spectator to conceive an emotion that "cannot be the reflection of any sentiment of the sufferer". Recall that the spectator's conception of the latter's emotion can be nothing but his own representation of what his own emotion would be in the other's situation (see §1.2 above). Then, since the spectator considers this situation to be a sad state of affairs, this leads him to conceive a sad emotion, whereas the man who has lost his reason, for his part, "laughs and sings". 27 26 In a previous footnote, we emphasized that Smith's imaginary change requires information about the other's situation (see §1.2 above, footnote 19). We can assume then that the more informed the spectator, the lower the conception bias. As has been suggested to me by Jerry M. Evensky, at The 2014 Meetings of the History of Economics Society, this conception bias may, therefore, disappear for "the supposed impartial and well-informed spectator" or the one that Smith also calls "the man within the breast" (TMS, III, 2, p. 130). 27 The conception bias and its consequences are also particularly salient in the case of our sympathy with the dead: "The idea of that dreary and endless melancholy, which the fancy naturally ascribes to [the] condition [of the dead], arises altogether from our joining to the change which has been produced upon them, our own consciousness of that change, from our putting ourselves in their situation, and from our lodging, if I may be allowed to say so, our own living souls in their inanimated bodies, and thence conceiving what would be our emotions in this case" (TMS, I, i, 1, p. 13).

Let us now show that Smith's imaginary change does not possess the second property according to which the spectator's belief about being in the other's situation would be maximal. Smith makes it explicit through another illustration in which he depicts a spectator who tries to minimize the foregoing conception bias while identifying with a sufferer:

In all such cases, that there may be some correspondence of sentiments between the spectator and the person principally concerned, the spectator must, first of all, endeavour, as much as he can, to put himself in the situation of the other, and to bring home to himself every little circumstance of distress which can possibly occur to the sufferer. He must adopt the whole case of his companion with all its minutest incidents; and strive to render as perfect as possible, that imaginary change of situation upon which his sympathy is founded. (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 21) But notwithstanding the efforts made by the spectator, as observed by [START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF], the fact remains that the "imaginary change of situation, upon which his sympathy is founded, is but momentary" (TMS, I, i, 4, p. 21). Consequently, Smith says, "[t]he thought of [his] own safety, the thought that [he himself] is not really the sufferer, continually intrudes itself upon [him]" (TMS, I, i, 4, p. 21). In other words, the spectator's awareness that the imaginary change of situation is just momentary diminishes his belief about being in the other's situation. It weakens the force of his conception, so that it cannot be maximal. So, while identifying with the other, he is continually aware that he is a separate person from the other.

To sum up, such a reading of Smith's imaginary change of situations can overcome [START_REF] Gordon | Sympathy, Simulation, and the Impartial Spectator[END_REF] and [START_REF] Sugden | Beyond Sympathy and Empathy: Adam Smith's Concept of Fellow-Feeling[END_REF] concerns about it implying the loss of the spectator's identity. Though identification with others involves not only a change of circumstances but also of person and character, the spectator cannot but retain his own identity. As a result, Smith's identification process does not satisfy the two foregoing properties. Even in the case where the spectator strives to render his imaginary change of situation as perfect as possible:

1) there remains an irreducible conception bias arising from the fact that he is not the other;

2) the force of his conception is not maximal because of his consciousness that he is a separate person from others.

So, contrary to what has been often claimed (L. Wispé, 1986, p. 314 and p. 318;K. Binmore, 1994, pp. 55-6;L. Montes, 2004, pp. 50-51;J. Rick, 2007, pp. 148-9), the Smithian spectator is invariably able to differentiate himself from others.

A characterization of the emotional result of imaginary change

Let us turn now to the features of the emotion resulting from the spectator's imaginary change of situation. As already suggested, the result of the non-fulfillment of both properties (1) and ( 2) is that the Smithian spectator necessarily feels an emotion distinct from that felt by the person with whom he identifies. However, the influence of (1) the conception bias and (2) the weakness of the force of conception on the emotional result shall be distinguished.

Since there is a conception bias inherent in Smith's imaginary change, "[w]e sometimes feel for another, a passion of which he himself seems to be altogether incapable; because, when we put ourselves in his case, that passion arises in our breast from the imagination, though it does not in his from the reality" (TMS, I, i, 1, p. 12). What has been shown in the previous subsection already put us on this track since an immediate consequence of the conception bias is that our conception of the other's emotion cannot be identical to the original emotion (see §2.2 above). 28 Yet, it is precisely this conception that gives rise to an emotion related to the other, thanks to the force of our conception (see §1.3 above). This is our conception of what our emotion would be in the other's situation -which is by its very nature, distinct from the other's real emotion-that is endowed with an emotional content. The result is that the emotion arising from our imaginary change of situation is necessarily distinct from the original one.

Let us now focus on the emotional content of our conception. Following Smith, this emotional content varies "in proportion to the vivacity of [our] conception" (TMS, I, i, 1, p. 9). However, as we have already argued, this vivacity cannot be maximal. This has another influence on the emotional result of identification, namely, that we can "never conceive […] that degree of passion which naturally animates the person principally concerned" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 21). 29 But that is not all! The weakness of our conception "not only lowers [our emotion] in degree, but, in some measure, varies it in kind, and gives it a quite different modification" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 22). To illustrate this point, Smith returns to the case of the spectator identifying with a sufferer. While comparing the spectator's emotion with the sufferer's emotion, he argues that 28 Whereas some contributions have noticed that the emotion resulting from Smith's imaginary change is never as intense as the original one (see [START_REF] Campbell | Adam Smith's Science of Morals[END_REF][START_REF] Dellemotte | Individu et coexistence sociale chez Thomas Hobbes et Adam Smith : une enquête sur le mythe fondateur de la science économique[END_REF][START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF], none mentions the fact that it is also never completely the same. In any event, such a characterization of the emotional result of Smith's imaginary change distance us from an intuitive understanding that it would be a more or less accurate copy of the other's emotion [START_REF] Levy | Sympathy and Approbation in Hume and Smith: a Solution to the Other Rational Species Problem[END_REF][START_REF] Montes | Adam Smith in Context: A Critical Reassessment of Some Central Components of His Thought[END_REF]. 29 Smith also writes that "the emotions of the spectator will still be very apt to fall short of the violence of what is felt by the [other]" (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 21).

what [the former] feel[s] will always be, in some respect, different from what [the latter] feels, and compassion can never be exactly the same with original sorrow. (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 22) Though both the spectator's and the sufferer's emotions reflect some sort of sorrow, this sorrow is not of the same kind. This difference arises from the fact that the spectator is aware that he is a separate person from the sufferer. Consequently, the sorrow that arises from the spectator's imaginary change of situation with the sufferer is not related to him but to the sufferer: it corresponds to compassion.

Conclusion: sympathy as a specific emotional result

Such a characterization of the emotional result of Smith's imaginary change of situation prompts us to consider Smithian sympathy as something other than the case in which the spectator's emotion is similar to the other's. Far from being trivial, such an interpretation of sympathy, as a feeling similar to the original one, led some commentators to view Smith's cases of "illusive sympathy" (TMS, II, i, 2, p. 71; italics added) as anything other than sympathy (see, for instance, [START_REF] Raphael | The Impartial Spectator: Adam Smith's Moral Philosophy[END_REF]. Now, as we have shown, Smith's imaginary change of situation systematically leads the spectator to feel an emotion distinct from the other. The question then becomes: under which conditions can we consider that the emotional result of the imaginary change of situation corresponds to what Smith calls "sympathy"? Smith makes his answer explicit while concluding his example of the spectator identifying with a sufferer. Though the sympathetic emotion -the spectator's compassion -is not similar to the original emotion -the sufferer's sorrow -these two sentiments, Smith says may […] have such a correspondence with one another, as is sufficient for the harmony of society. Though they will never be unisons, they may be concords, and this is all that is wanted or required. (TMS,I,i,[START_REF] Binmore | Game Theory and the Social Contract: Playing Fair[END_REF]p. 22) Consequently, contrary to what Nanay (2010) asserts, there is sympathy when the spectator's and the actor's emotions correspond with one another. However, such a correspondence does not entail, for Smith, that they feel a similar emotion. There is sympathy when the spectator's emotional reaction to the others' situation "concords" (in kind and intensity) with the other's emotion. In such a case, it is well known that the spectator is said to approve of the other's emotional reaction to his own situation (see TMS, I, i, 3); otherwise, he is said to disapprove of it.

As a result, there is no longer any reason to question the consistency between Smith's account of his imaginary change of situation and his analysis of moral evaluation.

Tribute:

But it is not the purpose of the present paper to confront the two authors' systems of sympathy. On this point see, for instance,[START_REF] Morrow | The Significance of the Doctrine of Sympathy in Hume and Adam Smith[END_REF],[START_REF] Fleischacker | Sympathy in Hume and Smith: a Contrast, Critique, and Reconstruction, inIntersubjectivity and Objectivity in Adam Smith and Edmund Husserl[END_REF] and[START_REF] Frazer | The Enlightenment of Sympathy: Justice and the Moral Sentiments in the Eighteenth Century and Today[END_REF].

On the fundamental separateness between individuals in Smith's analysis of sympathy, seeGriswold (1999, pp. 83- 91).

For an analysis of Hume's influence on Smith regarding the opposition to innatism, see for instance,Young (1997, pp. 32-3).

For all these reasons, I do not share Fleischacker's position that "almost immediately, in the second paragraph of the [opening] chapter [of the Theory of Moral Sentiments], Smith uses technical terms borrowed from Hume to make an anti-Humean point" (2012, p. 279). On the contrary, I believe that Smith embraces Hume's philosophy of knowledge in order to enrich his own system of sympathy.

[START_REF] Dellemotte | La cohérence d'Adam Smith, problèmes et solutions : une synthèse critique de la littérature après 1976[END_REF] himself concedes, Smith never uses the word "faculty" to refer to sympathy.

On the technical meaning of Humean belief, see also[START_REF] Lapidus | La Rationalité du Choix passionnel : En Quête de l'Héritage de David Hume[END_REF] 2010).

On illusive sympathy, see §1.1 above.

This article is in homage to Shirine Sabéran, a colleague and friend, who left us in June 2013. It owes a great deal to her professionalism, her benevolence and her friendship.

Acknowledgments:

Previous versions of this paper were presented at several conferences and workshops: The "Economics and Psychology in Historical Perspective" Conference (Paris, 2014), The History of Economic Society Conference (Montréal, Canada, 2014), Séminaire du LED (LED, 2014), 13th Summer Institute for the Preservation of the History of Economics (Richmond, USA, 2012), 14th Summer School in History of Economic Thought (Lisbon, Portugal, 2011), Séminaire des Après-Midis (PHARE, Paris, 2011). I would like to thank especially Elodie Bertrand, Ghislain Deleplace, Jean Dellemotte, Jerry Evensky, André Lapidus, David Levy, Sandra Peart, Shirine Sabéran, Nathalie Sigot and my referees. The remaining errors and omissions are mine alone.


domain: phys chim sdv spi

text:
Dalida Chouchi

Didier Gourgouillon

Mathilde Courel

Joaquim Vital

Manuel Nunes Da Ponte

The Influence of Phase Behavior on Reactions at Supercritical Conditions: The Hydrogenation of r-Pinene

In this paper, results on the hydrogenation of R-pinene, a liquid reactant, in supercritical (SC) CO 2 are presented. Visual observation of phase equilibria under the conditions of the reaction experiments was also performed. Much faster reaction rates were obtained when a two-phase system was present in the reactor than when a homogeneous, one-phase situation occurred. This phenomenon is attributed to the fact that SC CO 2 can dissolve extensively in the liquid reactant, leading to the formation of an "expanded liquid", which can dissolve large quantities of hydrogen. This seems to be the first time that this type of behavior is reported in the literature.

Introduction

Chemical reactions in supercritical fluid (SCF) media represent an expanding field. [START_REF] Noyori | Supercritical Fluids[END_REF][START_REF] Jessop | Chemical Synthesis in Supercritical Fluids[END_REF] One of the main advantages of using SCFs as solvents is their ability to dissolve large quantities of most gases. Carbon dioxide and hydrogen, for example, mix in all proportions [START_REF] Tsang | Phase equilibria in the H2/CO2 system at temperatures from 220 to 290 K and pressures to 172 MPa[END_REF] at temperatures above the critical temperature of CO 2 (304.1 K). If the other advantages over conventional liquid solvents, such as larger diffusion coefficients, lower viscosities, and nontoxicity, are added, SC CO 2 can be regarded as a potentially ideal solvent for carrying out hydrogenation reactions.

However, carbon dioxide has a serious drawback: it is a poor solvent for many substrates to be hydrogenated. Recently, Ha ¨rro ¨d and collaborators [START_REF] Harrod | Hydrogenation at Supercritical Conditions[END_REF] discussed the heterogeneously catalyzed hydrogenation of sunflower oil in two supercritical solvents, carbon dioxide and propane. They based their discussion on the phase diagram for ternary mixtures of oil + hydrogen + supercritical solvent in terms of the number of phases in contact with the catalyst. Because of the poor solubility of the oil in carbon dioxide, there are always two phases, liquid and gas, when the process is carried out in CO 2 . As a result, the concentration of hydrogen near the catalyst is small, and the positive effect of the presence of CO 2 on the reaction rate is thought to be due to viscosity reduction by dissolution in the liquid. In contrast, propane and oil can be made totally miscible. Only one (gas) phase contacts the catalyst when propane is used as a solvent, and very large increases in the reaction rates are obtained.

Bertucco and collaborators 5 studied a different hydrogenation reaction in CO 2 , where the system in contact with the catalyst was clearly biphasic. They also observed large increases in the reaction rate, although not as high as those observed in the work of Ha ¨rro ¨d et al.

Polyakoff et al. [START_REF] Poliakoff | A supercritical success story[END_REF] recently discussed these and similar results. They suggested that the liquid substrate dissolves a high quantity of CO 2 , becoming an "expanded liquid". Hydrogen would be highly soluble in this liquid, thus significantly increasing its concentration in the vicinity of the solid catalyst. Consequently, they concluded that "further research is needed to determine whether single phase behavior is essential for high efficiency in catalytic reactions".

Terpenes are a class of compounds with important industrial applications, especially in the fragrance and flavor industries. [START_REF] Albert | Flagrance and flavor chemicals[END_REF] Hydrogenation of these substances is commonly carried out for industrial purposes. On the other hand, most terpenes show a high affinity for CO 2 . There is, in fact, a large body of published research on phase equilibrium of terpenes + SC CO 2 (see, for example, Matos et al., [START_REF] Matos | Phase equilibria of natural flavours and supercritical solvents[END_REF] Akgu ¨n et al., [START_REF] Akgu ¨n | Phase behavior of essential oil components in supercritical carbon dioxide[END_REF] and Reverchon [START_REF] Reverchon | Supercritical fluid extraction and fractionation of essential oils and related products[END_REF] ). In general, supercritical CO 2 is highly soluble in most terpenes: at pressures close to the critical pressure, the liquid phase in a biphasic mixture can contain 80 mol % or more of CO 2 . Moreover, the critical pressures of these mixtures are reasonably low, often lower than 10 MPa.

It should therefore be easy to carry out experiments on hydrogenation reactions of terpenes in supercritical CO 2 , using either biphasic or single-phase mixtures, by small changes in the pressure. The results could represent a useful contribution to the discussion of the effect of phase behavior on catalytic efficiency.

We used the hydrogenation of R-pinene in SC CO 2 as a suitable model for that purpose. The hydrogenation of liquid R-pinene is well-known, as it is the first step in a series of reactions that converts a cheap and versatile raw material into a variety of valuable products (aromas and vitamins). 7 Figure 1 gives an example of a reaction in which R-pinene is used as a starting material for the synthesis of linalool.

Different metal-based catalysts can be used for the hydrogenation of R-pinene, such as Adams catalyst (PtO 2 ), Raney nickel, and carbon-supported metals (Pd/ C, Pt/C), depending on the selectivities and yields being sought. [START_REF] Cocker | The chemistry of terpenes. Part I. Hydrogenation of the pinenes and the careens[END_REF] The mechanisms of these catalytic reactions are generally well-known, and it is possible to control the stereoselectivity by adjusting the operating condi-tions. For example, Ilyna and Semikolenov recently proposed a mechanism for the hydrogenation of R-pinene on Pd/C catalysts to cis-and trans-pinane. [START_REF] Ilyna | Stereoselective hydrogenation of R-pinene to cis-pinane on Pd/C catalysts[END_REF] They showed that the selectivity toward cis-pinane is determined by two parameters: the hydrogen pressure and the reaction temperature.

At the start, the objectives of this work were to check the feasibility of hydrogenating R-pinene in SC CO 2 in the presence of a Pd/C catalyst and to examine the selectivity of the reaction under different pressures of CO 2 and H 2 . We chose CO 2 pressures corresponding to biphasic and monophasic conditions according to the data of Akgu ¨n et al. [START_REF] Akgu ¨n | Phase behavior of essential oil components in supercritical carbon dioxide[END_REF] To interpret the results obtained, a detailed study of the phase behavior under the conditions of the experiments (but without the presence of the catalyst) became necessary and was subsequently undertaken.

Experimental Section

2.1. Materials. Hydrogen and carbon dioxide with a stated purity of 99.998 mol % were obtained from Air Liquide. R-Pinene (purity ) 99%) and cis-pinane (purity > 99%) were obtained from Fluka. The catalyst was activated carbon-supported palladium (10 wt %) from Merck.

Hydrogenation Experiments.

Figure 2 is a schematic representation of the apparatus used for the hydrogenation of R-pinene with pressurized CO 2 . Reactions are carried out in a 316 SS reactor (R) with an approximately 40-cm 3 internal volume. Temperature control (323 K) is achieved through immersion in a thermostated water bath (stability better than 1 K, precision of (0.1 K). The stirring of the reaction mixture is achieved with a magnetic bar. The pressure inside the reactor is measured by a pressure transducer (PT) (Setra C204, precision of 0.1%).

The reactor is first flushed with low-pressure CO 2 and then loaded with 1 g of R-pinene and 0.02 g of catalyst. After that, CO 2 is introduced up to the desired pressure by means of a pressure generator (PG) (HIP, 87-6-5). When the temperature and pressure of the system are stable, H 2 is introduced in the reactor up to a total pressure of 14 MPa. This time is chosen as the starting time of the reaction (t ) 0).

During the reaction, samples are withdrawn at regular intervals from the top of the reactor through a highpressure switching valve (SV) (Rheodyne 7000) equipped with a 50-µL loop and connected to the reactor outlet (see Figure 2). An important consequence of this arrangement is that, when the system inside the reactor is biphasic, the samples are withdrawn from the gas phase. The additional volume of the loop induces a small pressure drop in the reactor, the extent of which depends on the working pressure. The content of the loop is then slowly depressurized at ambient temperature into a closed vial (V) filled with hexane in order to trap the R-pinene and pinane. Finally, the switching valve loop is washed twice with approximately 2 mL of hexane and then flushed with N 2 . The hexane fractions are collected together and analyzed by gas chromatograph (Varian 3800 GC) with a FID detector, equipped with a dimethylpolysiloxane column (CP-Sil 8 CB, 30 m long, 0.32 mm i.d., film thickness of 0.25 mm), working between 373 and 473 K with a heating rate of 15 K min -1 . The concentrations of R-pinene and pinane in the collected samples are determined using dodecane as the internal standard (response factor for R-pinene ) 0.90, response factor for pinane ) 0.81, precision of the method is better than 10%). The relative amounts of R-pinene and pinane in each sample taken from the reactor can then easily be calculated.

Phase Equilibrium Experiments.

To monitor the influence of pressure on the phase behavior of the system consisting of CO 2 , H 2 , R-pinene, and pinane during the reaction, we used a sapphire-windowed reactor (New Ways of Analytics) with an internal volume of approximately 50 cm [START_REF] Tsang | Phase equilibria in the H2/CO2 system at temperatures from 220 to 290 K and pressures to 172 MPa[END_REF] . This reactor is provided with a magnetically driven stirrer and anchor for efficient mixing of the components (max speed ) 2500 rpm), as well as a large sapphire window (diameter ) 36 mm, thickness ) 16 mm). Temperature control is achieved by means of a PID controller (Eurotherm 2216e) connected to a Pt-100 probe located in the reactor and two 100-W resistors inserted in the reactor walls. The pressure inside the reactor is measured with the same pressure transducer as used for hydrogenation experiments (Setra C204).

Results

All reaction experiments were performed at 50 °C, using 1 g of R-pinene and 0.02 g of catalyst. Five different experiments were carried out at CO 2 pressures of 8.0, 9.0, 9.5, 10.0, and 12.0 MPa. The total pressure of the system was 14 MPa in all cases and was reached by further introduction of H 2 .

Under these conditions, the initial concentration of R-pinene in the reactor varies from 4 to 11% of the CO 2 mass. The quantity of hydrogen cannot be calculated precisely, because of the lack of information on the densities of CO 2 + H 2 mixtures at high pressures. However, a rough calculation indicates that H 2 is in molar excess by 4-12 times in relation to the quantity required for the complete hydrogenation of 1 g of R-pinene. The results obtained in terms of mass percentages of pinane relative to R-pinene + pinane as a function of the reaction time are given in Table 1 and are plotted in Figure 3.

As the reactor used in these reaction experiments was a closed, no observation of the number of phases present was possible. Phase equilibrium experiments were separately performed in the previously described sapphire-windowed view cell. The main objective of these experiments was to determine the transition pressure from a two-phase (liquid-gas) system to a one-phase (fluid) system, under conditions of concentration that were similar to those in the reaction experiments. For this purpose, two separate experimental runs were carried out. In the first, 1 g of R-pinene was introduced into the cell, and CO 2 pressure was applied until all of the liquid disappeared and the system became monophasic. Subsequently, H 2 was added up to a pressure of 14 MPa. In the second run, instead of pure R-pinene, a 50/ 50 w/w liquid mixture of R-pinene + cis-pinane was used. Apart from this, the experiment was carried out as described for pure R-pinene. The purpose of the two different experiments was to mimic reaction conditions in the beginning (pure R-pinene) and at the midpoint (50/50 w/w mixture) of the reaction. However, no catalyst was added, to avoid any change of composition during the experiments. The transition pressures observed were 9.32 MPa for pure R-pinene and 9.37 MPa for the R-pinene + pinane mixture. In both cases, addition of H 2 did not induce any phase separation. The first result is in excellent agreement with the data presented by Akgu ¨n et al. [START_REF] Akgu ¨n | Phase behavior of essential oil components in supercritical carbon dioxide[END_REF] using static and dynamic methods.

C

Discussion

The results graphically represented in Figure 3 can be grouped in three different categories: the reactions at 8.0 and 9.0 MPa of CO 2 proceed at essentially indistinguishable, fast rates; the reactions at 10.0 and 12.0 MPa of CO 2 proceed at similar rates, but they are very slow; the reaction at 9.5 MPa of CO 2 is an intermediate case, where the reaction rate is low during the first 30 min and then increases significantly. It must also be remarked that, in the first two cases, the hydrogen pressure does not affect the reaction rates.

The phase equilibrium results obtained in this work determined that the first group (8.0-9.0 MPa) corresponds to biphasic conditions, whereas for the second group (10.0-12.0 MPa), the reaction proceeds in a single gas phase. For the intermediate case, the CO 2 pressure is very close to the transition pressure. It is possible, in fact, that the reaction initiates in a single phase and continues, after approximately 30 min, in two phases. There are three possible explanations for this phenomenon. (1) The sampling method induces a small pressure drop in the system, typically between 0.03 and 0.04 MPa. (2) The appearance of the reaction product pinane modifies the phase behavior. Indeed, pinane is slightly less soluble in CO 2 than R-pinene, and consequently, in our system, the one phase-two phase transition pressure increases as the reaction proceeds, as explained above. (3) The catalyst acts as a nucleus of condensation due to capillary forces and electrostatic interactions and leads to phase separation at surface or in the pores.

The hydrogenation of R-pinene in this work, therefore, was much faster under two-phase conditions than when a single phase contacted the catalyst. The reaction rate in each group did not depend on the quantity of H 2 , which in every case was present in large excess.

A possible explanation for this surprising result is that, under the conditions of this work, the limiting step for the catalysis might be the access of R-pinene, and not hydrogen, to the catalyst. Liquid mixtures of R-pinene and carbon dioxide at 8.0 and 9.0 MPa and 323 K have concentrations of R-pinene on the order of 10 mol. %. If the liquid surrounds the catalyst, R-pinene will have ready access to the metal. On the other hand, these liquid mixtures have a very high content of CO 2 and are a good model of the above-mentioned expanded liquids. Large amounts of gaseous hydrogen should be soluble in these liquids, maintaining a relatively high concentration of this substance close to the solid catalyst.

When single-phase conditions are obtained at higher CO 2 pressures, the concentration of R-pinene in the medium surrounding the catalyst is about 1 order of magnitude lower, on the order of 1 mol %.

A well-founded discussion of the factors involved would require adsorption data of R-pinene on Pd/C catalysts, so that quantitative considerations about the effect of the concentration differences of R-pinene in the vicinity of the metal might be produced. One might, however, speculate that this difference is the leading factor in this case.

Conclusions

The present case seems to be the first in which twophase conditions lead to better rates of hydrogenation than single-phase conditions. These findings call attention to important factors, such as the composition of liquid mixtures in the vicinity of the critical region and adsorption isotherms of the substrates on the catalyst.

Figure 1 .

 1 Figure 1. Synthesis of linalool from R-pinene through hydrogenation, oxidation, and pyrolitic ring cleavage.

Figure 2 .

 2 Figure 2. Schematic representation of the apparatus for hydrogenation reactions at high pressure: (MN) manometer, (MS) magnetic stirrer, (PG) pressure generator, (PT) pressure transducer, (R) reactor, (S) syringe, (SV) switching valve, (V) vial, (T) glass thermometer.

Figure 3 .

 3 Figure 3. Pd/C-catalyzed hydrogenation of R-pinene to pinane. Reaction yields as a function of time for different CO2 pressures: (b) PCO 2 ) 8.0 MPa; (O) PCO 2 ) 9.0 MPa; (9) PCO 2 ) 9.5 MPa; (2) PCO 2 ) 10.0 MPa, (4) PCO 2 ) 12.0 MPa.

Table 1 . Pd/C-Catalyzed Hydrogenation of r-Pinene to Pinane: Reaction Yields as a Function of Time for Different CO2 Pressures

 1

	PCO 2 ) 8 MPa	PCO 2 ) 9 MPa	PCO 2 ) 9.5 MPa	PCO 2 ) 10 MPa	PCO 2 ) 12 MPa
	time	pinane	time	pinane	time	pinane	time	pinane	time	pinane
	(min)	yield (%)	(min)	yield (%)	(min)	yield (%)	(min)	yield (%)	(min)	yield (%)
	5	6.3	5	17.2	7	16.5	11	4.2	5	5.9
	10	29.5	10	22.2	15	16.1	15	5.8	10	1.8
	15	54.6	15	43.7	30	28.4	20	5.9	15	2.9
	20	66.7	20	64.2	45	48.8	25	9.7	20	2.2
	25	74.3	26	76.7	60	72.8	30	11.3	25	3.8
	30	83.9	30	86.4	75	85.2	50	14.7	30	4.7
	40	85.1	40	92.7	90	88.8	80	24.5	45	6.8
	50	93.6	50	97.9	105	97	100	25.4	60	13.5
	62	100	60	100	110	98.5	105	35.5	80	17.6
									90	23.6
									92	28.4

Acknowledgment

D. Chouchi thanks the European Commission for a Marie Curie postdoctoral fellowship (TMR ERBFMBICT 972062). M. Courel also thanks the European Commission for a postdoctoral fellowship, granted through the Network Super-Clean Chemistry (TMR ERBFMRX-CT97-0104). All authors thank Fundac ¸a ˜o para a Cie ˆncia e a Tecnologia (Lisbon, Portugal) for additional support through Project PRAXIS/P/QUI/10075/1998.

Literature Cited