**Ten decimal places of are sufficient to give the circumference**

**of the earth to a fraction of an inch,**

**and thirty decimal places would give the circumference of the visible universe**

**to a quantity imperceptible to the most powerful microscope.**

**~Simon Newcomb**

Today is the 192nd day of the year; 192 is the smallest number that together with its double and triple contain every digit from 1-9 exactly once..*Number Gossip

**EVENTS**

**1663**John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid’s parallel postulate. See W. W. Rouse Ball, Mathematical Recreations and Essays, 6th edition, pp. 314– 315.*VFR

**1686**Leibniz published his ﬁrst paper on the integral calculus in Acta eruditorum.*VFR This paper contains the first appearance in print of the elongated s integral notation used today. He had used the symbol earlier in a manuscript on Oct 29, 1675.

**1700**Royal Prussian Academy of Sciences at Berlin founded. Leibniz was primarily responsible for the founding and directed it for sixteen years. [HM 2, p. 310; American Journal of Physics, 34(1966), p. 22]*VFR

**1731**Alexis-Claude Clairaut elected to the French academy. He was only eighteen. *VFR

**1738**Isaac Greenwood, the ﬁrst Hollis Professor at Harvard, was “ejected” from his chair for drunkenness. [I. B. Cohen, Some Early Tools of American Science, p. 36.] *VFR

**1811**Italian scientist Amedeo Avogadro published his memoire about the molecular content of gases. *TIS

**1814**Amp`ere submitted a paper on general solutions of diﬀerential equations. It contains thought-provoking remarks and interesting examples which had to wait several decades for proper understanding and recognition. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800– 1840, pp. 700ﬀ, 1389]*VFR

1859 The Current Big Ben (the bell) is first heard ringing in the Westminster clock tower. Why Big Ben? After Benjamin Hall (1802-67). In Aug 1856 the bell, with Hall's name inscribed on it, was cast, but cracked after tests in October 1857. The substitute was also defective but worked sufficiently well to be hung in Oct. 1858. Named Big Ben, it was first heard on 11 July 1859. Two months later it too cracked & fell silent for 4 years; it was repaired with help of Sir George Airy, astronomer royal, & rings to this day. *

**Oxford DNB**

**@ODNB**

**1976**K&E produced its last slide rule, which it presented to the Smithsonian Institution. A common method of performing mathematical calculations for many years, the slide rule became obsolete with the invention of the computer and its smaller, hand-held sibling, the calculator. (*

*This Day in Histor*y-Computer History Museum)

**1979**U.S. space station, Skylab, re-entered the Earth's atmosphere. It disintegrated, spreading fragments across the southeastern Indian Ocean and over a sparsely populated section of western Australia, where a cow died after being struck by a piece of falling debris. *TIS (

*Proving the potential effectiveness of weapons in space?*)

**In 1991**, a solar eclipse cast a blanket of darkness stretching 9,000 miles from Hawaii to South America, lasting nearly seven minutes in some places. It was the so-called eclipse of the century. A total solar eclipse - the moon passing between the sun and the earth - is the moon's shadow cast on the casting its shadow on the earth's surface. Total eclipses occur almost once per year, but are often over an ocean or remote countries. The solar eclipse on July 11, 1991, was a thrill for scientists. It traveled over the several astronomical observatories on the top of Mauna Kea. Their 14,000 feet elevation was actually above the cloud level, which obstructed the view for those below. *TIS

**2011**On this day "one year" ago German astronomer Johanne Galle discovered Neptune ... One Neptunian year that is! * mathematicus Thony Christie; On July 11, 2011, Neptune completed its first full barycentric orbit since its discovery on September 23, 1846, *Wik

**BIRTHS**

**1732 Joseph Jérôme Le Français de Lalande**, was a an astronomer, born in Bourg-en-Bresse, France. He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his

*Traité d'astronomie*in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS

**1811 Sir William Robert Grove**, British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS

**1857 Sir Joseph Larmor**born in Magheragall, Ireland.*VFR Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS

*today in Science also gives Binet's birthdate on July 11th, with a different description:*French psychologist who was a pioneer in the field of intelligence testing of the normal mind. He took a different approach than most psychologists of his day: he was interested in the workings of the normal mind rather than the pathology of mental illness. He wanted to find a way to measure the ability to think and reason, apart from education in any particular field. In 1905 he developed a test in which he had children do tasks such as follow commands, copy patterns, name objects, and put things in order or arrange them properly. He gave the test to Paris schoolchildren and created a standard based on his data. From Binet's work, "IQ" (intelligence quotient), entered the vocabulary. The IQ is the ratio of "mental age" to chronological age, with 100 being average.)

**1890**

**Giacomo Albanese**(11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in São Paulo, Brazil, in 1936. *Wik

**1902 Samuel Abraham Goudsmit**Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*TIS

**1922 J. W. S. Cassels**initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group,

*if*it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods.

His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik

**DEATHS**

**1382 Nicole Oresme**was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series. *SAU

Oresme was Bishop of Liseux and died there, but I was recently (2011) at the Cathedral and cold find no mark of his life there.

"His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the*Catholic Encyclopedia onlineintensio(the degree of heat at each point) and theextensio(e.g., the length of the heated rod): these two terms were often replaced bylatitudoandlongitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on thelatitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to thelongitudowas the abscissa at a given point, and a perpendicular at that point, proportional to thelatitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring thelongitudoandlatitudovary. Hence he defineslatitudo uniformisas that which is represented by a line parallel to the longitude, and any otherlatitudoisdifformis; thelatitudo uniformiter difformisis represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.

Besides the longitude and latitude of a form, he considers themensura, orquantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A formuniformiter difformishas the same quantity as a formuniformisof the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitudeuniformiter difformisbecame the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles."

**1733**

**Jakob Hermann**was a Swiss mathematician who made contributions to dynamics. *SAU

**1807**

**George Atwood**was an English mathematician best known for his invention of a low-friction pulley system.*SAU

**1871 Germain Sommeiller**French-Italian engineer who built the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorised on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS Note his death was only a few months before the opening of his great project.

**1909 Astronomer and mathematician Simon Newcomb**died in Washington D.C. He was such a revered scientist that President Taft attended his funeral.*VFR Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS

Newcomb is buried in Arlington National Cemetery

Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.

"The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention." He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy."

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM = This Day in History, Computer History Museum