Keywords: Galen, Galileo Galilei, Mechanics, Medicine, University of Padua, Paolo Sarpi, Pulsilogium, Pendulum, Santorio Santori

1.1. Sarpi, Santorio and Galileo on the Invention of the Pulsilogium

Attribution to Sarpi is entirely based on what Fulgenzio Micanzio (1570-1654) affirms in his biographyVita del padre Paolo (1646), in which he contends that not only two types ofpulsilogia (corresponding to A-B in our designation), but also the thermometer and the telescope were invented by the Venetian friar⁵. With the exception of only a few notes from his collection of thoughts (Pensieri, no.547) Sarpi’s scientific studies on the pendulum have not been preserved and the surviving testimonies do not permit us to judge with any historical accuracy what Sarpi’s contributions to the evolution of this instrument were. The brief notes he wrote in thePensieri, however, show that he had a particular interest in dynamics and that the topic was certainly among those he discussed with Santorio, the latter being his oldest and closest friend in Venice⁶.

In the case of Galileo, historians are mostly reliant on what Vincenzo Viviani (1622-1703), Galileo’s last and most faithful disciple, wrote in his biographyRacconto istorico della vita di Galileo (1654). Viviani writes that in about 1582-3 Galileo invented an instrument to measure the pulse when he was still a student of medicine in Pisa, and he afterwards described his invention to doctors⁷. As we shall see later, this claim has no historical basis, reflecting Viviani’s notorious lack of historical accuracy. Unlike Sarpi, however, attribution to Galileo can be supported with other evidence, in particular with a letter sent to Guidobaldo Del Monte (1545-1607) on 29 November 1602, in which Galileo describes some aspects of pendulum motion. Although the letter itself is not original, but is a second hand copy from another copy of Galileo’s original, there is no reason to doubt either its authenticity or its date. This letter has been studied by many historians with different purposes; our aim here is not to go through all its possible interpretations but to show that, whilst the letter clearly deals with some kind of experimentation with the pendulum, it does not imply any practical application, nor does it furnish any mathematical proof for the pendulum motion. Galileo simply refers to some experiments he performed (esperienze) and to a plausible mechanical explanation (senza trasgredire i termini della meccanica), though the mathematical law had not yet been found (è quello che cerco)⁸. And yet, there is more. Galileo refers to the harmonious movement of the pendulum as something already known, not as a discovery he made, rather adopting it as an ideal case (in which no friction but that of the air should occur) for his theory of motion of falling bodies on an inclined plane. Moreover, experiments that Galileo is said to have performed with two persons observing pendulums of the same length with equal weights swinging with different amplitudes up to 100 times and keeping their isochronism, do not stem from any actual experience: if actually performed, the results of these experiments would have rather contradicted such an assumption: at this stage Galileo’s theory was notoriously wrong as pendulums are indeed affected by the amplitude of their swing⁹. As already noted, Galileo himself makes no claims regarding inventions or practical applications resulting from his work on the pendulum. If he had actually developed any such inventions or applications he had no reason to hide them from a friend such as Guidobaldo, for describing them would have reinforced his point.

Misled by Viviani’s account but also by the fact that Galileo was later able to identify the geometrical proportions upon which the pendulum swings are based, many historians have mistakenly assumed that thepulsilogium was invented by Galileo and was able to furnish a direct reading of the pulse rate in term of beats per minute¹⁰. In the following paragraphs we will show that both hypotheses are groundless.

1.2. New Documents on Santorio and the Discovery of the Pulsilogium

The first contemporary and reliable testimony referring to an instrument calledpulsilogium appears as a quotation in a treatise on the pulse,De pulsibus libri duo (Padua, 1602)¹¹. The author was a physician, Eustachio Rudio from Belluno (1548-1612), who was a friend and colleague of Santorio at the College of Physicians in Venice as well as professor of practical medicine in Padua, the university where Galileo taught mathematics. As we shall see shortly, the fact that the testimony does not occur originally in a work of Santorio is particularly relevant, for it testifies to the spread of application of this instrument in a wider context. In his book, Rudio acknowledges Santorio’s invention in words that closely follow Santorio’s description one year later:

• I just want you to know that in our age (nostra aetate) an instrument – which it is possible to call apulsilogium – has been invented in order to discern the quickness and slowness of the pulse. Its author is Santorio Santori, a physician, a philosopher and a man provided with all kinds of erudition. This is a clearly wonderful event, and it represents a certain proof of the perspicacity and the keenness of wit of such a man. Thanks to this device, in fact, we can measure with exactness the movement and the rest of the pulse, and so the fastness and slowness of the present pulse can be compared with the one of previous days with absolute precision.¹²

Although the exact month of the publication cannot be established – for the printing licences of that period have not been preserved – there is no doubt that Rudio’s book was published well before the end of 1602, since there is another edition of this work published the same year in Frankfurt by Johann Spies (1540-1623) after the first Paduan edition.¹³ Spies’ edition bears the subtitleauctior and so it must have reached Frankfurt well before the end of 1602, a hypothesis further corroborated by the fact that Rudio relates that the instrument has already been invented and applied. As a result, we can conclude that, when Galileo writes to Guidobaldo, thepulsilogium was already known to Galileo’s colleagues in Padua. There is also the possibility that, since Galileo’s interest in studying the pendulum did not seriously begin prior to 1602, his interest was reawakened by Santorio’s discovery and Rudio’s announcement of it, a hypothesis that is further strengthened by the fact that Galileo took part as a subject in Santorio’s metabolic experiments¹⁴. This does not imply that Galileo relied on Santorio’s studies for his discoveries, it only testifies that the first historic record of an instrument using a pendulum acknowledges Santorio as its inventor, and that – as we will show in the following paragraphs – he was working, along with Galileo and Sarpi, on a legacy of shared ideas. Finally it is particularly noteworthy that no record has been found to support Viviani’s claim and all early historical quotations acknowledge Santorio’s as the inventor of thepulsilogium.

After Rudio’s announcement (1602) and Santorio’s first description (1603) many other physicians and scientists started being attracted to the possibilities opened by thepulsilogium. Some of these records are particularly interesting.

In 1611 Caspar Bartholin the Elder (1585-1629) published a small book collecting a series of opinions on medical and philosophical problems from across Europe. One of those is a report from the Venetian physician Antonio Fabri, who confirms Santorio’s invention of thepulsilogium and had the opportunity to witness its application to medical practice¹⁵. Ten years later (1621), Peter Lauremberg (1589-1635) a physician at the University of Rostok in Germany, was able to replicate and to successfully apply thepulsilogium to explore the usually imperceptible differences in the pulse rate (omnigena pulsuum discrimina)¹⁶. Lauremberg’s quotation is relevant also for another reason: since Santorio did not provide the design of his instrument until 1625, Lauremberg could not have copied its design from any printed editions. He says he was informed that Santorio was the inventor of such an instrument (qualia a Sanctorio excogitata accepimus) but he had to rely on either oral accounts or manuscript sheets of the instrument, a statement that supports Santorio’s later claim that his instruments were known and copied by his students and correspondents across Europe¹⁷. By the same token, Isaac Beeckman (1588-1637) paid particular attention to Santorio’s devices and took inspiration from them for his experiments on vibrating chords.¹⁸

With the exception of Beeckman, these quotations do not reveal much about the mathematical or scientific background of Santorio’s inventions: quite the contrary, many of them testify to his reluctance to share the secrets of his mathematical devices¹⁹. Unlike Galileo, we do not possess any of Santorio’s manuscripts that could reveal his studies. It is quite certain, however, that he had a good understanding of mechanics, due not only to his father’s military employment asbombardiere in Capodistria but also to the fact that he studied mathematics and music in his youth²⁰. Moreover, devices such as the anemometer and the water current meter that Santorio invented and personally suggested for use in naval equipment, offer a good testimony to this.

Although Rudio’s quotation does not specify when exactly the instrument was invented we can assume its date to be approximately 1590-1600. Relying on what Rudio says in theDe naturali atque morbosa cordis constitutione (Venice 1600) about Santorio’s forthcoming works, in fact, we can assume that Santorio’sMethodi vitandorum errorum omnium qui in arte medica contingunt libri XV (Venice 1603) containing the short entry on thepulsilogium was already part of it²¹. There are, however, other clues that suggest we should consider 1600 as the latest possible date of such an invention, for instance the fact that, in 1603, Santorio shows that he had performed many experiments with his instrument, being already able to distinguish between 133 differences (differentiae) in the frequency of the pulse.

Regrettably, the hypothesis of Santorio’s dependence on Galileo’s studies led scholars to completely neglect the direct reading of Santorio’s works, which reveal a different approach to the use of the pendulum that fits perfectly within Santorio’s programme for quantification in physiology. Indeed, the description of thepulsilogium in the fifth book of theMethodus vitandorum, a work mostly devoted to differential diagnosis, stresses the need to draw exact and certain indications in medicine. Furthermore, in the various types that we will be discussing inSection II, thepulsilogium represents the embodiment of Santorio’s ‘programme of quantification’ as a three-point method of empirical analysis:

• a)

  Measurement of a physiological process through definite parameters (perspiratio insensibilis→change in weight;fever→degrees of heat;pulse→frequency);

• b)

  Designing and manufacturing devices to use in order to guarantee certainty in measurement (statera medica,thermometers,pulsilogia, hygrometers,wind and water current meters);

• c)

  An essential part of repeated and controlled experimentation.

1.3. The Physics Behind the Pulsilogium

In Santorio’s earliest description (1603), thepulsilogium is ‘an instrument able to show all the differences in equal movements’ [Appendix A, Quotation I]. This statement, which will be explained insection II, highlights the most fundamental property of thepulsilogium, which consists in producing and recording equal intervals of time. In 1612 Santorio would reveal that the instrument was pendulum regulated [Appendix A, Quotation II] whereas in 1625 he would provide not only a drawing [Fig. 11] but also a short account of why it was capable of such regular movements. This account takes the form of a ‘caveat’ (at notandum) and, though it is not meant to provide any mathematical details, it reveals some clues about Santorio’s understanding of mechanics:

• It is quite noteworthy that by pushing the ball a little more or less hard, it does not change its frequency nor its velocity, as when the space reduces, the force decreases correspondingly (tantum amittitur de spacio quantum enim remittitur de violentia) [Appendix A, Quotation III].

This short sentence highlights that, covering different distances in the same time, distance and velocity must be in a direct proportion. In hisStoria del Metodo Sperimentale in Italia, Raffaello Caverni (1837-1900) claimed that in this passage Santorio assumed the absolute isochronism of the pendulum, yet, in the absence of Santorio’s manuscript, it is difficult to understand exactly how the Venetian physician could have reached such a conclusion²². Some hints come from the lexicon he adopts, which seems to be framed within the late medieval theory of ‘latitude of forms’ given to the use of expressions likeviolentiam <intendere vel>remittere, with which we will be dealing in the following paragraphs. If so however, Santorio’s explanation most certainly draws from an understanding of the Renaissance controversy on equilibrium, which updated and successfully transformed most of the medieval assumptions on dynamics.

As Jürgen Renn and Peter Damerow have shown in a pivotal contribution on the topic, the equilibrium controversy revolved around the behaviour of weights that are deflected from their position of equilibrium over the equal arms of a balance²³. The “equilibrium controversy” had important consequences in the development of early modern mechanics. A particularly important one, in our case, was acknowledged by the Venetian mathematician Giambattista Benedetti (1530-1590) in 1585 and stood in open contradiction to some principles of Aristotle’s physics²⁴ : relying on Archimedes’De aequi ponderantibus, Benedetti asserted that the weight, and so the momentum, of a body over a balance increases in proportion to the distance from the fulcrum²⁵ [Fig. 1]. As a result, if one of the two weights is lifted and the other is allowed to move freely downwards, it will arrive at the point of rest (viz. the centre of gravity) more rapidly if falling from a more distant position over the horizon and, vice versa, less rapidly if falling from a closer position, regardless its original weight²⁶. In short, it will acquire greater or lesser momentum (intendit aut remittit violentiam) according to the distance traversed so that, to smaller distances traversed would correspond less force and vice versa, exactly as in Santorio’s description²⁷. To understand this point we have to bear in mind that within the Aristotelian framework, the momentum of a body (violentia) was still related to its weight, which in this case changes depending upon its position.

The idea that weights had a different efficacy according to their position over the arms of the scale, was already known in Arabic science as the problem ofgravitas secundum situm (‘positional heaviness’). This concept was particularly important in the case of scales with unequal arms (staterae), where a smaller weight on the longest arm could counterbalance a greater one on the shortest [Fig. 2]. Being a case of equilibrium and an application of the principles of the scale, movement was chiefly conceived as obeying a circular motion. As Jurgen Renn and Peter Damerow put it: “[t]he proximity of the descent of a weight moving in constrained motion, on the one hand, and the natural motion of a weight to the centre of the world, on the other, is determined by the angle of contact between the circular path of constrained descent and the straight line of direct descent to the centre of the world.”²⁸.

Equally relevant were the outcomes that philosophers and engineers were able to draw from this debate in the early modern period. Del Monte, for instance, applied these principles to a particular case in which the centre of the world lies at the bottom of the circle described by the balance, a problem that seems to lie at the very foundation of Santorio’s and Galileo’s approach to the pendulum [Fig. 3]²⁹.

The indications that Santorio came to his conclusion from the development of this debate are many: the fact that he studied mathematics in Venice, where Benedetti’s legacy was well alive, and that he graduated in Padua, where Guidobaldo Del Monte (1545-1607) had studied; Santorio’s familiarity with statics in his long running experiments on metabolism as well as his reading of the works of Heron of Alexandria, which give considerable attention to the problem of equilibrium of weights³⁰. Furthermore, we found a confirmation of this theoretical proximity between Del Monte’s development and Santorio’s approach in some copies of the little-known second edition of the latter’sCommentaria in primam Fen primi libri Canonis Avicennae (Venice 1626) displaying some additional notes on instruments, not reported or displayed elsewhere. In one of these, Santorio states that all thepulsilogia keep constant proportions between their swings as their frequency increases or decreases according to the larger or smaller arcs of circumferences described by the pendulum (rotae portio) [seeAppendix A, Quotations IIIb]³¹.

In short, then, the question of the pendulum’s motion stems from the equilibrium of weights and if one considers that Santorio’s most famous invention was a platform scale (statera medica) designed to measure the metabolic dynamic, and that many of the instruments he invented imply complete familiarity with static principles (as the already mentioned anemometers and water current meters), the transition from one to another does not seem particularly surprising, nor does it require any reliance on Galileo’s studies [Figs. 4-6].

All the examples presented hitherto however, could lead to a reasonable explanation of the pendulum only if applied to a specific case: the vibration of cords. When a cord vibrates, in fact, the pitch remains constant even though the vibration – namely the space traversed between two consequent oscillations – is greater at the beginning than at the end. This is an empirical fact, not requiring the assumption of any theory, and, as seen, it could have been known to Santorio given his musical background. The idea of applying the positional heaviness and equilibrium to the study of vibrating cords must have been quite common in the early modern period, for we find this exact procedure in Isaac Beeckman (1588-1637).

On the 1st December 1630 Beekman notes in hisJournal that reading Santorio’sCommentary on Avicenna gave occasion to him to investigate the reason why cords of tortoise vibrate by passing different spaces in the same period, given the fact that the vibration is greater at the beginning than at the end³². The solution he finds reveals how the theory implied by Santorio’s instruments was understood in the immediate aftermath of their discovery:

• Let thenae be the rope from which the weight hangs perpendicularly. Let rise the same weight up tob; it is clear that, in this position, it has as much force to fall down as if it would not have been bound to the rope. Let dividebe into two equal parts, so that the anglebac will be the half of the right anglebae. As a result, the forcefb,gc which pulls downwards or that from up pushes downwards, is double more inb than it is inc, as it exercises its pressure only on the angleach, which is the half ofabf. Indeed, the particles that press the weightc (that whilst the weightc is at mid-way tend downwards according to the vertical line) affect that weight only for half of their virtue [Fig. 7]³³.

In the margin, Beekman notes that such a condition is only ideal, as experimenting with the same phenomenon in air with mass of different weights would produce different results according to the weights applied. As it clearly appears, then, the principle of positional heaviness is pivotal in understanding Santorio’s use of the pendulum in medicine, and from this standpoint it is equally important to note that many of Santorio’s followers substituted the namepulsilogium with one reflecting the principle from which it stems, calling itlibra sphygmica (‘sphygmic balance’)³⁴, a transition which in the history of technology would become even more apparent later on, in the case of pendulum scales, whereby the vertical thrust of a weight on a dish is counterbalanced by the inclination of a lever over a graduated scale [Fig. 8].

1.4. What does the Pulsilogium Measure?

Whatever the theoretical explanation behind thepulsilogium might have been, his understanding of the properties of the pendulum allowed Santorio to accurately collect, record and compare various data resulting from his measurement of the pulse. The physician had only to synchronise the swing of the pendulum with the frequency of the pulse and subsequently take note of the result. But what kind of measurement did use of thepulsilogium allow?

According to the statements we carefully collected from his various works and which are reproduced atAppendix A, thepulsilogium is intended ‘to measure the degree of distance’ (gradus recessus dimetiri) between healthy and unhealthy disposition in the body. Once measured, this distance becomes a proper quantity (quantitas recessus), and this possibly explains why Santorio uses the termsdegree andquantity interchangeably. The range of this distance – that we might better refer to today as ‘variability’ – is called by Santorio and by the Renaissance physicianslatitudo, or ‘range’, a term that could be applied to the neutral, healthy or diseased state of the body (latitudo neutralitatis, sanitatis,morbi). According to Santorio, in fact, the ‘latitude of health’ embraces also the ‘latitude of disease’ (latitudo morbi) as the last degree of its own range³⁵. The terminology adopted reveals that, once again, the Venetian physician is basing his conclusions on a particular development of the scholastic theory of the ‘latitude of forms’ (latitudo formarum).

Developed in the fourteenth century, especially in the works of English philosophers of the so-calledMerton School, this theory had already had an important precedent in the field of medicine where – at least from Galen onwards – the concept of degree played a pivotal role in understanding the action of drugs and temperaments on the body. It was however only in the medieval period that the concepts of degree and latitude overlapped and gave origin to a sophisticated theory of physical transformation in matter. According to thelatitude of forms, in fact, qualities such as heat, light and movement must be regarded as properties of a determinate substance that undergo a series of continuous changes. For this reason the theory was also known asintensio et remissio formarum, that is to say the capacity of forms to stretch and contract differently in corporeal substances. Being continuous as well as referred to a particular quality, these changes supposed aminimum andmaximum in the range of their variability (non gradus/gradus summus), and could be expressed theoretically by means of an incremental scale of degrees, usually comprehended between 0 and 8³⁶.

The transition from the concept of latitude to the use of quantitative parameters by means of instruments devised for this purpose represents one of the greatest breakthroughs in the history of science and, in medicine, the merit for this transition should be ascribed to Santorio. Most notably Santorio succeeded in adopting and systematically applying the notion of ‘magnitude’ (magnitudo) to the Galenic concept of equilibrium by converting the rapports of proportion/disproportion of bodily temperaments into linear segments of variable length (recessus) departing from or approaching to a mid-point representing the equilibrium³⁷. In this way he could then treat disease and healthiness as different regions over a scale of degrees, all of them accountable. Such an approach marked a radical departure from the practice of subjective appreciation of temperaments and bodily disposition which was dominant in any aspect of medical practice still in the seventeenth century. Before Santorio, degrees were used as theoretical entities, meant to classify the various aspect of a phenomenon and the idea of associating each degree with a real number was open to serious obstacles, related to the impossibility of setting determinate fixed limits on the range of variability of the phenomenon. This was even more the case in medicine, in which not only was the possibility of setting such limits openly rejected by Hippocrates and Galen, but its actual application was (and to some extent still is today) hindered by the peculiar constitution of each patient (idiosyncrasy). From this standpoint, it is particularly remarkable – but after all not surprising – that the transition from degree to quantity occurred chiefly in the field of medicine.

According to our study, however, this transition is still ongoing in the case of thepulsilogium. In Santorio’s account [Appendix A, Quotation I], in fact, the distance between themaximum andminimum range of the pulse frequency should be expressed as a linear scale between two points which he explicitly relates to the rarest and fastest pulse observable in normal conditions³⁸. Since we know that the measure of pulse rate increases geometrically but the measurement expressed by thepulsilogium is linear, the instrument was unable to provide a direct reading of pulse rate: this was not in fact its intended purpose.

1.5. Uses and Applications of the Pulsilogium

Thepulsilogium was meant to be used as a comparator. Its purpose was to reveal small variations of frequency allowing the physician to sketch out a reliable framework of the health trends in his patients [Appendix A, Quotation I-II]. The reasons why such variations were indeed considered to be ‘small’ were both practical and theoretical. As for the practical ones, Santorio repeatedly highlights the fact that any major increases or decreases in the pulse frequency are quite noticeable (sensibiles) and do not require the use of any particular instrument for them to be detected – although issues clearly arise as to how the objective value pinpointed at any time by such variations is determined. Theoretical reasons, are instead directly rooted in Santorio’s understanding of physiology as the process by means of which the body maintains (conservat) its normal functions by insensibly (insensibiliter) approaching or receding from the point of equilibrium; a process that in thepulsilogium is translated in the act of adding or subtracting degrees from a given number³⁹. More precisely, the device allows a comparative measurement of the pulse expressed as a difference between two or more consecutive measurements.

If the pulse which in one hour/day is found to be 70 degrees, is in the following one found to be 65, Santorio would record that it has decreased by 5 degrees. In this way, each successive measurement yields the difference between pairs of measurements. This means that Santorio’s measurements were basically collected and recorded in terms of ratios (proportiones): since the pulse frequency tends to remain constant in normal conditions that would give the same indication on the instrument scale. In other words, two consecutive measurements with the same result would have been marked as ratio 1:1 whilst regular increase or decrease of frequency could be reported as ratios of 1:2, 1:3, depending on the result found. On the other hand, irregular increases or decreases of the pulse frequency would have been recorded as simple comparison of degrees (60:55; 60:45, etc.). Santorio in fact specifies [Appendix A, Quotation I] that by means of the instrument it is possible ‘to observe all the ratios pertaining to the pulse’ (omnes proportiones observare) and we know from other accounts that the term ‘ratio’ (proportio) was sometime used quite literally, as Santorio used to collect results from its statical experiments just in terms of mathematical proportions⁴⁰. It is worth noting that, from a practical point of view and for the sake of medical diagnosis alone, the exact notion of the number expressed by each degree (in terms of beats per minute) is not necessary: it is enough to record the degree and monitor the trend of health in each patient.

Despite the fact that Santorio was not very keen on providing details on how he recorded his results, this conclusion follows directly from what he states in 1625 [Appendix A, Quotation III] and is further corroborated by the kind of practice that was adopted with the spreading of the instrument as a diagnostic tool by Marek Marci (1639) and Athanasius Kircher (1665) [Fig. 9-10], the latter in particular providing a very clear explanation of the kind of measurement permitted by instruments that are akin to or derived from thepulsilogium⁴¹.

When used in medical diagnosis, thepulsilogium required a pre-assessment of the general condition of the patient so that changes in frequency could be associated for instance with morbid conditions (especially fevers). As already noted, whereas great variations are easily perceived by any doctor, the smallest ones can be such that even a well-trained physician can fail to perceive them, thus leading to errors in diagnosis. In this sense, the invention of thepulsilogium serves to provide an objective appreciation of the values linked to any such variations. The point is clearly underlined by Józeph Struš (1510-1569), author of what was arguably the most influential sixteenth-century book on the pulse:

• In truth, there are more than fifteen simple pulses we already accounted for, but some of them are useless to a physician; others instead are useful but are impossible to be recognized at the human touch. […]. Those that are useful but cannot be detected by the touch (imperceptibiles) may nonetheless be converted to those already discussed and they are thepulsus longus,latus,altus and those opposed to these, that are the <pulsus>brevis,angustus andhumilis […].⁴²

The fact that thepulsus humilis is highlighted by Struš as ‘useful for the diagnosis but imperceptible’ can be profitably put in relation with the kind of analysis Santorio pursues in his investigations. Useful but imperceptible means that its existence can be logically deduced by the mathematical combination of all the other species of the pulse, but cannot be detected by the senses. This is indeed one of the most important concerns Santorio’s instrument is meant to address, as thepulsilogium aims at extending the doctor’s senses far beyond their natural limits in order to perceive what would otherwise remain obscure and unknown⁴³:

• […] by means of the pulsilogium we distinguish between thepulsus humilis and thepulsus invalidus in the following way: if the pulse that has previously been strong(durus) and frequent reduces its strength and frequency then it will be apulsus humilis, most of the time, in fact, thepulsus humilis does not decrease its frequency: when very slight the difference between the increase and decrease in frequencycannot be recognized by a physician without using the pulsilogium [Appendix A, Quotation VIIIb, see also Quotations IIIa and IIIb]. Our emphasis.

This passage appears to suggest application of thepulsilogium when pre-assessing the patient’s condition and determining how the pulse fits within the Galenic classification (magnus,durus,mollis,humilis, etc.). As Santorio recognises, in fact, frequencyper se is an equivocal parameter, inasmuch the ‘latitude of health’ might encompass different frequencies⁴⁴. As such, this classification provides the framework within which Santorio puts his instrument: having carried out a preliminary assessment of the general and invariant qualitative aspects of the pulse, the physician had only to measure the degree of frequency for each of them in terms ofaequalitas orinaequalitas. Others factors remaining the same, ‘equal pulses’ (pulsus aequales) resulted in having the same degree/frequency over thepulsilogium, whereas ‘unequal pulses’ (pulsus inaequales) resulted in showing different degrees/frequencies over time. In the latter case, each species of the pulse was susceptible of a range of variability (latitudo) specified as a particular region of the overall range of thepulsilogium scale marked as a difference between two or more degrees, and so as a numerical ratio (proportio). As we will show inSection II, the correct understanding of this point was essential to addressing the question of what Santorio’s 133 differences stand for.

By assigning a quantitative number to each species, Santorio possibly anticipated a method subsequently used by others, and especially adopted by John Floyer (1649-1734), though in the latter case the classification was provided in terms of beats per minute rather than degrees⁴⁵. Such a method could be used either as an application of the Galenic classification (marking the range of variability for each species) or as a method to correct some of its assumptions in the light of the measured frequency; this explains why Santorio emphasises that one of the main advantages of his instrument is its ability to better classify and distinguish betweenpulsus humilis anddebilis.

Such an approach is further revealing of Santorio’s understanding of how to use precision instruments in diagnosis. Thepulsilogium is not intended to replace the traditional physiology but to support it, by helping the physician to draw precise conclusions (indicationes) on the present condition of his patients and on the quantity of drugs and food to be supplied. Indeed Santorio clarifies that, whilst other factors are also important to evaluate the general condition of a patient, the doctor should be focusing only on those characteristics of the pulse that belongper se to its definition, and these are the motion and rest of the arteries. In the modern world, where every aspect of the human physiology has already been subjected to quantitative analysis, it is probably difficult to grasp how protracted and fruitless discussions on the exact nature of the pulse could be during and well before the early modern period, where a subjective interpretation of pulse frequency could result in a drastically different diagnosis, with an associated array of sometimes onerous and damaging treatments.

The need to draw a correct conclusion by means of instruments of precision would remain largely faithful to Santorio’s standards until the work of John Floyer (1649-1734) and Pierre Augustin Boissier de Sauvages (1706-1767). From this standpoint is interesting to note that, although in 1695 Guillaume Amontons tried to substitute Santorio’spulsilogium with a clepsydra⁴⁶ and in 1707 Floyer introduced a pocket watch for the direct reading of the pulse frequency, their new methods were not easily accepted (not least because Floyer’s methods were weirdly mixed with different notions of western and Chinese medicine). So much so that in 1752 Boissier De Sauvages and his students still proposed to rebuild a replica of thepulsilogium in order to avoid sterile discussion at the patient’s bedside⁴⁷.

Due to lack of his tabulated data, it remains unclear whether by means of thepulsilogium Santorio also pursued a statistical analysis of his patients according to their temperament, age and gender, but such an hypothesis is consistent with everything we know about feeling the pulse in the early modern period and the constant use of the plural in referring to the subjects of his experiments (sani /aegri homines) does suggest such an approach. What we can take for granted is that, due to its chiefly comparative use, coupled with advice to measure the pulse always in healthy men in order to obtain an assessment of the normal range, use of thepulsilogium entailed a repeated experimentation over long periods of time and in different environmental conditions.

Many of the details synthetically presented in this section will be now discussed analytically in the following sections concerned with the theoretical and technical issues faced during the reconstruction of this instrument.

2.1. Classification

A general classification of all the engravings presented in the 1625 edition of theCommentaria in primam Fen primi libri Canonis Avicennae constituted the second step.

By grouping pictures according to similarity in external shape and design, we classified them into three main types, that are hereby marked with letters (type) and numbers (model) in order to specify their variants [Table 1].

Despite some improvement in design,Pulsilogia A1-2 have been considered as belonging to the same type insofar both adopt a graduated beam (which in A1 is possibly a ruler), used vertically in the former case and horizontally in the latter.

Serious consideration was given to the extent to which the images could be relied upon as accurate illustrations of the instruments, as this is notoriously problematic when referred to the design of seventeenth-century instruments. It was possible in fact that the artist had limited access to the instruments with no time to study them in detail or that he produced the drawings from a description, without direct access to the instrument in question. However, due to their poor quality (the rough sketches provided by Santorio were meant as preliminaries to the elaborate plates he prepared for theDe instrumentis medicis), it is almost certain that Santorio either drew these images himself or was directly involved in their production. For the 1625 engravings represent the only available source we have for the originalpulsilogia, we had no other choice than to trust them, though we constantly checked their information against historical documents, both visual and written, and data provided by our experiments.

2.2. Collecting References and Establishing Criteria

A third step was to collect all the available descriptions provided by Santorio himself as referring to thepulsilogium [Appendix A].

Insofar it was not related to any particular device, Santorio’s earliest description [Appendix A, Quotation I] has been used as a standard description⁴⁸, although there is the possibility thatpulsilogia B1-2 worked on a slightly different principle.

For all the references he makes to them, Santorio’s accounts never relate the real functioning or mechanism of his devices, but only their purpose: a caution that he extended to all the other instruments in order to avoid plagiarism by his pupils. This notwithstanding, a comparative reading of these accounts is particularly useful, for it sets out the criteria for application, lists all the possible uses of thepulsilogium, and features some details that are noteworthy and summarized below:

Criteria

• a)

  Measurement must be always taken in healthy men;

• b)

  Measurement should define the minimal differences in the pulse variation, not the notable ones.

Uses

• a)

  Measuring the motion and rest of the artery;

• b)

  Exactly identifying the pulse frequency and enabling to repeat the control at any time;

• c)

  Identifying regularity/irregularity of the pulse;

• d)

  Recording and comparing data;

• e)

  Defining the range of normal/abnormal activity in each patient.

Details

• ➢

  The instrument is able to show 133 differences of the pulse frequency.

2.3. Recreating the Scale: [1] Motion and Rest

The first point listed underUses deserves particular attention. Indeed, whilst the measurement of the ‘pulse frequency’ (motus) can result in something intuitive for modern scholars to grasp, the idea of ‘rest’ (quies) might possibly not, thus requiring some explanation.

In Galenic medicine, therest constitutes an important therapeutic indication as it is revealing of qualitative pulse features such as itslatitudo andparvitas⁴⁹. In this case, rest (quies externa) refers to thedistensio of the artery and can be described as the time interval between two consecutive strokes of the pulse. As such, when the interval decreases (remittit), the velocity increases (intendit) and vice-versa. Accounting for both these values thepulsilogium should provide two types of indication but Santorio shows only one in his engravings. This led us to devote more serious consideration to the position of the scale of thepulsilogium A1 [Fig. 11]. Here the length, still numbered in degrees (gradus 80), runs from 0 degrees at the top to 80 at the bottom but, if it was meant to account for the increase of frequency alone, then the scale should have been reversed. Conversely, if one takes into account Santorio’s caveat about thepulsilogium measuring not only themotion but also therest of the artery, the scale shown might represent the interval of time (velocitas) and so the ‘greatness’ (magnitudo/latitudo) of the artery’s rest. This use might have been helpful especially in cases where the frequency didn’t perfectly match the regular oscillation of the pendulum. In this case, in fact, whilst the degree over the beam indicated the velocity, the frequency, that is to say the number of strokes per pendulum cycle, could be accounted for mentally. Conversely, when the strokes perfectly matched the swings, the degree revealed the frequency indicated by means of the white line drawn over the little ball A1 [Fig. 11], or by the small knot/wooden bead in A2 [Fig. 12, letter O]. We also know that Santorio used the A2 as a timekeeper in experiments on the temperature of light and fever, which confirms the idea that thepulsilogium provided a dual indication.

A good test for our hypothesis was the comparison with thedial pulsilogia (B1-2) where not only the reverse scale disappears, but degrees are in direct proportion to the increased frequency. Initially we thought that, by constantly using the device, Santorio realised that frequency was a sufficient indication for measuring the pulse, and that, being just its reverse, the rest could have been counted mentally. But this later proved to be a false trail. Santorio, in fact, uses thedial pulsilogia to measure the respiration cycle and seems to account mentally for the number of pulse beats within it [Appendix A, Quotation VII]. Besides, removing the scale indicating the ‘period of rest’ meant in fact the removal of the period of time, without which frequency could not be evaluated.

2.4. Recreating the Scale: [2] A Double Indication?

To better understand this point it is worth remembering that in late-Renaissance physics ‘frequency’ and ‘velocity’ were still considered unrelated parameters. As Stillman Drake has shown, at this point in history velocity was not the ratio of time elapsed to distance traversed but was expressed purely as a number of degrees that could be added or subtracted, exactly as Santorio does.⁵⁰ If the degree related to the interval of time disappears, then the degree of frequency must result in 0, because it happens in no time. Thus, the double indication provided by the beampulsilogium, (frequency/interval of time or rest), must be retained also in the B1-2 types, although possibly in a different and more subtle way.

As before, in this case a careful reading of Santorio’s quotations proves enlightening.

InAppendix A, Quotation VI, Santorio states that the dialpulsilogium (cotyla) measures bothtime andfrequency, allowing evaluation of the difference between diastolic and systolic pulse. Since, in Galenic medicine, inspiration corresponds to diastole, expiration to systole, he measured their difference by synchronising the swing of the pendulum at the lowest degree of the dial, say 1, in order to match the cycle of respiration and by subsequently increasing the degree over the dial in order to match the frequency of the pulse. In case of asynchrony, the number of pulse strokes could be accounted mentally. This represents a further proof that the kind of measurement Santorio was pursuing with the dialpulsilogium resulted in a comparison of degrees.

Whether or not the B1-2 had a particular mechanism that allowed the double registration of this value is not clear. Certainly these devices didn’t simply consist of a single thread wound around a pivot, for illustrations of both B models show a bulky box (cotyla) respectively underneath (B1) and behind the dial (B2) which would have been of no use in that case. This is also proved from a careful analysis of the B1 design [Fig. 13] that features both a moving hand and moveable dial (indeed the dial is shown rotated clockwise). It is also clear that, whatever the mechanism of thesepulsilogia might have been, the numeration over the dial (12-24 degrees) was intended to allow for improved measurement resolution.

Another important difference between the beam and the dialpulsilogia was the number of degrees on scale or dial. In A1, this scale is divided into 80 degrees [Fig. 11]. As already seen, in the doctrine of the ‘latitude of forms’(latitudo formarum) 8 stands for the maximum degree of intensity (gradus summus), so we can assume that Santorio’s intention was to divide this classic 8 degrees of intensity into tenths. This hypothesis could be corroborated not only by Santorio’s general understanding of physics, as described inSection I, but also by the fact that he used to assess the scale of his instruments – the thermometer for instance – on a minimum and maximum range of variability⁵¹. However, in keeping with what has been said before, the degree 0 would correspond to no time (being signalled in scholastic terms asnon gradus), so most of the scale intervals between 0 and 1 would represent time intervals too short to correspond to an actual range of the pulse in a healthy man. Thus it is possible that in the A2 Santorio completely suppressed the numbers between 0 and 1, and accounted for the real range of the pulse frequency (10-80) rather than for its ideal range (0-80), which would possibly explain why the A2 instrument has a scale of 70 divisions (that is to say 7x10) over the beam. A comparison withdial pulsilogia B1-2 shows in fact that the minimum degree is 1, not 0. It is noteworthy that the scale adopted was not common to all later examples ofpulsilogia: in Marci’spulsilogium we find a scale of 100 degrees whilst in Kircher’s the scale accounts for 50 degrees which means that it depended on the range and resolution sought by the physician at the time⁵².

2.5. Recreating the Scale: [3] Understanding the Expression “Differences of [Un]Equal Movements”

But there are also other aspects of Santorio’s description that deserve particular attention. InAppendix A, Quotation I, Santorio emphasises that by using thepulsilogium he had identified “133 differences of equal movements, starting from the slowest up to the fastest”. In his account, Santorio swaps the nameaequales andinaequales motiones, an aspect that left us completely puzzled initially.

The quotation reads as follows:

• […] exhibet enim instrumentumomnes aequalium motuum differentias, quae sunt centum et triginta tres incipiendo ab osservatione rarissimi motus usque ad creberrimum […]: totidem observanturdifferentiae [in]aequalium motionum. Ex cuius pulsilogii observatione primo colligimus qualibet die, et hora quantum aegri recedant in crebritate a statu naturali, secundo infallibilem notitiam praebet, qua hora desinat augmentum, incipiatque status, et declinatio: tertio observaturvirtute proportionum aequalium motionum in pulsilogio observatarum, quam crebritatem, quam intermissionem, et quietem externam quolibet individuum perpeti, et non perpeti potest.⁵³

Note that the termmotus is applied here alternately to the pulse frequency and to the motion of the pendulum, insofar at least as they match each other. We thought there might have been a mistake in the printed text, as most of Santorio’s quotations about instruments are inserted rhapsodically and sometimes contain easily identifiable imprecisions [for instance,Appendix A, Quotation VI]. Yet, the alternation is kept unchanged also in all the following editions of theMethodus vitandorum (Venice 1630, Geneva 1631-32).

We decided to proceed analytically, by looking at the meaning ofequality andinequality as referring to the pulse in Santorio’s and contemporary texts.

As noted inSection I, we knew thataequalitas referred to a pulse whose parameters are constant over time, whilstinaequalitas indicates a variation⁵⁴. Since thepulsilogium was able to assess only the frequency (motion and rest of the artery)inaequalitas should refer to the parameter whose range of variation could be assessed onlycaeteris paribus, that is all other factors remaining the same. This meant, of course, using the measurement within the framework of the traditional theory of the pulse, as frequency alone could not represent a reliable parameter in diagnosis. We knew also that equal pulses resulted in the same position over the beam, whilst differences could span within the range marked by each species distinguished by the Galenic rationale. We further assumed that Santorio applied thepulsilogium to define the exact range of each species, especially in fevers and other conditions in which frequency can be altered. Thus, insofar asaequalitas andinaequalitas are denoted by the same device and in a reverse way, Santorio using these expressions alternately is aFreudian slip revealing thepulsilogium’s capability to account for both of these values. As a result we amended the text to readdifferentiae aequalium motionum.

In the absence of further data it is impossible to understand fully how the 133 differences were distributed, but there is no compelling evidence that they had a linear distribution. These differences, would possibly result in figures annotated in a separate sheet or registered mentally by Santorio, for the number does not appear in any of the surviving drawings. Allowing that 133 is the result of 19x7 and that 7, as a number that accounts for differences in frequency, is openly acknowledged by Santorio in his reference to thepulsilogium D [Appendix A, Quotation IV], it is reasonable to assume that there were 7 overall genres into which the 133 were subdivided, but we don’t have enough information to decide upon which species or genre they referred.

2.6. Capacity of the Pulsilogium A2

In almost all his descriptions, Santorio highlights the fact that the slowest and fastest movements should also be referred to the measurements taken in healthy men (sani homines). This expression refers to a qualitative pre-assessment of the patient’s condition and resulted in a series of repeated experiments intended to identify the normal range of the pulse, firstly defined according to the general conditions of each individual and afterwards possibly extended to a wider sample. We found confirmation of the possible adoption of such a statistical approach in what Santorio says in a letter to Galileo dated 9 February 1615 about the sample of individuals used for his statical experiments; this sample encompassed 10,000 subjects for a period of over 25 years⁵⁵. Such an approach must have led him to assess the normal range of the pulse which, regardless of the historical capacity of the instrument, we know spans between 60-100bpm⁵⁶. This in turn gave us an insight into the overall length of the A2 that will be explained inSection III.

2.7. The Overlapping of Linear and Geometrical Measurement

A rather serious question that arose quite early in the reconstruction process, was to evaluate whether the overlapping of linear and geometrical progression in the evaluation of the pulse could have hindered the ability to use the instrument effectively.

The answer came from a reading of Santorio’s own account as well as from our experiments with thepulsilogium.

In Quotations III and VI Santorio explicitly states that thepulsilogium is meant to measure only small variations of the pulse, not the great ones (non quaerimus notabiles differentias sed illas minimas). By using thepulsilogium we noted that, when used in this way, the error resulting from the overlapping of linear and geometrical scale is for all practical purposes negligible. It should equally not be forgotten that the adoption of a linear scale does not constitute an historical proof against Santorio being aware of the so-called ‘law of the wire’ – that is, the pendulum period depends upon the square root of the distance from the point of suspension to centre-mass. In Marci’sDe proportione motuum (1639), in fact, a mathematical proof of this is clearly given and, nonetheless, the Bohemian physician still uses thepulsilogium in a way that is identical to that of Santorio.

2.8. Margin of Error

The engraving inFig. 12 shows a vertical line on the right-hand edge of the drawing which we interpreted as evidence that thepulsilogium A2 was attached to a wall or a fixed vertical stand. Indeed, as highlighted by Kircher⁵⁷, the perfect immobility of the pendulum’s support is an essential prerequisite for the correct functioning of the instrument. This detail led us to consider possible sources of error and the overall margin of error the instrument was subject to.

The advice given inAppendix A, Quotation I that the measurement must not only be ‘quick’ but also ‘exact’ (pro qua cognitione cito et exacte comparanda) shows that Santorio realised that the margin of error involved in thepulsilogium use was minimal and almost entirely due to the human operator. This aspect is highlighted in a quite rare and very short article devoted to Santorio’spulsilogium written in 1979 by Jeffrey Levett and Gyan Agarwal, whereby the effect of error introduced by the human operator is illustrated by reference to a system diagram that we have reproduced below [Table 2]⁵⁸.

Table 2. Levett and Agarwal’s System Diagram of Santorio’s pulsilogium.

Open in a new tab

As illustrated here, critical to the precision of this measurement is the operator’s ability to accurately synchronise pendulum motion with the patient’s pulse. Operator errors here will bias the error signal which will add or subtract an offset to the value of L in the function responsible for controlling pendulum rate. Thepulsilogium is modelled as part of a closed-loop control system employing negative feedback. The patient’s pulse rate provides the set-point (Block labelled S_x at upper left). The operator (O_x) has both tactile sense of the set-point and visual sense of the pendulum rate (Feedback to visual sense at lower right). Subtracting feedback from set-point produces an error signal – here labelled as ‘Asynchrony’. This error signal, whose magnitude and sense is proportional to the difference between feedback and set-point, is used to adjust the value of L in the function describing pendulum motion (Block at upper right). This in turn corrects the pendulum rate to drive the error toward zero. Assuming correct calibration, when zero error is achieved the value of L (Length of pendulum suspension cord), is an indirect indication the inter-pulse period.

3.1. Comparing Existing Replicas

To refine our ideas about design and materials we collected visual evidence by consulting replicas of the A2 found in at least four European museums that are listed below:

While useful from the general viewpoint of studying design and approach, a careful survey of these models quickly revealed that none of them were meant to be historically accurate reproductions; given their lack of both precision and historically informed criteria none of these replicas are faithful to Santorio’s original description ofpulsilogium A2. Almost all of them feature either no scale, or their scale is obviously wrong being assigned incorrect intervals sometimes assuming Santorio’s dependence on Galileo’s studies. Replica No. 4, for instance [Fig. 19], although similar in overall appearance to pulsilogium B1, is completely inconsistent with all historical references, for it not only assumes a direct reading of pulse rate in beats per minute (evidenced by the non-linear scale-shape), but its construction does not correspond to any historical account.

A further problem to be resolved was deciding on the correct orientation of the horizontal beam. Replica 2 [Fig. 17], shows the thread and bead on the uppermost face of the beam. In Replicas 1 [Fig. 16] and 3 [Fig. 18] however, the broad face of the beam is upright with thread and bead on one side. By drawing from a variety of historical sources but also from practical application our research has confirmed beyond reasonable doubt that, in use, the broad face would have been horizontal i.e. laid flat with the scale uppermost.

Relying on the design of Marci’spulsilogium as portrayed in the frontispiece of hisDe proportione motuum [Fig. 20a-b] it was in fact clear that, in order to be readily useful, the instrument could not have been arranged vertically when in use [as inFigs. 16 and18], an assumption that we further corroborated empirically. Indeed, operation of the pendulum with the beam in vertical orientation would be severely hampered by friction from an additional 90 degree bend in the thread and the thread being in contact with the rear face of the beam as shown atFig. 21(a) below, a problem that can be solved by simply laying the beam horizontally as shown inFig. 21(b).

It is also relevant to note that, in respect to A1, A2 introduced changes to improve repeatability, avoid interferences, and make operation less cumbersome. One of the defining characteristics of the A2 was in fact that it allowed swing rate to be adjusted and cord length read whilst the pendulum was still in motion. For instance, arranging for the pendulum pivot-point to be independently supported rather than hand-held removed error resulting from oscillation of the pivot-point as the hand was periodically pulled out of position by the swinging weight. As a result, we interpreted Santorio’s engraving inFig. 12 as representing the instrument in perspective, to allow the reader to grasp the overall functioning of the instrument, although it is also possible that, mounted on a wall, the instrument was used horizontally during measurement but inclined vertically afterwards (by means of a pivot connecting the beam to the wall) to allow the physician to have a clear reading whilst taking the pulse of his patient sitting down.

The abovementioned replica no 4 [Fig. 19], deserves particular attention. This is the Vergara-Caffarelli device which is supposed to be a replica of a Galileo’spulsilogium as reported by Vincenzo Viviani. And yet, since neither Galileo’s nor Viviani’s surviving works show either a drawing or a single reference to thepulsilogium, it is clear that the overall design for this replica was taken from Santorio’sCommentary to Avicenna’s Canon.

Despite being constructed by a competent and skilful physicist, the overall design of this replica is historically and technically flawed. From a technical point of view, it assumes that the pulsilogium type B consisted of simply a thread wound around an axle attached to a pointer which moves over a fixed dial. As anticipated earlier [2.4], however, it is clear fromFig. 13 that the design must be much more complex as its function depends also [B1] on the ability to rotate the dial relative to the frame. Of the two, however, the most important is the historical flaw, inasmuch the replica is equipped with a non-linear scale. As we have already shown, a division of thepulsilogium scale into beats per minute not only runs contrary to all the historical evidence found but would have been of no practical use to any early seventeenth-century physician, accustomed to detect great variation in pulse frequency without the help of any instrument.

3.2. Assumptions

Since examination of existing replicas proved them to be historically and technically inaccurate, we decided to go back to the texts and set out some principles which our replica should follow based on three assumptions:

• a)

  Homogeneity between past and present in accounting for an adult pulse rate range, that is to say 60 to 100 beats per minute (bpm);

• b)

  The measurement of the average healthy pulse frequency was taken each time from the approximate central range of the scale [as shown inFig. 12];

• c)

  In order to avoid the use of a much longer pendulum (too unwieldy for practical use), Santorio counted two pulse strokes per pendulum cycle.

Assumption a) is historically supported by the experiments of Johannes Kepler related in the introduction.

Assumption b) is backed by the fact that Santorio pre-assessed the patient’s pulse on a qualitative-diagnostic basis and measured preferably healthy men at rest, resulting in a middle position over the beam.

Assumption c) results from pre-assessment of the instrument application as referred to the average healthy pulse.

3.3. Outline Design and Materials

Materials have been chosen based on clues deriving from Santorio’s quotes, and although many of them did not present particular problems (being just paper, thread and wood) we have been compelled to use brass instead of lead for the swinging ball, since the use of lead is prohibited by the current UK Health and Safety regulations⁵⁹.

In his 1625 description [Appendix A, Quotation IV] Santorio refers to a thread [Fig 12, letter B], made of linen or silk, whose length is controlled by being wound around a tapered peg. Furthermore,Fig. 12 shows what appears to be either a knot, or a little wooden bead (Letter O) fixed to the thread over the scale, and a pendulum bob (Letter E) that consisted of a leaden ball. From historical records, and from surviving examples of early 17th Century Italian furniture, we know that Italian cabinet makers commonly used wood such as European Lime (Tilia vulgaris), for carcases and frame-work. Being Venetian from Capodistria (today Koper in Slovenia), Santorio also had access to wood from the Croatian forests⁶⁰. Since there is no record of the actual wood used to make the beam and a suitably sized piece of English light oak was available, that is what was used in the first reconstruction⁶⁰.

A similar historical approach has been adopted in selecting material for the pendulum bob⁶¹. Although the weight and dimension of the ball does not affect the pendulum isochronism, a historically accurate replica must take into account these details. In estimating the size of the bob from what is known of other components, we realised that it could not have been pistol shot because that would be too small; therefore, it is most likely that a musket ball was used⁶². Santorio himself uses the termpila plumbea (leaden bullet) to refer to gunshot wound, and we also know from archaeological evidence that 17^th Century musket balls came in a variety of sizes ranging from 16 to 20mm diameter and weights from 22 to 35g depending on the composition of the ball. Practical considerations dictate, however, that lighter bobs would be preferred as, in the case of a portable device as the A2 might also have been⁶³. In conclusion, this suggests that the pendulum bob should weigh about 30g.

3.4. Dimensions of the Instrument

One of the most serious problems we faced in our attempt to recreatepulsilogium A2 was defining the unit of measurement for the length of the scale and beam. As for this aspect, we couldn’t rely on any available source so we had to proceed empirically by adapting modern knowledge to ancient problems. A preliminary consideration was that, although Santorio’s instrument did not directly measure pulse frequency in beats per minute, the scale used could not be completely arbitrary as the physician was dealing with a phenomenon whose limits, in normal conditions, tend to remain constant. In this sense, we had to draw a distinction between the apparently arbitrary nature of the resolution adopted (that could span either 50 or 100 degrees as shown in Kircher’s and Marci’s examples), and the nature of the phenomenon to be measured, which demands precise parameters. As a consequence, in order to understand, replicate and subsequently test limits of the instrument, it was essential to determine the overall length of the scale and, from that, the dimensions of the instrument⁶⁴. To that end, and to render the analysis readily understood in modern terms, it is necessary to relate pulse rate in beats per minute, although, where necessary for clarification, conversion back to inter-pulse period will also be made.

To get an idea of the rough dimensions of the instrument, we considered first the normal range of the pulse. The drawing inFig. 12 shows a scale of 70 divisions/degrees. Working on the assumption that at two pulse strokes per pendulum cycle this scale covers the pulse rate range of 60 to 100 beats per minute, the change in suspension cord length to accommodate that range has to be 643mm [seeAppendix B]. Therefore, the interval between adjacent scale divisions is: 643/70 = 9.186mm. Overall length of the instrument is determined by the measurement range and the space required to fit components to control the thread. In order to measure pulse rate in the range 60 to 100 bpm at two pulse beats per pendulum cycle, the change in suspension cord length – and therefore the scale length, is 643 mm. In our reconstruction [Fig. 22] a few cm were added to extend the measurement range slightly.

Tapered peg and thread hole were positioned according to proportions taken from the woodcut image, so overall length was just short of 1.0 m. Although width of the beam is for practical purposes immaterial, in the interests of historical accuracy this dimension was estimated from the proportions inFig. 12.

A final question might arise as to why, given the nature of Santorio’s pursuit – dealing with small variations of pulse rate in a healthy man – the overall instrument encompasses such a long range. The answer lies in what Santorio and his followers relate as an actual use of thepulsilogium. The Venetian physician states in fact that ‘[t]he instrument showsall the differences in equal movements starting from the slowest up to the fastest’ [Appendix A, Quotation I], which means that it could account at least for the entire range of the ‘latitude of health’ (latitudo sanitatis, neutralitatis et morbi), which is what we felt confident to assume. As seen, this entry by Santorio is confirmed also by later accounts, such as Lauremberg’s, who relates thepulsilogium being used to exploreomnigena pulsuum discrimina⁶⁵. Finally, if the assumption made inSection I.5 is solid, then each region of thepulsilogium was meant to correspond to a given species of the pulse, whose range was expressed in decimals of degree.

3.5. Applications

Based on Santorio’s written records we can safely assume that he designed his instruments so that the bead would be in the middle of his scale when a normal healthy degree of the pulse was measured. To achieve this condition in our recreation, it was calculated that for the pendulum swing to synchronise with two pulse beats per full cycle at 70 beats per minute the distance between the centre of the pendulum bob and the underside of the beam has to be 73cm [seeAppendix B]. After adjusting the tapered peg to set this length, the bead was moved along the linen thread to centre-scale and locked in that position. As stated above, in order to cover the normal healthy range, the limits must be at least 643mm apart, this being the required change in cord length to measure between 60 and 100 beats per minute.

3.6. Practical Reliability

As part of a series of public engagement activities, held as joint events between the Centres for Medical History and Biomedical Modelling and Analysis of the University of Exeter, Dr Joanne Welsman and David Taylor conducted a series of tests to address the question of how reliable was thepulsilogium in terms of practical measurements. Some of these tests took place at the Honiton Festival of Imagination (2016) whilst others at the South Devon University Technical College (SDUTC) in Newton Abbot (UK). In the latter, measurements were taken by students with no background in early modern medicine, using replicas of Santorio’spulsilogium A2. Students took measurements in a kind of doctor-patient session, whereby two different students (doctors) were asked to use our replica to match the pulse rate of a third one (the patient) and record the measurement obtained. As expected, a slight increase or decrease of pulse rate due to environmental or psychological factors in the ‘patient’ was acknowledged, overall however, it turned out that the difference between measurements was negligible and almost exclusively attributable to the ability of the student taking the measurement to match pendulum swing to pulse rate.

Supplementary Materials