Physics · Mechanics · Grade 7

History of physics: al-Biruni, Ulugh Beg

How did al-Biruni measure the density of gold, and Ulugh Beg the latitude of Samarkand?

The situation

A thousand years ago, al-Biruni, who was born in Khorezm, weighed gold, silver and precious stones on a balance, and also weighed the water they displaced — and compiled a table very close to modern values. Four centuries later, Mirzo Ulugh Beg had a sextant of almost 40 metres radius built in Samarkand and measured the noon height of the Sun throughout a whole year. Today this tradition is carried on by the Large Solar Furnace in Parkent and the research reactor in the town of Ulugbek. What instruments did they measure with, and how accurate were the results?

Topic

History of physics: scientists of Central Asia. How al-Biruni measured density, Ulugh Beg's sextant and al-Farghani's nilometer

Key ideas

Relative density
Meridian sextant and latitude
Physics in Uzbekistan

Formulas

s = \frac{P_{1}}{P_{3}} = \frac{ρ}{ρ_{water}}

Relative density (al-Biruni’s method): $P_{1}$ is the weight in air, $P_{3}$ is the weight of water displaced by the sample.

\frac{1}{ρ} = \frac{x}{ρ_{A u}} + \frac{1 - x}{ρ_{A g}}

A gold–silver alloy: the volumes add up, and $x$ is the mass fraction of gold.

h = 90^{\circ} - φ + δ

The noon height of the Sun: $φ$ is the latitude of the place, $δ$ is the declination of the Sun ( $- ε \leq δ \leq ε$ ).

φ = 90^{\circ} - \frac{h_{summer} + h_{winter}}{2}, ε = \frac{h_{summer} - h_{winter}}{2}

Latitude and the obliquity of the ecliptic from measurements at the two solstices.

q = σ T^{4} \Rightarrow T = \sqrt[4]{q / σ}

The equilibrium temperature of a sample at the focus of a solar furnace: the absorbed flux is balanced by radiation (a grey body, no convection); $σ = 5.67 \cdot 10^{- 8}$ W/(m²·K⁴).

Theory

Al-Biruni: knowledge begins with measurement

Abu Rayhan al-Biruni was born in 973 on the outskirts of the city of Kath in Khorezm and spent the end of his life in Ghazni (sources give the year of his death as anywhere from 1048 to 1052). He insisted that precious stones should be told apart not only by colour but also by their specific gravity and hardness. For this he made a conical vessel himself: the vessel is filled with water, and the water displaced by the immersed sample runs through a side tube into the pan of a balance and is weighed. The ratio $P_{1} / P_{3}$ is the density of the sample relative to water. At the beginning of the 12th century al-Khazini, who worked in Merv, described al-Biruni’s vessel in “The Book of the Balance of Wisdom” (1121) and entered al-Biruni’s results into his table (correcting some and adding his own measurements): gold 19.05 (now 19.32), mercury 13.56 (13.55), lead 11.32 (11.34). The value for gold in the table is the average of ten measurements: water of a volume equal to 100 mithqals of gold weighed from 5 mithqals 1 danaq 1 tassuj to 5 mithqals 2 danaqs. Try it in the experiment: with a small sample, the smallest stone — 1 tassuj — gives a noticeable error, so the sample should be as large as possible (according to the sources, al-Biruni also recommended this). This is exactly what lies at the basis of the secular scientific outlook: measurement, repeated checking and analysis of error. Al-Biruni also noted that the speed of light is incomparably greater than the speed of sound. For more on density and flotation, see the “Mass and density” and “Why doesn't a ship sink?” experiments.

The Ulugh Beg Observatory and the stages of astrophysics

Mirzo Ulugh Beg (1394–1449) had a three-storey observatory built in the 1420s on a hill near Samarkand. Its main instrument was the Fakhri sextant, dug into the ground in the plane of the meridian: its radius is about 40 m (40.04 m in the sources), so 1° of the arc is almost 70 cm and 1′ almost 1.2 cm. At noon a ray of sunlight passes through the aperture at the centre of the arc (at the top) and throws an image of the Sun on the arc, and its height is read from the scale: in summer the image falls close to the bottom of the trench, in winter higher up. Half the difference between the heights at the summer and winter solstices is the obliquity of the ecliptic $ε$ , and their mean gives $90^{\circ} - φ$ . Ulugh Beg found ε = 23°30′17″ (the true value for that epoch was ≈ 23°30′48″) and the latitude of Samarkand φ = 39°37′33″ (today ≈ 39°40′). Atmospheric refraction makes the Sun appear slightly higher — more so when it is low; switch it off in the experiment and see how the result changes. The catalogue in the tables of the “Zij-i Sultani” (1437) contains about 1000 stars (from 992 to 1018 in the sources). Later stages: the telescope (Galileo, 1609–1610), spectral analysis (Kirchhoff and Bunsen, 1859–1860), galaxies and the expansion of the universe (Hubble, 1924–1929), and today’s space telescopes.

Al-Farghani, Ibn Sina and the history of optics

The book “Elements of Astronomy” by Ahmad al-Farghani (9th century) was translated into Latin in the 12th century, and the author became known in Europe as “Alfraganus”. According to the sources, in 861 he supervised the building of a new nilometer on Roda (Rawda) Island in present-day Cairo. A nilometer works as communicating vessels: the well is connected to the river by tunnels, so the water level in it equals the level of the river ( $p_{0} + ρ g h$ is the same on both sides) and is read from the cubit marks on the central column. According to tradition, a flood of 14 cubits was considered sufficient, and 16 cubits a sign of an abundant harvest. Ibn Sina (980–1037, born near Bukhara) in “The Book of Healing” explained the motion of a thrown body by the “inclination” (mayl) imparted to it and held that, without external resistance, this inclination is preserved indefinitely — a thought close to the idea of inertia. The history of optics: Ibn al-Haytham (11th century) explained vision by light coming from an object to the eye; Newton regarded light as a stream of particles, Huygens as a wave; Young’s interference (1801–1803) showed its wave nature, Maxwell’s theory (1860s) showed that it is an electromagnetic wave, and Einstein’s photon (1905) showed its quantum nature.

Stages of atomic and nuclear physics, the scientific and technological revolution

Radioactivity (Becquerel, 1896) and the electron (Thomson, 1897) showed that the atom is not indivisible. Rutherford’s experiment (1909–1911) revealed the atomic nucleus, while the Bohr model (1913) and quantum mechanics (1925–1927) explained the electron shells. The neutron (Chadwick, 1932) clarified the composition of the nucleus; the fission of the uranium nucleus (Hahn and Strassmann, 1938) and the first nuclear reactor (Fermi, 1942) began nuclear power. From the middle of the 20th century the results of physics began to pass into technology very quickly — reactors, the transistor (1947), the laser (1960), computers: this is called the scientific and technological revolution. Elementary particle physics is described today by the “Standard Model”.

Physics in Uzbekistan: schools, institutes, results

The Physical-Technical Institute was founded in November 1943; on the basis of its departments the Institute of Nuclear Physics (1956), the Institute of Electronics (1967) and the “Physics–Sun” Scientific Production Association (1987; 1986 in some sources) came into being. Scientists who created scientific schools: U. A. Arifov (1909–1976) — physical electronics (the interaction of ions with the surface of a solid), director of the PTI and in 1956–1962 director of the INP; S. A. Azimov (1914–1988) — cosmic rays and high-energy physics, the PTI now bears his name; S. V. Starodubtsev (1914–1967) — radiation solid-state physics, one of the organisers of the INP. The VVR-SM research reactor of the INP was started in September 1959 at a power of 2 MW and upgraded to 10 MW in 1978–1980 (sources give different years). At the reactor and cyclotrons, isotopes for medicine are produced (technetium-99m generators, iodine-131 and others), gold in ore is determined by neutron activation analysis, and silicon is doped with neutrons — nuclear physics in the national economy. The Large Solar Furnace in Parkent: construction began in 1981 and it was commissioned in the summer of 1987: 62 heliostats, a 54 × 42 m concentrator (10 700 mirrors), a power of 1000 kW, and up to 3000 °C at the focus. According to many sources, on 26 July 1928 in Tashkent B. P. Grabovsky and I. F. Belyansky transmitted a moving image electronically with the “Telephot” apparatus, which is why Tashkent is called one of the birthplaces of television; historians dispute who was first in electronic television (V. Zworykin, F. Farnsworth) — more in the “Radio communication and radar” experiment.

What the model simplifies

1 mithqal ≈ 4.25 g is taken (it varied with period and region); water temperature 20 °C; the smallest weight of the balance is 1 tassuj. The motion of the Sun uses a two-term equation of the centre, with dates in the modern calendar; the obliquity of the ecliptic takes its value for 1437; refraction uses Bennett’s formula. The observatory and sextant are an approximate reconstruction, and the arc of the sextant is taken to cover altitudes of 20°–80°. The hydrography of the Nile is simplified, 1 cubit ≈ 0.5 m. In the solar furnace the sample is a grey body (absorptivity = emissivity), the spot at the focus is Gaussian, mirror and beam losses are covered by an efficiency of ≈ 0.55, direct radiation follows the Meinel–Laue model, the sample is a disc 3 mm thick, and convection is 20 W/(m²·K).

Did you know?

Al-Khazini writes that al-Biruni made the neck of the conical vessel so narrow that even a single grain of millet noticeably changed the water level; and he bent the side tube and made holes in it so that the water would not hang in it.
The exact site of the Ulugh Beg Observatory was unknown for a long time: its remains were found in 1908 by the archaeologist V. L. Vyatkin. The underground part of the Fakhri sextant survives to this day.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.