Koen Vermeir

Sacrobosco

Polony

Ailhaud, Arnoud, Dacher Cagliostro ; Le Comte De Saint-Germain

CURING THE FAITHFUL MESMERISM AND THE HISTORICAL IMAGINATION

CNRS) 1

'Il ne faut être que médiocrement versé dans la lecture des Auteurs, pour ne pas ignorer que la doctrine annoncée par M. Mesmer, a formé pendant un siècle une opinion dominante qui, dans l'histoire de tant de sectes fâcheuses pour la Médecine, offre une époque très remarquable.' (Thouret 1784, p. 1) 'Le magnétisme sera donc désormais la pierre de touche avec laquelle on jugera du degré de santé de chaque individu, lequel se trouvera préservé de toutes les maladies. Paracelse, Maxwell, le Chevalier Digby, tous les Médecins sympathiques, cabalistiques, spagiriques, magnétiques, tous ceux qui ont proposé les talismans, un remède universel ;

Introduction

During the famous siege of the city of Breda in 1625, the city garrison was afflicted with the scurvy in a most dreadful degree. When the Prince of Orange heard of this, he was afraid the city would surrender to the enemy. He sent letters and three small phials of medicinenormally not enough for the recovery of 2 patients. It was told, however, that two or three drops would give a healing virtue to a gallon of liquor. Not even the commander of the army knew about the cheat. The effect of this delusion was astonishing. Many were quickly and perfectly recovered. Even those who had not been able to move their limbs for months were fully cured, cheerful with the wondrous medicine that came directly from the Prince. This episode was recorded by Frederic Vander Mye, one of the physicians present, and it was retold by John Haygarth 175 years after the facts (Haygarth 1800, p. 26).

Haygarth, physician and fellow of the Royal Societies of London and Edinburgh, published

Of the imagination in the wake of the Mesmer controversy, in order to expose a new and curious cure that was the latest vogue in Bath. The physician unmasks this new cure by means of trick trials, revealing that not the alleged cure but the imagination of the patients had restored them to health. He compared this episode explicitly with animal magnetism (p. 4).

Both the story of the siege of Breda and the reference to mesmerism performed the same function: they were called in as historical confirmation of the imagination's curious powers, disturbing as well as curing the body. Haygarth did active historical interpretation in bringing these episodes together and in appropriating them for his argument that the imagination, not the popular cure, was effective.

In this article, I will show that historical interpretation and appropriation played a crucial role in the Mesmer controversy. In writing histories of animal magnetism, physicians would develop the central arguments against mersmerism that would shape the later controversy.

First, these physicians argued that animal magnetism had a long genealogy, and was derivative of 16 th and 17 th century speculations. According to the medical establishment, this tradition was suspect, however, full or error and speculation, and it had already been rejected in the course of the 17 th century, when experimental philosophy had dispelled such vain superstitions. Second, they claimed that animal magnetism is not real but only an effect of the imagination. They based themselves on medical explanations made in older, now paradigmatic cases, and they explored the parallels with the contemporary discourse about mesmerism.

It is striking that, despite these historicizations of animal magnetism, the concept of the imagination is used uncritically and is not historicized. Also in the secondary literature on the mesmerism debate, the imagination is taken for granted or is contextualised only to a limited degree. It is the aim of this paper to historicize the concept of imagination that determined the mesmerism controversies by closely studying how the concept was used and from which sources it was derived. In this way, we will get a new perspective on this crucial aspect of the Mesmer debates, which will allow us to reinterpret this episode in the historiography of the imagination.

Historiographies of medical magnetism

Historiographical time is not linear. Sometimes, history seems to run at different speeds, with long continuities, sudden changes and unexpected jumps. Classical authors have kept their presence over the centuries, while forgotten historical figures can suddenly become like contemporaries. Such unexpected historical presences and resurrections played a crucial role in the controversy surrounding Franz-Anton Mesmer and his disciples. 2 One of the first critical assessments of mesmerism by the medical establishment was a historiographical account of animal magnetism. 3 Michel-Augustin Thouret, one of the first and youngest members of the recently founded Société Royale de Médicine, argued that Mesmer's theory was not at all original. In 1784, he published a book detailing the origins of Mesmer's theories in an obscure and suspect tradition of magnetic cures. He accused Mesmer of reviving these forgotten authors, of actualising theories that were in fact justly rejected by previous generations (Thouret 1784, p. xiii-xv). In the course of this analysis, Thouret developed some explicit reflections on the usefulness of historiography. Some historical distance is necessary for judging current controversies, Thouret (1784, p. viii) claimed. Knowledge about previously discarded systems can help in judging new ones. Indeed, many old superstitions are still present, according to Thouret, albeit in a different guise. He sketches a historiograpical picture in which theories of intelligences, enchantments and demonic possessions as well as astrology and animal magnetism succeeded each other as explanations of seemingly extraordinary phenomena. 4 Every time, these phenomena were allegedly well established by observation and experience, 'mais si l'on y regarde de près, si l'on se reporte avec quelque attention sur l'histoire de ces opinions, on verra en quoi consistait le prestige & l'erreur ' (ibid., p. 127, 170). By established skills, charlatans are able to present facts convincingly and create an alluring spectacle that convinces spectators of its veracity. Unfortunately, Thouret argues, the enlightenment, the sciences and increased knowledge of the world have not been good protections against the illusions of the imagination and the tricks of these charlatans. A major problem is that past rebuttals fall into oblivion, and 'quand la scène du monde ne présente que des hommes neufs & dépourvus d'expérience en ce genre, la crédulité reprend tous ses droits ' (ibid., p. 248). What we should do is to educate ourselves about such errors and deceptions by reading about similar cases.

Thouret sets out to write a history of errors and impostures as an epistemic remedy against deception and illusion in the sciences.

Together with his colleague Charles-Louis-François Andry, Thouret had already written a historical and critical assessment of the use of the magnet in medicine, read in 1779 for the Royal Society of Medicine, and they were considered experts in the history of medical magnetism (Andry & Thouret 1782). Medical magnetism was a hotly debated topic at the and educational curricula. The same is true for Mesmer's contemporaries, who were actively reviving or rejecting older sources in specific ways in order to bolster their arguments. 3 Cf. Azouvi (1985), Schaffer (2010). time, and both authors accepted the magnet's medicinal properties (which were different from its iron drawing properties). They tried to separate the wheat from the chaff, however, rejecting the more 'extravagant errors' of the 'sympathetic magnetism' or 'magnetic medicine' in a footnote (Ibid., p. 538; 582 n. 151). Mesmer's early practice is treated as part of the orthodox medical magnetism and gets reviewed rather positively, although they thought that Mesmer exaggerated the efficacy of his cures (Ibid., p. 566-568). When Mesmer abandoned the use of the magnet, however, and claimed he could do the same cures without its help, Thouret was flabbergasted. If Mesmer did not use a magnet, what could the active agent be? Maybe Mesmer used a hidden magnet during his cures, yet he empathically denied he did (Thouret 1784, p. 192-5)? Mesmer himself claimed that he was able to channel a universal agent, previously by means of a magnet, but now he could use his own body to that effect. This, however, meant for Thouret that Mesmer used the term 'magnetism' only metaphorically. Indeed, Mesmer's supposed universal fluid had some striking properties contradicting conventional magnetism, such as reflecting in mirrors and not being ferromagnetic (Thouret 1784, p. 232 ff.).

Mesmer's later practices, therefore, had to be placed in a different historiography, together with authors who considered magnetism the ultimate panacea and who treated of it metaphorically and expansively. This was exactly the heterodox strand of 'sympathetic magnetism' that Andry and Thouret had announced but left aside (even if many of the authors discussed belonged to both 'orthodox' and 'heterodox' strands). They already hinted in a footnote that these 'ancient pretensions' were recently renewed (by Mesmer) in a new guise, adapted to modern physics. This strand of 'sympathetic magnetism ' included Paracelsus, Vanhelmont, Goclenius, Burgravius, Santanelli, Tenzel, Wirdig, Maxwell, Kircher, etc., authors who studied magnetism in connection with the animal economy, and used it for healing of wounds and as a general treatment of diseases. Thouret's argued that Mesmer's theories were an almost exact revival of this strand, which was developed mainly in the sixteenth and seventeenth centuries. They proposed an art of curing by very particular external means, functioning by means of an actio in distance, hence the analogy with magnetism. This actio in distance was supported by a universal fluid, but this was only a physical name proposed in more enlightened times for what had been previously called the world soul, the spirit of nature, astrological influences, sympathies or occult qualities (Thouret 1784, p. 6-7). For Thouret, all these concepts could be substituted because they amounted to the same kind of medical theory.

In much of the book, Thouret endeavours a one to one comparison between Mesmer's published doctrines and the work of William Maxwell, an obscure author who was considered to have systematised the medico-magnetic claims of more famous physicians such as Paracelsus and Jan Baptiste Van Helmont. 5 Thouret believed that such opinions had long been contested and rejected, and he singled out the Italian physician Francesco Redi as a key figure who had refuted the old magnetic medicine: 'En cherchant à s'assurer par l'expérience de tant de faits adoptés de son tems, il en découvrit la fausseté, & tout le systême ancien du magnétisme, à l'appui duquel on les avait avancés, fut entierement abandonné' (Thouret 1784, p. 243). 6 Didn't the partisans of the new medico-magnetism fear the same fate, Thouret asks? They took all from the old system and only changed some of the most obvious errors.

Thouret's whole endeavour was to shed doubt on Mesmer's system by exploring its suspect historiographical lineage. Other critics took a similar approach. The physician Jean-Jacques Paulet gave a short historiographical denouncement in the first part of his L'Antimagnetisme and the two royal commissions that were charged with investigating Mesmerism accepted Thouret's historiographical analysis and conclusions. Historiography was deemed so important in the debates about animal magnetism that a priority dispute emerged between physicians about who was first in discovering that Mesmer's system resembled that of Paracelsus (Joyand 1786a; 1786b).

A history of errors

Historiographies of errors were popular in the early modern period and the enlightenment, and they had specific cultural functions. In 1625, for instance, the physician Gabriel Naudé (1657) wrote a history of magic in the context of a renewed interest in Paracelsianism. He exposed false accusations of magic by ignorant people who treated all learned men as magicians, and explained that these 'magicans' were in fact physicians or natural philosophers. Others rather sought to write a natural history of magic, in which magical and spiritual phenomena would be established experimentally (Glanvill 1666). 7 On the one hand, histories of magic could make magic look alien and surpassed; it was a means to disenchantment. Naudé made 'magic' 5 Late eighteenth century commentators referred to Maxwell (1679), but his authorship is contested. The same text circulated in manuscript in the first half of the seventeenth century and was published, with some additions or omissions, as Boulton (1656) and Irvine (1656) in English and then as Maxwell (1687) in German. Kassell (2007) argues that the text was probably written by Maxwell in the 1630s, because of a reference to a conversation with Robert Fludd. Poma (2009) believes Irvine was probably the author. Because our eighteenth century actors referred to Maxwell, we will do so too. 6 For the fragile nature of Redi's results, however, see Baldwin (1995). 7 See Kahn 2001, Kassell 2006. it into a category mistake by credulous people. On the other hand, natural histories of magic aspired to make magic up to date with the newest experimental procedures. Later historiographies of 'errors', often also referring to magical beliefs, like those by Pierre Bayle and Thomas Browne, were meant as a means to enlightenment. These critical histories were to make the people less credulous, and to show them critical strategies to unmask impostures or illusions. 8 Thouret's analysis can be understood as part of this long tradition. 9 The enlightenment he promoted, however, was only for the elite, as the vulgar were inveterate and desired too much to be deceived (Thouret 1784, p. 249).

The aim of Thouret's historiography was to render the ancient tradition of sympathetic magnetism actual and alien at the same time. This tradition was prominently present in actual practices and theories, but simultaneously, it was an old sect that had been justly rebuffed a long time ago. Mesmer and his followers took a very different view of their history. Mesmer's doctoral dissertation on the influence of the stars on the body, presented in 1766 at the faculty of Medicine in Vienna, was derived from the 1746 edition of De imperio solis ac lunae in corpora humana by the respected London physician Richard Mead. Mesmer's critics had not read his dissertation and only saw a tenuous link between Mead's book and Mesmer's later published work, focusing more on the resemblances with the sympathetic magnetism of Maxwell and others.10 Indeed, although his universal fluid kept its cosmic proportions, Mesmer had changed his theories and practices over time, and his debt to Mead was less pronounced. As Mesmer himself relates in his Mémoire, he had started to use magnets and electricity in his therapies, and later combined all these strands in his theory of animal magnetism (Mesmer 1779, p. 5-9). Thouret considered Mesmer's personal trajectory also important for judging him, and he remarked on the change of emphasis in Mesmer's work, from magnetic medicine to the heterodox sympathetic magnetism (Thouret 1784, p. 228). He stressed the local and national character of specific superstitions and claimed that Mesmer adapted his theories according to these local fashions and superstitions, from a focus on astral influences toward magnetic healing.

In his Mémoire, Mesmer (ibid., p. 4-5) embraced the idea that he had recovered the remains of a truth recognised in primitive societies but misinterpreted by them. Contemporary physicians were wrong in covering these 'ruins' with disdain. When Thouret placed Mesmer explicitly in a long tradition of sympathetic magnetism, however, Mesmer refused to acknowledge this genealogy. He denied having red Maxwell, and preferred to see his work in a more respectable lineage of Descartes and Newton (Réceuil 1784, p. 465). 11 In contrast, Charles Deslon, physician to the Comte d'Artois and Mesmer's most prominent disciple, accepted the mesmerist's pedigree in a primitive and rejected tradition. He did not see this as a setback but rather as an asset. He took the traditional perspective of a practitioner standing in a long but disowned tradition. Surely, something in it must be true if so many people have defended these techniques and phenomena over the ages: 'L'Histoire de tous les Peuples nous en offre la trace' (Deslon, 1784, p. 28). What is more, if it weren't true, people would not react so vehemently against it. 12 He explained the opposition of the establishment by their vested interest in the status quo. They do not want their remedies to be superseded by new discoveries and hence oppose every revolutionary doctrine. Despite his tumultuous relationship with Mesmer, he believes that his mentor is due a lot of credit because 'il nous a rappelé de grandes vérités tombées, non dans le mépris, mais dans l'oubli.' Mesmer has had the great talent to find the gems in forgotten practices, to resurrect this lost ancient wisdom and bring everything together in one system (Ibid., p. 30).

Antoine Court de Gébelin, imaginative historian of mankind's Golden Age, lodge-brother of Voltaire and Franklin, placed Mesmerism in yet another relationship with history. As an enthusiastic patient cured by Mesmer, he strongly defended Mesmer's theories, and saw in them a way to better understand ancient civilizations. His life project, published in different instalments in Le Monde primitif, analysé et comparé avec le monde moderne, was a reassessment of advanced primitive civilizations. He supposed that the force of animal magnetism would have been stronger, better observable and more constant in times not yet degenerate. The ancients had therefore better access to these wondrous phenomena, but this had given occasion to all kinds of misguided theories and opinions, which were transmitted to us only in a weakened and degraded sense. The newly discovered agent of animal magnetism will give us a precious key for uncovering and reinterpreting these misunderstood theories and practices. The evil eye, for instance, discussed in ancient times, was in fact an effect of animal magnetism, just like the Royal touch, and other old and new practices. Before, one could 'neither deny nor believe' in these accounts, but 'le Magnétisme animal [les] remettrait sous 11 See also Hervier (1784, p. 11-3) for a physician who places Mesmer in the lineage of Descartes and Newton. See Anon. (Observations, 1784) for a critique of Thouret's comparison between Mesmer and Maxwell. 12 'Si le Magnetisme n'étoit rien on ne le combattroit pas avec autant d'acharnement. L'Histoire de tous les Peuples nous en offre la trace. On la trouve chez les Egyptiens, chez les Chinois, jusques chez les Sauvages. La Nature elle-même l'indiquoit, lorsque l'Art de la Médecine étoit encore ignoré. Quelques Grands Hommes l'ont deviné; les Physiciens de tous les siècles l'ont supposé. C'est assurément quelque chose qu'une idée qui germe de puis tant de siècles & dans autant de têtes savantes.' (Deslon, 1784, p. 28) leur vrai point de vue.' 13 Maybe de Gébelin would have integrated animal magnetism in his interpretations of primitive civilization in the next volumes of his Le Monde primitif.

Unfortunately, he relapsed in his illness shortly after publishing his eulogy of Mesmer. He died under Mesmer's hands while undergoing therapy, attached to a tub of magnetized water. 14 Thouret's book is not only a historiography of a discredited tradition. He also develops a historical epistemology in analysing why observations can be problematic and lead to illusions. William Godwin, London based man of letters and radical political thinker, based his introduction to the translation of the Commission's report on Thouret's book. He endorses Thouret in proclaiming: 'Perhaps the history of the errors of mankind, all things considered, is more valuable and interesting than that of their discoveries.' Moreover, according to Godwin, we should look into 'what different instruments were necessary to deceive mankind in an ignorant and an enlightened age'. 15 The history or errors is also a history of deceptions and their unmasking. This history too was part of a long tradition, with canonical aspects and paradigmatic examples. Thouret inscribes himself in this tradition by his constant referral to the same paradigmatic cases: the convulsionaries of Saint-Médard, the posessions of Loudun, Greatrakes the stroker and the exorcisms of Gassner (especially relevant because of his controversy with Mesmer). Thouret would also follow the paradigmatic solution physicians had proposed for understanding each of these cases: all these curious phenomena were attributed to the imagination. 16 While Thouret spends much time historicizing medical magnetism, he unquestioningly adopts discourse about the imagination he finds in his sources.

We will see that this striking imbalance has crucial consequences for the development of the mesmerism controversy. It is the aim of this paper to historicize the concept of the imagination that was persistently evoked by all sides of the debate.

13 Gébelin (1784, p. 164) 14 See Anon. (Recueil 1784, p. 169-174). 15 Franklin (1785, p. xvii-iii). According to Godwin, however, truth is boring, while error is the pure and simple creation of the mind, where she can exert all her boundless faculties in beautiful and interesting extravagancies. We find here thus an aesthetic of error, betraying a deeper fascination with 'mystery' and 'superstition' and its imaginative potential. 16 The lexical change between the first and second part of Thouret's book is striking (the change occurs around page 24). He describes the tradition of sympathetic magnetism, propounded by sixteenth and seventeenth century physicians, as a hypothesis and speculative system. Although these systems have now been rejected as a result of the experimental philosophy, in their own times, these theories had 'brilliant destinies' (p. 126-7). In contrast, when he describes the convulsionaries of Saint-Médard, the nuns of Loudun, etc. (who were allegedly unmasked by contemporary physicians) in the second part, he refers to imposture, illusion and error. His suggestion that these resemble Mesmer's practices is therefore much more damaging than the comparison of Mesmer's theories with sympathetic magnetism.

Judging mesmerism

On the 12 th of March, 1784, Louis XVI named nine commissioners from the Faculty of Medicine and from the Academy of Sciences to investigate animal magnetism. 17 The result of the commission's work is well known. In their eloquently written report (the 'Bailly report'), they argued that Mesmer's universal magnetic fluid did not exist and that the perceived effects were all due to the imagination. They came to this conclusion by means of a set of carefully orchestrated experiments exploring the necessary and sufficient conditions for the perceived effects (Rapport, p. 32ff). They performed trick trials, making the patients believe that they were being magnetised when in fact nothing was going on, and yet the patients felt sensations or even fell into convulsions. Or the commissioners already started the magnetisation unbeknown to the patients, with no perceptible effects as a result. The imagination, they concluded, was able to produce the various sensations and other effects Mesmer attributed to animal magnetism. At the same time, the magnetization procedures had no effect when the action of the imagination was precluded.

Although supporters of mesmerism pointed out some of the logical, epistemological and practical flaws of the report, the commissioners' dismissal of mesmerism as an effect of the imagination would have a marked impact on the discussion. Commentators have stressed the radical and novel nature of the commission's conclusions and that they created the first deliberate psychological tests. 18 It has not been appreciated, however, that earlier critics of Mesmer had already attributed the effects on his patients to the force of the imagination. In 1780, Jacques De Horne, physician to the Comtesse d'Artois, was already convinced 'que l'imagination de ceux qui se soumettent à ces singulieres épreuves en détermine souvent ou en augmente au moins l'impression. Tout son art [de Mesmer] ne consiste peut-être qu'à profiter habilement des moyens qui lui présente une imagination exaltée, affoiblie ou trompée ' (15-16). Real physicians are used to grasp and estimate the whole span of the imagination, knowing its various resources, and they will not be so easily fooled. Mesmer's supporters, such as De Gébelin, contested bitterly these accusations by De Horne as well as 17 Borie, Sallin, d'Arcet, Guillotin from the Faculty of Medicine and Franklin, Le Roy, Bailly, Lavoisier and de Borie from the Academy of Sciences. The latter died during the procedures and was replaced by the physician Majault. 18 Riskin (2002, p. 217) has argued that previous accounts of the imagination gave it a power over the body, while the commission's conclusions were innovative in giving it power over the senses. In fact, the power of the imagination over the senses was the most traditional (as a typical explanation of madness), while the extent of its powers over the body had been strongly contested during the previous centuries. similar ones by other physicians such as Bacher and de Vauzesmes (Gébelin in Receuil, 124-33).

It was Thouret's official analysis, however, that would make the largest impact and that was taken up by the commissioners. On the same date of the creation of the commission, Thouret was charged by the Royal Society of Medicine to explore the precursors of animal magnetism.

The Society approved the report in an extensive and widely distributed censure report on the 9 th of July 1784. 19 The commissioners explicitly followed Thouret's historiographical analysis, and accepted the critical part of the book in which he attributed the mesmeric effects to the imagination (Rapport, p. 70-2). The commission's experimental procedures, especially the trick trials meant to uncover the powers of the imagination, were particularly striking.

Contrary to prevailing historiographical opinion, however, there is a more complex history to be told here as well. 20 The point here is not to take away credit from the commission by pointing at precursors, but to get a better historical insight of how the commission came to put forward the imagination as the central agent in mesmerism. Historians have explored contemporary discussions of the imagination to better understand the arresting conclusion of the commission. 21 The definitions of the imagination put forward by Descartes, Diderot or Condillac are, however, not the most relevant context for understanding the discussions about the mesmeric imagination. Many different and more complex conceptions of the imagination were at play in the early modern period and the enlightenment. On one of these notions in particular, we will focus in this article.

What is the imagination?

When Mesmer's supporters heard the judgement of the medical establishment, they reacted confoundedly and indignantly. What the commissioners meant by 'imagination' was not at all clear to them. Deslon asked: 'Qu'est-ce que l'imagination?' (Deslon 1784, p. 19). He complained that the commissioners did not even try to define it, taking a very easy road indeed, because it insulated their own explanation from targeted criticism. Deslon continued by repeatedly asking 'Est-ce l'imagination [...] ?' (ibid., p. 23), calling into question the properties the commission seemed to attribute to this extraordinary faculty. Antoine Servan 19 It was printed e.g. in Thouret (1784), Franklin (1785), and the Journal de médecine, chirurgie, pharmacie 1784, n° 62, Octobre, 341-51. 20 Riskin (ibid.), Kaptchuk (1998) have characterised these trials as the first blind assessment tests. Note that Kaptchuk (2009) has pointed at earlier trick trials. Indeed, sources in the mesmerism controversy and earlier refer to many older trick trials and blind assessment tests (e.g. Paulet 1784, p. 187; Hecquet 1733, p. 197) 21 Riskin (2002), Azouvi (1976) was equally dumbfounded: 'qu'est-ce qu'ébranler l'imagination, frapper l'imagination?' (Servan 1784, p. 70), he wondered. They tried to make some sense of the concept themselves.

Deslon referred to an accepted distinction between a metaphysical and a physical imagination, as an activity of conception versus a subtle fluid in our body, but it was not clear to which of the two the commission attributed these special powers. Servan also considered the imagination to consist of a subtle fluid, not unlike Mesmer's universal fluid. Nicolas Bergasse tried his own account of the imagination. 'Ce que c'est l'imagination', (122) he explained: it is the faculty that makes absent objects present by means of similar impressions, and it acts on the organisation of our body, developing or constraining it. Interestingly, when they were reflecting about the powers of the imagination, they referred to sixteenth and seventeenth century authors such as Michel de Montaigne and Nicolas Malebranche, who were part of a tradition that had long contemplated the wondrous forces of the imagination. 22 In an Exposé about their experiments, read by Jean Sylvain Bailly for the Académie des Sciences, the commissioners from the Académie went into more detail about the force of the imagination they had put forward in their report. In this exposé, it is clear that they made a strong distinction between 'physical' and 'moral' causes (and with 'moral', they meant nothing else than 'not physical'). This presupposition actually followed from their initial question: does Mesmer's universal fluid exist? Does there exist a real physical cause of the mesmeric phenomena, or else? If the question is framed this way, their only alternative to a physical fluid was a non-physical cause. Furthermore, 'real' and 'physical' became conflated in an interesting way. As a result, the effects of 'moral' causes were transformed into something 'illusory'. Refuting the reality of Mesmerism seemed to presume a non-physical cause, in a sense 'illusionary'. The imagination was a good candidate, because of some ingrained connotations of the imagination, coming from different traditions, in which the imagination was associated with 'non-physical' and with 'illusions'. Bailly wrote: 'La recherche d'un agent qui n'existe pas, sert donc à faire connoître une puissance réelle de l'homme ; [...] Mais cette action ne peut être regardée comme physique ; nous ne voyons pas qu'elle dépende d'un fluide communiqué ; elle est entièrement morale.'23 (Bailly 1784, p. 15) The problem remained, however, how to explain these 'physical' effects by means of 'nonphysical' causes, after presupposing such a neat distinction between the two. Bailly asserts: 'ce sont des faits pour une science encore neuve, celle de l'influence du moral sur le physique' (Ibid., p. 11).

Of course, this science was not new. Physicians had been writing about the physical effects of the imagination for centuries. In fact, traditionally, the imagination was the faculty that connected mind and body. The status of the imagination was therefore somewhat ambiguous, falling in between the opposite poles of body and mind. In general, however, most early modern philosophers and physicians held that the imagination was the highest material faculty of the soul, hence its pre-eminent status for explaining all kinds of 'psychosomatic' diseases. A strong distinction between 'physical' and 'moral', and placing the imagination on the 'moral' side, makes explaining its 'real' and 'physical' effects more difficult.

Furthermore, these 'real' effects become quite 'unreal'. This is noticeable in the report of the commissioners. They go into great length detailing the sensations people felt during mesmerism, and attribute them to the imagination. The implication is that these were not 'real' symptoms, however, but illusory feelings induced by an overstrained sensibility. 24 Even the more spectacular convulsions are not 'real' effects, but fleeting and illusory phenomena that tell us nothing about the real state of the body. These 'physical' effects become characterised as illusions, i.e. as phenomena that have no real substance (associated with trickery or stage magic). This is even more clearly the case in the writings of the commission's immediate predecessors on this topic. De Horne, who attributes mesemeric effects to the power of the imagination, writes that good physicians know the tricks of the imagination, and that curing 'real diseases' are not in the imagination's power (De Horne 1780, p. 9). The imagination can only create illusionary symptoms. Thouret, who uses a distinction between the 'physical' and the 'moral' similar to the commissioners' (e.g. Thouret 1784, p. 68, 106), asserts multiple times that the imagination creates 'illusions'. 25 These are not 'illusions' in the head of a patient, as most of the traditional thinking about the imagination would have it, but perceptible and attestable effects, often extraordinary, such as convulsions, superhuman strength or speaking in tongues.

Nevertheless, such effects are illusionary, because they do not reflect the real condition of the body (e.g. Ibid., pp. 146-9, 175-9). They are fleeting effects, like the tricks of impostors or thaumaturgic illusions, in De Horne's terminology. According to these authors, the imagination is not able to create real cures, and by implication, the patients do not suffer from 'real' diseases. The imagination is only able to deliver temporary relief or a minimal improvement if the patient's disease is 'real'. In contrast, the commissioners, after spending fifty pages on the illusionary effects the imagination generates, at least spend two sentences recognizing that the imagination can have some power to cure. This is quickly dismissed, however, because its destructive powers are far greater, especially if procedures are used with violent effects, as is the case with the mesmeric 'crises' (Rapport 1784, p. 74). The 'real' powers of the imagination to cure are therefore rejected in favour of a close analysis of its illusionary effects.

Powers of imagination

It is curious that the medical and scientific establishment opposed the imagination to animal magnetism. We have seen two strategies, employed by the critics of animal magnetism and elaborated, in particular, by Thouret: first, animal magnetism had a suspect lineage in rejected doctrines, and second, animal magnetism was not real but rather an effect of the imagination.

These two arguments become conflated and problematic, however, when we look deeper into Thouret's historiography of magnetic medicine. Indeed, all the major historical figures in the tradition of sympathetic magnetism that Thouret discussed, such as Paracelsus, Van Helmont and Maxwell, held that magnetism and imagination were closely related phenomena. 26 They were all part of a tradition that claimed that the imagination had wondrous powers and, in particular, could act outside the body on other humans and even on inanimate objects. They saw the imagination as a cosmic power. As Oswald Croll, a disciple of Paracelsus writes 'The imagination of man is a magnet that attracts beyond a thousand miles.' 27 This power of the imagination was thought to work by means of a subtle spirit, imponderable but corporeal.

For Jan Baptista Van Helmont, a seventeenth century Flemish physician notorious for his heterodox ideas, magnetism and imagination are closely intertwined. The magnet itself is endowed with sensation and imagination, which it needs for knowing its position and for moving to the iron or to the poles (Van Helmont 1648, § 142). The imagination, both of man and of things, works by more or less incorporeal effluvia (Ibid., §159). For Van Helmont, this 26 For this tradition of medical magnetism, see Poma (2009); for the tradition of the transitive powers of imagination, see Godet (1982), Giglioni (2000), Vermeir (2004). 27 Croll (1608 p. 38): 'Imaginatio Hominis est magnes attrahens ultra mille milliaria: imo quicquid vult in Exaltatione sua, ex quatuor Elementis ad se attrahit. Efficax autem non est Imaginatio, nisi prius rem conceptam attrahat per vim Imaginationis attractivã, ut ex fe quasi spiritum nativum Imaginationis Architectum procreet: postea Imaginatio quasi ingravidata imprimit ,quae licet non fit tangibilis, instar venti tamen est corporea.' Cf. also the 18th century discussion in Barchusen (1723, p. 406), referring to this passage: 'Imaginationem enim hominis esse magnetem attrahentem ultra mille milliaria: imo quicquid vult in exaltatione sua, id ex quatuor elementis ad se attrahere.' is the deeper cause of the magnetic process, by means of which magnets can attract iron or effect cures at a distance. About the weapon salve, a cure which works by anointing the blood-stained weapon rather than the wound, he writes: 'The natural imagination of the unguent [itself] is therefore the general cause of magnetism and the particular cause of the cure.'28 Not only the magnetic salve's imagination cures at a distance, however; also man's magnetic imagination has wonderful powers in Van Helmont's system. Similarly, William Maxwell's magnetic system is predicated on the imagination. He starts his book with aphorisms in which the power of the imagination is central: the imagination has a dominating power over the body (Maxwell 1679, aphorism 2) and works by means of the vital spirit. He who wants to work great things will have to know how to work this spirit or to join his imagination to the imagination of the soul of the world (Ibid., aphorism 7); by means of this connection, he can affect objects and men at a distance. The spirits of one body can be communicated to another body, for instance, and Maxwell suggests that the imagination is involved in this process. The first conclusion of the book also explains that the imagination can work beyond its own body, affecting others. The book, however, will rather focus on related phenomena, i.e. on managing and enhancing the flow of spirits by means of specific recipes. Indeed, he wants to explain recipes for creating 'magnets', i.e. prepared substances that strongly attract and channel these subtle spirits.

There is therefore an important distinction to be made. Early critics of the weapon salve and magnetic cures, such as Michael Döring, Tobias Tandler or Andreas Libavius already attributed their efficacy to the psychosomatic power of the imagination of the patient, exalted by the confidence inspiring practices of the physician. 29 The action of the imagination proposed by Paracelsus, Van Helmont and Maxwell was radically different, however. Van Helmont explained that such cures are not 'superstitious': the imagination of the sick person does not anticipate anything, nor does he need to have confidence or implicit faith in the cure or in the physician (Van Helmont 1648, §13). It is a 'real' cure and the imagination of the patient is not at play. Magnetic cures are effective because of the action of a 'cosmological imagination' in which things as well as man participate. In some of these cures, it is the imagination of the physician that is the most important, in others, it is the imagination of the object.

Such ideas belong to a longer and broader tradition of the powers of the imagination. Four different levels of this power were often distinguished: the power on the proper body (one of the strongest examples is the creation of stigmata), the power of the imagination of the mother on the foetus (imprinting images on the unborn child, or deforming it), the power on other bodies (as in magnetic cures) or the power on inanimate objects (e.g. creating apparitions in the sky). 30 Physicians had been debating for centuries how far these powers extended, and they disagreed widely. 31 A weak power on the proper body (e.g. blushing) was considered evident, and also the power on the foetus was generally accepted in the seventeenth century, while the existence of stronger powers was very controversial. One controversial point was the possibility to explain away miracles or the efficacy of relics by means of such a strong imagination, and physicians such as Pomponazzi or Van Helmont hinted at such explanations. Some of the central issues this conception of the imagination tried to address were the phenomena of communication, contagion and action at a distance, which could be thought in terms of magnetism as well as of imagination. To illustrate again the proximity of between two: Maxwell explained the effect of the mother's desires on the unborn child one time as an effect of the power of her imagination (conclusion 1) and another time as a magnetic phenomenon ('The Weapon-Salve'). 32

Historicizing the imagination

Thouret's analysis of these seventeenth century authors only focuses on magnetism and he does not mention their theories of imagination, even if these theories coincide. There is only one exception: he mentions the tradition power of imagination once, when he explains in general that the most diverse phenomena are relegated to magnetism by these authors, including the marvellous powers of the imagination, and in particular its effects on the foetus (Thouret 1784, p. 107). He does not reject these powers, but he offers no reflection on the relation between imagination and magnetism, and, especially, he does not discuss the relation between their concepts of imagination and his own use of the term. Yet this more 'magical' conception of the imagination was not completely abandoned at the turn of the nineteenth century, as is often suggested. 33 In the 7 th volume of the Encyclopédie Méthodique of Medicine, published in 1798, the first article on the imagination, written by he physician, 30 See Vermeir 2004; for an explicit classification in similar terms, see e.g. Bacon (1989, vol 2, p. 654). 31 See e.g. Fienus (1608), Pico Della Mirandola (1501) for important critical contributions to this discussion 32 Maxwell also rewrites a Helmontian story about the power of imagination in magnetic terms. 33 Cf. Daston & Park (2001).

natural historian and mineralogist Louis-Claude-Henri Macquart, devotes only a few lines to its function in genius and sensibility and to some of its more evident psychosomatic effects. In contrast, he devotes several pages to the refutation of the idea that the imagination can imprint images on the foetus. After this analysis, the author goes on with recounting many 17 th century stories about its marvellous psychosomatic powers. In fact, these powers of imagination were widely discussed in, for instance, the works by the physicians Benjamin Bablot and Jean-Baptiste Demangeon. 34 Thouret's criticism fits in a different historiography of the imagination. It is based on paradigmatic cases in which wondrous phenomena, attributed to God or the Devil, were unmasked by physicians as natural, or as artificial, i.e. the effect of imposture. Thouret based himself on traditional medical interpretations of healing or prophecy, such as the healing practiced by Greatrakes and Gassner, the posessions of Loudun and prophets of the Cevennes and Saint-Médard. A key source for his interpretation was Le naturalisme des convulsions by the Jansenist physician Philippe Hecquet. 35 Hecquet wrote this polemical work during the controversy around the convulsionaries of Saint-Médard which raged in the 1730s, when Jansenists experienced convulsions and other 'miraculous' effects at the tomb of François de Pâris (1690-1727), a popular Jansenist ascetic. Hecquet sought to distance himself from his fellow Jansenists, especially the theologians who supported the convulsionaries, by attributing these so called 'miracles' to an overheated imagination (a judgement that would be followed by a committee of 30 physicians two years later). Hecquet referred to the fantastical fancies and grotesque imaginations of these 'vaporous ladies' (Hecquet 1733, p. 130-1) and detailed how the imagination could affect the body by prompting convulsions and other effects. This was material Thouret eagerly used. Hecquet also repeatedly stressed the erotic powers as a deeper cause behind these convulsions, an opinion we see mirrored fifty years later, first in Thouret and then in Bailly's (1957) secret report of the Mesmerism investigation, addressed only to the King.

If we look closer at Hecquet's work, however, we see that he uses the whole spectrum of the concept of imagination to support his claims. Indeed, he needed to make the imagination as strong as possible, so it could be used to explain all these wondrous 'miracles' that beset the convulsionaries. He even attributes the appearance of stigmata on the bodies of the convulsionaries as an effect of their strong imaginations (Hecquet 1733, p. 121) -traditionally a very controversial position for its potential to naturalize real miracles. Most strikingly, however, is that he explains the contagiousness of the convulsions by means of an imagination that acts outside the body by imprinting material spirits. The imagination's power to act at a distance is attested by many authorities, according to Hecquet (Ibid., p. 36-41). In analogy to the air, transmitting sensible species, the agitated blood and spirits of the convulsionary imprint their nature on the elastic spirits of the air. By oscillations, these spirits transmit these impressions to other people, who become affected by them. These spirits even carry the ideas, which they contracted in the body of the convulsionary, and, after being transmitted through the air, they go through the nose, ears or pores of the skin of the spectators. In this way, these impressions and ideas will imprint the latter's animal spirits and thus affect their imagination. As a result, the spectators are like vibrating strings, activated by an action at a distance, reacting in unison. (Interestingly, this analogy was used traditionally in the magical literature, and was repeated by Bailly and the commissioners.) 36 In this way, the convulsionaries multiply, in a natural way. In a later passage, Hecquet explains that there exists a homogeneous 'air' in all female bodies (Ibid., p. 178ff.), which establishes a natural harmony between them and makes them especially vulnerable for these kinds of contagions.

Ideas and feelings are transmitted by waves through different spirits, internal as well as external to the body, because these spirits are in essence all alike. These spirits, Hecquet stresses, are material (Ibid., p. 181). 37 It turns out that Thouret's authorities -used in his argument to promote the imagination rather than animal magnetism as an explanatory principle -adhere to a system that, in essence, conflates the two. For Hecquet, the imagination is akin to a material effluvium between bodies, even if he rephrases this traditional idea in more fashionable, Newtonian terminology of waves and oscillations. For the Paracelsians and Helmontians too, the imagination works on distant bodies by means of subtle vapours. 38 This early modern imagination therefore strongly resembles animal magnetism, although it stands in stark contrast with Thouret's concept of imagination. Thouret, therefore, historicised animal magnetism by tracing back its roots, but he took an unhistorical imagination for granted. As a result, Thouret and the commissioners either suppressed troubling historical views on the imagination, or projected 36 E.g. Bailly (1784, p. 14); Rapport (1784, p. 68). See also Van Helmont (1648 §151), using the 'sympathetic' vibrations in unison lute strings as a metaphor for the universal spirit that causes sympathies and as a metaphor for the powers of imagination. 37 For an analysis of the role of the imagination in the Cevennes case and later 18 th century reverberations, see Vermeir 2004. 38 Of course, not all these doctrines are the same. But in respect to what interests us here, the question framed by Thouret and the commissioners in terms of an opposition between imagination and animal magnetism, all these doctrines conflate this neat distinction.

back their own ambivalent concept of the imagination in their interpretations of the past authors they enlists in their argument. This, it can be surmised, is a consequence of how Thouret and the commissioners formulated their opposition to Mesmer in the first place, and how they framed their basic question: is animal magnetism the result of a real agent or is it an effect of the imagination? Such a question precludes the possibility of an imagination that works externally by means of a real material agent. Supporters of animal magnetism of course did not agree with this framing of the question. They challenged the criticism of their adversaries on different grounds. Deslon chided the commission for focussing on the 'illusionary' sensibilities that were generated or not during the trials of the commission, instead of looking at the real curative effects and medical results of his practices (Deslon 1784, p. 9-10). 39 Later commentators argued that it was not the hypothesis of a universal magnetic agent that should have been tested, which was only that -a hypothesis, but rather the efficacy of the magnetic procedures (Colquhoun 1833, p. 67).

The moral versus the physical

More important, however, is the argument by Mesmer's disciples that the imagination and animal magnetism might be different but need not be independent causes (e.g. Bergasse 1784, p. 129). If this were to be the case, the way the commission had framed the question might be seriously flawed. Some went even further, suggesting like Servan that the imagination could be a modification of this elementary magnetic fluid (Servan 1784, p. 59, 64). 40 Everyone agrees that physicians cannot explain anything of the animal economy without taking recourse to the 'animal spirits', 'ce fluide aussi nécessaire qu'inconnu, ' Servan writes (Ibid., p. 66), and this fluid might thus very well be a form of the universal magnetic fluid. Of course, the commission had tried to establish that there was no real fluid interacting between the mesmerist and the patient, be it a magnetic fluid or a fluid emitted by the imagination. What they had tried to show is that there were only symptoms or effects if the patient's imagination was involved. So both animal magnetic fluids and the material effluvia of the imagination had to be rejected. Nevertheless, as Servan spelled out, if the hypothetical magnetic fluid was akin to the imagination of the patient, interacting and interfering with it, the results experiments are not so clear cut. For instance, Servan argued, if the patient's imagination was expressly distracted by the commissioners during the treatment, in order to test whether animal magnetism had effects without the action of the patient's imagination, the commissioners manipulated the spirits of the imagination of the patient. Indeed, they were drawing these spirits to certain places in the body depending on where they directed the patient's attention.

In this case, because the patient's spirits were occupied, they could not receive the imprints of the spirits transmitted by the animal magnetism (Ibid., p. 71-2) and therefore the magnetic procedure would be without effects. According to Thouret, the fact that Mesmer had developed a materialist version of the former 'spiritual' theories was a sign of enlightenment (Thouret 1784, p. 103-4). Mesmer's supporters, however, resorted to an older opinion, conflating the powers of magnetism and imagination, the physical and the moral.

When a second commission appointed by the King, with members selected from the Royal Society of Medicine, presented their report on animal magnetism, they broadly concurred with the 'Bailly report'. They were more cautious in attributing the effects to the imagination, however. They suggested instead that most of the mesmeric effects were probably due to physical causes such as touching. Interestingly, one of the commissioners, the physician and botanist Antoine Laurent de Jussieu, wrote a dissenting report (Jussieu 1784). One of the problems both commissions had to deal with is that it is problematic for logical reasons to demonstrate experimentally that something does not exist. As Jussieu pointed out: one real fact is enough to establish the existence of a phenomenon (of course, this 'fact' has to be very well attested, which brings in another set of challenges). Man is subject to many causes, moral as well as physical, and Jussieu agreed that many of the phenomena seen were not attributable to animal magnetism. They were probably due to other physical causes or to the imagination. Nevertheless, Jussieu believed that there were a limited amount of well established facts, indicating that there was a real phenomenon behind the magnetizers' practice, and he proposed an alternative explanation to Mesmer's theory. Jussieu posited a vital principle, animal heat, which escapes the body and mingles with the electric fluid in the atmosphere. It can enter another body and produce changes there, relative to the state of the body it has left and the one it now penetrates. This animal heat is therefore not a general agent acting the same everywhere, but it is dependent on moral and physical circumstances and can create specific effects in particular bodies. This theory, distinct in some respects, nevertheless comes close to alternative theories of animal magnetism and the power of imagination. Probably unwittingly, Jussieu revived an old tradition in yet another way.

One of the crucial issues in the debate is how cures, crises, diseases or even ideas and other effects can be communicated between bodies. Mesmer's followers, Jussieu, as well as many authors in the tradition of the powers of the imagination, they all posit a material effluvium that carries these effects between bodies. They all do this in their specific way, and some even suggest that this fluid can be directed by the will or imagination of the physician. In contrast, the commission did agree that we emanate fluids, and that these insensible perspirations form an imponderable atmosphere around us, but its properties are similar to the ordinary properties of other atmospheres: '[ce fluide] ne peut se communiquer qu'infiniment peu par l'attouchement, ne se dirige ni par des conducteurs, ni par le regard, ni par l'intention' (Rapport 1784, p. 73). Bailly maintained that the imagination can act on the imagination of another man, but only by 'moral means', that is, only by perceptible gestures and signs, not by an exchange of imponderable vapours (Bailly 1784, p. 14-5). 41 For Thouret too, it was the imagiantion that had to explain the actio in distans of the mesmerist cures, but this action was 'moral', not physical (Thouret 1784, p. 212). In the end, different sides in the debate could agree that the imagination was involved in mesmerist cures, but there was wide disagreement on what this imagination was supposed to be. In the course of these discussions, the neat concept of the imagination was exploded; new interpretations were proposed and older models became revived.

In the wake of the controversy sparked by the work of Thouret and the commissioners, the practice and theory of animal magnetism would be transformed. Animal magnetism became divided into different schools, it went out of favour during the revolution, and was later again revived in different guises in Paris as well as internationally. One of the consequences of this debate was the emergence of a new competing historiography of animal magnetism. Although the academic histories continued to follow the path drawn by Thouret, supporters of animal magnetism became interested in the sixteenth-and seventeenth-century tradition of the powers of the imagination for intrinsic reasons. As we have seen, early mesmerists avoided this tradition, probably because they preferred a material magnetic fluid, devoid of spiritual connotations, in order to be accepted by colleagues as enlightened physicians. Also the early critics of animal magnetism avoided referring to this tradition, despite their familiarity with it, because it would call into question their concept of imagination and their neat distinction between moral and physical causes. Only after mesmer's followers, in response to the commissions' criticism, came to associate the imagination with the universal magnetic fluid did people start to adopt and actualise again some of the ideas from this tradition. Animal magnetism created a new self-image by consciously integrating the legacy of Paracelsus, Van Helmont and even Pomponazzi in their genealogy, especially for their theories of the imagination. 42 As Colquhoun wrote: 'their works were consigned to neglect and oblivion [...] until, in recent times, when the subjects of which they treated again began to attract a considerable share of the public attention, they were sought after with avidity, drawn forth from their obscurity, carefully studied, and appealed to by the professors of animal magnetism in support of their principles and practices' (Colquhoun 1833, pp. 23-33, citation p. 33). Partly because of his own doing, the tradition that Thouret thought obsolete and rejected became alive again. And as a result, the professors of animal magnetism would reconcile themselves with the imagination, paving a path towards a future that, in much current historiography, is recognised as 'psychology'.

Conclusion

This article is less about Mesmer than about the controversy that developed around him in the 1780s, and in which he was a relative bystander. I have stressed the role of historiography in this controversy, and I have argued that early accounts of the history of animal magnetism were crucial in setting the agenda and the framework of the debates. Physicians turned historiographers, such as Thouret and Paulet, argued, firstly, that animal magnetism was heir to a tradition of medical magnetism rejected long ago, and, secondly, that animal magnetism was not real but all the effects prompted by the magnetizer's cures were illusions of the imagination. In invoking the imagination, these physicians elaborated a long medical tradition of naturalizing wondrous phenomena. Interestingly, however, when they historicized animal magnetism, pointing out similarities and differences between conceptions of magnetism over time, these physicians did not refer to changes in the concept of imagination. Their own concept of imagination -referring to a paradoxical power of the patient's imagination to have 'illusionary' effects on the patient's body -was markedly unhistorical.

It has been the aim of this paper to historicize the mesmeric imagination in a specific sense, namely, by exploring in detail the historical sources used by the participants in the debates themselves. By reflecting on their selective reading and historicization of these sources, we uncover the deeper structure and development of the Mesmerism controversy. Curiously, in 42 Also John Webster's theory of the powers of imagination was associated with mesmerism by contemporary commentators, for instance. See e.g. Brydges (1809, pp. 306-309).

the theories of the heterodox medico-magnetic tradition that were supposed to resemble Mesmer's doctrine, magnetism was closely related to the imagination. In this tradition, the imagination was akin to magnetism because it could act at a distance, even outside the body.

Mesmer's critics did not reflect on the fact that their own concept of imagination was the polar opposite -especially in relation to magnetism -from concept of imagination in the sources they were reading. Even more curiously, the medical authorities cited by Mesmer's critics and on which they based their critical analysis of Mesmerism, used a concept of imagination similar to the one used in the heterodox tradition. Here too, the imagination was imbued with a power to transmit ideas and impressions to others, by a material process, resembling the action of animal magnetism itself. While their sources suggested the imagination and magnetism were closely related phenomena, Mesmer's critics instead constructed a concept of imagination that had to be its polar opposite.

I have argued that the strict dichotomy between moral and physical causes, supposed by Mesmer's critics, was a consequence of their aim of unmasking animal magnetism as unreal.

Hence, the imagination, seen as the moral force responsible for the perceived physical effects, became the creator of 'illusions'. In their responses, the supporters of animal magnetism constructed the imagination very differently. Their solution came close to the position of the heterodox medico-magnetic tradition. Finally, they would integrate this seventeenth-century tradition explicitly in their genealogy.

The mesmerism controversy was a crucial and high profile moment in the history of the imagination. The medical and scientific establishment 'spiritualised' the imagination, but this made the effects of the imagination rather 'unreal' or 'illusionary'. The commission did not have the last word, however. As a response to their judgement, the supporters of magnetism embraced the imagination as an explanatory category, but radically transformed its meaning.

In the wake of this controversy, many different notions of the imagination were developed, still underexplored in historiography, enriching medical theories as well as the nascent cultural movement of Romanticism.

Koen Vermeir, CNRS (UMR 7219, SPHERE); Univ Paris Diderot, Sorbonne Paris Cité, F-75013 Paris, France. A first version of this article was presented at the conference « Le mesmérisme en contexte. Nouveaux regards sur un mouvement pluriel, 1780-1840 » 19 june

2009, Versailles and Paris.

Of course, a lot of work goes into keeping authors readable for a contemporary audience. The fact that Aristotle is intelligible for us, for instance, is due to strong traditions of scholarship and centuries of interpretative work

This is still the standard historiography up to today, constructing a genealogy from demonic possession to Mesmer, Charcot and Freud. See e.g.[START_REF] Harrington | The Cure Within: A History of Mind-Body Medicine[END_REF].

Bayle (1697);[START_REF] Browne | Pseudodoxia Epidemica[END_REF]; see e.g. Vermeir 2011.

Paulet explicitly sees himself in the lineage of Naudé, who, he claimed, had also attacked the magnetic doctrines of Gaffarel and others(Paulet 1784, p. 14).

But seeSchaffer (2010), who focuses on Mesmer's place in the historiography of medical astrology.

Montaigne (1992, Ch. XXI, p. 97-106);[START_REF] Malebranche | De la recherche de la vérité[END_REF]

We will come back later to the significance of this quote, which is in fact about the communication of the imagination between people.

See alsoAzouvi (1976)

See note 16 for the important lexical changes between the two parts of Thouret's book.

'Est igitur naturalis phantasia unguenti, causa magnetismi, & causa curationis propria, non imaginatio componentis.' (Van Helmont 1648, § 173; see also§74-6)

See Poma (2009, pp. 137-9).

Bablot (1788),[START_REF] Demangeon | Considérations Physiologiques sur le pouvoir de l'imagination maternelle durant la grossesse[END_REF] 1829; 1834)

For the Saint-Médard case, see e.g.[START_REF] Cottret | Jansénismes et Lumières[END_REF],[START_REF] Kreiser | Miracles, convulsions, and ecclesiastical politics in early eighteenth-century Paris[END_REF],[START_REF] Maire | Les Convulsionnaires de Saint-Médard; Miracles, convulsions et prophéties à Paris au XVIIIe siècle[END_REF].

In this respect, I think[START_REF] Riskin | Science in the age of sensibility: the sentimental empiricists of the French enlightment[END_REF] is mistaken in claiming that mesmerism was an extreme version of the sensibility paradigm in science. Its adversaries interpreted and presented it as such, but Deslon, for instance, explicitly repudiated too much focus on sensations and sensibilities.

For a sceptical reaction on this proposal, seePaulet (1785).

This is in fact a traditional position in the debate on the powers of the imagination. See e.g.[START_REF] Malebranche | De la recherche de la vérité[END_REF].


Denis Flaig

Christian Ochsenfeld
email: christian.ochsenfeld@cup.uni-muenchen.de

Combining the Advantages of Semi-Direct Schemes and Linear-Scaling Self-Consistent Field Methods

Keywords: SCF, Hartree-Fock, Density-Functional Theory, linear scaling, integral storage

A new stored-integral self-consistent field (SCF) scheme is presented for both Hartree-Fock (HF) and density-functional theory (DFT), that combines the advantages originally attributed to the direct and also linear-scaling SCF methods with those of traditional indirect or semi-direct approaches. By storing the densityscreened two-electron integrals in the first time-consuming SCF iteration, recalculation of integrals can be almost entirely avoided in subsequent iterations as the one-particle density matrix is shown to be quite representative for the one in later iterations. For the dominant exchange-type contractions speed-ups of typically 1.5-3.7 are observed.

I. INTRODUCTION

Since its introduction in the 1980s [1-3] the direct self-consistent field (SCF) method has become the standard procedure for the iterative solution of both the Hartree-Fock (HF) and Kohn-Sham equations in density functional theory (DFT) for large molecules. The direct method avoids storage of the a priori N 4 four-center two-electron integrals (as it is done in integral indirect schemes; with N as the number of Gaussian-type basis functions) and in this way overcomes limitations with respect to memory or storage capacities. Although this entails a recomputation of the two-electron integrals in each SCF iteration, the advan-

tage is that for screening negligible two-electron integrals the one-particle density matrix is available, which contrasts the case of an indirect SCF scheme where integrals are calculated beforehand. In this way, not only typically many more integrals can be neglected, but also linear-scaling methods can be devised that exploit the locality of the one-particle density matrix (see, e.g., Ref. [START_REF] Ochsenfeld | Reviews in Computational Chemistry[END_REF] for an overview). Although recently semidirect approaches [START_REF] Mitin | [END_REF]6] have been introduced that avoid to read back all of the stored integrals, using a screening with density matrices as well, they still require the calculation and storage of a quadratic number of integrals.

In our present work, we present a modified quasi-indirect or semi-direct SCF scheme, which allows for both linear scaling and efficient reuse of integrals. The accuracy and scaling behavior of the conventional direct or linear-scaling schemes is fully unchanged, since the same integrals are employed for forming the integral contractions and only the way they are stored or recalculated is changed. Efficiency is illustrated for various systems for the dominant exchange part.

II. APPROACH

With the present work we aim for a new stored-integral Hartree-Fock SCF method which preserves the favorable scaling of the direct and linear-scaling methods. The fundamental concept of the new approach is to avoid the computation of a quadratic number of ERIs prior to the SCF iterations by exploiting the sparsity of the density matrix not only for the reading of integrals, but also for calculating and storing them. For this purpose integrals are stored not before the first iteration, but in an early SCF iteration, typically in the first costly iteration where a full and meaningful one-particle density matrix is available for the screening, so that negligible integral-density products can be discarded. The preselection is performed according to the well-established density based Schwarz screening:

|P νσ • (µν|λσ)| ≤ |P νσ | • (µν|µν) 1 2 • (λσ|λσ) 1 2
(1)

As will be shown, the second iteration is typically a good choice for the storage iteration for two main reasons: On the one hand the initial guess of the first iteration, e.g. obtained by a superposition of atomic densities (SAD), is still quite poor for a meaningful integral selection.

In addition, since the initial guess density matrix is extremely sparse, the calculation of the On the other hand, storing in a later than the second iteration, would sacrifice too much of the potential gain of time. Furthermore, we will show below that the density matrix in the second iteration is typically already quite representative for the converged density matrix and in this way a good choice for a realistic selection process of the integrals.

For minimizing the overhead of storage access, the present method is developed for an integral storage in core memory (although of course disc-based storage is also possible in principle). This means, that for large molecules or basis sets, additional criteria for the integral selection are essential, although the memory (or disc) capacities on personal computers increase steadily. Therefore within the memory limitations we adapt the well-established criteria of time and size estimates in semi-direct SCF theory [3] and improve the time criterion by counts of floating point operations needed for integral evaluation.

In order to play out the strength of the CFMM [7] and LinK methods [8,9] within linearscaling SCF schemes, the current methods need to form the exchange and Coulomb part separately. Here, the exchange part is typically three to five times more time-consuming than the Coulomb part depending on integral thresholds, basis sets and the molecular system.

Therefore the focus of the present work is on the exchange part. However, the method can as well been established for the near-field integrals needed for the Coulomb part.

III. IMPLEMENTATION

The new stored-integral method was implemented into a development version of Q-Chem [START_REF]Development version of the program package Q-Chem[END_REF]. Fig. 1 outlines the implementation, which is composed of three main steps. The first iteration is fully identical to a conventional direct SCF, based on the default initial guess, the superposition of atomic densities (SAD), which typically results in a fast computation of the first iteration. The second iteration is the iteration where the integrals are selected, screened, calculated and stored to the main memory. In the following iterations a modified screening is performed, the required integrals are read back from memory, and additional integrals are calculated, if necessary.

Within the selection run a Schwarz screening that accounts for the corresponding density matrix is performed. Moreover, additional selection criteria for the decision which integrals to store are applied: i.e. estimates for size and time. Since neither the effective size of This holds in particular if difference densities are employed and the Fock matrix is build incrementally [2,3]. The second factor, the time for calculating an integral can be estimated by counting necessary floating point operations n flop for a chosen integral evaluation path for each integral class divided by the number of integrals per class. Here an integral class is defined as set of integrals sharing the same momentum type and degree of contraction for the bra and ket. Fig. 2 shows the correlation between time and number of floating point operations per integral class for the cyclic S 6 allotrope. The time within the second SCF iteration, averaged for 50 exchange builds to be statistically balanced, is compared to the number of floating point operations for different integral classes. Only if an integral class exceeds a minimum number ϑ flop of floating point operations the corresponding integrals are selected for storage. Within the current implementations the threshold ϑ flop is not user defined but is the result of the size criteria ϑ size and available memory capacities.

Once the exact number of ERIs selected for storage is known, all the memory for integral storage may be allocated at a time. Then, as the ERIs are batchwise calculated as usual, ERIs belonging to the same shell quartet are written consecutively to the integral buffer.

For future addressing the offset for each shell quartet is additionally stored.

By a modified screening procedure in the following iterations, the decision is made, which integrals are significant according to (difference) densities and the Schwarz inequality and, moreover, which of them can be read back from the memory or need to be calculated. Within the present scheme the necessity for calculating new integrals upon the iteration process may thus have two causes: Firstly, changes of the difference density matrix within the SCF iteration process that influence the density based Schwarz screening. Secondly, if due to memory constraints not all integrals were storable (as defined by the separate selection criteria ϑ size and ϑ flop ). Any additionally needed integrals are calculated and contracted batchwise like in the conventional direct procedure. Fig. 3 shows the best possible theoretical speed-ups of the stored-integral method as compared to the direct scheme, assuming that the stored-integral method could save the full time for integral evaluation and if the time for storage access and other overhead were completely neglected. The maximum theoretical speed-up is plotted against the percentage of exchange time, which is required by the integral evaluation within the direct method. For example, if the percentage was 66.7 % (two-thirds), the stored-integral method would at best be three times faster than the direct one for building one exchange matrix. The ratio for integral formation and contraction can be strongly dependent on the computer architecture, so that speed-ups may vary to some extent. These considerations illustrate the optimal limit that one may aim for and allow to assess the efficiency of our present implementation.

Certainly, in real timings, the time for storage access becomes clearly noticeable and, moreover, the time for the calculation of integrals within the second iteration remains:

For comparison, Tab. I lists the CPU time for each component of the stored-integral and direct method. As test case, a DNA fragment with one base pair deoxyadenosine and deoxythymidine DNA(A-T) 1 [START_REF] Doser | [END_REF] is considered. All timings were performed on one core of an Intel(R) Xeon(R), 2x CPU E5420 (quadcore), 64 GB RAM. For the stored-integral method the time for selection, storage and reading of the integrals is listed, in addition to screening, calculation, and contraction. The integral selection for storage is based on the second density matrix. For iterations 3 to 8 the total time over all these iterations is given for each component (where always incremental Fock builds were employed). Besides the specific iteration time also the total time for the SCF is shown. The percentage always refers to the total exchange time of the stored-integral or direct method, respectively. Within the direct method the percentage of the total integral evaluation time is about 65.5 % with respect to the total exchange time. Of course the stored-integral method cannot save the integral evaluation within the second iteration (13.6 %), but only (and for the best case) the integral evaluation within the reading iterations 3 to 8 (51.9 %). Therefore the best possible speed-up for this example is g = 2.08. The assumption, that the time for the calculation of additional integrals within the iterations 3 to 8 is negligible, proves to be correct here:

It decreases to about 0.5 % of the exchange time. Clearly, this is where the stored-integral method takes its speed-up from. On the contrary, additional time need to be spent for the The overall speed-up of the stored-integral method depends on different aspects, which are considered in the following. First of all, Tab. II reveals its dependence on the integral threshold and SCF convergence criterion, again for the example of DNA(A-T) 1 . For variable integral thresholds a constant convergence criterion was used and vice versa. The speed-up increases with the tightness of the integral thresholds, because the ratio of time for screening, calculation and contraction shifts to a domination of the integral calculation time. As CPU time can only be saved in the third and later iterations, but not in the first and second one, the speed-up increases the tighter the convergence criteria and the more iterations are needed.

Moreover, the speed-ups depend of course on the chosen basis set and molecular system.

Once again, the speed-ups increase, if the integral evaluation is more expensive within the later iterations of the direct SCF method compared to the screening and contraction steps.

Therefore the largest speed-ups are reached e.g. for heavy atoms with non-split valence basis sets, including high momentum types. In Tab. III several benchmark calculations are arranged according to increasing speed-ups of the stored-integral with respect to the direct SCF for the formation of the exchange part. For example, using the cc-pVQZ basis set and a convergence criterion of ϑ SCF = 10 -7 and an integral threshold of ϑ Int = 10 -10 , the percentage of the integral evaluation in the reading iterations with respect to the total exchange time reaches 78 % for the cyclic S 6 molecule and speed-ups of 3.70 are achieved as compared to the best possible speed-ups of 4.55.

The test cases described so far were all based on the first calculated density matrix (i.e., of the second iteration), without the use of additional criteria ϑ size and ϑ flop , that means 100 % of integrals selected by the first calculated density matrix were stored. However, for large systems, due to memory limitations, the additional criteria ϑ size and ϑ flop may be essential and their effect on the described stored integral method is considered in the following. Firstly, the effect of ϑ size is shown in Tab. IV for the example of DNA(A-T) 1 and a TZP basis. Here, the percentage of stored and additionally calculated integrals are listed for three cases:

• In the direct method (case 1) no integrals are stored. • In the second case, all integrals as selected by the second density matrix are stored.

• In the third case, of density selected integrals only those integrals are stored for which the Schwarz estimates are larger than ϑ size = 10 -4 .

The data in Tab. IV indicate, that the selection by ϑ size = 10 -4 strongly enlarges the number of additional ERIs required in later iterations: For example in the third SCF iteration 24.98 % instead of 0.76 % in case of full storage 100 % (32.39 GB) need to be calculated additionally, while the memory requirements are reduced to 68.45 %(22.17 GB). As consequence of the high percentage of additional required integrals in later iterations the speed-up with respect to the direct method typically quickly decreases, if a large additional criterion ϑ size needs to be set due to memory restrictions. For the example of DNA(A-T) 1 and a TZP basis it reduces from 1.55 to 1.40, if ϑ size is set to 10 -4 .

For another example, the cyclic S 6 allotrope (cc-pVQZ basis, integral threshold ϑ Int = 10 -8 , convergence criterion ϑ Int = 10 -5 ), where the evaluation time for ERIs of different integral classes strongly differs, the effect of the second additional storage criterion, the time estimates (cf. Fig. 2) is considered. The selection of integrals according to the number of floating point operations per integral ϑ flop proves to be very efficient: It leads to a speed-up of 2.70, as compared to 2.79 if all integrals are stored, and reduces the memory capacities from 100 % (31.02 GB) to 61.76 % (19.16 GB). In contrast a selection according to the product of total degree of contraction and total momentum type shows a speed-up of 2.53 using roughly the memory as above. The third most primitive option, to avoid storing integrals once the memory limit is hit, leads to a speed up of 1.44. This clearly smaller speed-up is reached, since the most primitive option employs no time criteria and the default integral ordering does not start with the most expensive integrals.

For the investigation of the scaling behavior, three model system are considered: Linear alkanes, helical oligopeptides, and fragments of amylose, which can be systematically enlarged. Due to rising memory requirements a small 6-31G* basis set and a rather loose integral threshold of ϑ int = 10 -7 are employed for the investigation of the scaling behavior, so that the overall speed-ups of the stored-integral methods are comparatively small (see also Tab. III). Tab. V compares the direct case with a conventional semidirect method and the present stored-integral method. Besides the total CPU time for the formation of the exchange part and its scaling behavior, also the memory requirements and its scaling are listed for the two stored-integral cases. The storage selection of the present stored-integral method is again based on the Schwarz estimates including the first calculated density matrix. In contrast, the conventional semidirect method selects the integrals by Schwarz estimates prior to the SCF iterations and therefore does not include maximum elements of the one-particle density matrix. Since such a selection quickly results in a lack of memory, e.g. 152.49 GB would be required for Alk 160 , additional estimates of time and size are used for the semidirect method. The criteria for time and size are kept constant for each example and are chosen in a way that the maximum memory requirements for the largest molecule can be satisfied. For this purpose a suitable selection for ϑ size and ϑ flop is made: ϑ size is throughout set to 10 -4 and from the remaining selection, according to the time estimates ϑ flop , only the more expensive half of integrals is stored in each case. Comparison of the total time for the semidirect and direct case shows that for the chosen basis set and integral threshold the linear scaling behavior of the direct method pays off already for the second smallest molecules within the series of examples. For larger molecules the conventional semidirect method becomes more and more inefficient compared to the direct method, because the calculation of the integrals chosen prior to the SCF cycle scales quadratically. This problem is solved by the new stored-integral method, where the favorable scaling behavior of the CPU time of the direct method is preserved. The linear scaling also holds for the memory requirements for storing the two-electron integrals.

V. CONCLUSION

In our present work, we have introduced a new stored-integral SCF method that combines the advantages of semi-direct or quasi-indirect SCF methods with those of linear-scaling methods. The key is to use the first computed one-particle density matrix for screening the significant two-electron integrals and then storing the corresponding integrals for subsequent iterations. It is shown that typically the first computed density matrix (following the cheap SAD guess iteration that is almost negligible in time) is sufficiently accurate for preselecting the integrals, so that only a few integrals need to be recomputed in later iterations. The speed-ups depend on the molecular system, the basis set, and the chosen thresholds, where for exchange-type contractions an acceleration by factors of typically 1.5-3.7 are observed, which is relatively close to the optimum of estimated speed-ups. Our scheme is not only useful for the calculation of energetics, but will also accelerate the calculation of molecular properties (see e.g. [12,13]), where relatively tight convergence thresholds are required. Also, with the availability of computers with more core memory, the possibilities for storing integrals and avoiding their recalculation will increase, which underlines the usefulness of the present approach. Response to the reviewers' comments (manuscript TMPH-2010-0289)

Referee 1

The authors have implemented a semi-direct SCF scheme that scales linearly with the molecular size. This is an obvious improvement of modern efficient SCF codes. The presented test calculations show that it was worth the effort as the code can become faster by almost a factor of 3.

The manuscript contains lots of technical information that might be of interest for other developers. The authors should consider whether all details have to be reported. The manuscript is though very well written.

We thank the referee for the positive comments. Although we agree that there are many technical details included and we reconsidered whether they are necessary, we do believe that they might be useful for other research groups. Also, the second referee asked for some more technical details, which we included in brief.

I would write Gaussian-type instead of Gauss-type.

Changed accordingly.

Referee 2

This paper shows the efficiency gain of calculating the HF exchange matrix by storing and reusing AO integrals instead of calculating them at every SCF cycle (the the so-called direct method). In the early years of HF, all the AO integrals were stored. The direct method allowed the efficient HF calculation of large systems on computers with small amount of memory. It makes sense to revisit the 'indirect' method with the amount We thank the referee for the positive statements and thank in particular for pointing out the unclear 'i/o' notation. We always meant memory access (and not disc access), therefore we replaced the term 'i/o' by 'storage access'.

2. The authors did not describe how the integrals are stored and indexed in memory. This info is technically important as it affects how RAM and cache are used efficiently, especially considering additional integrals are added as the SCF goes on.

We added a paragraph in the 'implementation' section that explains (in short) the essential details of storage organisation and indexing. As the first calculated density matrix shows to be typically quite good for a meaningful integral selection, the present scheme does not employ any additional storage in later iterations. Preliminary tests with additional integral storage in later iterations showed that speed-ups were hardly affected: The additional computational effort for storage organisation and (little) savings compensate each other.

3. It is not totally accurate to say that this method is good for 'the applicability of HF and DFT methods to large systems' as the authors wrote in the last sentence of the conclusion. The method trades space for speed, and thus squeezes the memory required for 'large systems'. There aren't too many GBs of memory for each core on a typical motherboard. On the other hand, the method would be effective when combined with sharedmemory parallel calculations to take the full advantage of the processing power of multicores and large memory that comes with them.

We agree with the referee that it is better to separate prefactor reductions and the treatment of larger molecules in the present context. We changed the manuscript accordingly.

  very fast and the time negligible as compared to the total SCF cycle.

  nor the effective time for its calculation is known in advance, one has to use estimates. For the integral size the conventional Schwarz estimates provide an upper bound[3]. An additional user-defined threshold ϑ size allows the selection of large integrals for storage, since such integrals are most probably reused within the SCF iteration process.

  , modified screening and reading of integrals, so that the overall speed-up reduces to 1.51 as compared to the best possible speed-up of 2.08.

-FIG. 2 :FIG. 3 :

 23 FIG. 1: Outline of the semidirect implementation

(

TABLE II :

 II ). a) Influence of the integral threshold ϑ Int and b) of the convergence criterion ϑ SCF on speed-ups g = t dir. /t sem. for the formation of the exchange part for the DNA(A-T) 1 system. For a) ϑ SCF = 10 -4 is used throughout and for b) ϑ Int = 10 -10 .

	Molecular Physics Molecular Physics			Page 14 of 21
						14 15
	a) -log(ϑ Int )	6	7	8	9	10
	speed-up	stored int. 1.36 1.43 1.47 1.49 1.52 direct
	ite. task b) -log(ϑ SCF )	t [s] (p [%]) t [s] (p [%]) 3 4 5 6	7
	1 total 2 screen a calc b speed-up contr. c 17 (8.8) 17 (5.6) 5 (2.6) 5 (1.7) 3 (1.5) 3 (1.0) 40 (20.6) 40 (13.6) 1.35 1.52 1.60 1.65 1.68 select d 3 (0.1) --P o F r F o r P
	store e e e		9 (4.6)	-	-
	total screen a 16 (8.2) 12 (4.0) 73 (37.6) 62 (20.5) e r e r
	3-8 total calc b contr. c R 1 (0.5) 156 (51.9) R 0 (0.2) 60 (19.9) read f 96 (49.5) -e e -total 116 (59.8) 234 ( 77.7) 194 (100) 301 (100) v i e v i e
			w w
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						y y

a density-based Schwarz screening (modified if necessary) b calculation of ERIs c contraction of calculated ERIs with density matrix d selection of expensive and large ERIs e storage of selected ERIs f reading and contraction of stored ERIs Page 13 of 21 URL: http://mc.manuscriptcentral.com/tandf/tmph URL: http://mc.manuscriptcentral.com/tandf/tmph

TABLE III :

 III Speed-ups for the formation of the exchange part for different molecular systems and basis set for two different thresholds. In addition, the energy difference between the tighter thresholds (7/10) and the lower ones (5/8) is listed. SCF = 10 -α and integral threshold ϑ Int = 10 -β b Absolute value of the energy difference between the use of 7/10 and 5/8 thresholds

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	molecule	basisset	speed-up	b ∆E[µH]
			a 5/8 a 7/10
	alkane C 20 H 42 DNA (AT) 1 peptide Gly 6 F o r	6-31G* SVP TZP	1.39 1.51 1.55 1.68 1.59 1.72	7 2 20
	carbohydrate Glu 2 perfluor. silane Si 6 F 18 cc-pVTZ 2.10 2.39 cc-pVDZ 1.83 2.07 P	15 70
	sulfur ring S 6 e	cc-pVQZ 2.79 3.70	13
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a α/β denotes a convergence criterion ϑ

TABLE IV :

 IV Percentage of stored integrals in the second iteration and additionally calculated integrals in later iterations for DNA(A-T) 1 , basis set TZP, convergence criterion ϑ SCF = 10 -5 , integral threshold ϑ int = 10 -8 and threshold for integral storage ϑ size . The ratio refers to the number of calculated integrals within the second SCF iteration (4347.95 millions). For all cases an incremental Fock build is used.

		Molecular Physics		Page 16 of 21
	direct SCF o F r	store iter. 2 iter. 3 ite. 4 iter. 5 iter. 6 calculate 0.00 92.00 81.93 68.37 54.98
	no ϑ size	100.00	0.76	0.13	0.00	0.00
	ϑ size = 10 -4 P	68.43	24.98 17.65	9.25	3.46
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TABLE V :

 V Total CPU times t (in seconds) for the formation of the exchange part, memory requirements m (in gigabytes) and scaling behavior (n x ) for linear alkanes Alk n (n C atoms), helical peptides Gly n (n glycine units), and amylose fragments Glu n (n glucose units) (basis set 6-31G*, convergence criterion ϑ SCF = 10 -5 , integral threshold ϑ Int = 10 -7 ). The stored-integral scheme of the present work (P-screening) is compared to the direct SCF using LinK and to a semidirect scheme, which does not include the density matrix for the integral selection (no P-screening), but size and time estimates (see text for details). For the dependence of the speed-ups on basis sets, integral thresholds and convergence criteria see Tab. III (e.g., for larger basis sets larger speed-ups are expected).

	Page 17 of 21		Molecular Physics
						Prof. Dr. Christian Ochsenfeld
						Chair of Theoretical Chemistry
						Department of Chemistry
						University of Munich (LMU)
						Butenandtstr. 7 (C)
						D-81377 Munich
						christian.ochsenfeld@cup.uni-muenchen.de
						www.cup.uni-muenchen.de/pc/ochsenfeld/
						Phone: +49/89-2180-77920
							+49/89-2180-77921 (Secretary)
	r o F			Fax:	+49/89-2180-77919
		stored-integral no P-screening P-screening/LinK P	direct/LinK
	molecule a (N bas )	t b (x t ) e	m c (x m )	t b (x t )	m c (x m )	t	b (x t )
	Alk 10 Alk 20	(194) (384) 34 (1.95) 0.62 (2.18) 23 (1.97) 1.44 (2.03) 30 (1.60) 9 0.14 6 0.36 10 e r
	Alk 40	(764) 108 (1.68) 2.84 (2.21) 59 (1.37) 4.20 (1.56) 80 (1.43) R
	Alk 80	(1524) 344 (1.68) 11.66 (2.05) 145 (1.30) 9.81 (1.23) 191 (1.26) e
	Alk 160 Gly 3 Gly 6 Gly 12	(3044) 1136 (1.73) 47.26 (2.02) 343 (1.24) 21.03 (1.10) 421 (1.14) (221) 19 0.25 13 0.71 20 v i e (419) 72 (2.08) 1.14 (2.37) 49 (2.07) 3.04 (2.27) 68 (1.91) (815) 263 (1.95) 5.31 (2.31) 166 (1.83) 11.21 (1.96) 214 (1.72) w
	Gly 24 Glu 1 Glu 2 Glu 4 Glu 8	(1607) 835 (1.70) 23.00 (2.16) 416 (1.35) 29.36 (1.42) 520 (1.31) (204) 18 0.27 13 0.73 20 (389) 72 (2.15) 1.23 (2.35) 49 (2.06) 3.37 (2.37) 67 (1.87) O n l (759) 235 (1.77) 5.33 (2.19) 147 (1.64) 11.23 (1.80) 187 (1.54) (1499) 747 (1.70) 21.67 (2.06) 375 (1.38) 27.99 (1.34) 476 (1.37) y
			a number of basis functions
			b scaling exponent of the total exchange time
			c scaling exponent of memory requirements

URL: http://mc.manuscriptcentral.com/tandf/tmph

  of memory per processor (core) now is in the GB range. Thus, this paper represents a technical progress especially in combination with linearscaling HF and is thus publishable. This reviewer has the following comments: 1. The authors mentioned 'i/o' at several places. It is not clear what they meant here since all the integrals are stored in-core.

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Acknowledgments C.O. acknowledges financial support by the Volkswagen Stiftung within the funding initiative 'New Conceptual Approaches to Modeling and Simulation of Complex Systems'.