Unities and a Unifier Hermann Helmholtz

Unifiers and Diversifiers
Science is largely a bipartisan endeavor. Most scientists have no difficulty identifying
with one of two camps, which can be called, with about as much accuracy
as names attached to political parties, theorists and experimentalists. An astute
observer of scientists and their ways, Freeman Dyson, has offered a roughly
equivalent, but more inspired, division of scientific allegiances and attitudes. In
Dyson’s view, science has been made throughout its history in almost equal measure
by “unifiers” and “diversifiers.” The unifiers, mostly theorists, search for
the principles that reveal the unifying structure of science. Diversifiers, likely to
be experimentalists, workto discover the unsorted facts of science. Efforts of the
scientific unifiers and diversifiers are vitally complementary. From the great bodies
of facts accumulated by the diversifiers come the unifier’s theories; the theories
guide the diversifiers to new observations, sometimes with disastrous results
for the unifiers.
The thermodynamicists celebrated here were among the greatest scientific unifiers
of the nineteenth and early twentieth centuries. Three of their stories have
been told above: of Sadi Carnot and his search for unities in the bewildering
complexities of machinery; of Robert Mayer and his grand speculations about
the energy concept; of James Joule’s precise determination of equivalences among
thermal, electrical, chemical, and mechanical effects. Continuing now with the
chronology, we focus on the further development of the energy concept. The
thermodynamicist who takes the stage is Hermann Helmholtz, the most confirmed
of unifiers.

A Joule Sketch

Osborne Reynolds, who met Joule in 1869, gives us this impression of his manner
and appearance in middle age: “That Joule, who was 51 years of age, was rather
under medium height; that he was somewhat stout and rounded in figure; that
his dress, though neat, was commonplace in the extreme, and that his attitude
and movements were possessed of no natural grace, while his manner was somewhat
nervous, and he possessed no great facility of speech, altogether conveyed
an impression of simplicity, and utter absence of all affectation which had characterized
his life.”
Joule married Amelia Grimes in 1847, when he was twenty-nine and she
thirty-three; they had two children, a son and a daughter. Amelia died in 1854,
and “the shocktook a long time to wear off,” writes Joule’s most recent biographer,
Donald Cardwell. “His friends and contemporaries agreed that this never
very assertive man became more withdrawn.” About fourteen years later, Joule
fell in love again, this time with his cousin Frances Tappenden, known as
“Fanny.” In a letter to Thomson he writes “an affection has sprung up between
me and my cousin you saw when last here. There are hindrances in the way so
that nothing may come of it.” The “hindrances” prevented marriage, and eventually
Fanny married another man.
Joule’s political leanings were conservative. He had a passionate, sometimes
irrational, dislike of reform-minded Liberal politicians such as William Gladstone and John Bright. In a letter to John Tyndall, he wrote, “The fact is that Mr. Gladstone
was fashioning a neat machine of ‘representation’ with the object of keeping
himself in power. . . . Posterity will judge him as the worst ‘statesman’ that England
ever had and the verdict with regard to that Parliament will be ditto, ditto.”
Joule had a personality that was “finely poised,” as another biographer, J. G.
Crowther, puts it. On the one hand he was conducting experiments with unlimited
care and patience, and on the other hand fulminating against Liberal politicians.
He feared that too much mental effort would threaten his health. In 1860,
a new professorship of physics was created at Owens College in Manchester, and
Joule could have had it, but he decided not to apply, as he explained in a letter
to Thomson: “I have not the courage to apply for the Owens professorship. The
fact is that I do not feel it would do for me to overtaskmy brain. A few years
ago, I felt a very small mental effort too much for me, and in consequence spared
myself from thought as much as possible. I have felt a gradual improvement, but
I do not thinkit would be well for me to build too much on it. I shall do a great
deal more in the long run by taking things easily.”
Joule’s life was hectic and burdensome at this time, and he may have felt that
he was near breakdown. Amelia died in 1854, the brewery was sold in the same
year, and the experiments with Thomson were in progress. During the next six
years, he moved his household and laboratory twice. After the second move, he
was upset by an acrimonious dispute with a neighbor who objected to the noise
and smoke made by a three-horsepower steam engine Joule included in his apparatus.
The neighbor was “a Mr Bowker, an Alderman of Manchester and chairman
of the nuisances committee, a very important man in his own estimation
like most people who have risen from the dregs of society.”
During this same period, Joule narrowly escaped serious injury in a train
wreck, and after that he had an almost uncontrollable fear of railway travel. At
the same time, he loved to travel by sea, even when it was dangerous. In a letter
to Fanny, he described a ten-mile trip to Tory Island, in the Atlantic off the coast
of Ireland, where his brother owned property: “Waves of 4 to 600 feet from crest
to crest and 20 feet high. Dr Brady who was with us and had yachted in the
ocean for 25 years said he was never in a more dangerous sea. However the
magnificence of it tookaway the disagreeable sense of danger which might have
prevailed.”
In some measures of scientific ability, Joule was unimpressive. As a theorist,
he was competent but not outstanding. He was not an eloquent speaker, and he
was not particularly important in the scientific establishment of his time. But
Joule had three things in extraordinary measure—experimental skill, independence,
and inspiration.
He was the first to understand that unambiguous equivalence principles could
be obtained only with the most inspired attention to experimental accuracy. He
accomplished his aim by carefully selecting the measurements that would make
his case. Crowther marvels at the directness and simplicity of Joule’s experimental
strategies: “He did not separate a quantity of truth from a large number of
groping unsuccessful experiments. Nearly all of his experiments seem to have
been perfectly conceived and executed, and the first draft of them could be sent
almost without revision to the journals for publication.”
For most of his life, Joule had an ample independent income. That made it
possible for him to pursue a scientific career privately, and to build the kind of intellectual independence he needed. Crowther tells us about this facet of Joule’s
background:
As a rich young man he needed no conventional training to qualify him for a
career, or introduce him to powerful future friends. His early researches were
pursued partly in the spirit of a young gentleman’s entertainment, which happened
to be science instead of fighting or politics or gambling. It is difficult to
believe that any student who had received a lengthy academic training could
have described researches in Joule’s tone of intellectual equality. The gifted
student who has studied under a great teacher would almost certainly adopt a
less independent tone in his first papers, because he would have the attitude
of a pupil to his senior, besides a deference due to appreciation of his senior’s
achievements. A student without deference after distinguished tuition is almost
always mediocre.
Joule was not entirely without distinguished tuition. Beginning in 1834, and
continuing for three years, Joule and his brother Benjamin studied with John
Dalton, then sixty-eight and, as always, earning money teaching children the
rudiments of science and mathematics. The Joules’ studies with Dalton were not
particularly successful pedagogically. Dalton tookthem through arithmetic and
geometry (Euclid) and then proceeded to higher mathematics, with little attention
to physics and chemistry. Dalton’s syllabus did not suit Joule, but he benefited
in more-informal ways. Joule wrote later in his autobiographical note, “Dalton
possessed a rare power of engaging the affection of his pupils for scientific truth;
and it was from his instruction that I first formed a desire to increase my knowledge
by original researches.” In his writings, if not in his tutoring, Dalton emphasized
the ultimate importance of accurate measurements in building the
foundations of physical science, a lesson that Joule learned and used above all
others. The example of Dalton, internationally famous for his theories of chemical
action, yet self-taught, and living and practicing in Manchester, must have convinced
Joule that he, too, had prospects.
Joule’s independence and confidence in his background and talents, natural
or learned from Dalton, were tested many times in later years, but never shaken.
His first determination, in 1843, of the mechanical equivalent of heat was ignored,
and subsequent determinations were given little attention until Thomson
and Stokes took notice at the British Association meeting in 1847.
When Joule submitted a summary of his friction experiments for publication,
he closed the paper with three conclusions that asserted the heat-mechanicalworkequivalence
in the friction experiments, quoted his measured value of J,
and stated that “the friction consisted in the conversion of mechanical power to
heat.” The referee who reported on the paper (believed to have been Faraday)
requested that the third conclusion be suppressed.
Joule’s first electrochemistry paper was rejected for publication by the Royal
Society, except as an abstract. Arthur Schuster reported that, when he asked Joule
what his reaction was when this important paper was rejected, Joule’s reply was
characteristic: “I was not surprised. I could imagine those gentlemen sitting
around a table in London and saying to each other: ‘What good can come out of
a town [Manchester] where they dine in the middle of the day?’ ”
But with all his talents, material advantages, and intellectual independence, Joule could never have accomplished what he did if he had not been guided in
his scientific workby inspiration of an unusual kind. For Joule “the study of
nature and her laws” was “essentially a holy undertaking.” He could summon
the monumental patience required to assess minute errors in a prolonged series
of measurements, and at the same time transcend the details and see his work
as a quest “for acquaintance with natural laws . . . no less than an acquaintance
with the mind of God therein expressed.” Great theorists have sometimes had
thoughts of this kind—one might get the same meaning from Albert Einstein’s
remarkthat “the eternal mystery of the world is its comprehensibility”—but experimentalists,
whose lives are taken up with the apparently mundane tasks of
reading instruments and designing apparatuses, have rarely felt that they were
communicating with the “mind of God.”
It would be difficult to find a scientific legacy as simple as Joule’s, and at the
same time as profoundly important in the history of science. One can summarize
Joule’s major achievement with the single statement
J 778 ft-lb per Btu,
and add that this result was obtained with extraordinary accuracy and precision.
This is Joule’s monument in the scientific literature, now quoted as 4.1840
kilogram-meters per calorie, used routinely and unappreciatively by modern students
to make the quantitative passage from one energy unit to another.
In the 1840s, Joule’s measurements were far more fascinating, or disturbing,
depending on the point of view. The energy concept had not yet been developed
(and would not be for another five or ten years), and Joule’s number had not
found its niche as the hallmarkof energy conversion and conservation. Yet Joule’s
research made it clear that something was converted and conserved, and provided
vital clues about what the something was.

Living Force and Heat

Living Force and Heat
Joule believed that water at the bottom of a waterfall should be slightly warmer
than water at the top, and he made attempts to detect such effects (even on his
honeymoon in Switzerland, according to an apocryphal, or at any rate embellished,
story told by Thomson). For Joule this was an example of the conservation
principle that “heat, living force, and attraction through space . . . are mutually
convertible into one another. In these conversions nothing is ever lost.” This
statement is almost an expression of the conservation of mechanical and thermal
energy, but it requires some translation and elaboration.
Newtonian mechanics implies that mechanical energy has a “potential” and a
“kinetic” aspect, which are linked in a fundamental way. “Potential energy” is
evident in a weight held above the ground. The weight has energy because work
was required to raise it, and the workcan be completely recovered by letting the
weight fall very slowly and drive machinery that has no frictional losses. As one
might expect, the weight’s potential energy is proportional to its mass and to its
height above the ground: if it starts at a height of 100 feet it can do twice as
much workas it can if it starts at 50 feet.
If one lets the weight fall freely, so that it is no longer tied to machinery, it does no work, but it accelerates and acquires “kinetic energy” from its increasing
speed. Kinetic energy, like potential energy, can be converted to work with the
right kind of machinery, and it is also proportional to the mass of the weight. Its
relationship to speed, however, as dictated by Newton’s second law of motion,
is to the square of the speed.
In free fall, the weight has a mechanical energy equal to the sum of the kinetic
and potential energies,
mechanical energy kinetic energy potential energy. (1)
As it approaches the ground the freely falling weight loses potential energy, and
at the same time, as it accelerates, it gains kinetic energy. Newton’s second law
informs us that the two changes are exactly compensating, and that the total
mechanical energy is conserved, if we define
mv2
kinetic energy (2)
2
potential energy mgz. (3)
In equations (2) and (3), m is the mass of the weight, v its speed, z its distance
above the ground, and g the constant identified above as the gravitational acceleration.
If we represent the total mechanical energy as E, equation (1) becomes
mv2
E mgz, (4)
2
and the conservation law justified by Newton’s second law guarantees that E is
always constant. This is a conversion process, of potential energy to kinetic energy,
as illustrated in figure 5.2. In the figure, before the weight starts falling it
has 10 units of potential energy and no kinetic energy. When it has fallen halfway
to the ground, it has 5 units of both potential and kinetic energy, and in the
instant before it hits the ground it has no potential energy and 10 units of kinetic
energy. At all times its total mechanical energy is 10 units.
Joule’s term “living force” (or vis viva in Latin) denotes mv2, almost the samething as the kinetic energy , and his phrase “attraction through space” means
mv2
2
the same thing as potential energy. So Joule’s assertions that living force and
attraction through space are interconvertible and that nothing is lost in the conversion
are comparable to the Newtonian conservation of mechanical energy.
Water at the top of the falls has potential energy only, and just before it lands in
a pool at the bottom of the falls, it has kinetic energy only. An instant later the
water is sitting quietly in the pool, and according to Joule’s principle, with the
third conserved quantity, heat, included, the water is warmer because its mechanical
energy has been converted to heat. Joule never succeeded in confirming
this waterfall effect. The largest waterfall is not expected to produce a temperature
change of more than a tenth of a degree. Not even Joule could detect that
on the side of a mountain.
Joule’s mechanical view of heat led him to believe further that in the conversion
of the motion of an object to heat, the motion is not really lost because heat
is itself the result of motion. He saw heat as the internal, random motion of the
constituent particles of matter. This general idea had a long history, going back
at least to Robert Boyle and Daniel Bernoulli in the seventeenth century.
Joule pictured the particles of matter as atoms surrounded by rapidly rotating
“atmospheres of electricity.” The centrifugal force of the atmospheres caused a
gas to expand when its pressure was decreased or its temperature increased.
Mechanical energy converted to heat became rotational motion of the atomic
atmospheres. These speculations of Joule’s markthe beginning of the development
of what would later be called the “molecular (or kinetic) theory of gases.”
Following Joule, definitive workin this field was done by Clausius, Maxwell,
and Boltzmann.

Mechanical Equivalents

Joule made the crucial addition of mechanical effects to his system of equivalences
by following a time-honored route to scientific discovery: he made a fortunate mistake. In the fourth of his electrochemistry papers he reported electric
potential data (voltages, in modern units) measured on voltaic cells whose
electrode reactions produced oxidation of zinc and other metals. He believed,
mistakenly, that these reaction potentials could be used in much the same way
as reaction heats: that for a given reaction the potential had the same value no
matter how the reaction was carried out. This interpretation is not sanctioned by
modern thermodynamics unless cell potentials are measured carefully (reversibly).
Joule and his contemporaries were unaware of this limitation, however, and
the mistake led Joule to calculate electrical and thermal equivalents for the process
in which dissolved oxygen is given “its elastic condition,” the reaction
O2 (solution) O2 (gas).
Joule’s result was an order of magnitude too large. But mistaken as it was quantitatively,
the calculation advanced Joule’s conceptual understanding immensely,
because he believed he had obtained electrical and thermal equivalents for a
mechanical effect, the evolution of oxygen gas from solution. In Joule’s fertile
imagination, this was suggestive. In the fourth electrochemistry paper, he remarked
that he had already thought of ways to measure mechanical equivalents.
He hoped to confirm the conclusion that “the mechanical and heating powers of
a current are proportional to each other.”
In this serendipitous way, Joule began the determinations of the mechanical
equivalent of heat for which he is best known today. The first experiments in
this grand series were performed in 1843, when Joule was twenty-four. In these
initial experiments, he induced an electrical current in a coil of wire by rotating
it mechanically in a strong magnetic field. The coil was contained in a glass tube
filled with water and surrounded by insulation, so any heating in the coil could
be measured by inserting a thermometer in the tube before and after rotating it
in the magnetic field. The induced current in the coil was measured by connecting
the coil to an external circuit containing a galvanometer. Although its
origin was entirely different, the induced current behaved the same way as the
voltaic current Joule had studied earlier: in both cases the current caused heating
that followed the I 2R-law.
In the final experiments of this design, the wheel of the induction device was
driven by falling weights for which the mechanical effect, measured as a mechanical
workcalculation, could be made directly in foot-pounds (abbreviated
ft-lb): one unit was equivalent to the workrequired to raise one pound one foot.
Heat was measured by a unit that fit the temperature measurements: one unit
raised the temperature of one pound of water 1 Fahrenheit (F). We will use the
term later attached to this unit, “British thermal unit,” or Btu.
In one experiment, Joule dropped weights amounting to 4 lb 12 oz ( 4.75 lb)
517 feet (the weights were raised and dropped many times), causing a temperature
rise of 2.46 F. He converted the weight of the glass tube, wire coil, and water
in which the temperature rise occurred all into a thermally equivalent weight of
water, 1.114 lb. Thus the heating effect was 2.46 F in 1.114 lb of water. If this
same amount of heat had been generated in 1 lb of water, the heating effect would
have been . Joule concluded that in this case (517)(4.75)
(2.46)(1.114)
2.74 F
1
ft-lb was equivalent to 2.74 Btu. He usually determined the mechanical workequivalent to 1 Btu. That number, which Thomson later labeled J to honor Joule,
was
(4.75)(517)
J 896 ft-lb per Btu
(2.74)
for this experiment. This was one determination of the mechanical equivalent of
heat. Joule did thirteen experiments of this kind and obtained results ranging
from J 587 to 1040 ft-lb per Btu, for which he reported an average value of 838
ft-lb per Btu. The modern “correct” value, it should be noted, is J 778 ft-lb per
Btu.
If the 27% precision achieved by Joule in these experiments does not seem
impressive, one can sympathize with Joule’s critics, who could not believe his
claims concerning the mechanical equivalent of heat. But the measurements Joule
was attempting set new standards for experimental difficulty. According to Reynolds,
the 1843 paper reported experiments that were more demanding than any
previously attempted by a physicist.
In any case, Joule was soon able to do much better. In 1845, he reported another,
much different determination of the mechanical equivalent of heat, which
agreed surprisingly well with his earlier measurement. In this second series of
experiments, he measured temperature changes, and calculated the heat produced,
when air was compressed. From the known physical behavior of gases
he could calculate the corresponding mechanical effect as workdone on the air
during the compression.
In one experiment involving compression of air, Joule calculated the workat
11230 ft-lb and a heating effect of 13.628 Btu from a measured temperature rise
of 0.344 F. The corresponding mechanical equivalent of heat was
11230
J 824 ft-lb per Btu.
13.628
Another experiment done the same way, in which Joule measured the temperature
change 0.128 F, gave the result J 796 ft-lb per Btu. Joule’s average for the
two experiments was 810 ft-lb per Btu. This was in impressive, if somewhat
fortuitous, agreement with the result J 838 ft-lb per Btu reported in 1843.
Joule also allowed compressed air to expand and do workagainst atmospheric
pressure. Temperature measurements were again made, this time with a temperature
decrease being measured. In one of these expansion experiments, Joule
measured the temperature change 0.1738 F and reduced this to 4.085 Btu. The
corresponding workcalculation gave 3357 ft-lb, so
3357
J 822 ft-lb per Btu.
4.085
Joule did two more experiments of this kind and measured the temperature
changes 0.081 F and 0.0855 F, giving J 814 and J 760 ft-lb per Btu.
When Joule’s colleagues looked at these results, the first thing they noticed
was the accuracy claimed for measurements of very small temperature changes.
In Joule’s time, accurate measurement of one-degree temperature changes was difficult enough. Joule reported temperature changes of tenths of a degree with
three or four significant digits, and based his conclusions on such tiny changes.
As William Thomson remarked, “Joule had nothing but hundredths of a degree
to prove his case by.” Yet, most of Joule’s claims were justified. He made temperature
measurements with mercury thermometers of unprecedented sensitivity
and accuracy. He told the story of the thermometers in an autobiographical note:
“It was needful in these experiments to use thermometers of greater exactness
and delicacy than any that could be purchased at that time. I therefore determined
to get some calibrated on purpose after the manner they had been by
Regnault. In this I was ably seconded by Mr. Dancer [J. B. Dancer, a well-known
Manchester instrument maker], at whose workshop I attended every morning for
some time until we completed the first accurate thermometers which were ever
made in England.”
Joule demonstrated the heat-mechanical-workequivalence with a third gas
expansion experiment that incorporated one of his most ingenious experimental
designs. In this experiment, two constant-volume copper vessels, one evacuated
and the other pressurized with air, were connected with a valve. The connected
vessels were placed in a calorimeter, the valve opened, and the usual temperature
measurements made. In this case, Joule could detect no net temperature change.
Air expanding from the pressurized vessel was cooled slightly, and air flowing
into the evacuated vessel was slightly heated, but no net temperature change was
observed.
This was what Joule expected. Because the combined system consisting of the
two connected vessels was closed and had a fixed volume, all of the workwas
done internally, in tandem between the two vessels. Workdone by the gas in one
vessel was balanced by workdone on the gas in the other; no net workwas done.
Heat equivalent to zero workwas also zero, so Joule’s concept of heatmechanical-
workequivalence demanded that the experiment produce no net
thermal effect, as he observed.
The next stage in Joule’s relentless pursuit of an accurate value for the mechanical
equivalent of heat, which he had begun in 1847, was several series of
experiments in which he measured heat generated by various frictional processes.
The frictional effects were produced in a water-, mercury-, or oil-filled
calorimeter by stirring with a paddle-wheel device, the latter being driven by
falling weights, as in the 1843 experiments. The workdone by the weights was
converted directly by the paddle-wheel stirrer into heat, which could be measured
on a thermometer in the calorimeter.
Of all Joule’s inventions, this experimental design, which has become the bestknown
monument to his genius, made the simplest and most direct demonstration
of the heat-mechanical-workequivalence. This was the Joule technique reduced
to its essentials. No complicated induction apparatus was needed, no
calculational approximations, just falling weights and one of Joule’s amazingly
accurate thermometers.
With the paddle-wheel device and water as the calorimeter liquid, Joule obtained
J 773.64 ft-lb per Btu from a temperature rise of 0.563 F. Using mercury
in the calorimeter, he obtained J 773.762 and 776.303 ft-lb per Btu. In two
further series of experiments, Joule arranged his apparatus so the falling weights
caused two cast-iron rings to rub against each other in a mercury-filled calorimeter;
the results J 776.997 and 774.880 ft-lb per Btu were obtained.
Joule described his paddle-wheel experiments in 1847 at an Oxford meeting of the British Association for the Advancement of Science. Because his previous
papers had aroused little interest, he was asked to make his presentation as brief
as possible. “This I endeavored to do,” Joule recalled later, “and a discussion not
being invited the communication would have passed without comment if a
young man had not risen in the section, and by his intelligent observations created
a lively interest in the new theory.”
The silence was finally broken. The young man was William Thomson, recently
installed as professor of natural philosophy at Glasgow University. Thomson
had reservations about Joule’s work, but he also recognized that it could not
be ignored. “Joule is, I am sure, wrong in many of his ideas,” Thomson wrote to
his father, “but he seems to have discovered some facts of extreme importance,
as for instance, that heat is developed by the friction of fluids.” Thomson recalled
in 1882 that “Joule’s paper at the Oxford meeting made a great sensation. Faraday
was there, and was much struckby it, but did not enter fully into the new views.
. . . It was not long after when Stokes told me he was inclined to be a Joulite.”
George Stokes was another rising young physicist and mathematician, in 1847 a
fellow at Pembroke College, Cambridge, and in two years to be appointed Lucasian
Professor of Mathematics, the chair once occupied by Newton.
During the three years following the Oxford meeting, Joule rose from obscurity
to a prominent position in the British scientific establishment. Recognition came
first from Europe: a major French journal, Comptes Rendu, published a short
account of the paddle-wheel experiments in 1847, and in 1848 Joule was elected
a corresponding member of the Royal Academy of Sciences at Turin. Only two
other British scientists, Faraday and William Herschel, had been honored by the
Turin Academy. In 1850, when he was thirty-one, Joule received the badge of
British scientific acceptance: election as a fellow of the Royal Society.
After these eventful years, Joule’s main research effort was a lengthy collaboration
with Thomson, focusing on the behavior of expanding gases. This was one
of the first collaborative efforts in history in which the talents of a theorist and
those of an experimentalist were successfully and happily united.

Equivalences

The theme that dominated Joule’s research from beginning to end, and served as
his guiding theoretical inspiration, was the belief that quantitative equivalences
could be found among thermal, chemical, electrical, and mechanical effects. He
was convinced that the extent of any one of these effects could be assessed with
the units of any one of the other effects. He studied such quantitative connections
in no less than eight different ways: in investigations of chemical effects converted
to thermal, electrical, and mechanical effects; of electrical effects converted
to thermal, chemical, and mechanical effects; and of mechanical effects
converted to thermal and electrical effects.
At first, Joule did not fully appreciate the importance of mechanical effects in
this scheme of equivalences. His earliest workcentered on chemical, electrical,and thermal effects. In 1840, when he was twenty-two, he started a series of five
investigations that was prompted by his interest in electrochemistry. (Joule was
an electrochemist before he was a physicist.) First, he demonstrated accurately
that the heating produced by an electrical current in a wire is proportional to the
square of the current I and to the electrical resistance R—the “I2R-heating law.”
His experimental proof required temperature measurements in a “calorimeter” (a
well-insulated, well-stirred vessel containing water or some other liquid), electrical
current measurements with an instrument of his own design, and the invention
of a system of absolute electrical units.
Joule then invested considerable effort in various studies of the role played
by his heating law in the chemical processes produced in electric cells. He
worked with “voltaic cells,” which supply an electrical output (the modern flashlight
battery is an example), and “electrolysis cells,” which consume an electrical
input (for example, a cell that decomposes water into hydrogen gas and oxygen
gas). In these experiments, Joule operated an electrolysis cell with a battery of
voltaic cells. He eventually arrived at the idea that the electrical currents generated
by the chemical reaction in the voltaic cell carried the reaction’s “calorific
effect” or “chemical heat” away from the primary reaction site either to an external
resistance where it could be converted to “free heat,” according to the I 2Rheating
law, or to an electrolysis cell where it could be invested, all or partly, as
“latent heat” in the electrolysis reaction.
To determine the total chemical heat delivered to the electrolysis cell from the
voltaic cells, call it Qe, Joule found the resistance Re of a wire that could replace
the electrolysis cell without causing other electrical changes, measured the current
I in the wire, and calculated Qe with the heating law as I2Re. He also measured
the temperature rise in the electrolysis cell doubling as a calorimeter, and
from it calculated the free heat Qt generated in the cell. He always found that
Qe substantially exceeded Qt; in extreme cases, there was no heating in the cell
and Qt was equal to zero. The difference Qe Qt represented what Joule wanted
to calculate: chemical heat converted to the latent heat of the electrolysis reaction.
Representing the electrolysis reaction’s latent heat with Qr, Joule’s calculation
was
Qr Qe Qt.
This is the statement Joule used in 1846 to determine several latent heats of
electrolysis reactions with impressive accuracy. It is a complicated and exact
application of the first law of thermodynamics, which Joule seems to have understood
in terms of inputs and outputs to the electrolysis cell. That is evident
in the last equation rearranged to
Qt Qe Qr,
with Qe an input to the cell, Qr an output because it is lost to the reaction, and
Qt the difference between the input and output (see fig. 5.1). This was a balancing
or bookkeeping kind of calculation, and it implied a conservation assumption:
the balanced entity could not be created or destroyed within the cell. Joule did
not have a name for the conserved entity. It would be identified six years later
by Rudolf Clausius and William Thomson, and called “energy” by Thomson.
Although he had not arrived at the energy concept, Joule clearly did have, wellahead of his contemporaries, a working knowledge of the first law of
thermodynamics.
Joule’s electrochemistry papers aroused little interest when they were first
published, neither rejection nor acceptance, just silence. One reason for the indifference
must have been the extraordinary nature of Joule’s approach. The
input-output calculation was difficult enough to comprehend at the time, but in
addition to that, Joule used his measured heats of electrolysis reactions to calculate
heats of combustion reactions (that is, reactions with oxygen gas). For
example, he obtained an accurate heat for the hydrogen combustion reaction,
2 H2 O2 2 H2O,
which is just the reverse of the water electrolysis reaction,
2 H2O 2 H2 O2,
and therefore, Joule assumed, its heat had the same magnitude as that of the
electrolysis reaction.
This was an exotic way to study a combustion reaction. Joule’s first biographer,
Osborne Reynolds, remarks that “the views they [the electrochemistry papers and
others of Joule’s early papers] contained were so much in advance of anything
accepted at the time that no one had sufficient confidence in his own opinion or
was sufficiently sure of apprehending the full significance of the discoveries on
which these views were based, to venture an expression of acceptance or rejection.”
We can imagine a contemporary reader puzzling over the papers and finally
deciding that the author was either a genius or a crank.
But for Joule—apparently unconcerned about the accessibility or inaccessibility
of his papers for readers—the complicated method was natural. His primary
interest at the time was the accurate determination of equivalences among thermal,
electrical, and chemical effects. He could imagine no better way to tackle
this problem than to use electrical and calorimetric measurements to calculate
the thermal effect of a chemical effect.

A Holy Undertaking James Joule

The Scientist as Amateur
James Joule’s story may seem a little hard to believe. He lived near Manchester,
England—in the scientific hinterland during much of Joule’s career—where his
family operated a brewery, making ale and porter. He did some of his most important
workin the early morning and evening, before and after a day at the
brewery. He had no university education, and hardly any formal training at all
in science. As a scientist he was, in every way, an amateur. Like Mayer, who was
also an amateur as a physicist, Joule was ignored at first by the scientific establishment.
Yet, despite his amateur status, isolation, and neglect, he managed to
probe more deeply than anyone else at the time (the early and middle 1840s) the
tantalizing mysteries of conversion processes. And (unlike Mayer) he did not
suffer prolonged neglect. The story of Joule’s rapid progress, from dilettante to a
position of eminence in British science, can hardly be imagined in today’s world
of research factories and prolonged scientific apprenticeships

Strange Success

The final episode in this life full of ironies will seem like the ultimate irony.
Recognition of Mayer’s achievements finally came, but hardly in a way deserved
by a man who had endured indifference, rejection, breakdown, cruel medical
treatment, and reports of his own death. In the early 1860s Mayer, now peacefully
tending his vineyards in Heilbronn, suddenly became the center of a famous
scientific controversy.
It all started when John Tyndall, a popular lecturer, professor, and colleague
of Michael Faraday at the Royal Institution in London, prepared himself for a
series of lectures on heat. He wrote to Hermann Helmholtz and Rudolf Clausius
in Germany for information. Included in Clausius’s response was the comment
that Mayer’s writings were not important. Clausius promised to send copies of
Mayer’s papers nevertheless, and before mailing the papers he read them, apparently
for the first time with care. Clausius wrote a second letter with an entirely
different assessment: “I must retract the statements in my last letter that
you would not find much of importance in Mayer’s writings; I am astonished at
the multitude of beautiful and correct thoughts which they contain.” Clausius
was now convinced that Mayer had been one of the first to understand the energy
concept and its conservation doctrine. Helmholtz also sent favorable comments
on Mayer, pointing especially to the early evaluation of the mechanical equivalent
of heat.
Tyndall was a man who loved controversy and hated injustice. Because his
ideas concerning the latter were frequently not shared by others who were
equally adept in the practice of public controversy, he was often engaged in
arguments that were lively, but not always friendly. When Tyndall decided to be
Mayer’s champion, he embarked on what may have been the greatest of all his
controversies. As usual, he chose as his forum the popular lectures at the Royal
Institution. He had hastily decided to broaden his topic from heat to the general
subject of energy, which was by then, in the 1860s, mostly understood; the title
of his lecture was “On Force.” (Faraday and his colleagues at the Royal Institution
still preferred to use the term “force” when they meant “energy.”)
Tyndall began by listing many examples of energy conversion and conservation,
and then summarized Mayer’s role with the pronouncement, “All that I have
brought before you has been taken from the labors of a German physician, named
Mayer.” Mayer should, he said, be recognized as one of the first thermodynamicists,
“a man of genius arriving at the most important results some time in advance
of those whose lives were entirely devoted to Natural Philosophy.” Tyndall
left no doubt that he felt Mayer had priority claims over Joule: “Mr. Joule published
his first paper ‘On the Mechanical Value of Heat’ in 1843, but in 1842
Mayer had actually calculated the mechanical equivalent of heat.” In the gentlemanly
world of nineteenth-century scientific discourse, this was an invitation to
verbal combat. It brought quickresponses from Joule and Thomson, and also
from Thomson’s close friend Peter Guthrie Tait, professor of natural philosophy
at the University of Edinburgh, and Tyndall’s match in the art of polemical
debate.
Joule was the first to reply, in a letter published in the Philosophical Magazine.
He could not, he said, accept the view that the “dynamical theory of heat” (that
is, the theory of heat that, among other things, was based on the heat-workconnection)
was established by Mayer, or any of the other authors who speculated on the meaning of the conversion processes. Reliable conclusions “require experiments,”
he wrote, “and I therefore fearlessly assert my right to the position
which has been generally accorded to me by my fellow physicists as having been
the first to give decisive proof of the correctness of this theory.”
Tyndall responded to Joule in another letter to the Philosophical Magazine,
protesting that he did not wish to slight Joule’s achievements: “I trust you will
find nothing [in my remarks] which indicates a desire on my part to question
your claim to the honour of being the experimental demonstrator of the equivalence
of heat and work.” Tyndall was willing to let Mayer speak for himself; at
Tyndall’s suggestion, Mayer’s papers on the energy theme were translated and
published in the Philosophical Magazine.
But this did not settle the matter. An article with both Thomson and Tait listed
as authors (although the style appears to be that of Tait) next appeared in a
popular magazine called Good Words, then edited by Charles Dickens. In it,
Mayer’s 1842 paper was summarized as mainly a recounting of previous work
with a few suggestions for new experiments; “a method for finding the mechanical
equivalent of heat [was] propounded.” This was, the authors declared, a
minor achievement, and they could find no reason to surrender British claims:
On the strength of this publication an attempt has been made to claim for Mayer
the credit of being the first to establish in all its generality the principle of the
Conservation of Energy. It is true that la science n’a pas de patrie and it is
highly creditable to British philosophers that they have so liberally acted according
to this maxim. But it is not to be imagined that on this account there
should be no scientific patriotism, or that, in our desire to do justice to a foreigner,
we should depreciate or suppress the claims of our countrymen.
Tyndall replied, again in the Philosophical Magazine, pointedly directing his
remarks to Thomson alone, and questioning the wisdom of discussing weighty
matters of scientific priority in the pages of a popular magazine. He now relaxed
his original position and saw Joule and Mayer more in a shared role:
Mayer’s labors have in some measure the stamp of profound intuition, which
rose, however, to the energy of undoubting conviction in the author’s mind.
Joule’s labours, on the contrary, are in an experimental demonstration. True to
the speculative instinct of his country, Mayer drew large and weighty conclusions
from slender premises, while the Englishman aimed, above all things, at
the firm establishment of facts. And he did establish them. The future historian
of science will not, I think, place these men in antagonism.
Tait was next heard from. He wrote to one of the editors of the Philosophical
Magazine, first offering the observation that if Good Words was not a suitable
medium for the debate of scientific matters, neither were certain popular lecture
series at the Royal Institution. He went on: “Prof. Tyndall is most unfortunate in
the possession of a mental bias which often prevents him . . . from recognizing
the fact that claims of individuals whom he supposes to have been wronged have,
before his intervention, been fully ventilated, discussed, and settled by the general
award of scientific men. Does Prof. Tyndall know that Mayer’s paper has no
claim to novelty or correctness at all, saving this, that by a lucky analogy he got
an approximation to a true result from an utterly false analogy?” Even if the polemics had been avoided, any attempt to resolve Joule’s and
Mayer’s conflicting claims would have been inconclusive. If the aim of the debate
was to identify once and for all the discoverer of the energy concept, neither
Joule nor Mayer should have won the contest. The story of the energy concept
does not end, nor does it even begin, with Mayer’s speculations and Joule’s experimental
facts. Several of Kuhn’s simultaneous discoverers were earlier, although
more tentative, than Joule and Mayer. In the late 1840s, after both men
had made their most important contributions, the energy concept was still only
about half understood; the modern distinction between the terms force and energy
had not even been made clear. Helmholtz, Clausius, and Thomson still had
fundamentally important contributions to make.
Those who spend their time fighting priority wars should forget their individual
claims and learn to appreciate a more important aspect of the sociology of
science: that the scientific community, with all its diversity cutting across race,
class, and nationality, can, as often as it does, arrive at a consensus acceptable
to all. The final judgment in the Joule-Mayer controversy teaches this lesson. In
1870, almost a decade after the last Tyndall or Tait outburst, the Royal Society
awarded its prestigious Copley medal to Joule—and a year later to Mayer.