Video: The Michelson-Morley Experiment,
by David L. Goodstein1 |
Popular Fallacies in the History of Science
(2002-10-08) Heliocentric "Copernican" System
Did the idea of an heliocentric system originate with Copernicus?
No. The idea is far more ancient than that...
of Pontus (387-312 BC)
deserves credit for suggesting that the Earth rotates around an axis,
he did not yet place the Sun at the center of the Solar system
(in spite of what some reports are still stating).
Copernicus (1473-1543) himself credits
of Samos (c.310-230 BC) for the idea of an heliocentric system.
This heliocentric idea is not explicited in the only surviving work of Aristarchus,
where the distances and sizes of the Moon and the Sun are
However, Aristarchus makes it clear that he estimated the Sun
to be much bigger than the Earth (although he still underestimated
its true size). This may indeed have suggested to him that the smaller body
ought to be revolving around the larger one.
Actually, the heliocentric views of Aristarchus are precisely known to us from the
short account given in "The Sand Reckoner"
by his illustrious (younger) contemporary,
Archimedes of Syracuse (287-212 BC).
Incidentally, Archimedes was then seeking
to present as "nonsensical" the belief in an
infinite Cosmos, which Aristarchus advocated...
Plutarch (c. 45-125) reports that
Seleucus of Seleucia
(born c. 190 BC) was championing the heliocentric system
and teaching it as an established fact, in the second century BC
(Seleucia was an important Greek city
in Mesopotamia, on the west bank of the
At that exact same time, however,
of Rhodes (190-120 BC) reverted to the geocentric belief
and was instrumental in killing the heliocentric idea altogether
Little Heath (1861-1940)].
The idea was strongly suppressed by
Reviving it took more than a little courage from
the early followers of Copernicus.
Tell me, why do people always say it was natural for Man to assume that the Sun
went round the Earth, rather than that the Earth was rotating?
Obviously, because it just looks as though the Sun is going round the Earth.
Well, what would it have looked like, if
it had looked as though the Earth was rotating !?
(in TED talk by Richard Dawkins
(2003-10-15; e-mail) Galileo's Assistants
Who was Galileo's assistant for his famous experiment?
The legendary experiment, which allegedly took place at the
Leaning Tower of Pisa, consisted in dropping two different
weights simultaneously from the top of the Tower and supposedly
recording their simultaneous arrivals on the ground...
Well, one of Galileo's assistant, Vincenzio Viviani (1622-1703),
did play a major role in this, but not in the way you might expect, as
Viviani was not even around to witness the event, if it ever occurred!
Some Assistants and/or Noted Disciples of Galileo's
When he became Galileo's assistant in October 1638,
Viviani was only a 16-year old youth from Florence, whose promising aptitude for
mathematics had earned him the commendation of Galileo's patron,
the Grand Duke Ferdinand II of Tuscany.
By that time, the ageing Galileo had already lived under house arrest for 5 years
in Arcetri. He had lost his eyesight in 1637
and he welcomed the live-in presence of the devoted Viviani, who wrote and read for him.
When Galileo died in the evening of January 8 of 1642, he was surrounded
by only three people: His own son, Vincenzio Galilei (1606-1649),
his junior assistant Vincenzio Viviani and his famous new
senior assistant, Evangelista Torricelli, who had joined him only weeks before:
Evangelista Torricelli (1608-1647)
an orphan who studied at the University of Sapienza under a former student
and close friend of Galileo's, Benedetto Castelli (1578-1643).
Torricelli served as Castelli's secretary from 1626 to 1632.
According to Dava Sobel (author of the bestseller "Galileo's Daughter")
Torricelli had first written to Galileo in the summer of 1632
to tell him how he had been converted to the Copernican views by reading Galileo's own
Dialogue on the Two Chief World Systems, Ptolemaic and Copernican, the very book
which would seal the Inquisition's case against Galileo in 1633
(and have him condemned to spend the rest of his life under house arrest).
In 1640, Torricelli wrote a treatise on the motion of bodies
(Trattato del Moto) in which he described experimental evidence for
the laws of falling bodies expressed by Galileo.
As he was dying and needed help to polish his final scientific thoughts,
Galileo made Torricelli his assistant in October 1641.
When Galileo passed away a few weeks later,
Torricelli succeeded him as professor at the Florentine Academy and as
court mathematician to the Grand Duke Ferdinand.
Torricelli kept working with Vincenzio Viviani, Galileo's younger assistant.
In 1643, the two men invalidated Galileo's own theory about the inability
of aspiration pumps to raise water above a certain height
[of less than 10 m]. Torricelli and Viviani
suspected that the limited tensile strength of water was not
at fault, despite what Galileo had conjectured, but that the weight of the liquid
column was of crucial importance.
They transposed the effect to mercury and observed that if a mercury-filled glass
tube is inverted into a bowl of mercury without letting any air in,
then the level of mercury in the tube stabilizes at a height of about 760 mm
over the level of the liquid in the bowl.
In 1644, Torricelli correctly stated that the cavity above the mercury in the
tube contains "absolutely nothing" and that the mercury is pushed up
the tube by the pressure of the air in the atmosphere, which varies slighlty from
day to day. Torricelli is thus remembered as the inventor of the
(Note that the "Torricellian vacuum" in the tube actually contains mercury vapor at
extremely low pressure, but this is largely irrelevant.)
When Torricelli died in 1647, Viviani suceeded him in the position Galileo
had occupied only a few years earlier.
In 1654, a dozen years after Galileo's death,
Viviani began writing the first biography of Galileo.
He clearly embellished things a little...
In particular, the colorful narration of the experiment at the
Leaning Tower of Pisa
is a fiction invented by Viviani...
The Leaning Tower of Pisa and the Alleged "Experiment"
What the Italians call "la Torre pendente di Pisa"
is a bell tower, whose seven bells were used until 1950.
The architect Bonnano Pisano began its
construction on August 9, 1173 in the Campo dei Miracoli
(Pisa's "Field of Miracles").
When the building reached the 3rd level (about 10 years later),
its leaning was already pronounced, and construction stopped for 90 years.
The main tower was completed between 1275 and 1284
by Giovanni Di Simone, who compensated for the
tilt by giving the building a slight banana shape.
The architect Tommaso Pisano (son of Andrea Pisano)
finally added the top belfry between 1350 and 1372.
In Galileo's times, more than two centuries later,
the Leaning Tower of Pisa was pretty much what it is today:
A building of about 14 700 000 kg
rising 58.363 m above its foundations,
with a 4 m overhang that would increase steadily
(at a rate of about 1.2 mm per year)
if it was not for regular heroic countermeasures...
Galileo's "famous experiment" at the Leaning Tower of Pisa
probably never took place. Galileo himself never claimed to have performed the
deed, and the fantastic decorum described by Viviani is even more unlikely.
The experiment would have been largely inconclusive anyway,
except to disprove the gross misconception [wrongly] attributed to
according to which the speed of falling objects ought to be proportional
to their weights (this much is easily proven wrong by less dramatic experiments which
Galileo did perform).
Galileo may have meant to do the grand experiment,
but the idea probably occurred to him at a time when it could not be conveniently
carried out, because he no longer lived next to the Tower:
Galileo moved from Pisa to Padua in 1591.
He had began to study falling bodies only two years earlier, in 1589.
Three years earlier, in 1586, the Dutch engineer Simon Stevin
had already accomplished the key experiment by releasing simultaneously,
from a height of 30 feet, two very different pieces of lead (1 pound and 10 pounds)
and observing that the sounds of their impacts "could not be separated".
For the record, such experiments only "work" properly in
where a feather and a ball of lead do fall at the same rate.
(Otherwise, a given shape, size and speed imply a certain value of the
air resistance which does constitute a lesser percentage of the weight
of an heavier object.)
Astronaut David R. Scott successfully performed Galileo's experiment
(using a feather and a hammer)
on the lunar surface, on August 2, 1971
The same result is routinely demonstrated [at a much lesser cost]
with an evacuated sealed tube containing two very different objects,
usually a feather and a coin...
Other problems exist when conducting such experiments with the "technology"
of Galileo's time, including a curious systematic error (due to muscle fatigue)
when people are attempting to release simultaneously balls of different weights.
A tribute to the observational skills of Galileo was that he recorded negative
results to similar experiments which could be explained this way...
So much for the simplicity of legendary "experiments".
Was Newton really born the year Galileo died?
No. Galileo died 361 days before the
birth of Newton.
The death of one and the birth of the other occurred in different Julian years
(1641 and 1642)
and in different Gregorian years (1642 and 1643).
The year is the same (1642) only when the death of Galileo is recorded
in the Gregorian calendar (then prevalent in Italy) and the birth of Newton
is recorded in the Julian calendar (still prevalent in England at the time).
Another complication may arise for Julian dates between January 1 and March 24
(included) recorded in England before 1752.
The legal year in England, under the old [Julian] calendar, changed on
In other words, Newton was 6 days old on December 31, 1641 and clearly 7 days old on
the following day, which was legally January 1, 1641.
On the other hand, Gregorian years have always been incremented on January 1.
To disambiguate the relevant dates, it's customary to specify either "O.S."
(Old Style) or "N.S." (New Style) after the year number.
For example, the birthdate of Joseph Priestley
is properly given as:
Wednesday, 13 March 1733 (O.S.)
Priestley himself would have said that he was born in 1733.
Nevertheless, any consistent chronological list of scientists should indicate 1734 as the year
of Priestley's birth (the exact Gregorian date was 24 March 1734 ).
Primitive Roman calendars
evolved into a somewhat variable system which featured 12 short months and,
on some years, a thirteenth month
(called either Intercalaris or Mercedonius)
whose length was ultimately decided politically...
This dubious system was replaced by an early form of the
introduced by Julius Caesar in 45 BC.
After a rough start and too many leap years, the Julian calendar
was given its final form by Augustus, and every fourth year was made a leap
year starting with AD 8.
Our current calendar is only a slight modification
of the latter Julian calendar.
It's known as the Gregorian calendar because it was introduced under the
authority of Gregory XIII, né Ugo Boncompagni (1502-1585),
who was Pope from 1572 to 1585.
The Gregorian reform of the calendar was actually engineered by the astronomer
(1538-1612) after preliminary work by
The aim was to make seasons correspond permanently
to what they were under the Julian calendar in AD 325,
at the time of the First Ecumenical Council of the Christian Church,
Council of Nicea, when rules were adopted for the date of
(usually, the first Sunday after a full moon occurring no sooner than March 21).
10 days were dropped in 1582 (October 15 followed October 4)
and new rules were devised to have only 97 leap-years in 400 years
(instead of 1 in 4).
adopted the "new" calendar only much later.
In particular, the earliest valid Gregorian date in England
(and in what was then known as the American Colonies) is September 14, 1752,
which followed September 2, 1752 (the discrepancy had
grown from 10 to 11 days by that time, because the year 1700 was not a leap year
in the Gregorian calendar).
This happened more than a century after Newton's birth,
which was thus still recorded as Christmas day of 1642,
although the year in Italy was already 1643.
On the other hand, it is correct to remark that
was born (January 8, 1942) exactly 300 years after the death of Galileo
(January 8, 1642) since both events were recorded in the same Gregorian calendar.
This is the following relation between the vectorial and scalar potentials A
and f, which would otherwise be defined with more leeway.
In a classical context, this equation has some aesthetic appeal,
as it makes the d'Alembertians of A and f
respectively proportional to the density of current and the density of charge...
In a quantum context not anticipated by Lorenz at the time,
the potentials have a real significance of their own,
which is happily consistent with that gauge :
[ In SI units, or Giorgi's MKSA system.]
The thing is very often misspelled "Lorentz Gauge" (with a "t") because of
a fallacious attribution to Hendrik Antoon Lorentz
(1853-1928; Nobel 1902).
The relation was published in 1867 by the Danish physicist
Ludwig V. Lorenz (1829-1891).
The Danish spelling is Ludvig Valentin Lorenz.
At the time, the future Dutch physicist
H.A. Lorentz was only 14 years old.
Ironically, it turns out that Ludwig Lorenz is best remembered for the relation he
established in 1880, building on earlier work (1878)
by the young H.A. Lorentz
about the theoretical index of refraction of a dielectric substance.
This result is now known as the
Spelling bee, anyone?
As the Internet grows, are authors getting it right ?
Before 2008, I was assuming that nobody used both spellings in the same page,
which is not quite true. Some Internet authors either discuss both spellings
(like I'm doing here) or they think it's a good idea to let people discover
their pages with either spelling...
(Others simply make an occasional involuntary typo.)
All told, that remark increases slightly the percentage of "correct" pages
(i.e., the ratio of pages containing the correct spelling to pages containing either spelling)
as given by the following formula, where R, W and B are the numbers of pages containing
the right spelling, the wrong one and both (respectively):
R / (R + W - B) = 1 / [ 1 + (W - B) / R )
The right-hand-side is just a trick to enter each number only once...
It also goes to show that B merely acts as a deduction from W.
If we counted as correct just the pages which have only the right
spelling, B would be like a deduction from R instead.
Different numbers are for different Google snapshots taken on the same day.
They indicate that the quantitave result of Google queries is to be taken with a grain of salt.
If we assume that the pages which quote the wrong spelling have remained a fixed portion
(3%) of the pages which properly discuss the Lorenz gauge,
then we can estimate that there were only about a dozen such pages back in 2003.
The present page was one of the happy few!
(2002-10-08) On the Origins of the Special Theory of Relativity
Was Einstein the first to formulate the (Special) Theory of Relativity?
The secret to creativity is knowing how to hide your
sources. Albert Einstein (1879-1955)
What is now known as the
Theory of Relativity
was first completely formulated by the prolific French mathematician
J. Henri Poincaré (1854-1912), who published key results with
a relativistic perspective in 1898, 1900, 1904 and on June 5, 1905.
Albert Einstein discovered the whole thing independently and published his original
paper on the subject on
June 30, 1905.
Einstein later added the adjective "special" to describe this initial theory,
to the 1915 theory of General Relativity,
his relativistic theory of gravitation (of which Einstein stands as the
undisputed sole author).
Neither Einstein nor Poincaré ever quoted each other on the subject.
Both, however, often cite
Hendrik A. Lorentz (1853-1928) who put forth the relevant
coordinate transform in 1899 and 1904,
incorporating the so-called FitzGerald-Lorentz contraction, which had been
George FitzGerald (1851-1901) in 1889
(and, independently, by Lorentz himself in 1892)
to explain the negative result of the
experiment of 1887.
Lorentz himself credited
Sir Oliver Lodge (1851-1940) for
first publishing the idea (in 1893).
The full Lorentz transform was first proposed in
1897 by Joseph Larmor (1857-1942)
of Ireland (who is credited for the discovery, in the same year, of the
for the power radiated by an accelerated charge).
10 years earlier (in 1887)
Woldemar Voigt (1850-1919)
had proposed a coordinate transform which explained the Michelson-Morley result
(and the transverse Doppler shift )
but featured an erroneous overall scale factor implying some asymmetry between
the stationary and the moving system, against relativistic principles.
Yet, in hindsight, Voigt's idea of involving time as a coordinate was a key breakthrough.
H.A. Lorentz and Voigt were in touch, but it took years
for Lorentz to adopt this viewpoint and find a
correct transform with the desirable symmetry.
Voigt also introduced modern tensors into physics,
a key element in Einstein's own General Theory of Relativity.
The symbol "c" for the speed of light (Einstein's constant)
was introduced in 1894 by a famous student of Voigt's, Paul Drude (1863-1906).
Drude used "c" for electromagnetism, but in an optical context he retained the symbol "V"
which had been introduced by James Clerk Maxwell.
Einstein himself used "V" until 1907.
The famous equation E = m c 2 has been spotted
several times times before Albert Einstein proposed it, in September 1905.
Such reports include:
1904: Friedrich Hasenöhrl (1874-1915) a teacher of
The Special Theory of Relativity did not take off until 1908, when
Max Planck (1858-1947) put his considerable weight in the balance and wrote
a paper on the subject.
The same year,
Minkowski expresssed the Maxwell-Lorentz equations [of electromagnetism]
relativistically in tensor form,
and showed that Newton's theory of gravity was not consistent
with Special Relativity.
The whole controversy
may have been one of the reasons why Relativity was not
mentioned in 1921 when Einstein was awarded the Nobel prize.
Instead, Einstein was officially rewarded for his 1905 explanation of the laws of
the photoelectric effect, which may be construed as a
discovery of the photon.
In 1912 (the year Poincaré died)
had even proposed that Lorentz and Einstein
share the Nobel prize for Special Relativity, because:
[...] the merits of both investigators [are] comparable.
Some authors have felt that Einstein's huge fame was not entirely deserved, but calling him
is certainly not fair: Just like any other genius in history,
Albert Einstein had to build on the work of his elders. Period.
Most of Einstein's precursors were about 25 years older than himself.
They were all the heirs of Maxwell
(1831-1879) who died the year Einstein was born...
Maxwell's key contribution was his set of
differential equations unifying electricity and magnetism,
and predicting electromagnetic propagation at a fixed celerity.
Their mathematical form seemed to make them only valid in some fixed "aether".
Relativity was born with the gradual realization that
Maxwell's equations should hold unchanged
even for observers in relative uniform motion.
The nontrivial coordinate relations postulated by the
Lorentz transform allowed just that.
Before Maxwell, those who paved the road include a few French physicists:
Augustin Jean Fresnel (1788-1827)
was born on the de Broglieestate.
(His mother was the daughter of the overseer. His father worked for a few years
as an architect for the family of the future
Fresnel was educated at Caen and at the
Ecole Polytechnique (X) in Paris
[just like this writer, on both counts, incidentally].
Fresnel is best remembered for the type of lenses now named after him
(featuring concentric grooves) which are used in lighthouses,
spotlights, flat plastic magnifiers, etc.
Among other fundamental scientific investigations,
Fresnel showed that two light beams polarized in perpendicular planes
do not exhibit optical interference,
thus establishing the transverse nature of lightwaves
(whereas sound in a fluid is a longitudinal wave).
Fresnel also investigated light in a moving medium:
In this context, we call Fresnel coefficient of drag
a parameter f whose dependence on the refractive index (n)
was found empirically by Fizeau and explained by Einstein:
1 - 1/n2
Armand Hippolyte Louis Fizeau (1819-1896)
discovered the Doppler effect in 1848,
independently of Christian Doppler
(1803-1853) who wrote on the subject in
1842: The effect is sometimes
called Doppler-Fizeau, especially in French texts.
In 1849, Fizeau gave the first direct experimental value of the speed of light,
by using a rotating toothed wheel (Fizeau wheel)
and a distant mirror.
In 1851, he used interferometry to investigate how the speed of a moving liquid affects
the celerity of light propagating in it.
He obtained a result intermediary between what would be expected of a wave
bound to the medium (like sound in a fluid)
and something independent of it.
Einstein explained this relativistically.
Jean Bernard Léon Foucault (1819-1868) is still
remembered for the pendulum experiment named after him,
which detects the rotation of the Earth by mechanical means.
In 1851, he first demonstrated this publicly,
under the dome of the Panthéon in Paris.
Foucault is on record as the inventor of the gyrocompass (1852).
Electric currents induced in a metallic mass (eddy currents) were discovered by
Foucault; they are now often called Foucault currents.
He improved on Fizeau's method to measure the speed of light
(using a mirrored wheel instead of a toothed wheel).
Foucault proved the speed of light to be greater in air than in water,
as is consistent with an undulatory phenomenon.
(2016-11-16) Who really discovered natural radioactivity ?
Abel Nièpce de Saint-Victor discovered radioactivity before Becquerel.
The credit for the discovery of radioactivity
is usually given to Henri Becquerel (1852-1908)
who received half of the 1903 Nobel prize in physics for that.
His celebrated serendipitous discovery entailed processing an unexposed photographic plate which had been
stored in the dark next to
potassium uranyl sulfate. That event took place on March 1, 1896.
However, the very same observation with uranium salts and photographic plates
had been made 39 years earlier (in 1857) by
Nièpce de Saint-Victor (1805-1870) whose first cousin
Nicéphore Niépce (1765-1833)
had invented photography in 1826.
That early discovery was duly heralded as major
at the time (1857) in particular by the chemist
(1786-1889)who was then the superior of Abel Niepce.
Chevreul is one of the
French scientists whose names appear on the Eiffel Tower.
However, tthe World was apparently not quite ready for that yet...
By the time of Becquerel's own discovery (1896) the previous work of
Niépce de Saint-Victor had apparently been all but forgotten...
Curiously enough, one of the few noteworthy physicists who did
notice in due time was Becquerel's own father!
Edmond Becquerel (1820-1891)
fully discussed the future discovery of his son in a book he published in 1868
(La lumière, ses causes et ses effets).
At the time, the younger Becquerel was 16,
but it's hard to believe he never read the book of his father.
The record clearly shows that he had totally forgotten about the book
28 years after its publication, since he never mentioned it.
His father was no longer around to point that out to him...
(2002-10-05) The Oil-Drop Experiment [to measure electron charge]
Did Robert A. Millikan (1868-1953) design the famous experiment which helped him earn a Nobel prize?
Much of the credit should have gone to his graduate student
who was not even named a co-author of the key relevant paper.
Originally, Millikan reproduced an
experiment involving drops of water,
conceived by J.J. Thompson and E. Regener.
On this subject, let's quote
who is sympathetic to Millikan:
Unfortunately the single-droplet method had a serious flaw. The water
evaporated too rapidly to allow accurate measurements. Millikan, Begeman and a new
graduate student named Harvey Fletcher discussed the situation and decided to try to do
the experiment with some substance that evaporated less rapidly than water. Millikan
assigned to Fletcher the job of devising a way to do the experiment using mercury or
glycerin or oil.
Fletcher immediately got a crude apparatus working, using tiny droplets of watch
oil made by means of a perfume atomizer he bought in a drugstore. When he focused his
telescope on the suspended oil droplets, he could see them dancing around in what is
called Brownian motion, caused by impacts of unseen air molecules. This itself was a
phenomenon of considerable current scientific interest. When Fletcher got the busy
Millikan to look through his telescope at the dancing suspended droplets of oil, Millikan
immediately dropped all work on water, and turned his attention to refining the oil-drop
A couple of years later (around 1910) Fletcher and Millikan had produced two
results. One was an accurate determination of the unit electric charge (called e) from
observing the rate of fall or rise of oil drops in gravitational and electric fields, and the
other was a determination of the product Ne, where N is a separate constant called
Avagadro's number. The product Ne came out of observations of Brownian motion.
Millikan approached his student Fletcher with a deal. Fletcher could use a published
paper as his Ph.D. thesis, but only if he was sole author. Millikan proposed that Fletcher
be sole author on the Brownian motion work and that he, Millikan be sole author on the
unit electric charge work. This is the source of the assertion that Millikan mistreated his
graduate students. No doubt Millikan understood that the measurement of e would
establish his reputation, and he wanted the credit for himself. Fletcher understood this
too, and he was somewhat disappointed, but Millikan had been his protector and
champion throughout his graduate career, and so he had little choice but to accept the
deal. The two men remained good friends throughout their lives, and Fletcher saw to it
that this version of the story was not published until after Millikan's death, and after his
Fletcher (1884-1981) himself summarized his collaboration with Millikan
in the June 1962 issue of Physics Today.
There were in fact 5 papers involved; Millikan is named as sole author of
the first (and most important) one, Fletcher is named as the sole author of 2 others
(including the one he used as his doctoral dissertation) and the last two
appeared with both names as joint authors.
(2005-08-19) About Customary Physical Units
Errata about physical units and noteworthy physical quantities.
As we compiled a rather large catalog of physical units over the years,
we found a large number of errors throughout the literature.
They propagate at an alarming rate.
We've lost track of most of the sources, but feel compelled to
post the following list of errata, as a public service.
(If you must know, this list is sorted alphabetically with respect to the
main unit, scale, quantity, or concept involved.)
These have been thoroughly investigated, so we may hope to avoid the same
embarrassment as one author who made a similar claim (about the rarely-used
"poncelet" unit) and got it wrong!
We did pay particular attention to wrong
claims that we found more than once...
At times, it really looks like nobody ever bothers to check mathematical facts.
One particularly startling example is our first entry,
about the Beaufort rating of an 18 mph wind, for which we have yet to find a
single correct table!
An 18 mph wind should be rated "Force 5" (not 4) in the
A square centimeter candle
is 60 candelas (not the other way around).
The mean curvature is the half-sum (not the sum) of the principal curvatures.
One gram of radium has an activity of 9 curies (not just one curie); out of
this, 1/9 is from the direct decay of radium nuclei, 8/9 is from subsequent
decays of all the decay products of radium (the proportions are exact under
"equilibrium" conditions, where the relative concentrations remain constant).
As a unit, the day remains 86400s,
but the "mean solar day" increases.
The density of the Earth is not 5.2, but 5.52 (more precisely,
Ordinary screws and corkscrews are dextrorsum (not sinistrorsum).
A logarithmic spiral's evolute is congruent but usually not equal to itself.
The frigorie (1000 negative gram-calories) is a unit of energy, not power.
According to modern tables for the density of water, the old definition of the
UK gallon implied measurement at about 16.3333°C (61.4°F),
not 15.18°C (since that definition was
enacted at a time when the liter was not exactly equal to a cubic decimeter:
998.859 g/L "then" is 998.887 g/L "now".)
The moment of inertia of the Earth is about
8´10 37 kg×m 2
(not 10 42 ).
A jansky is not a
W/m2/Hz, it is 26 orders of magnitude smaller!
was born in the Gregorian year 1643 (Julian Christmas day 1642).
The "pascal per square meter" is not a unit of pressure; the "pascal" is.
A poncelet is not 100 W, but 980.665 W (100 kgm/s).
The spat (whole sphere) is a unit of solid angle,
it is not a planar angle.
A torr is not quite equal to a
millimeter of mercury (it's 0.14 ppm less).
"Water" units of pressure are conventional
units which do not depend on the actual density of water
(under conditions prevailing during measurement).
A meter of water is defined either as precisely 9806.65 Pa
or roughly 9806.38 Pa
(using a conventional density of either 1 kg/L or 999.972 g/L).
(2007-11-02) The True Face of Adrien-Marie Legendre
A case of mistaken identity.
Before I wrote the first version of this article,
every biography of the great
(1752-1833) showed a lithograph which was also associated
with an unrelated contemporary politician
The godfather of Louis Legendre was "officier de bouche" of the Queen.
Louis himself served as a sailor for 10 years before setting up shop as
a butcher in Saint-Germain-des-Prés (Paris).
He was a leader in the Storming of the Bastille
(July 14, 1789).
In spite of his lack of education and problems with diction, his early enthusiasm for
revolutionary ideas got him elected to the National Convention and he served as
The allegiances of Louis Legendre to various
revolutionary leaders changed several times.
He was already suffering from dementia when he got elected to what would be
his last position, at the Conseil des 500.
(1752-1797) politician unrelated to the
The above lithograph
is signed by François-Séraphin Delpech (1778-1825)
who is also known for his later collaboration with Zéphirin Belliard (1798-fl.1843?)
on a portrait of
the young Adolphe Thiers
The Encyclopedia Britannica
has erroneously presented the above as a reproduction by Delpech of a painting
due to Belliard, although Louis Legendre died the year before Zéphirin Belliard
The Belgian writer
Jacques Noizet correctly identified this picture with portrait number 13
in another lithograph representing the entire political group of Louis Legendre
(les Montagnards) as of 1793.
That picture appears, for example, on page 678 of Dictionnaire d'Histoire de France
The whole issue had been actively discussed on the Internet for several months
before I became aware of the controversy, as
Jean-Bernard François (2007-10-31) quoted my own
thumbnail rendition of the
coat-of-arms of Adrien-Marie Legendre (of which I have since published a better
I then discovered
obscure record showing that the library of the Institut de France
had a portrait of the mathematician Adrien-Marie Legendre, which had been totally
overlooked! It appears in a sketchbook of 73 caricatures
(73 portraits-charge de membres de l'Institut)
next to a similar caricature of Fourier (heads in full color, bodies lightly drawn in pencil).
After securing a great contact at the library of the Institut de France
(from a retired French librarian, Jeanne Refleu,
the widow of my late math teacher Lucien Refleu)
I failed to follow through for several months. I just posted my discovery here,
without fetching the actual picture...
This grabbed the attention of the aforementioned Jean-Bernard François
(a.k.a. Infofiltrage ) who did the legwork and
kindly presented me with a
photograph of the relevant
page from that sketchbook (on 2008-12-28).
Thus, the caricature at right seems to be
the only extant portrait of the great mathematician!
Album de 73
des membres de l'Institut (1820) by
Julien-Léopold Boilly (1796-1874)
(wrongly attributed to his father, Louis-Léopold Boilly, 1761-1845)
Courtesy of Biliothèque de l'Institut de France
In the U.S. at least
the above drawing is clearly in the public domain (as a straight
reproduction of a two-dimensional work
created well before 1888 by someone who died well before 1938).
True Face of Legendre... The word is spreading !
A color picture of the original page depicting
Legendre and Fourier is on the
that issue, with an
by Bill Casselman, graphics editor of the
Notices of the American Mathematical Society (AMS).
2009-11-11: My own prepublication e-mail buzz about the above.
2009-11-14: The full-sized caricature appears automatically on the pages of Wikipedia
dedicated to Legendre, in
A correct tiny thumbnail also appears in the list
of the 72 scientists who have their names on the Eiffel Tower
It is clear that the aforementioned article of Peter Duren in the Notices of the American
Mathematical Society (Dec. 2009) has done more than all previous efforts to
popularize this unique portrait of Adrien-Marie Legendre.
On 20009-11-12 (e-mail) Robin Whitty
wrote: M. Legendre may rest easy in his grave,
although he might feel it ironic that it should be
that particular likeness that the efforts
of 21st century scholars would produce !
a digital painting by an artist identified as
(2008-08-25) Group portrait of 35 major
mathematicians (out of necessity, some faces are purely fictional).
(2015-02-04) Portraits of Ambroise Paré (1510-1590)
Popular pictures don't match the portrait authentified by his descendants.
At left is the painting still most commonly used to evoke the famous surgeon.
At right is the true portrait inherited by his descendants...
The "correct" portrait was unearthed by
Dr. Claude Stéphen Le Paulmier,
who made it the centerpiece of his 1884 biography of Paré, entitled:
D'après de nouveaux documents découverts
aux archives nationales et des papiers de famille (avec un portrait inédit de Paré).
There was at least one question about this (by someone signing "Firmin")
in one printed ancestor of Internet forums:
L'intermédiaire des chercheurs et curieux (1043, 49, p.897, June 1904).
Dr. Le Paulmier obtained that previously unpublished portrait from the archives
of the descendants of Catherine Paré and Claude Hedelin.
He could establish that it was painted just after the second wedding of Ambroise Paré.
(2012-09-16) On the lack of iconography for Apollonius of Perga Apollonius of Tyana is unrelated to the mathematician !
To anyone primarily interested in science or mathematics, there's only one
worth remembering: Apollonius
of Perga (262-190 BC). Just like there's only one
Archimedes worth mentioning.
However, one unrelated
Apollonius of Tyana
became extremely famous, a couple of centuries later, as a religious figure
(which some have likened to Christ).
All coins and statues made in the image of "Apollonius"
are meant to represent that other man, as the slightest bit of research will show...
(2017-12-10) The missing portraits of Robert Hooke (1635-1703).
Did Isaac Newton really destroy them? (Probably not.)
Robert Hooke (1635-1703)
and Isaac Newton (1643-1727)
were major scientific rivals who had been bitterly feuding since 1686.
In 1703, Hooke died and Newton took over the Presidency of the
It seems that Hooke had commisioned at least two portraits
of himself but none of them were ever seen after his death...
At some obscure point in History, someone saw fit to put those two facts together and the
legend was born that Newton had his revenge after his rival's death by unhanging
from the walls of the Royal Society
any portrait of Hooke which had fallen under his care (Newton wasn't a nice man).
In that urban legend, there was supposedly just one such portrait,
thereafter known as the missing portrait of Hooke.
In the milder version of the story, Hooke's portrait was just left to decay unattended in some damp storage.
In the more dramatic version, Newton himself destroyed a portrait bequeathed
to the Royal Society. That's is now part of folklore...
For example, Newton is shown slashing Hooke's portrait in the final scene of
of Thomas Hobbes (produced in 2008-2009 by the
Royal Shakespeare Company)/
My own guess is that Newton had little to do with the missing portrait(s):
There's evidence to suggest that Hooke had thyroid eyes,
which can be responsible for stunning female faces
(e.g., Bette Davis or Susan Sarandon)
as well as uneasing male looks (e.g., Marty Feldmann or
Hooke may have disliked his own appearance so much that he
rejected any portrait of himself as either ugly or inaccurate.
He wouldn't have it either way.
He didn't want to leave a bad image for posterity. Literally.
Hooke's Looks :
Hooke had (at least) two portraits of himself made.
They're both lost.
The entry for 16 October 1674 in Hooke's personal diary gives a clue.
"At Garaways [Coffee House]. Left off taking tobacco — Mr Bonust drew picture."
In this, Hooke probably misspelled the name of
a noted portrait engraver of the time.
We don't know if Bownest's sketch ever got turned into a proper engraving or painting.
Hooke knew several other portraitists, including
Mary Beale (1633-1699) who made a portrait of his
mentor, colleague and friend, Robert Boyle (1627-1691).
However, there is no extant trace of a portrait of Hooke anywhere now.
Neither in the inventory of Hooke's
possessions after his passing nor in the records of gifts made to the Royal Society.
Therefore, we must fall back to several written descriptons of Hooke which say that
he had dark hair, a pointed chin,
prominent bulging grey eyes (bilateral proptosis)
a hunched back and an emaciated figure.
Using two extant written descriptions of Hooke,
the history painterRita Greer
has created a series of modern portraits of Robert Hooke.
She's been volunteeing since her retirement
(in 2003) to restore Hooke's rightful place in History.
The lack of a portrait of Hooke was hindering the proper memorializing of Hooke and
the portraits made by Greer are a welcome remedy.
The picture at left is a close-up of a portrait painted by Greer in 2004.
Robert Hooke (by Rita Greer, 2004)
The Seal of Robert Hooke
An imprint of the seal
of Robert Hooke exists at the County Record Office on the Isle of Wight, next to Hooke's
It presumably bears a likeness of Hooke at the time when he started to wear
on a regular basis (mid to late 1670s).
(2017-12-10) The Involuntary Hoax of
Dr. Lisa Jardine (1944-2015).
Her enduring blunder hinders the memorializing of two major scientists.
Like most biographers of Hooke, the late Lisa Jardine was lamenting
the lack of a portrait of Robert Hooke.
Unfortunately for her, as she was getting her biography of Hooke ready for
publication, it was realized that a painting attributed to Mary Beale (1633-1799)
could not possibly be a portrait of John Ray as previously advertised
(it doesn't look at all like other well-documented portraits of Ray).
Robert Hooke certainly knew Mary Beale. Although we don't know for sure,
it's thus quite possible that Beale was once commissioned by Hooke to do
a portrait of himself.
That flimsy bit of circumstancial evidence was enough of an incentive
to make Dr. Jardine succomb to wishful thinking and jump to the conclusion
that the previously misidentified portrait was the long-lost portrait of Hooke.
She shose to ignore the fact that the picture doesn't fit any
element in the well-known descriptions of Hooke's appearance, dark hair,
emaciated figure, hunched back, pointed chin and --above all-- prominent bulging grey eyes.
After presenting rather flimsy circumstancial evidence, Dr. Jardine threw caution
to the wind and thought she could safely put the full portrait on the cover of a
biography of Hooke, thus offering it to the World as the new
official portrait of Robert Hooke. She wrote:
I propose to claim this portrait as Robert Hooke's until it is proved to me that this is in fact
recognisably a portrait of somebody else. Since I discovered my Hooke I confess that I have
found it much easier to reconjure in my own mind the man to match the image.
I hope my portrait of Hooke will make it possible for the reader of this book to do likewise.
For Hooke, I believe, is a man we should learn to treat with affection, in and for himself,
as well as to admire.
A stunned reviewer called it a hitherto unknown portrait of Hooke.
Jardine's challenge was met as soon as her book was out (and the cover wisely publicised).
It was a very easy thing to do,
as discussed below:
The portrait is merely a faithful reproduction of an earlier
woodcut representing a major scientist of the previous generation
J.B. Van Helmont (1577-1644)
surrounded by his son and their family arms. Positive identification if there ever was one!
The only surprise is that the protrait had not been correctlty identified earlier!
The misidentified picture is still all over the Internet.
Sadly, Jardine's blunder now hinders also the correct depiction
of Van Helmont, who is just as significant for Science as Hooke.
To the best of my knowledge, the late Dr. Jardine never publicly apologized for this.
Nor did the publisher try to minimize the consequences:
The wrong portrait was knowingly put on the spline of the paperback edition (I own a copy).
The non-buldging non-blue right eye is still on the front cover (in a peephole).
The full portait iself is reproduced twic inside twice (once the color plates).
The blunder made on the first edition is nowhere corrected; it's not even mentioned.
This is robbing that portrait of it correct place in the History of Science:
(2017-12-10) Jan Baptist Van Helmont (1577-1644)
Tribulations of a great portrait...
Legend has it that the picture at right once belonged to the Anglo-Irish naturalist
Sir Hans Sloane, first Baronet (1660-1743).
Sloane was elected FRS in 1685 and served as
President of the Royal Society from 1727
(suceeding Newton) to 1741.
He was an avid collector noted for bequeathing his personal collection to the Britsh People,
thus bringing about the foundation of the British Museum (1753).
Watson thought that the portrait had been made around 1674 by
Mary Beale (1633-1699)
and represented the parson-naturalistJohn Ray (1627-1705)
who had spelled his own name John Wray until 1670.
He bequeathed the portrait to the British Museum.
Upon his death, in 1787, they took possession of it, but nobody noticed that
Watson's identification couldn't possibly be correct, as the portrait looks
very different from all known depictions of John Ray.
The mistake was thus allowed to stand for two more centuries...
An etching of the exact same portrait is found in the 1648 edition of...
Lisa Jardine had been looking for the lost portrait(s) of Robert Hooke
for a number of years and she cntracted a terminal case of wishful thiking when she learned
about the mislabeling. She hastily relabeled it a portrait of Robert Hooke without a
shred of evidence (disgarding all pieces of evidence invalidating such a hasty conclusion).
In print, she simply challenged anybody to prove "to her" that it was the portrait of
somebody else. Unexpectedly and unfortunately for her, this was a surprisingly
easy thing to do...
The challenge was met immediately (2004) independently, by
William B. Jensen (University of Cincinatti)
and Dr. Andreas Pechtl
(Johannes Gutenberg University of Mainz).