A Dictionary of Science

compound, Fe2(SO4)3; rhombic; r.d. 3.097; decomposes above 480°C. It is obtained by heating an aqueous acidiÜed solution of iron(II) sulphate with hydrogen peroxide:

2FeSO4 + H2SO4 + H2O2 → Fe2(SO4)3 +

2H2O

On crystallizing, the hydrate Fe2(SO4)3. 9H2O is formed. The acid sulphate Fe2(SO4)3.H2SO4.8H2O is deposited from solutions containing a sufÜcient excess of sulphuric acid.

irradiance Symbol E. The *radiant Ûux per unit area reaching a surface; in SI units it is measured in watts per square metre (W m–2). Irradiance refers to electromagnetic radiation of all kinds,

iwhereas *illuminance refers only to visible radiation.

irradiation Exposure to any form of radiation; often exposure to *ionizing radiation is implied. See also food preservation.

irrational number A number that cannot be expressed as the ratio of two inte-

gers. An irrational number may be a *surd, such as √2 or √3, which can be expressed to any desired degree of accuracy but cannot be assigned an exact value. Al-

ternatively, it may be a *transcendental number, such as π or e. Compare rational number.

irreversibility The property of a system that precludes a change to the system from being a *reversible process. The paradox that although the equations describing the bodies in a system, such as Newton’s laws of motion, Maxwell’s equation, or Schrödinger’s equation are invariant under *time reversal, events involving systems made up from large numbers of these bodies are not reversible. The process of scrambling an egg is an example. The resolution of this paradox requires the concept of *entropy using *statistical mechanics. Irreversibility occurs in the transition from an ordered arrangement to a disordered arrangement, which is a natural trend, since changes in a closed system occur in the direction of increasing entropy. Irreversibility also occurs in processes that violate T symmetry. According to the *CPT theorem, processes that violate CP also violate T and hence

are irreversible. This has been observed in some weak interactions.

irreversible reaction See chemical reaction.

irrigation The provision of water for crops by artiÜcial methods; for example by constructing ditches, pipe systems, and canals. Irrigation can lead to problems when the water leaches trace elements from the soil; selenium, for example, can be toxic to both local fauna and Ûora. Irrigation can also increase the salinity of the soil, if diverted rivers are used to provide the water. Evaporation of surface water leaves a crust of salt, which can drain down to deeper layers of the soil.

irritability See sensitivity.

IR spectroscopy See infrared spectroscopy.

ischium The most posterior of the three bones that make up each half of the *pelvic girdle. See also ilium; pubis.

isentropic process Any process that takes place without a change of *entropy. The quantity of heat transferred, δQ, in a reversible process is proportional to the change in entropy, δS, i.e. δQ = TδS, where T is the thermodynamic temperature. Therefore, a reversible *adiabatic process is isentropic, i.e. when δQ equals zero, δS also equals zero.

Ising model A simpliÜed model of a magnetic system consisting of an array of magnetic spins. Spins may have one of two values and interactions occur with nearest neighbours. There are also random thermal Ûuctuations depending on the temperature of the system. At low temperatures there is a net magnetization as a result of alignment of spins. At high temperature there is no net magnetization. The model was Ürst proposed by the German physicist Ernst Ising (1900–98), who studied the one-dimensional case in 1924. The two-dimensional case for a square lattice was solved exactly by Lars Onsager in 1944. Only approximate solutions have been found for threedimensional models. The Ising model is very important in statistical mechanics and can be used to investigate other types of phase transition.

islets of Langerhans Small groups of cells in the pancreas that function as an endocrine gland. The alpha (or A) cells secrete the hormone *glucagon, the beta (or B) cells secrete *insulin, and the delta (or D) cells secrete *somatostatin. The islets are named after their discoverer, the German anatomist and microscopist Paul Langerhans (1847–88).

iso- PreÜx denoting that a compound is an *isomer, e.g. isopentane (CH3CH- (CH3)C2H5, 2-methylbutane) is an isomer of pentane.

isobar 1. A line on a map or chart that joins points or places that have the same atmospheric pressure. 2. A curve on a graph representing readings taken at constant pressure. 3. One of two or more nuclides that have the same number of nucleons but different *atomic numbers. Radium–88, actinium–89, and thorium–90 are isobars as each has a *nucleon number of 228.

isobaric spin See isotopic spin.

isocline A line on a map or chart joining points or places of equal magnetic dip (see geomagnetism).

isocyanate See cyanic acid.

isocyanic acid See cyanic acid.

isocyanide See isonitrile.

isocyanide test A test for primary amines by reaction with an alcoholic solution of potassium hydroxide and trichloromethane.

RNH2 + 3KOH + CHCl3 → RNC + 3KCl + 3H2O

The isocyanide RNC is recognized by its unpleasant smell. This reaction of primary amines is called the carbylamine reaction.

isodiaphere One of two or more nuclides in which the difference between the number of neutrons and the number of protons is the same. A nuclide and its product after losing an *alpha particle are isodiapheres.

isodynamic line A line on a map or chart joining points or places at which the total strengths of the earth’s magnetic Üeld are equal (see geomagnetism).

isoelectric point The pH of a medium at which a protein carries no net charge and therefore will not migrate in an electric Üeld. Proteins precipitate most readily at their isoelectric points; this property can be utilized to separate mixtures of proteins or amino acids.

isoelectronic Describing compounds that have the same numbers of valence electrons. For example, nitrogen (N2) and carbon monoxide (CO) are isoelectronic molecules.

isoenzyme See isozyme.

isogamy Sexual reproduction involving the production and fusion of gametes that are similar in size and structure. It occurs

in some protoctists, e.g. certain proto- i zoans and algae. Compare anisogamy.

isogonal line A line on a map or chart joining points or places of equal magnetic declination (see geomagnetism).

isolating mechanism Any of the biological properties of organisms that prevent interbreeding (and therefore exchange of genetic material) between members of different species that inhabit the same geographical area. These mechanisms include seasonal isolation, in which the *breeding seasons of the different populations do not overlap; and behavioural isolation, in which different

*courtship behaviour in the populations ensures that mating takes place only between members of the same species. Both these are examples of premating mechanisms. Postmating mechanisms include hybrid infertility and inviability.

isoleucine See amino acid.

isomerase Any of a class of *enzymes that catalyse the rearrangement of the atoms within a molecule, thereby converting one isomer into another.

isomerism 1. (in chemistry) The existence of chemical compounds (isomers) that have the same molecular formulae but different molecular structures or different arrangements of atoms in space. In structural isomerism the molecules have different molecular structures: i.e. they may be different types of compound or they may simply differ in the position of the functional group in the molecule.

Structural isomers generally have different physical and chemical properties. In stereoisomerism, the isomers have the same formula and functional groups, but differ in the arrangement of groups in space. Optical isomerism is one form of

this (see optical activity). Another type is cis–trans isomerism (formerly geometrical isomerism), in which the isomers have different positions of groups with respect to a double bond or central atom (see illustration).

Octahedral complexes can display cis– trans isomerism if they have formulae of the type MX2Y4. Octahedral complexes with formulae of the type MX3Y3 can display a different type of isomerism. If the three X ligands are in a plane that includes the metal atom and the three Y ligands are in a different plane at right angles, then the structure is a mer-isomer (meridional). If the three X ligands are all on one face of the octahedron and the three Y ligands are on an opposite face, then it is a fac-isomer (facial). See also ambidentate; e–z convention. 2. (in physics) The existence of atomic nuclei that have the same atomic number and the same mass number but different energy states.

isomers See isomerism.

isometric 1. (in technical drawing) Denoting a projection in which the three axes are equally inclined to the surface of the drawing and lines are drawn to scale. 2. (in crystallography) Denoting a system in which the axes are perpendicular to each other, as in cubic crystals. 3. (in physics) Denoting a line on a graph illustrating the way in which temperature and pressure are interrelated at constant volume.

isomorphism The existence of two or more substances (isomorphs) that have the same crystal structure, so that they are able to form *solid solutions.

isonitrile (isocyanide; carbylamine) An organic compound containing the group –NC, in which the bonding is to the nitrogen atom.

iso-octane See octane; octane number.

isopoly compound See cluster compound.

isoprene A colourless liquid diene, CH2:C(CH3)CH:CH2. The systematic name is 2-methylbuta-1,3-diene. It is the structural unit in *terpenes and natural *rubber, and is used in making synthetic rubbers.

isospin See isotopic spin.

isostasy The theoretical equilibrium that tends to exist in the earth’s crust. If this equilibrium is disturbed, for example

as a result of erosion or deposition, compensatory movements in the earth’s crust occur: areas of deposition sink, whereas areas of erosion rise. Continental ice sheets have been an important cause of isostatic movements of the earth’s crust. The growth of ice sheets and the resulting additional mass of the ice is compensated by the downward deÛection of the lithospheric plate and the displacement of asthenospheric material (see asthenosphere) beneath it. When the ice melts, the displaced material Ûows back causing the overlying lithospheric plate to rise.

isotactic polymer See polymer. isotherm 1. A line on a map or chart

distinction between them. The use of the word ‘spin’ implies only an analogy to angular momentum, to which isotopic spin has a formal resemblance.

isotropic Denoting a medium whose physical properties are independent of direction. Compare anisotropic.

isozyme (isoenzyme) One of several forms of an enzyme in an individual or population that catalyse the same reaction but differ from each other in such properties as substrate afÜnity and maximum rates of enzyme–substrate reaction (see michaelis–menten curve).

IT (information technology) The use of computers and telecommunications equipment (with their associated microelectronics) to send, receive, store and manipulate data. The data may be textual, numerical, audio or video, or any combination of these. See also world wide web.

iteration The process of successive approximations used as a technique for solving a mathematical problem. The technique can be used manually but is widely used by computers.

Jacob–Monod hypothesis The theory postulated by the French biologists François Jacob (1920– ) and Jacques Monod (1910–76) in 1961 to explain the control of *gene expression in bacteria (see operon). Jacob and Monod investigated the expression of the gene that codes for the enzyme β-galactosidase, which breaks down lactose; the operon that regulates lactose metabolism is called the *lac operon.

jade A hard semiprecious stone consisting either of jadeite or nephrite. Jadeite, the most valued of the two, is a sodium aluminium pyroxene, NaAlSi2O6. It is prized for its intense translucent green colour but white, green and white, brown, and orange varieties also occur. The only important source of jadeite is in the Mogaung region of upper Burma. Nephrite is one of the amphibole group of rock-forming minerals. It occurs in a variety of colours, including green, yellow, white, and black. Important sources include Siberia, Turkistan, New Zealand, Alaska, China, and W USA.

jadeite See jade.

Jahn–Teller effect If a likely structure of a nonlinear molecule or ion would have degenerate orbitals (i.e. two molecular orbitals with the same energy levels) the actual structure of the molecule or ion is distorted so as to split the energy levels (‘raise’ the degeneracy). The effect is observed in inorganic complexes. For example, the ion [Cu(H2O)6]2+ is octahedral and the six ligands might be expected to occupy equidistant positions at the corners of a regular octahedron. In fact, the octahedron is distorted, with four ligands in a square and two opposite ligands further away. If the ‘original’ structure has a centre of symmetry, the distorted structure must also have a centre of symmetry. The effect was predicted theoretically by H. A. Jahn and Edward Teller in 1937.

jasper An impure variety of *chalcedony. It is associated with iron ores and as a result contains iron oxide impurities that give the mineral its characteristic red or reddish-brown colour. Jasper is used as a gemstone.

jaw The part of the vertebrate skeleton that provides a support for the mouth and holds the teeth. It consists of two bones, the upper jaw (maxilla) and the lower jaw (mandible). Members of the Agnatha lack jaws.

Jeans instability Instability in a cloud of gas in space due to Ûuctuations in the density of the gas, causing the matter in the cloud to clump together and lead to gravitational collapse. The conditions under which this occurs were worked out by Sir James Hopwood Jeans (1877–1946) in terms of Newtonian gravity. The analogous analysis of this problem using general relativity theory is the basis of the theory of *structure formation.

jejunum The portion of the mammalian *small intestine that follows the *duodenum and precedes the *ileum. The surface area of the lining of the jejunum is greatly increased by numerous small outgrowths (see villus). This facilitates the absorption of digested material, which is the prime function of the jejunum.

jellyÜsh See cnidaria.

Jenner, Edward (1749–1823) British physician, who is best known for introducing smallpox vaccination to Britain in 1796 (announced two years later), using a vaccine made from cowpox.

jet A variety of *coal that can be cut and polished and is used for jewellery, ornaments, etc.

jet propulsion (reaction propulsion)

The propulsion of a body by means of a force produced by discharging a Ûuid in the form of a jet. The backward-moving

jet of Ûuid reacts on the body in which it was produced, in accordance with Newton’s third law of motion, to create a reactive force that drives the body forward. Jet propulsion occurs in nature, the squid using a form of it to propel itself through water. Although jet-propelled boats and cars have been developed, the main use of jet propulsion is in aircraft and spacecraft. Jet propulsion is the only known method of propulsion in space. In the atmosphere, jet propulsion becomes more efÜcient at higher altitudes, as efÜciency is inversely proportional to the density of the medium through which a body is Ûying. The three principal means of providing jet propulsion are the turbojet, the ramjet, and the rocket. The turbojet is an airbreathing *heat engine based on the *gas

jturbine, used to power jet aircraft. The ramjet is also an air-breathing engine, but compression of the oxidant is achieved by the forward motion of the device through the atmosphere. This enables the compressor and turbine of the gas turbine to be dispensed with and the remaining system consists simply of an inlet diffuser, a combustion chamber in which fuel is burnt, and a jet nozzle through which the products of combustion are discharged. Used in guided missiles, the ramjet must

be accelerated to its operating velocity before it can Ûy (see also pulse jet). These two forms of jet propulsion, being airbreathing engines, can only be used in the earth’s atmosphere. The *rocket, however, carries its own oxidant and can thus be used in space. See also ion engine.

jet stream A narrow wind current that occurs in the earth’s atmosphere above

the lower troposphere (see earth’s atmosphere). The wind Ûows towards the east at speeds of between 60 km/h (summer) and 125 km/h (winter).

jeweller’s rouge Red powdered

haematite, iron(III) oxide, Fe2O3. It is a mild abrasive used in metal cleaners and polishes.

j-j coupling A type of *coupling in many-fermion systems, such as electrons in atoms and nucleons in nuclei, in which the energies associated with the spin– orbit interactions are much higher than the energies associated with electrostatic

repulsion. *Multiplets of many-electron atoms having a large atomic number are characterized by j-j coupling. Multiplets in the *shell model of nuclei characterized by j-j coupling are invoked to explain the *magic numbers of nuclei. The multiplets of many atoms and nuclei are intermediate between j-j coupling and *Russell– Saunders coupling (intermediate coupling).

joint The point of contact between two (or more) bones, together with the tissues that surround it. Joints fall into three classes that differ in the degree of freedom of movement they allow: (1) immovable joints, e.g. the *sutures between the bones that form the cranium; (2) slightly movable joints, e.g. the *symphyses between the vertebrae of the spinal column; and (3) freely movable or synovial joints, e.g. those that occur between the limb bones. Synovial joints include the ball- and-socket joints (between the limbs and the hip and shoulder girdles), which allow movement in all directions; and the hinge joints (e.g. at the knee and elbow), which allow movement in one plane only. A synovial joint is bound by ligaments and lined with *synovial membrane.

humerus ligament

synovial membrane synovial fluid cartilage

ulna

a hinge joint (the elbow)

pelvis (socket)

cartilage

synovial membrane

ligament

head of femur (ball)

synovial fluid

a ball-and-socket joint (the hip)

Types of freely movable joint

Joliot-Curie, Irène (1897–1956) French physicist, daughter of Marie and Pierre *Curie, who was educated by her mother and her scientist associates. In 1921 she began work at the Radium Institute, becoming director in 1946. In 1926 she married Frédéric Joliot (1900–58). They shared the 1935 Nobel Prize for chemistry for their discovery of artiÜcial radioactivity the previous year.

joliotium See transactinide elements.

Joly’s steam calorimeter An apparatus invented by John Joly (1857–1933) to measure the speciÜc heat capacity of a gas at constant volume. Two equal spherical containers are suspended from the opposite ends of a balance arm. One sphere is evacuated and the other contains the sample gas. The whole apparatus is enclosed in a steam bath, the speciÜc heat capacity of the sample gas being calculated from the difference between the masses of the water that condenses on each sphere.

Josephson effects Electrical effects observed when two superconducting materials (at low temperature) are separated by a thin layer of insulating material (typically a layer of oxide less than 10–8 m thick). If normal metallic conductors are separated by such a barrier it is possible for a small current to Ûow between the conductors by the *tunnel effect. If the materials are superconductors (see superconductivity), several unusual phenomena occur:

(1)A supercurrent can Ûow through the barrier; i.e. it has zero resistance.

(2)If this current exceeds a critical value, this conductivity is lost; the barrier then only passes the ‘normal’ low tunnelling current and a voltage develops across the junction.

(3)If a magnetic Üeld is applied below the critical current value, the current density changes regularly with distance across the

junction. The net current through the barrier depends on the magnetic Üeld applied. As the Üeld is increased the net current increases from zero to a maximum, decreases to zero, increases again

to a (lower) maximum, decreases, and so on. If the Üeld exceeds a critical value the superconductivity in the barrier vanishes

and a potential difference develops across the junction.

(4) If a potential difference is applied across the junction, a high-frequency alternating current Ûows through the junction. The frequency of this current depends on the size of the potential difference.

A junction of this type is called a Josephson junction; two or more junctions joined by superconducting paths form a

Josephson interferometer. Such junctions can be used in measuring fundamental constants, in deÜning a voltage standard, and in the highly accurate measurement of magnetic Üelds. An important potential use is in logic components in high-speed computers. Josephson junctions can switch states very quickly (as low as 6

picoseconds). Moreover they have very j low power consumption and can be

packed closely without generating too much heat. It is possible that computers based on such devices could operate 50 times faster than the best existing machines. The effects are named after Brian Josephson (1940– ), who predicted them theoretically in 1962.

joule Symbol J. The *SI unit of work and energy equal to the work done when the point of application of a force of one newton moves, in the direction of the force, a distance of one metre. 1 joule = 107 ergs = 0.2388 calorie. It is named after James Joule.

Joule, James Prescott (1818–89) British physicist. In 1840 he discovered the relationship between electric current, resistance, and the amount of heat produced. In 1849 he gave an account of the *kinetic theory of gases, and a year later announced his best-known Ünding, the *mechanical equivalent of heat. Later, with William Thomson (Lord *Kelvin), he discovered the *Joule–Thomson effect.

Joule heating The production of heat in a conductor as a result of the passage of an electric current through the conductor. The quantity of heat produced is given by *Joule’s law (def. 1).

Joule’s laws 1. The heat (Q ) produced when an electric current (I) Ûows through a resistance (R) for a time (t) is given by Q = I2Rt. 2. The *internal energy of a given

mass of gas is independent of its volume and pressure, being a function of temperature alone. This law applies only to *ideal gases (for which it provides a deÜnition of thermodynamic temperature) as in a real gas intermolecular forces would cause changes in the internal energy should a change of volume occur. See also joule–thomson effect.

Joule–Thomson effect (Joule–Kelvin effect) The change in temperature that occurs when a gas expands through a porous plug into a region of lower pressure. For most real gases the temperature falls under these circumstances as the gas has to do internal work in overcoming the intermolecular forces to enable the expansion to take place. This is a deviation from *Joule’s law (def. 2). There is usually also a

j deviation from *Boyle’s law, which can cause either a rise or a fall in temperature since any increase in the product of pressure and volume is a measure of external work done. At a given pressure, there is a particular temperature, called the inversion temperature of the gas, at which the rise in temperature from the Boyle’s law deviation is balanced by the fall from the Joule’s law deviation. There is then no temperature change. Above the inversion temperature the gas is heated by expansion; below it, it is cooled. The effect was discovered by James Joule working in collaboration with William Thomson (later Lord Kelvin).

Jovian Relating to the planet Jupiter.

JUGFET See transistor.

jugular vein A paired vein in the neck of mammals that returns blood from the head to the heart. It joins the subclavian vein at the base of the neck.

jumping gene See transposon.

junction detector (solid-state detector)

A sensitive detector of *ionizing radiation in which the output is a current pulse proportional to the energy falling in or near the depletion region of a reversebiased *semiconductor junction. The Ürst types were made by evaporating a thin layer of gold on to a polished wafer of n- type germanium; however, gold–silicon devices can be operated at room temperature and these have superseded the ger-

manium type, which have to be operated at the temperature of liquid nitrogen to reduce noise. When the gold–silicon junction is reverse-biased a depletion region, devoid of charge carriers (electrons and holes), forms in the silicon. Incoming ionizing radiation falling in this depletion region creates pairs of electrons and holes, which both have to be collected in order to give an output pulse proportional to the energy of the detected particle.

Junction detectors are used in medicine and biology as well as in space systems.

junction transistor See transistor.

Jupiter The largest planet in the *solar system and the Üfth in order from the sun (778.41 × 106 km distant). Its equatorial diameter is 142 985 km and its *sidereal period is 11.86 years. Viewed through an optical telescope it appears as an elliptical disc crossed by a number of bands. With a *radio telescope thermal radiation can be detected from the Jovian stratosphere indicating a temperature between 100 and 130 K. Microwave nonthermal emission can also be detected from the Jovian *Van Allen belts. The planet has at least 63 satellites, the largest of which, Io, has a diameter of 3242 km (see galilean satellites). A planetary ring of rocks was discovered in 1979 by the US Galileo probe.

Jurassic The second geological period of the Mesozoic era. It followed the Triassic, which ended about 213 million years ago, and extended until the beginning of the Cretaceous period, about 144 million years ago. It was named in 1829 by A. Brongniart after the Jura Mountains on the borders of France and Switzerland. Jurassic rocks include clays and limestones in which fossil Ûora and fauna are abundant. Plants included ferns, cycads, ginkgos, rushes, and conifers. Important invertebrates included *ammonites (on which the Jurassic is zoned), corals, brachiopods, bivalves, and echinoids. Reptiles dominated the vertebrates; the Ürst Ûying reptiles – the pterosaurs – and the Ürst primitive bird, Archaeopteryx, appeared.

juvenile hormone A hormone secreted by insects from a pair of endocrine glands (corpora allata) close to the brain. It inhibits metamorphosis and maintains the presence of larval features.

kainite A naturally occurring double salt of magnesium sulphate and potassium chloride, MgSO4.KCl.3H2O.

Kainozoic See cenozoic.

kalinite A mineral form of *aluminium potassium sulphate (Al2(SO4)3.K2SO4. 24H2O).

kallidin See kinin.

Kaluza–Klein theory A type of

*uniÜed-Üeld theory that postulates a generalization of the general theory of relativity to higher than four space–time dimensions. In Üve space–time dimensions this gives general relativity and electromagnetic interactions. In higher space–time dimensions Kaluza–Klein theories give general relativity and more general *gauge theories. A combination of Kaluza–Klein theory and *supersymmetry gives rise to *supergravity, which needs eleven space–time dimensions. In these theories it is proposed that the higher dimensions are ‘rolled up’ to become microscopically small (a process known as spontaneous compactiÜcation) with four macroscopic space–time dimensions remaining. It is named after Theodor Kaluza (1885–1954) and Oscar Klein (1894–1977).

kame An isolated mound of rock particles, originally formed at the lower end or side of a slow-moving glacier. The mound consists of layers of gravel and sand, which were transported by meltwater and left behind when the ice melted. See also esker.

kaolin (china clay) A soft white clay that is composed chieÛy of the mineral kaolinite (see clay minerals). It is formed during the weathering and hydrothermal alteration of other clays or feldspar. Kaolin is mined in the UK, France, the Czech Republic, and USA. Besides its vital importance in the ceramics industry it is also used extensively as a Üller in the

manufacture of rubber, paper, paint, and textiles and as a constituent of medicines.

kaon A K-meson. See meson.

karst A type of broken limestone terrain, characterized by Üssures (grikes) and depressions (dolines). A typical karst landscape, lacking vegetation, resembles an area paved with large slabs of limestone. Rainwater percolates through the Üssures into the rock beneath, where it can follow bedding planes and form underground streams, which carve out caves. Surface streams may disappear down *sink holes.

karyogamy The fusion of nuclei or nuclear material that occurs during sexual reproduction. See fertilization.

karyogram (idiogram) A diagram representing the characteristic features of the *chromosomes of a species.

karyokinesis The division of a cell nucleus. See meiosis; mitosis.

karyotype The number and structure of the *chromosomes in the nucleus of a cell. The karyotype is identical in all the *diploid cells of an organism.

katal Symbol kat. A non-SI unit of enzyme activity deÜned as the catalytic activity of an enzyme that increases the rate of conversion of a speciÜed chemical reaction by 1 mol s–1 under speciÜed assay conditions.

Kater’s pendulum A complex *pendulum designed by Henry Kater (1777–1835) to measure the acceleration of free fall. It consists of a metal bar with knife edges attached near the ends and two weights that can slide between the knife edges. The bar is pivoted from each knife edge in turn and the positions of the weights are adjusted so that the period of the pendulum is the same with both pivots. The period is then given by the formula for a simple pendulum, which enables g to be calculated.