Advances in Historical Studies
2014. Vol.3, No.1, 68-81
Published Online February 2014 in SciRes (
Open Access
Spreading Newtonian Philosophy with Instruments:
The Case of Atwood’s Machine
Salvatore Esposito1, Edvige Schettino2
1I.N.F.N., Naples Unit, Naples, Italy
2Department of Physics, University of Naples “Federico II”, Naples, Italy
Received June 13th, 2013; revised July 20th, 2013; accepted July 29th, 2013
Copyright © 2014 Salvatore Esposito, Edvige Schettino. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any
medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution Li-
cense all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Salvatore
Esposito, Edvige Schettino. All Copyright © 2014 are guarded by law and by SCIRP as a guardian.
We study how the paradigm of Newton’s science, based on the organization of scientific knowledge as a
series of mathematical laws, was definitively accepted in science courses—in the last decades of the
XVIII century, in England as well as in the Continent—by means of the “universal” dynamical machine
invented by George Atwood in late 1770s just for this purpose. The spreading of such machine, occurring
well before the appearance of Atwood’s treatise where he described the novel machine and the experi-
ments to be performed with it, is a quite interesting historical case, which we consider in some detail. In
particular, we focus on the “improvement” introduced by the Italian Giuseppe Saverio Poli and the sub-
sequent “simplifications” of the machine, underlying the ongoing change of perspective after the defini-
tive success of Newtonianism. The case studied here allows recognizing the relevant role played by a
properly devised instrument in the acceptance of a new paradigm by non-erudite scholars, in addition to
the traditional ways involving erudite scientists, and thus the complementary role of machine philosophy
with respect to mathematical, philosophical or even physical reasoning.
Keywords: Atwood’s Machine; Giuseppe Saverio Poli; Newtonianism
The XVIII century was characterized by a widespread inter-
est for natural philosophy, driven by public lecture courses and
the publication of popular texts in addition to the traditional
forms of transmission of knowledge. The scientific societies
and academies created during the scientific revolution played
an increasingly larger role than universities, thus becoming the
cornerstone of organized science (McClellan, 2003; Gillispie,
1980). In England, the presidency of Sir Isaac Newton to the
Royal Society from 1703 to his death in 1727 obviously led
British science to be dominated by Newtonian ideas and ex-
periments, and the structure itself of Newtonian physics, that is
scientific knowledge organized as a series of mathematical laws,
became the model for all sciences. However, due to this use of
mathematics, very few people—in England and abroad—were
able to understand Newton’s ideas, so that an army of popular-
izers, lecturers and textbook writers was required in order to
widespread Newtonianism: this occurred precisely in the early
XVIII century, continuing for about half a century.
The rapid dissemination of Newton’s science came first via
the members of the Royal Society, both British and Continental
(Feingold, 2004), and an important role was played by Hugue-
nots (Baillon, 2004; see also Gibbs, 1986), i.e. French Protes-
tants who had been expelled from France as early as 1685. In
this respect, a key contributor to the success of Newtonian sci-
ence was John Theophilus Desaguliers, whose work of dis-
semination extended well beyond his lectures and publications.
Indeed, for example, in 1715 Desaguliers also performed ex-
periments on colors before members of the French Académie
Royale des Sciences, thus paving the way to a wider recogni-
tion of the validity of Newtons theories in France, and much the
same took place before diplomatic audiences from Spain, Sicily,
Venice and Russia (Stewart, 1992). The Dutch Willem Jacob’s
Gravesande was present to the demonstration of 1715, and later
became a decisive spokesman of Newtonian science in the
Netherlands, a country which already played in the XVII cen-
tury a significant role in the advancement of the sciences, in-
cluding Isaac Beeckman’s mechanical philosophy and Chris-
tiaan Huygens’ work on the calculus and in astronomy (Jacob,
1988). The Netherlands became the first Continental country to
adopt Newtonianism, with Amsterdam becoming the center of
European publishing, thanks, again, to French exiles, while in
France the struggle against Cartesianism lasted for some time,
the Newtonianism attracting mainly people dissatisfied with
French society and the Catholic Church, like Voltaire. A similar,
or even deeper struggle, was fought in the Germanic world,
where Newton’s science contended against the prestige of
Leibniz’s philosophy, this resulting in the long-lasting Newto-
nian-Wolffian controversy (Calinger, 1969): in the XVIII cen-
tury, Germany was always hesitant about the mechanization of
nature, and eventually Newton’s mechanics was incorporated
into the dominant German academic philosophy. Instead, New-
ton’s science filtered quite early into different parts of Italy,
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notwithstanding the Inquisition looked with suspicion on these
ideas, not least because they came from a Protestant country.
The traditional way to disseminate Newtonian natural phi-
losophy was, of course, through academic courses: before the
XVIII century, indeed, science courses were taught almost ex-
clusively through formal lectures. Thus, in the first instance,
scientists, mathematicians and philosophers of Holland, France,
Germany and Italy read Newton’s books and taught the ideas to
their students. The structure of courses, however, began to
change in the first decades of the XVIII century, when physical
demonstrations were added to academic lectures, and popular
lectures were introduced in response to the growing demand for
science. For example, Pierre Polinière was among the first indi-
viduals to provide demonstrations of physical principles in the
classroom: he presented experimental demonstrations of his
own devising before students at the University of Paris (Hanna,
1972), his lectures proving so popular that in 1722 he presented
a series of experiments before Louis XV, King of France. In
particular, in physics, such a change coincided with the institu-
tionalization of the course in Experimental Physics (Schettino,
Now, still in the XVIII century, what we now could call “re-
search centres” of the newborn physics, were not necessarily
distinct from the places devoted to the transmission of knowl-
edge, i.e. schools, colleges, etc. The success of a theory also
passed through its acceptance by “students”, i.e. scholars not
yet acquainted with it, who then contributed actively in the
dissemination of novel ideas. In other words, if the first accep-
tance of a given doctrine was disputed at a rather “high” level
between leading scientists and philosophers (as a reminiscence
of the philosophical disputations of earlier centuries), the de-
finitive one was played in lecture halls before non-experts. An
illuminating example of this mechanism is just the general
achievement of Newton’s mechanics, expressed in his Principia
(Newton, 1726). While its acknowledgement by leading school-
ars is well documented in the literature [see, for example
(Westfall, 1971); see also (McCormmach, 2004)], the same is
unfortunately not true for its thorough acceptance by “stu-
dents”1; in this paper, we will focus just on this last historical
If treatises of natural philosophy played a major role in the
“high” level debates, the writing and the circulation of practical
textbooks for the courses in Experimental Physics (or similar
other ones) became essential for the dissemination and accep-
tance of the novel ideas among “students”. In the following
Section we then review this issue. Far from being exhaustive,
we focus just on the most known scholars and their textbooks in
England and in the Continent, by concentrating on the period
immediately following that influenced directly by Newton.
Instead, in the further Section we enter into the heart of the
subject matter hereof, by showing how the invention of a “uni-
versal” dynamical machine by George Atwood, described along
with the experiments to be performed with it in an accompany-
ing treatise, contributed substantially to the final, general
achievement of Newton’s mechanics. The invaluable work of
Jean-Hyacinthe de Magellan and especially that, much less
known, of Giuseppe Saverio Poli in the rapid spreading of
Awood’s machine outside England is considered in a following
Section, where the subsequent key changes and “simplifica-
1See, however, the beautiful review by Schaffer on the role of “machine
philosophy” in the XVIII century’s England (Schaffer, 1994).
tions” underlying the ongoing change of perspective are pointed
out as well. Finally, in the concluding section, we summarize
what discussed in order to provide a rapid overview of the his-
torical case studied.
Newtonian Textbooks of Natural Philosophy in
the Post-Newtonian Age
Newtonian doctrines spread in the first quarter of the XVIII
century thanks to elementary or complex textbooks by English
authors such as J. T. Desaguliers, or the Dutch ones W. J. ‘s
Gravesande and Pieter van Musschenbroek, and the Frenchman
Jean Antoine Nollet. The complexity of Newtonian thought
expressed itself in several different ways, and in the following
we will give a glimpse of such diversity.
Newton’s Experimenter Successor
The first English disciples of Newton tried to give an expe-
rimental basis especially to ideas that he had not sufficiently
formalized (such as that of ether and that of interparticle forces),
so that the results obtained by Newton by means of a complex
relationship between inductive and deductive reasoning became
truths demonstrable directly with experiments.
The Newtonian method underwent a profound remodeling
with Desaguliers, a member of the Christ Church College who
held popular Newtonian lectures at Oxford, where he had much
success in his activity (Hall, 1972). After moving to London in
1710, he was welcomed into Newtonian circles of the capital
and was then (1714) elected fellow of the Royal Society, later
becoming the curator of the Royal Society, a position that was
earlier held by Francis Hauksbee. Desaguliers published many
works on the Philosophical Transactions about experiments on
heat, mechanics and electricity. In particular, he correctly real-
ized that the physical quantities then used for describing the
motion of a body, i.e. the momentum for the Newtonians and
the vis viva for the Leibnizians, were different concepts, and
that the Newtonian one was to be preferred because better sup-
ported by experiments.
As curator of the Royal Society, Desaguliers performed ex-
periments that were repetitions of those already described by
Newton, although there were more complex experiences such
as those aimed at finding a similarity between the electric force
and the force of cohesion [for a thoughtful examination of the
studies by Newton on the internal structure of matter, see for
examples (Thackray, 1970)]. However, Desaguliers’ reputation
as a scientist was sealed (apart by his three awards from the
Royal Society) by publication of a two volume work about A
Course of Experimental Philosophy (Desaguliers, 1734, 1744),
whose first volume was published in 1734, while the second
volume's publication came 10 years later in 1744. The first
volume deals with mechanics, with an explanation of the basics
of Newtonian science, while the second volume contains mate-
rial oriented toward practical application of scientific findings.
Desaguliers contributed significantly to the wide spread of
Newtonian-oriented textbooks also by translating Edme Ma-
riotte’s Traité du mouvement des eaux et des autres corps
fiuides (Mariotte, 1718), as well as ’s Gravesande’s Latin trea-
tise on Physices elementa mathematica, experimentis confir-
mata (‘s Gravesande, 1747). In addition, he also wrote several
texts, among which we recall The Newtonian system of the
world, the best model of government: An allegorical poem
(Desaguliers, 1728) and A dissertation concerning electricity
Open Access
(Desaguliers, 1742), which received a prize awarded by the
French Académie de Bordeaux.
Instrumental Philosophy in the Netherlands
The introduction of Newtonian science in the Netherlands
and, more in general, in the Continent came through’s Grave-
sande (Hall, 1972). Educated at the University of Leiden, in
1714 he had the opportunity to be part of the delegation sent to
England by the Dutch States General to congratulate King
George Ion his accession to the throne, and just during his (one
year) stay in London he attended sessions of the Royal Society,
later being elected to membership, and made acquaintance of
Newton and, especially, Desaguliers. On his return to Holland,
‘s Gravesande was appointed professor of astronomy and
mathematics at the University of Leiden, and in 1720 published
the first of the two volumes on Physices Elementa Mathematica,
experimentis confirmata (‘s Gravesande, 1747), already men-
tioned above.
Written in Latin, this first Newtonian-oriented textbook on
natural philosophy was of course accessible to all educated
readers in Europe, but the English translation performed by
Desaguliers in the same year of its publication certainly con-
tributed to its rollout. In the discussion on the infinite divisibil-
ity of matter and on small real particles of which it was com-
posed, Newton’s hypothesis on particle different shape and size
was not discussed by ‘s Gravesande, but simply ignored: his
position in favor of Leibniz’s theses had revived the debate on
the vis viva. Instead, ‘s Gravesande agreed with Newton about
the role played by short-ranged forces of attraction and repul-
sion acting on the fundamental particles, the rising of liquids by
capillary action being considered as an example supporting the
Newtonian theory (such phenomena were treated as Queries in
Newton’s Opticks (Newton, 1718). ‘s Gravesande’s treatise dis-
played a complete adhesion to Newtonian approach, not only
about the structure of matter and short- and long-ranged forces,
but also on questions of mechanics and astronomy. However,
he took no position about ether; rather, on this topic, ‘s Grave-
sande showed to follow the ideas of his teacher Hermann
Boerhaave, three chapters being devoted to the discussion on
the fire and its nature (Thackray, 1970).
In the third decade of the XVIII century, Dutch science en-
joyed a period of great splendor with ‘s Gravesande’s successor
in Leiden, Pieter van Musschenbroek (Struik, 1979; Kryzha-
novskii, 1991), who followed the same approach introduced by
his predecessor. The lectures delivered by Musschenbroek,
indeed, maintained the excellent reputation that Boerhaave and
‘s Gravesande earned to the University of Leyden, where stu-
dents interested to experimentation flocked from all over
Europe. The Musschenbroeks were scientific instruments’ ma-
kers since the seventeenth century, Joost (1614-1693) being the
founder. His sons Samuel and Johan continued such activity,
specializing themselves in the construction of microscopes,
telescopes and air pumps, all of them being typical instruments
used at that time. Pieter and Jan were the sons of Johan, and
both had an excellent education, his teacher being Boerhaave;
however, while Pieter decided to pursue his academic studies,
Jan chose to continue the family business.
Pieter van Musschenbroek began his academic career in 1719
in Duisburg, where he taught mathematics and philosophy, and
then, after a temporary moving to Utrecht, finally (in 1739)
came to Leiden, where he succeeded to ‘s Gravesande. His lec-
tures were characterized by a systematic use of experimental
devices, many of them being constructed by his brother Jan.
Skillfully designed models, illustrating the use of those ma-
chines and the experiments that could be run with them, sup-
plemented the textbooks written by Pieter, among which we
find the Elementa physicae of 1734 (Musschenbroek, 1734) and
the Institutiones physicae of 1748 (Musschenbroek, 1748). The
large diffusion of these text books also increased the demand
for instruments constructed by Jan: both universities and pri-
vate science amateurs wanted to buy them for their demonstra-
tions. The demand increased to such an extent that the manu-
facturers of scientific instruments began to reproduce the same
models of Jan: it’s well known, for example, that the instru-
ments made by George Adams in the cabinet of George III of
England were inspired just by those models. The fame of Pieter
van Musschenbroek spread rapidly throughout Europe, and his
works were translated into German, French and English, in
addition to further editions of the Elementa physicae, including
the Neapolitan one of 1745.
French Newtonianism
The Newtonian science was introduced in France through
Dutch scholars. Newton’s Opticks, considered as a book of ex-
perimental physics, was well and quite soon received (a transla-
tion into French was published as early as 1720 (Newton, 1720),
given the pronounced experimentalism of the Académie des
Sciences, while the diffusion of the Principia encountered some
more difficulty. An initial English corpuscular approach, fol-
lowed by the experimental Newtonianism in France, gave then
way to the typically Dutch fluidic approach, this change being
facilitated by some Newton’s early reflections on the ether,
published only in 1744 (Hall, 1995). This transition from dis-
continuous to continuous proved very heuristic, especially in
the studies about electricity.
Charles-Francois de Cisternai Dufay realized, after many ex-
perimental observations, that two different kinds of electric-
ity—the vitreous and the resinous ones—existed: together with
his collaborator Jean Antoine Nollet, he proposed to explain
electrical phenomena starting from the existence of two oppo-
site fluid currents, gave off by electrified bodies. The success of
the fluidic approach was accompanied by the abandonment of
the idea on the homogeneity of matter, and fire, ether and elec-
tric fluids were conceived as substances different from ordinary
Like many other young scholars from all over Europe, Nollet
(Heilbron, 1981) was attracted by the fame of ‘s Gravesande
and moved to Leyden to follow his lectures. On his return from
Holland, after a visit to London, where he was admitted into the
Royal Society, in 1735 he succeeded to Pierre Polimière who
taught at the College of the University of Paris, and in 1740
became a member of the Academic des Sciences. Nollet’s con-
tribution to the spread of experimental physics was quite re-
markable and his treatises, among which we mention the Le-
cons de physique experimentale (Nollet, 1743-1748), published
in six volumes between 1743 and 1748 and often reprinted,
enjoyed enormous popularity. This textbook offered many ex-
periments on electricity, and thanks to a very substantial con-
tribution by Voltaire, Nollet could realize many instruments,
about 350, with which he performed experiments both during
public lectures and in his physics courses.
It was, instead, quite difficult for the Newtonian astronomy,
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based on the concept of action at a distance, to be introduced in
France, given the wide spread of the Cartesian theory of vor-
tices. Through the reading that the Dutch scholars had made of
Newton’s works, however, Voltaire reinterpreted the Principia
along empiricist lines (Arouet, 1738), thus reconciling it with
the experimentalism of the French Académie des Sciences.
Although in the general scholion of Newton’s Principia it is
shown that the theory of vortices is incompatible with Kepler’s
law, the conflict between Cartesianism and Newtonianism con-
tinued to persist during the XVIII century. Also, a great theo-
retical debate concerning the theory on the shape of the Earth
emerged. The contrast between the Cartesian idea of the Earth
lengthened at the poles—as early measurements performed by
the astronomer G. Cassini seemed to show—against the idea of
Newton on the flattening at the poles due to the proper motion
of the planet, found a definitive solution only with the meas-
urements of Earth’s curvature at the equator and at the Arctic
Circle (de la Condamine, 1751; Clairaut, 1743). This theoretical
debate did not find room in empiricist oriented textbooks, but it
should be stressed that such studies led later to the development
of rational mechanics, carried on by mathematics scholars such
as P. L. M. de Maupertuis, A. C. Clairaut, L. Euler, J. B.
d’Alembert and the Bernoullis, who were poorly interested in
Experimental Science in Italy
Physics textbooks that privileged an empirical approach were
inspired, in Italy, by the works by ‘s Gravesande and Muss-
chenbroek, and the University of Naples, in particular, was
among the first to introduce in 1734 the teaching of experi-
mental physics. The sponsor of the institution of this chair was
the Grand Chaplain Celestino Galiani, a great supporter of
Newtonian ideas, who entrusted the chair to Giuseppe Orlandi
(Schettino, 2001). The intent to pursue a teaching based on the
inductive method, as practiced in the Dutch universities for
over ten years, was clear already from a letter by Galiani to the
Grand Chaplain:
“In the beginning, a preface will be present in which I will
show how the true way of philosophizing is nothing but by
means of experiments; and compare the state of philosophy
among scholastics lasted for many centuries with the present,
started by so many talented scholars who used to look at the
book of Nature and study the characters with which it is written,
which are observation, experiments and geometry” [a complete
transcription of the letter, in Italian, is in (Palladino, 1985)].
It is evident, however, that in order to perform experiments,
as claimed by the followers of empiricism, several machines
were required, i.e. instruments by means of which the laws of
physics could be inductively derived. For this reason, Orlandi
adopted the Elementa physicae by Musschenbroek, where the
necessary devices were skillfully depicted, but added to it a
long appendix on astronomy—De rebus coelestibus tractatus.
The first Naples edition of this textbook appeared in 1745
(Musschenbroek, 1745), with a long introduction written by
Antonio Genovesi under the meaningful title Disputatio phys-
ico-historica de rerum corporearum origine et constitutione,
where the illustrious Neapolitan follower of the Enlightenment
attempted to give a first, brief but insightful history of physics
from ancient times to XVIII century [about the Disputatio by
Genovesi and on his attempt to oppose the philosophical inter-
ferences encountered in Newtonian oriented textbooks, see
(Torrini, 1994)].
Giovanni Maria Della Torre, entrusted with the teaching of
experimental physics in the Royal Archigymnasium in Naples,
was the author of a very successful textbook published between
1748 and 1749 in two volumes (Della Torre, 1748-1749). The
first volume—Scienza della Natura generale—was devoted to
general physics, that is Della Torre expounded about “matter,
extent, strength, mobility and motion”, while in the second
one—Scienza della Natura particolare—topics related to Earth
science were discussed, that is about “Earth’s shape and size,
internal structure, surface and atmosphere”. The Della Torre’s
textbook was different, especially in the second volume, from
the most authoritative ones by Musschenbroek and ‘s Grave-
sande, where biology and geology were omitted, as well as
almost all of chemistry and meteorology. The historical and
critical notes about “ancient conceptions and their links with
recent results”, though always present in Newtonian oriented
textbooks, were so many in the Della Torre’s treatise that raised
strong debates (Torrini, 1994). In this book, as well as in any
contemporary textbook, the use of mathematics was always
theorized, but scientific theories were explained without resort-
ing to analytic calculations. This, however, did not mean that
theories were not addressed in a rigorous way: for example, in
Section IV of the second volume, detailed theorems were pre-
sent in order to justify the laws of optics and catoptrics. As in
the Lecons by Nollet, a large part was devoted to the descrip-
tion of instruments, especially microscopes, with fully spherical
lenses (invented by Della Torre himself), which limited the
problem of spherical aberration. Della Torre acquired such a
skill in experimenting with microscopes that was famous
throughout Europe: J. J. de Lalande, who traveled in Italy be-
tween 1765 and 1766, had him in high regard, and quoted him
often in his book Voyage en Italie (de Lalande, 1769), and the
same applies to Nollet, who had the opportunity to meet him
during his stay in Naples in 1750.
Later in the XVIII century, starting from 1770’s, a new gen-
eration of enlightened scientists, who were educated at the
University of Padua, where they had very strong links with
scientific circles in England, began to impose in the academies
of the Kingdom of Naples (Borrelli, 2000). Giuseppe Saverio
Poli was one among these who, having had the opportunity to
stay in Cambridge and meet George Atwood (Toscano, 2009),
was the first to publish a new, Newtonian oriented textbook
(Poli, 1781a) where the novel machine invented by the English
scholar was illustrated with a choice of experiments.
Now, however, one step back is needed in order to fully un-
derstand the change of perspective that occurred in the last
quarter of the XVIII century, and that further influenced the
subsequent transmission to “students” of physics results.
Atwood and the General Achievement of
Newton’s Mechanics
The Atwood’s machine changed the way of propagating
Newtonian mechanics, and had also a prominent role in the
definitive success of Newtonianism, though this fact is not al-
ways correctly realized or even considered. In the following we
will focus just on this issue, while in the subsequent section, we
will show how Poli and others contributed to the widespread
use of Atwood’s machine (and, in particular, to a specific use of
it) in the Continent.
Open Access
Popular Lecturer in Cambridge
Biographical notes on Rev. George Atwood are scarce, and
mainly related to his record in the Alumni Cantabrigienses list
(Venn, 1922-1958) or other similar records in England [see
(Cole, 1970)]. He was the first of three sons (with James and
Thomas) by Isabella Sells of Inglesham, Wiltshire, and Thomas
Atwood, the curate of the parish of St. Clement Danes, West-
minster, where George was baptized on 15 October 1745. After
attended the Westminster School, starting in 1759, as a king’s
scholar, he entered Trinity College in Cambridge on 5 June
1765 as a pensioner (i.e. he paid for his own keep in College),
and was then elected to a scholarship on Lent 1766, being also
awarded with the Members’ prize in the same year. He gradu-
ated (as third Wrangler) with a B. A. in 1769, being first
Smith’s prizeman in the same year, and received his M. A. in
1772. Meanwhile, in October 1770, Atwood became a Fellow
of Trinity College and taught there, also becoming a tutor in
1773. His lectures in the observatory over the Great Gate of
Trinity College were well attended and received because of
their delivery and their experimental demonstrations. He pub-
lished descriptions of his demonstrations in 1776 (Atwood,
1776), the year he was elected Fellow of the Royal Society:
they consisted of simple experiments to illustrate mechanics,
hydrostatics, electricity, magnetism and optics. One of the
many students who attended Atwood’s popular lectures was
William Pitt, who later (in 1783) achieved the high office of
British Prime Minister. In 1784 Atwood was then hired to a
major post in the customs office as part of Pitt’s campaign for
administrative rationalization: he “rendered important financial
services to Pitt, who bestowed upon him a sinecure office, as
one of the patent searchers of the Customs, with a salary of
£500” (Venn, 1922-1958).
Atwood is now best known for a textbook on Newtonian
mechanics, A Treatise on the Rectilinear Motion and Rotation
of Bodies (Atwood, 1784), published in 1784, where he also
describes in detail a machine, now known as Atwood’s machine
(see below). In the same year he also published a second work,
An Analysis of a Course of Lectures on the Principles of Natu-
ral Philosophy (Atwood, 1784), which is an expanded version
of his Cambridge course which he had first given detail in
Most of other Atwood’s published works (Cole, 1970) con-
sists of the mathematical analysis of practical problems, in-
cluding a review for Pitt in which he analyzed the cost of bread
and attempted to rationalize the standards for it. A particular
mention merit his works on the stability of ships (Atwood,
1796-1798), where he extended the theories of Euler, Bougier
and others to account for the stability of floating bodies with
large angle of roll, and for which, in 1796, he was awarded the
Copley Medal of the Royal Society. Finally, he also wrote on
the construction of arches (Atwood, 1801) and on the design of
a new iron London Bridge over the Thames at Blackfriars.
Atwood died “unmarried” (Venn, 1922-1958) on July 1807
and buried at St. Margaret’s, Westminster, where his brother
Thomas had succeeded his father as curate.
A Novel Machine
The name of Atwood is almost entirely related to the dy-
namical machine he invented between 1776 and 1779: the story
of the development of this machine and the spreading of its
existence throughout Europe is, by itself, worth-mentioning,
and will be considered in some detail here and in the next sec-
tion. Its scope, according to textbooks appeared since the end of
1700s till recent times, would be just that of conducting ex-
periments proving the laws of rectilinear (and rotational) mo-
tion of bodies, with particular reference to motions ruled by
gravity. As we will see, such a (reductive) purpose of Atwood’s
machine was established only after the general achievement of
Newton’s mechanics, that is from the end of the XVIII century
onward, but in the Cambridge of 1770s and 1780s it served just
to fulfill definitively such achievement before young students
and scholars who later disseminated the Newtonian paradigm.
The machine is described in Atwood’s Treatise of 1784
(Atwood, 1784), but its diffusion outside England dates back to
the end of 1770s (see next Section). As well known, it consists
(see Figure 1) just of two balanced cylinders linked by a silk
cord suspended over a pulley, where additional weights can be
attached (and removed) to either cylinder in order to provide a
net (or zero) force acting on the system.
It is quite instructive to follow closely how Atwood devised his
ingenious machine, starting from his first considerations about
the classical problem of experimenting on the free fall of bod-
The most obvious method would be to observe the actual
descent of a heavy body, as it falls toward the earth by its
natural gravity: but in this case it is manifest, that on ac-
count of the great velocity generated in few seconds of
time, the height from which the observed body falls must
be considerable. […]
Figure 1.
The plate in Atwood’s
of 1784 (Atwood,
1784) with the illustration of the novel machine built
by Adams.
Open Access 73
If to remedy this inconvenience bodies be caused to de-
scend along inclined planes, according to the experiments
of the celebrated author [Galileo] of this theory, by vary-
ing the proportion of the plane’s height to their lengths,
the force of the acceleration may be diminished in any ra-
tio, so that the descending bodies shall move sufficiently
slow to allow of the times of motion from rest being ac-
curately observed; and the effects of the air’s resistance to
bodies moving with these small velocities will be abso-
lutely insensible: the principal difficulty however which
here occurs, arises from the rotation of the descending
bodies, which cannot be prevented without increasing
their friction far beyond what the experiment will allow of
(Atwood, 1784: pp. 295-296).
Notably, here the “principal difficulty” is with what theory
already knows (as explained in the first half of the book),
namely that the acceleration of a rotating body while descend-
ing along an inclined plane is reduced with respect to the case
where rotation does not occur, and thus gravity is the sole cause
of such effect. While this is not accounted for in many modern
textbooks, the problem envisaged by Atwood is not the consid-
eration of the effect of rotation (he knew the correct reduction
factors: 5/7 for a sphere and 2/3 for a cylinder), but simply the
super position of two effects (rotation and gravity) that could
cause—in Atwood’s mind—not a univocal acceptance of the
Newtonian paradigm. This attitude is confirmed one page after
in the Treatise, where other, different problems with the in-
clined plane are envisaged.
There are no means separating the mass moved from the
moving force; we cannot therefore apply different forces
to move the same quantity of matter on a given plane, or
the same force to different quantities of matter. Moreover,
the accelerating force being constant and inseparable from
the body moved, its velocity will be continually acceler-
ated, so as to render the observation of the velocity ac-
quired at any given instant impossible (Atwood, 1784: p.
298) 2.
The first problem is that, with a given inclined plane (i.e.
height to length ratio) it is not possible to study the dependence
of the force acting upon the body on its mass, thus proving
Newton’s second law of motion. The second, more involved
experimental problem is instead the impossibility to measure
the velocity of the body at any desired instant of time, since it
continually changes, and thus the impossibility to prove the
time law for the velocity in the uniformly accelerated motion.
What is, then, Atwood’s aim? Surprisingly enough, he is
aware that Newton’s second law will be generally confirmed
only when considering the effect of variable forces, but the
inadequacy of the experimental conditions of the epoch forced
him to turn to constant forces (as in the free fall or in the mo-
tion along an inclined plane). This, however, does not mean for
him to make any other concession to the ease of the experiment
(again, as is instead the case in the free fall or in the motion
along an inclined plane).
Although it might be difficult to reduce the effects of vari-
able forces on the motion of bodies to experimental test, yet the
laws observed during the motion of bodies acted on by constant
2Note that, according to Atwood’s terminology, “moving force” is for force,
“accelerating force”, for acceleration; and “quantity of matter”, for mass.
forces, admit of easy illustrations from matter of fact. But in
order to render experiments of this kind satisfactory, they
should comprehend the properties of the moving forces, the
quantities of matter moved, and the velocity acquired, as well
as the spaces described and times of description: which general
properties of uniformly accelerated motion are not so much
considered in books of mechanical experiments as the subject
seems to demand (Atwood, 1784: p. 294).
The boundaries of the problem are, thus, well depicted: how
is it possible to device a series of experiments with a single
machine with which force, mass, velocity, distances and times
are dealt with? Without previous suggestions by other authors
(which is, instead, the case of Desaguliers, as mentioned above,
who simply improves Galilei’s experiment on free falling bod-
ies), Atwood focuses his attention on pulleys, already worthy of
consideration by men of science since many centuries. But here
the change of perspective is crucial: a conventional device em-
ployed in statics as a simple machine is transformed in At-
wood’s hands into a carefully scaled dynamically device capa-
ble of being subjected to mathematical analysis for the illustra-
tion of the Newtonian paradigm. In this light, indeed, a consis-
tent interpretation can be given to a number of kinematics and
dynamics problems—just theoretical exercises, not directly re-
lated to his machine—appearing in Atwood’s Treatise, most of
which not at all considered in subsequent textbooks3.
In the instrument constructed to illustrate this subject ex-
perimentally, A, B represent two equal weights affixed to
the extremities of a very fine and flexible silk line: this
line is stretched over a wheel or fixed pulley abcd, move-
able round a horizontal axis: the two weights A, B being
precisely equal and acting against each other, remain in
equilibrium; and when the least weight is superadded to
either (setting aside the effects of friction) it will prepon-
derate (Atwood, 1784: p. 299).
The general problems envisaged above (too short falling
times—in free fall or on an inclined plane—require very large
distances traveled by the falling body, upon which, however,
acts a non negligible friction force, the body reaching also too
great velocities near the end of its motion) disappear at once: a
small mass unbalance induces small accelerations and veloci-
ties, thus preventing unnecessary large falling height and, then,
neglecting the action of air resistance. But Atwood’s aim is a
precise confirmation of Newton’s laws, and if the realization of
accurately balanced weights, as well as small while removable
additional weights, is leaved to the art of skilled craftsmen, the
possible friction developed by the axle of the pulley merits
appropriate considerations.
When the axle is horizontal it is absolutely necessary that
it should be supported on friction wheels, which greatly
diminish, or altogether prevent the loss of motion which
would be caused by the friction of the axle, if it revolved
on an immoveable surface (Atwood, 1784: p. 338).
3To this regard, it is quite illuminating what writes still in 1922 a reviewer
of Atwood’s Treatise, evidently considered just as a modern textbook:
“though written in 1784, some of its pages are greatly superior to those in
many of the textbooks now in use in schools, and one is particularly im-
pressed by the stress laid on experimental verification of the various laws of
mechanics, and by the extreme care shown in the planning and execution of
the experiments proposed” (Hall, 1922).
Open Access
Such an apparently tricky mechanism, introduced earlier
probably by the French clockmaker Henry Sully (Sully, 1726),
was installed by Atwood on the top of the cylindrical column of
his machine, upon which a weight operated clock is as well
mounted in order to perform time measurements, while a ruler
with “a scale about 64 inches in length graduated into inches
and tenths of an inch” is added on another vertical column to
allow measurements of the distances covered by the bodies su-
spended on the string. The assemblage with the wheels is, in-
terestingly enough, a removable piece of the machine: Atwood
was, indeed, creating a device capable of studying rectilinear
motions as well as rotation of bodies, to which almost half of
his Treatise is devoted. The recognition of this important sec-
ond part of mechanics will be lost in subsequent descriptions of
Atwood’s machine in textbooks—and further copies of the
machine itself will no longer show the removable assemblage
with the friction wheels—but it should not fall into oblivion the
fact that Atwood was originally aimed to conceive a “univer-
sal” machine suited for studying both rectilinear and rotational
motion. This is clearly testified by a number of interesting and
intriguing experiments, proposed in his Treatise, to be realized
with the aid of additional accessories sketched in figures 84 -
88 of the book (Atwood, 1784). However, while the main part
of the machine “was executed with great mechanical skill,
partly by Mr. L. Martin, and partly Mr. G. Adams, mathemati-
cal instrument makers in London” (Atwood, 1784: p. 337),
such accessories, especially the principal one drawn in figure
84 of (Atwood, 1784), were never realized, probably for the
change of working interests; see the biographical notes above.
Thus, Atwood’s machine was subsequently associated only to
the studies on rectilinear motion under the action of a constant
Displaying the Newtonian Paradigm
How did Atwood obtain a satisfactory illustration of the
Newtonian paradigm with his machine? The first step is, obvi-
ously, to reproduce the Galilei’s law of proportionality between
the traveled distances s and the square of the elapsed time t in
the uniformly accelerated motion: s t2. Under the “action of
the constant force m” (m, here the unbalanced net moving force,
corresponds to the weight of 1/4 oz of matter; it is considered as
a standard quantity in Atwood’s experiments),
if the times of motion be 1 second, 2 seconds, and 3 sec-
onds, the spaces described from rest by the descending
weight A in those times will be 3 inches, 3 × 4 = 12 inches,
and 3 × 9 = 27 inches respectively; the spaces described
from rest being in a duplicate ratio of the times of motion
(Atwood, 1784, p. 318).
The second step is to study the dependence of s on the accel-
eration a of the descending body, here obtained—in units of the
free fall value g—from the ratio of the unbalanced mass to the
total mass of the bodies on the pulley (in modern terms, a/g =
It appears from these experiments, that when the times are
the same, the spaces described from rest are as the accel-
erating force (Atwood, 1784: p. 320)
(recall that “accelerating force” means just acceleration). That
is to say, s a. What else about the equation of motion regard-
ing the distance traveled? Obviously, that a 1/t2:
The latter part of the experiment shows, that if the space
described remains the same, while the time description is
diminished, the force of acceleration must be increased in
a duplicate proportion of the times’ diminution (Atwood,
1784: p. 321).
From these three experiments, then, the full time law that, in
modern terms, we write as s = 1/2 at2, is completely derived4.
Next, Atwood considers experiments suitable for obtaining
the law for the velocity, whose measurement with the machine
is particularly intriguing (and, mainly, feasible). Indeed, let us
suppose with Atwood that the instantaneous velocity of the
descending body is requested when it passes at a certain height.
Then a ring is placed at that height on the column with the ruler,
whose ring is designed to remove the additional, unbalanced
mass (whose length exceeds ring’s diameter) while allowing the
passage of the main body upon which it is affixed. In such a
way, and from now on, the pulley is completely balanced, and
the two bodies continue to move with constant velocity, whose
value is easily obtained from the ratio of the distance traveled
in a given time. With this trick, the law for the velocity can be
tested experimentally even when a constant force is applied to
the body, and the first result to be obtained is the proportional-
ity between the instant velocity and the time elapsed: v t.
During the different times 1 second, 2 second, 3 seconds,
etc. the velocities generated will be those of 6 inches, 12
inches, and 18 inches in a second respectively, being in
the same proportion with the times wherein the given
force acts (Atwood, 1784: p. 324).
It appears therefore, that if different forces accelerate the
same body from quiescence during a given time, the ve-
locities generated will be in the same proportion with
these forces (Atwood, 1784: p. 326)
(again, “forces” means “accelerating forces” or, simply, accel-
eration), that is to say, v a in a constant time. Finally, as
above, the complete law v = at is obtained by means of propor-
if bodies be acted in by accelerating forces, which are in
the proportion of 3:4, and for times, which are as 1:2, the
velocities acquired will be in the ratio of 1 × 3 to 2 × 4, or
as 3 to 8 (Atwood, 1784: p. 326).
The story, however, does not end here, as could be hastily
expected. Indeed, other two experiments are described to show
that, for bodies accelerated through the same space s, v a
(Atwood, 1784: p. 327) and, conversely, under the action of the
same acceleration a, v s (Atwood, 1784: p. 328). That is to
say, in modern terms, v = 2as.
Finally, and more importantly, “the moving force must be in
the same ratio as the quantities of matter moved,” which is
Newton’s second law of dynamics (Atwood, 1784: p. 328):
Experiments to illustrate this truth may be comprised in the
subjoined table.
4According to the introductory mathematical chapter in the Treatise, At-
wood never uses absolute equations, so that any physical law is always
expressed as a proportion. Thus, in the present case, the factor 1/2 does not
appear, and the final result is rather written as s/s = at2/at2. The same
applies below, though we will use modern notations for simplicity of expla-
Open Access 75
Quantities of
matter moved
Spaces described
in inches
Velocities acquired
in inches in a second
m 64 m 1/64 12 12
3/2 m 96 m 1/64 12 12
3/4 m 48 m 1/64 12 12
From the first three columns it is evident that the “moving
force” is equal to the product of the “quantity of matter moved”
times the “accelerating force”, or, in modern notations, F = ma.
It is interesting to compare such a result, directly obtained from
experiments, with the original Newtons formulation of the se-
cond law in terms of momentum variation rather than accelera-
tion [see the discussion in (Westfall, 1971)].
The accuracy of the conclusions reached by Atwood obvi-
ously depends on the sensitivity of his machine and on possible
systematic errors primarily related to friction and to the prompt-
ness of the experimenter for time measurements. This last point
was considered only in broad outline by Atwood, who just
warned possible other experimenters to train with the “simulta-
neous” activation of the pendulum clock with the start of the
descending body. This is evidently—a priori—the major source
of inaccuracy, and we will back on it in the next Section. The
friction issue, including air resistance, has been already dealt
with above, but here we mention the fact that Atwood did not
limit himself to simply state that “the effects of friction are
almost wholly removed by the friction wheels” (Atwood, 1784:
p. 316). Indeed, he quantified such assertion by making a pre-
liminary experiment:
If the weights A and B be balanced in perfect equilibrium,
and the whole mass consists of 63 m, according to the
example already described, a weight of 1 1/2 grains, or at
most 2 grains, being added either to A or B, will commu-
nicate motion to the whole, which shows that the effects
of friction will not be so great as a weight of 1 1/2 or 2
grains (Atwood, 1784: p. 316).
Note that a mass of 1 m corresponded to 1/4 oz (and thus 63
m 16 oz), while 480 grains accounted for 10 oz (and thus 2
grains 1/240 oz), so that the sensitivity of the pulley was ex-
tremely high. With his device, Atwood was then able to meas-
ure accelerations as low as 1/64 of the free fall value (Atwood,
1784: p. 305), an unprecedented accuracy in such studies.
This fact was also the reason for the subsequent fortune of
Atwood’s machine.
Other Topics in the Treatise
The description of the machine and the discussion of the ex-
periments performed with it occupy only about 10% of At-
wood’s Treatise , so that we cannot leave the issue without even
a rapid mention of the remaining topics covered in the book,
again aimed at establishing the Newtonian paradigm. The major
part of them is devoted to display the theory regarding rectilin-
ear motion, mainly related to the experiments later considered,
with few intriguing exceptions.
One of these, which is worth to mention, is the discussion of
the resistance opposed to spherical bodies when impinging on
given substances. According to Atwood, the resistance force FR
depends, of course, on the substance considered, this effect
being parameterized by the penetration depth δ, and is propor-
tional to the square of the diameter D of the body; in modern
notation: FR δ D2 (Atwood, 1784: p. 40).
The only other “exceptions” we here point out regard, instead,
the affair related to the concepts of momentum and vis viva.
Although Atwood discusses at length such issues in Section IX
of his Treatise (Atwood, 1784: p. 356), he introduces the rele-
vant quantities well before. The momentum q = mv is intro-
duced in the discussion of (a particular case of) what we now
call the theorem of momentum:
The moving force which communicates, and the force of
resistance which destroys the motion of bodies in the
same time, will be in a compound ratio of the quantities of
matter in the moving bodies, and velocities generated or
destroyed (Atwood, 1784: p. 36).
In modern notation, for given time interval, F mv. Analo-
gously, the vis viva mv2 is introduced in the discussion of (a
particular case of) what we now call the theorem of kinetic
If bodies unequal in quantities of matter, be impelled from
rest through equal spaces, by the action of moving forces
which are constant, these forces are in a duplicate ratio of
the last acquired velocities, and the ratio of the quantities
of matter jointly (Atwood, 1784: p. 29).
That is, in modern notation, for a constant force acting for a
given distance, F mv2. Echoes of the not yet extinguished
polemic with the Leibnizian view of mechanics in terms of
living forces are present in Section IX of the Treatise, where
Atwood considers the “conservatio motus” introduced by Da-
niel Bernoulli in discussing (one-dimensional) impact of bodies.
While we cannot enter here in such an issue, and thus refer the
interested reader to the existing literature (see, for example,
(Schaffer, 1994) and references therein), we only mention how
Atwood posed the physical question. How define the momen-
tum q of a body in motion? In terms of mv (Atwood, from
Newton) or, rather, mv2 (Bernoulli, from Leibniz)? Atwood’s
answer was intimately related to the physical properties of
(one-dimensional) impact of bodies: according to him, Ber-
noulli’s conservatio motus necessarily implied q = mv.
The only other polemic present in the Treatise is with J.
Smeaton about the role of friction. While the natural philoso-
pher Atwood was trying to design frictionless machines, the
engineer Smeaton set out to measure friction’s effects. The
different attitudes are evident: while friction is seen by Atwood
as an obstacle to the clear manifestation of the perfect Newto-
nian laws of Nature, it is instead an important piece of consid-
eration for engineers and engine makers. Additional, interesting
details on this polemic, here only trivialized, may be found in
(Schaffer, 1994), where a special emphasis is given on what
dubbed as social function of friction.
Finally, few words should be said on the second great topic
of the Treatise, that is rotation of bodies. Indeed, Atwood’s
book is as well a splendid example of XVIII century’s treatise
on the mechanics of rigid bodies, with a number of interesting
examples and applications, an idea of which may be formed
just by looking at the drawings at the end of the book. A clear
definition for the centre of gravity is given, together with a
discussion of its relevance for rigid body’s motion. Also, the
concept of moment of inertia is already present in Atwood’s
Treatise, implicitly introduced in the cardinal law for the rota-
Open Access
In any revolving system, the force which accelerates the
point to which the moving force is applied, is that part of
the acceleration of gravity which is expressed by a frac-
tion, of which the numerator is the square of the distance
at which the force is applied from the axis, multiplied into
the moving force, and the denominator the sum of all the
products formed by multiplying each particle of the sys-
tem into the square of its distance from the axis of motion
(Atwood, 1784: p. 345).
In formulae, a = r2 F/I (I being the moment of inertia), which
is just a particular case of the law for the torque M.
Other key, general results for the rotation of rigid bodies are
considered and discussed in the Treatise, but their punctual
reconstruction is here unnecessary: Atwood’s main aim of the
general achievement of the grandiose Newtonian paradigm has
been, probably, well illustrated from what discussed above.
The Spreading of Atwood’s Machine:
G. S. Poli and J. H. De Magellan
The direct spreading of Atwood’s machine outside the bor-
ders of England was due mainly to the work of two scholars,
who were eyewitnesses of the experiments performed by At-
wood with his novel machine: namely, the Portuguese J. H. de
Magellan and the less known Italian G. S. Poli.
A Newtonianist in Naples
Giuseppe Saverio Poli was born in Molfetta, Italy where he
completed his first studies at the Jesuit College which, together
with the Convent of the Dominicans, culturally animated this
small agricultural and fishing town [the most recent biography
of Poli is in (De Gennaro, 2006)]. In 1764 his family arranged
for him to study at the University of Padua, where he graduated
in Medicine, and in 1771 moved to Naples practicing as a doc-
tor at the Ospedale degli Incurabili and, one year later, he was
entrusted with the teaching of Geography and History at the
“Nunziatella” Military Academy. It was during this period that
Poli resumed his studies (began in Padua) on electricity and, in
1772-3 he published two books on the formation of and effects
induced by thunder and lightning (Poli, 1772; Poli, 1773). In
the second of these books, Poli described a series of experi-
ments conducted by himself and questioning about one of the
main theories of Benjamin Franklin, i.e. about the adiather-
manous property of glass (Franklin was the first, in 1751, to
suppose that glass is completely impermeable to heat rays). Poli
did not know an explanation for some observed anomalies of
electrified glass, but noted that they were not justified by
Franklin’s dominant theory. Nevertheless, to explain with his
model also the insulating effect that the glass sometimes dis-
played, Poli resorted to the existence of two forms of electricity,
which he called “by source and by contact” (Schettino, 2000).
As a result of his success within the scientific community in
Naples, in 1775 Poli was entrusted with the important task of
traveling on behalf of the King of Naples, in order to acquire
scientific instruments for the Military Academy and also to
study the cultural institutions of the major European capitals.
This “scientific” journey lasted five years, but very few details
are known about it (Toscano, 2009); some information about
his stay in Cambridge and the meeting with Atwood may be,
however, deduced from his later textbook (Poli, 1781a).
Meanwhile, spurred by a group of reforming intellectuals, in
1778-1779 Ferdinand IV of Bourbon founded in Naples two
important institutions: the Royal Academy of Sciences and
Humanities, and the Medical School of the Ospedale degli In-
curabili (Borrelli, 2007; Borrelli, 2000). Director of the School
was Giovanni Vivenzio, who urged the authorities in order to
establish in it the teaching of Experimental Physics, with the
related “theater” where experiments could be performed ac-
cording to the Newtonian address. The intention of those re-
formers was to create a new kind of doctors, updated on the
latest scientific results, and Vivenzio was able to obtain that the
examinations of Anatomy and Experimental Physics were
mandatory, and that students could not graduate without a good
knowledge on these subjects.
The teaching of Experimental Physics was entrusted to Poli,
who was informed in late 1780, when still in England: this was
an opportunity to ask the famous instrument maker Jesse
Ramsden (Webster, 1986), encountered in his stay in England,
to build the new machine invented by Atwood in order to study
the physical laws of kinematics and dynamics.
The Atwood Machine Arrives in the Continent
According to Poli, Atwood’s machine he commissioned to
Ramsden would have been useful in his teaching to the young
students of the Medical School, as clearly highlighted in the
inaugural lecture which he held for the start of the course in
Experimental Physics (Poli, 1780). Such inaugural lecture was
printed by the Royal Printing Office (Stamperia Reale), this
showing the importance given to that course. The same inten-
tion may be deduced from another inaugural lecture, printed in
the subsequent year, that for the course in Experimental Physics
for the cadets of the “Nunziatella” Military Academy (Poli,
1781b): here Poli laid the foundations for how he dealt with the
study of Nature.
In the meantime, Poli had left England and, in this same year,
he gave to the press his textbook on the Elementi di Fisica
Sperimentale (Poli, 1781a), already mentioned above. The par-
ticular relevance of this first edition5 of the Elementi follows
from the fact that for the first time a plate appears in it, en-
graved by de Grado, with the illustration of Atwood’s machine
(note that Atwood’s Treatise was published only three years
later, in 1784). The instrument illustrated in this textbook was
the copy ordered to and built by Ramsden; its story, along with
those of the other first models of Atwood’s machine is quite
The copy purchased by Poli for his course at the Medical
School and at the Military Academy in Naples arrived in Mar-
seille in October 1782 and was delivered to the countess Zuc-
cheri Stella, who took charge of sending it to Naples so that it
could be delivered to Poli:
Dal Sig. Gioacchino Bettalli di Parigi mi fu spedito una
cassa contenente istrumenti fisici, e pezzi dell’istoria na-
turale, la quale lui mi dice avere avuto ordine dal Sig. Cav.
Poli di recapitarmela; questa essendomi alla fine giunta,
non sapendo io se il d. Sig. Cav. Poli si trova costì, o al-
trove; e dall’altra parte sapendo per relazione del mio
cugino l’Abbate Boscovich, che la d.a cassa deve servire
per uso di codesta Università, ho stimato mio dovere
spedirla alla direzione di V. S., sicura, che darà ordini, che
5The first Neapolitan edition of 1781 is rarely mentioned in the literature,
while the second Neapolitan edition of 1787 is often quoted as the first one.
Open Access 77
sia essa consegnata a chi compete [Countess Zuccheri
Stella to Marquis Della Sambuca, 19 October 1782, in
(Borrelli, 2000)]6.
Some months before, another Atwood’s machine, built by
Adams, arrived in the port of Genoa: it was delivered to Ales-
sandro Volta in May 1781:
Al mio arrivo qui ho trovato le sei Casse di Macchine pro-
venienti da Londra, ch’io già sapeva da qualche tempo
essere giunte in Genova [...] Credo non sarà discaro a V.
E. ch’io Le faccia particolarmente conoscere l’indicata
Macchina del Sig. Atwood, la quale riunisce i due più
grandi pregi di facilità ed esattezza nelle sperienze che si
fanno con essa [Volta to Count Firmian, 1 May 1781, in
(Volta, 1951)]7.
These are the only two Atwood’s machine that reached Italy
in 1781-1782. While Poli had been in Cambridge to see At-
wood demonstrating his machine, thus deciding to order a copy
of it for his course in Naples, Volta didn’t. It was the Portu-
guese Joao Jacinto de Magalhaes, who met Atwood in England,
to write to Volta, then teaching at Pavia, and inviting him to
subscribe to Atwood’s forthcoming Course of Lectures [J. H.
Magellan to A. Volta, 9 April 1779, in (Volta, 1951)] and, later,
to one of the four prototypes of Atwood’s machine built be-
tween 1780 and 1782, to be addressed to the Physics Labora-
tory of the University of Pavia [J. H. Magellan to A. Volta, 21
November 1780, in (Volta, 1951)].
Better known to the English-speaking world by the name
under which he published most of his works, Jean-Hyacinthe de
Magellan (Pierson, 1979) was born in Portugal in 1722 and, at
the age of eleven, went to an Augustinian monastery in Coim-
bra where he spent the next twenty years living and studying.
The scientific tradition among the Coimbra Augustinians (who
knew and studied the works of Newton) allowed him to become
familiar with science, particularly astronomy, and after received
permission from Pope Benedict XIV to leave the order, in 1755
Magellan started a “philosophical tour” through Europe, finally
settling in 1764 in England. Although he produced no particu-
larly relevant scientific works (the large part of which related to
scientific instruments), he is known chiefly for his wide circle
of acquaintances and for acting as an intermediary in dissemi-
nating new information, mainly about chemistry and experi-
mental physics. Among the people he met during his life, we
mention only very few names, including A. Lavoisier and J. J.
Rousseau in France, Atwood and J. Priestley in England, Volta
and many others. His work and notoriety earned him member-
ship in the Royal Society of London (1774), the Academia das
Ciencias of Lisbon (1780) and the American Philosophical
Society of Philadelphia (1784), as well as corresponding mem-
bership in the science academies in Paris, Madrid, Bruxelles
6“Mr. Gioacchino Bettalli in Paris sent out to me a case containing physics
instruments and several specimens of natural history. He writes that he was
commissioned by Mr. Poli to send me that case. Having arrived such a case,
since I do not know if Mr. PoIi is there or somewhere else, while knowing
from my cousin, the Abbé Boscovich, that the said case shall serve for use in
this University, I have thought it my duty to send it to your lordship, sure
that you will give orders that it be given to who be due.”
7“On my arrival I found the six boxes with the machines coming from Lon-
don, about which I already knew since some time to be arrived in Genoa [...]
I think it will not be displeasing to Your Excellency that I make known to
You the aforesaid machine of Mr. Atwood, which combines the two greatest
advantages of ease and accuracy in the experiences that we can do with it.”
and St. Petersburg.
Magellan published the letter quoted above to Volta in a
pamphlet of 1780 (Villas-Boas, 2000), where he described the
new Atwood’s machine for studying dynamics, four years be-
fore Atwood himself succeeded in publishing his Treatise de-
scribing all the properties of his device.
Cette machine, dans son état actuel, rend sensible les loix
du mouvement uniformément acceleré, ou reiarde, de
meme que celles du mouvement uniforme, sans employer
qu’un éspace moindre de cinq pieds & demi; ce qui la
rend extremement commode & tres avantageuse dans un
Cours de Physique. La simplicité & l’exactitude avec
laquelle cette machine rend ce genre d’expériences a la
portée des sens, sont éncore son plus grande mérite: car
vous savez que les observations sur la chute des corps, &
lacceleration de leurs vitesses, démandent des operations
très delicates, fort difficiles, & asséz laborieuses: & ce qui
plus est, tout-a-fait impraticables dans un Cours régulier
de Physique Experimentale (Villas-Boas, 2000)8.
In the additions et corrections to his pamphlet, Magellan stated
explicitly that there were four machines that were being built:
Tandis qu’on imprimoit cette Lettre, j’eus occasion de
faire les observations et rémarques suivantes, on exami-
nant, comme je vous l’ai promis, Monsieur, la machine
qui vous est destinée; & une autre que j’envoyerai aussitot
a mon ancien Confrere, les tres-R.P.D. Joachim de l’As-
sumption, Chanoine Regulier d’un mérite sort distingue,
actuellement Professeur de Physique dans le Monastere
Royal de Chanoines Reguliers Lateranenses de S. Au-
gustin a Mafra, pres Lisbonne. Ces deux machines sont
marquées avec les N. 3 & 4; parcequ’en effet, on n’a pas
éncore fait plus, que deux autres machines de cette espèce
jusqu’a present, meme en y comprénant celle de l’in-
venteur (Villas-Boas, 2000)9.
The same news (evidently taken by Magellan) is reported in
the letter by Volta mentioned above: “la Macchina che mi è
giunta è la terza appena che sia stata fatta, non essendosene fino
ad ora fabbricate più che due altre, compresavi quella dell’
illustre inventore” [Volta to Count Firmian, 1 May 1781, in
(Volta, 1951)]10.
Contrary to what sometimes appeared in literature (Magellan,
1780), it is thus evident that the first copy of Atwood’s ma-
8“This machine, in its present form, allows the demonstration of the laws of
the uniformly accelerated or retarded motion, as well as those of uniform
motion, by using a space less than five and a half feet; making it extremely
useful and profitable within a Course of Physics. The simplicity and accu-
racy with which this machine makes this kind of experiments within the
reach of the senses, remain his greatest merit, since you know that the ob-
servations on falling bodies and their accelerations require very delicate,
difficult and laborious operations; and, what is more, all of them is imprac-
ticable in a regular course of Experimental Physics”.
9“While printing this Letter, I had occasion to make the following comments
and observations, when examining the machine that is for you, Sir, as I have
promised to you, and another one that I have to send as soon as possible to
my former colleague, the very R. H. Don Joachim de l’Assumption, a very
distinguished Canon Regular, currently Professor of Physics in the Royal
Monastery of Lateran Canons Regular of S. Augustine in Mafra, near Lis-
bon. These two machines are marked with N. 3 and 4; indeed, we have not
yet built more than two other machines of this kind until now, including also
that of the inventor”.
10“The machine that has come to me is just the third to have been made, no
more than two others having been produced, including that of the illustrious
Open Access
chine—that “marked” with N. 2—was that realized by Rams-
den on behalf of Poli.
Intriguing Changes
As recalled above, the major source of errors in the experi-
ments performed with Atwood’s machine came from the
As recalled above, the major source of errors in the experi-
ments performed with Atwood’s machine came from the possi-
ble non simultaneous activation of the pendulum clock with the
start of the descending body, such ability being left to the
promptness of the experimenter. Poli apparently remedied to
such possible inconvenience: indeed, the machine manufac-
tured by Ramsden had a novelty compared to those built by
Adams, that is a lever that allowed the experimenter just to start
simultaneously the motion of the pendulum and the fall of the
Le parti principali di cui è composta questa nuova Mac-
china, sono l’asta verticale AB dell’altezza di cinque piedi
e mezzo, divisa in 64 pollici; le cinque picciole ruote C, D,
E, F, G; i tre sostegni H, I, S, il pendolo K, ed i pesi
convenienti. [...] Come in fatti lo stesso Autore mi ha
dimostrato, che anche nella massima velocità, che si suol
dare al peso 0, la resistenza, che l’aria fa su di esso, a
mala pena supera quella del peso di un grano. [...] V’è
nell’asta AB una molla, guarnita di un bottoncino P,
mercé la cui pressione si fa sì che nel medesimo istante
cadano i due sostegni H ed I, e quindi che il Pendolo K
ch’era arrestato dal sostegno I, incomincia ad oscillare nel
punto stesso, che il grave 0 incomincia a discendere. A
codesto picciolo meccanismo si è data la massima per-
fezione dal felicissimo genio del celebre Ramsden (Poli,
1781) 11.
In Figure 1, reproduced here from the Atwood’s Treatise,
we find the original design of the machine: all the models built
by Adams conform to such design. In these early prototypes,
there are two vertical arms: one supports the pendulum clock
for the measurement of time, while the other arm supports the
ruler and the latches for the two weights with the gear of the
pulley. The machine realized by Ramsden, instead, has a dif-
ferent making: as it is evident from the plate engraved by de
Grado for the 1781 edition of Poli’s Elementi (see Figure 2),
there is a single vertical arm (parallelepiped-shaped) supporting
both the pendulum clock and the latches for the two weights.
The trigger mentioned above is as well anchored to the single
vertical arm, allowing an easy start of the experiments. Con-
vinced that such a trigger would have reduced the measurement
errors, Poli directly spoke of this improvement with Atwood
who, however, did not appear entirely persuaded of its effec-
11“The main parts that make up this new machine are: the vertical arm AB
with a height of five feet and a half, divided into 64-inches; five tiny wheels
C, D, E, F, 0, H; three holders H, I, S; the pendulum K; and suitable weights.
[...] In fact, as the author himself has shown me, even in the case of the
maximum speed usually reached by the weight 0, the resistance offered by
the air on it barely exceeds that of the weight of one grain. [...] In the verti-
cal arm AB there is a spring, provided with a button P, through the pressure
of which it causes the two holders Hand I to open at the same moment, and
therefore the pendulum K, which was kept idle by the holder I, begins to
oscillate at the same moment in which the weight 0 begins to descend. The
highest perfection of this small mechanism is due to the happy talent of the
renowned Ramsden”.
Figure 2.
The plate in the first edition of Poli’s Elementi (Poli,
1781) with the illustration of Atwood’s machine built by
tiveness, or, rather, was convinced that it would not have im-
proved the measurements. Nevertheless, as a matter of fact,
Atwood mentioned this problem—though giving only a broad
outline of it—in his Treatise, this being probably a reminis-
cence of Poli’s advice (Atwood, 1784: p. 308). Interestingly
enough, the machines that were built later (during the XIX
century) had all this trigger, though the instrument makers
chose to use two vertical arms instead of only one, by keeping
separate the pendulum clock from the weights.
The set of five friction wheels was quite immediately simpli-
fied: in the 1801 edition of the Traité eleméntaire de Physique
by A. Libes (Malaquias & Thomaz, 1994), for example, At-
wood’s machine was already represented with just a simple
pulley on the top of a vertical arm with a ruler. Even without
resorting to such extreme simplifications, it is nevertheless a
matter of fact that, in any of the copies realized in the XIX
century, the removable apparatus with the friction wheels in the
Open Access 79
original prototype was replaced by a fixed one: the original
intent of a “universal” machine for translational and rotational
motions disappeared.
An apparent exception to such boost to simplify is given by
Poli’s Elementi (Poli, 1781) which, in any of its 23 editions
(ranging from 1781 to 1837, i.e. well beyond the death of Poli),
Atwood’s machine is invariably depicted as in the 1781 edi-
tion12, this being evidently related to the original instrument
that Poli had at his disposal. It is interesting to note that, al-
though Poli himself gave a simplified presentation in his trea-
tise of Atwood’s machine and of the experiments that could be
performed with it, as any other author did, nevertheless he
stressed his will to revisit the subject in a later work:
Tutte le rapportate dottrine riguardanti la discesa de’ gravi,
rintracciate mirabilmente dall’immortal Galileo, render si
possono sensibilissime, ed evidenti, mercé di una Mac-
china inventata, non è molti anni, dal Signor Atwood,
Professore di Fisica nell’Università di Cambridge, e mio
rispettabile Collega nella Società R. di Londra. Conver-
rebbe scrivere un intiero trattato per dare una compiuta
idea di siffatta Macchina, e per indicare la maniera, onde
si debbono con essa istituire tutti gli esperimenti. Sarà
questo in qualche parte il soggetto di un’altra mia Opera
(Poli, 1781).13
However, not only Poli did not add a specific chapter on this
subject in any of the subsequent editions of his Elementi, but he
did not publish even any other work regarding Physics, de-
voting himself in those years to the writing of a major work
concerning testaceans (De Gennaro, 2006).
A Different Use
The small (but relevant) changes introduced in the realization
of copies of Atwood’s machine seen above were, of course,
functional to a better operation of the machine, but the “sim-
plification” of it as a whole intervened already at the beginning
of the XIX century does not call for a similar explanation. This
can be searched, instead, by looking at the use that scholars
made of the machine which, as already envisaged in the quota-
tion above from Poli’s Elementi, was substantially different
from the original Atwood’s intention. Even more explicitly than
Poli, the following words by Volta are illuminating:
V.E. può giudicare di qui se [la Macchina] è novissima: lo
è tanto, che non è comparsa ancora l’Opera che il Sig.
Atwood medesimo promette di pubblicare sopra questa
sua Macchina di Dinamica, dove la descrizione ne sarà
più compiuta di quella che or ci dà il Sig. Magellan [...]
Ho ripetute io già le principali sperienze proposteci in
essa ne’ 14 problemi, e le ho variate in più maniere; e
sempre l’esito ha corrisposto alla teoria con una preci-
12An irrelevant difference appearing since the second edition concerns only
the initial position of the pendulum: in the 1787 edition, it is sketched at the
starting of the oscillation, rather than at rest.
13“Any result concerning the falling of bodies, as admirably deduced by the
immortal Galileo, can be made extremely accurate and evident by means of
a machine invented, not many years ago, by Mr. Atwood, Professor of
Physics at the University of Cambridge and my respected colleague at the
Royal Society of London. It would be appropriate to write an entire treatise
in order to give an idea of such a machine and to describe how any experi-
ment could be performed with it. This will be somewhere the subject of
another work of mine”.
sione, che maggiore desiderar non si potrebbe. Le leggi
della caduta dei gravi son messe così chiaramente e dis-
tintamente sott’occhio, che anche chi nulla conoscesse
della teoria, vi è tosto condotto e le intende a maraviglia.
Da qualche giorno che ho messo alla prova la Macchina
non so quasi occuparmi d’altro, tanta e la soddisfazione
che ne ritraggo [Volta to Count Firmian, 1 May 1781, in
(Volta, 1951)]14.
What was the original motivation for the construction of the
machine—that of displaying the Newtonian paradigm—has
now been changed: its use was quite soon limited just to per-
form several illustrative experiments on the falling of bodies
with a single and accurate device. This is, indeed, the use made
of Atwood’s machine since the end of the XVIII century until
recent times (whereas, sometimes, the experimental study on
the falling of bodies is replaced by generic studies on uniform
and uniformly accelerated motion).
The reasons for this apparent change of mind are, again,
contained in the quotation above: the machine arrived in the
Continent well before the appearance of the Treatise where
Atwood explained its original use, while the description of the
experiments that could be performed with it was spread only
through the work of the eyewitnesses Poli and, especially, Ma-
gellan. While, on the one hand, this implied a rapid fortune of
Atwood’s machine, given the success of the Poli’s Elementi
with its 23 editions and the indefatigable work as intermediary
of Magellan, on the other hand it evidently allowed the subse-
quent scholars to make (only) a different use of the machine,
given the already occurred achievement of the Newtonian para-
digm. Furthermore, Atwood himself contributed indirectly to
such direction, since he never reissued the 1784 edition of his
Treatise, having later changed his interests, as recalled above.
The structure of Newtonian physics is, as well known, based
on the organization of scientific knowledge as a series of ma-
thematical laws and, according to early codification by Galilei,
such laws require experimental validation. In the XVIII cen-
tury, physical demonstrations took place in different ways and
for different audiences, ranging from academic courses to po-
pular lectures. In the present paper, we have shown how the
Newtonian paradigm was definitively accepted in science
courses—in England as well as in the Continent—by means of
the dynamical machine invented by Atwood in late 1770s just
for this purpose. Although being aware that the ultimate test of
Newton’s mechanics would have come from experiments
showing the effect of variable forces, the experimental condi-
tions of his epoch forced Atwood to turn to constant forces, for
which he designed a single machine in order to test, in simple
experiments, all the kinematical and dynamical laws for those
14“Your Excellency will judge from this whether [the machine] is new: it is
so much new that has not yet appeared the work that Mr. Atwood himself
has promised to publish about his dynamical machine, where it will be given
a more complete description of what we now have from Mr. Magellan [...] I
have already repeated the key experiments proposed by him in the reported
14 problems, having changed them in several ways; the results always con-
formed to the theory with an accuracy, that you could not desire more. The
laws on the falling of bodies are made so clear and distinct, that even those
who know nothing of the theory are led to fully understand them. I tested the
machine since few days, and I almost cannot take care of other things, so
great is the satisfaction I feel with it”.
Open Access
forces, as coming out from Newton’s mechanics. Particularly
relevant is the mechanism he devised to measure the velocity
acquired by the body during its accelerated motion: in Galilei’s
inspired experiments on the free fall or on the motion along an
inclined plane, indeed, only the proportionality between the
traveled spaces and the square of the elapsed time could be
established. But, probably, the astonishing result was the un-
precedented accuracy with which Atwood tested the Newtonian
laws of motion, being able to measure acceleration as low as
1/64 of the free fall value. As described in his Treatise of 1784,
Atwood’s original aim was not limited to the mechanical laws
of the rectilinear motion, the machine having to serve also for
studying the rotation of bodies (in the Treatise, a number of
experiments are described concerning this topic, with the aid of
additional parts, never effectively realized), but such an in-
credible accuracy catalyzed the interest of any of the subse-
quent scholars who used the machine in their demonstrations.
The spreading of Atwood’s machine outside England oc-
curred well before the appearance of the Treatise, where it was
described along with the experiments to be performed with it.
In fact, some scholars who had the opportunity to attend At-
wood’s demonstrations in Cambridge in the late 1770s, realized
immediately the importance of the novel machine, and dis-
seminate the news, even subscribing (or suggesting the sub-
scription to other scholars) to the acquisition of copies of that
machine. Thus, it was the Portuguese Magellan the first to pub-
lish (in 1780) a pamphlet where the new machine was broadly
described, along with a set of experiments concerning uniform
and accelerated motion, in the form of a letter addressed to
Volta in Pavia. Instead, it was the Italian Poli to report (in 1781)
for the first time an illustration of the novel machine, realized
on the copy ordered to the instrument maker Ramsden, in his
textbook where a choice of experiments are described as well.
The model manufactured by Ramsden (the second one ever
realized, including the original one owned by Atwood) intro-
duced an additional device, suggested by Poli, in order to trig-
ger the simultaneous activation of the pendulum clock and the
start of the descending mass. Clearly aimed at a better operation
of the machine and, consequently, at a reduction of the meas-
urement errors, this additional lever was always included in
later copies of the machine during the XIX century, irrespective
of the “simplification” of Atwood’s machine (the removable set
of five friction wheels was replaced by a fixed set of wheels or
even just a simple pulley) that was going on already at the very
end of XVIII century.
Such changes which were occurring on the machine are em-
blematic of the different use made of it. Once Newton’s me-
chanics was definitively accepted in academic courses as the
only possible theory of motion, Atwood’s machine did not
serve anymore as a device displaying the success of the Newto-
nian paradigm. Its use then changed accordingly: several illus-
trative experiments on the falling of bodies, or even just on uni-
form or uniformly accelerated motion may be performed with a
single and accurate machine. This is, indeed, the use made of
Atwood’s machine until now.
The historical case studied here, therefore, allows us to rec-
ognize the relevant role played by a properly devised instru-
ment in the acceptance of a new paradigm by non-erudite scho-
lars, in addition to the traditional ways followed by erudite ones
(almost exclusively considered in the literature), where mathe-
matical, philosophical or even physical reasoning certainly do-
minates over machine philosophy.
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