Galvanometer

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An early D'Arsonval galvanometer showing magnet and rotating coil A moving coil galvanometer. Wellcome M0016397.jpg
An early D'Arsonval galvanometer showing magnet and rotating coil

A galvanometer is an electromechanical measuring instrument for electric current. Early galvanometers were uncalibrated, but improved versions, called ammeters, were calibrated and could measure the flow of current more precisely.

Contents

A galvanometer works by deflecting a pointer in response to an electric current flowing through a coil in a constant magnetic field. Galvanometers can be thought of as a kind of actuator.

Galvanometers came from the observation, first noted by Hans Christian Ørsted in 1820, that a magnetic compass's needle deflects when near a wire having electric current. They were the first instruments used to detect and measure small amounts of current. André-Marie Ampère, who gave mathematical expression to Ørsted's discovery, named the instrument after [1] the Italian electricity researcher Luigi Galvani, who in 1791 discovered the principle of the frog galvanoscope – that electric current would make the legs of a dead frog jerk.

Galvanometers have been essential for the development of science and technology in many fields. For example, in the 1800s they enabled long-range communication through submarine cables, such as the earliest transatlantic telegraph cables, and were essential to discovering the electrical activity of the heart and brain, by their fine measurements of current.

Galvanometers have also been used as the display components of other kinds of analog meters (e.g., light meters and VU meters), capturing the outputs of these meters' sensors. Today, the main type of galvanometer still in use is the D'Arsonval/Weston type.

Operation

Diagram of D'Arsonval/Weston type galvanometer. As the current flows from + through the coil (the orange part) to -, a magnetic field is generated in the coil. This field is counteracted by the permanent magnet and forces the coil to twist, moving the pointer, in relation to the field's strength caused by the flow of current. Galvanometer scheme.svg
Diagram of D'Arsonval/Weston type galvanometer. As the current flows from + through the coil (the orange part) to , a magnetic field is generated in the coil. This field is counteracted by the permanent magnet and forces the coil to twist, moving the pointer, in relation to the field's strength caused by the flow of current.

Modern galvanometers, of the D'Arsonval/Weston type, are constructed with a small pivoting coil of wire, called a spindle, in the field of a permanent magnet. The coil is attached to a thin pointer that traverses a calibrated scale. A tiny torsion spring pulls the coil and pointer to the zero position.

When a direct current (DC) flows through the coil, the coil generates a magnetic field. This field acts against the permanent magnet. The coil twists, pushing against the spring, and moves the pointer. The hand points at a scale indicating the electric current. Careful design of the pole pieces ensures that the magnetic field is uniform so that the angular deflection of the pointer is proportional to the current. A useful meter generally contains a provision for damping the mechanical resonance of the moving coil and pointer, so that the pointer settles quickly to its position without oscillation.

The basic sensitivity of a meter might be, for instance, 100 microamperes full scale (with a voltage drop of, say, 50 millivolts at full current). Such meters are often calibrated to read some other quantity that can be converted to a current of that magnitude. The use of current dividers, often called shunts, allows a meter to be calibrated to measure larger currents. A meter can be calibrated as a DC voltmeter if the resistance of the coil is known by calculating the voltage required to generate a full-scale current. A meter can be configured to read other voltages by putting it in a voltage divider circuit. This is generally done by placing a resistor in series with the meter coil. A meter can be used to read resistance by placing it in series with a known voltage (a battery) and an adjustable resistor. In a preparatory step, the circuit is completed and the resistor adjusted to produce full-scale deflection. When an unknown resistor is placed in series in the circuit the current will be less than full scale and an appropriately calibrated scale can display the value of the previously unknown resistor.

These capabilities to translate different kinds of electric quantities into pointer movements make the galvanometer ideal for turning the output of other sensors that output electricity (in some form or another), into something that can be read by a human.

Because the pointer of the meter is usually a small distance above the scale of the meter, parallax error can occur when the operator attempts to read the scale line that "lines up" with the pointer. To counter this, some meters include a mirror along with the markings of the principal scale. The accuracy of the reading from a mirrored scale is improved by positioning one's head while reading the scale so that the pointer and the reflection of the pointer are aligned; at this point, the operator's eye must be directly above the pointer and any parallax error has been minimized.

Uses

Closed-loop galvanometer-driven laser scanning mirror DynAXIS L.jpg
Closed-loop galvanometer-driven laser scanning mirror

Probably the largest use of galvanometers was of the D'Arsonval/Weston type used in analog meters in electronic equipment. Since the 1980s, galvanometer-type analog meter movements have been displaced by analog-to-digital converters (ADCs) for many uses. A digital panel meter (DPM) contains an ADC and numeric display. The advantages of a digital instrument are higher precision and accuracy, but factors such as power consumption or cost may still favor the application of analog meter movements.

Modern uses

Most modern uses for the galvanometer mechanism are in positioning and control systems. Galvanometer mechanisms are divided into moving magnet and moving coil galvanometers; in addition, they are divided into closed-loop and open-loop - or resonant - types.

Mirror galvanometer systems are used as beam positioning or beam steering elements in laser scanning systems. For example, for material processing with high-power lasers, closed loop mirror galvanometer mechanisms are used with servo control systems. These are typically high power galvanometers and the newest galvanometers designed for beam steering applications can have frequency responses over 10 kHz with appropriate servo technology. Closed-loop mirror galvanometers are also used in similar ways in stereolithography, laser sintering, laser engraving, laser beam welding, laser TVs, laser displays and in imaging applications such as retinal scanning with Optical Coherence Tomography (OCT) and Scanning Laser Ophthalmoscopy (SLO). Almost all of these galvanometers are of the moving magnet type. The closed loop is obtained measuring the position of the rotating axis with an infrared emitter and 2 photodiodes. This feedback is an analog signal.

Open loop, or resonant mirror galvanometers, are mainly used in some types of laser-based bar-code scanners, printing machines, imaging applications, military applications and space systems. Their non-lubricated bearings are especially of interest in applications that require functioning in a high vacuum.

A galvanometer mechanism (center part), used in an automatic exposure unit of an 8 mm film camera, together with a photoresistor (seen in the hole on top of the leftpart). Autoexpmeter.JPG
A galvanometer mechanism (center part), used in an automatic exposure unit of an 8 mm film camera, together with a photoresistor (seen in the hole on top of the leftpart).

Moving coil type galvanometer mechanisms (called 'voice coils' by hard disk manufacturers) are used for controlling the head positioning servos in hard disk drives and CD/DVD players, in order to keep mass (and thus access times), as low as possible.

Past uses

A major early use for galvanometers was for finding faults in telecommunications cables. They were superseded in this application late in the 20th century by time-domain reflectometers.

Galvanometer mechanisms were also used to get readings from photoresistors in the metering mechanisms of film cameras (as seen in the adjacent image).

In analog strip chart recorders such as used in electrocardiographs, electroencephalographs and polygraphs, galvanometer mechanisms were used to position the pen. Strip chart recorders with galvanometer driven pens may have a full-scale frequency response of 100 Hz and several centimeters of deflection.

History

Hans Christian Ørsted

The deflection of a magnetic compass needle by the current in a wire was first described by Hans Christian Ørsted in 1820. The phenomenon was studied both for its own sake and as a means of measuring electric current.

Schweigger and Ampère

The earliest galvanometer was reported by Johann Schweigger at the University of Halle on 16 September 1820. André-Marie Ampère also contributed to its development. Early designs increased the effect of the magnetic field generated by the current by using multiple turns of wire. The instruments were at first called "multipliers" due to this common design feature. [2] The term "galvanometer," in common use by 1836, was derived from the surname of Italian electricity researcher Luigi Galvani, who in 1791 discovered that electric current would make a dead frog's leg jerk.

Poggendorff and Thomson

Thomson mirror galvanometer, patented in 1858. Thomsons mirror galvanometer, 1858. (9663806048).jpg
Thomson mirror galvanometer, patented in 1858.

Originally, the instruments relied on the Earth's magnetic field to provide the restoring force for the compass needle. These were called "tangent" galvanometers and had to be oriented before use. Later instruments of the "astatic" type used opposing magnets to become independent of the Earth's field and would operate in any orientation.

An early mirror galvanometer was invented in 1826 by Johann Christian Poggendorff.[ citation needed ] The most sensitive form of astatic galvanometer, the Thomson galvanometer, for which Thomson coined the term mirror galvanometer, was patented in 1858 by William Thomson (Lord Kelvin). Thomson's mirror galvanometer was an improvement of a design invented by Hermann von Helmholtz in 1849. [3] Thomson's design was able to detect very rapid current changes by using small magnets attached to a lightweight mirror, suspended by a thread, instead of a compass needle. The deflection of a light beam on the mirror greatly magnified the deflection induced by small currents. Alternatively, the deflection of the suspended magnets could be observed directly through a microscope.

Georg Ohm

The ability to measure quantitatively voltage and current allowed Georg Ohm, in 1827, to formulate Ohm's Law – that the voltage across a conductor is directly proportional to the current through it.

D'Arsonval and Deprez

The early moving-magnet form of galvanometer had the disadvantage that it was affected by any magnets or iron masses near it, and its deflection was not linearly proportional to the current. In 1882 Jacques-Arsène d'Arsonval and Marcel Deprez developed a form with a stationary permanent magnet and a moving coil of wire, suspended by fine wires which provided both an electrical connection to the coil and the restoring torque to return to the zero position. An iron tube between the magnet's pole pieces defined a circular gap through which the coil rotated. This gap produced a consistent, radial magnetic field across the coil, giving a linear response throughout the instrument's range. A mirror attached to the coil deflected a beam of light to indicate the coil position. The concentrated magnetic field and delicate suspension made these instruments sensitive; d'Arsonval's initial instrument could detect ten microamperes. [4]

Edward Weston

D'Arsonval/Weston galvanometer (ca. 1900). Part of the magnet's left pole piece is broken out to show the coil. D'Arsonval ammeter movement.jpg
D'Arsonval/Weston galvanometer (ca. 1900). Part of the magnet's left pole piece is broken out to show the coil.
Weston galvanometer in portable case Weston galvanometer 6h440s49d 4j03cz922 dl full size.jpg
Weston galvanometer in portable case

Edward Weston extensively improved the design. He replaced the fine wire suspension with a pivot and provided restoring torque and electrical connections through spiral springs rather like those of a wristwatch balance wheel hairspring. He developed a method of stabilizing the magnetic field of the permanent magnet, so the instrument would have consistent accuracy over time. He replaced the light beam and mirror with a knife-edge pointer that could be read directly. A mirror under the pointer, in the same plane as the scale, eliminated parallax observation error. To maintain the field strength, Weston's design used a very narrow circumferential slot through which the coil moved, with a minimal air-gap. This improved linearity of pointer deflection with respect to coil current. Finally, the coil was wound on a light-weight form made of conductive metal, which acted as a damper. By 1888, Edward Weston had patented and brought out a commercial form of this instrument, which became a standard electrical equipment component. It was known as a "portable" instrument because it was affected very little by mounting position or by transporting it from place to place. This design is almost universally used in moving-coil meters today.

Initially, laboratory instruments relying on the Earth's own magnetic field to provide restoring force for the pointer, galvanometers were developed into compact, rugged, sensitive portable instruments essential to the development of electro-technology.

Taut-band movement

The taut-band movement is a modern development of the D'Arsonval-Weston movement. The jewel pivots and hairsprings are replaced by tiny strips of metal under tension. Such a meter is more rugged for field use. [5] [6]

Types

Some galvanometers use a solid pointer on a scale to show measurements; other very sensitive types use a miniature mirror and a beam of light to provide mechanical amplification of low-level signals.

Tangent galvanometer

A tangent galvanometer is an early measuring instrument used for the measurement of electric current. It works by using a compass needle to compare a magnetic field generated by the unknown current to the magnetic field of the Earth. It gets its name from its operating principle, the tangent law of magnetism, which states that the tangent of the angle a compass needle makes is proportional to the ratio of the strengths of the two perpendicular magnetic fields. It was first described by Johan Jacob Nervander in 1834 (see J.J. Nervander, “Mémoire sur un Galvanomètre à châssis cylindrique par lequel on obtient immédiatement et sans calcul la mesure de l’intensité du courant électrique qui produit la déviation de l’aiguille aimantée,” Annales de Chimie et de Physique (Paris), Tome 55, 156–184, 1834. and J. Venermo and A. Sihvola, "The tangent galvanometer of Johan Jacob Nervander," IEEE Instrumentation & Measurement Magazine, vol. 11, no. 3, pp. 16–23, June 2008.) and in 1837 by Claude Pouillet. [7]

A tangent galvanometer consists of a coil of insulated copper wire wound on a circular non-magnetic frame. The frame is mounted vertically on a horizontal base provided with levelling screws. The coil can be rotated on a vertical axis passing through its centre. A compass box is mounted horizontally at the centre of a circular scale. It consists of a tiny, powerful magnetic needle pivoted at the centre of the coil. The magnetic needle is free to rotate in the horizontal plane. The circular scale is divided into four quadrants. Each quadrant is graduated from 0° to 90°. A long thin aluminium pointer is attached to the needle at its centre and at right angle to it. To avoid errors due to parallax, a plane mirror is mounted below the compass needle.

In operation, the instrument is first rotated until the magnetic field of the Earth, indicated by the compass needle, is parallel with the plane of the coil. Then the unknown current is applied to the coil. This creates a second magnetic field on the axis of the coil, perpendicular to the Earth's magnetic field. The compass needle responds to the vector sum of the two fields and deflects to an angle equal to the tangent of the ratio of the two fields. From the angle read from the compass's scale, the current could be found from a table. [8] The current supply wires have to be wound in a small helix, like a pig's tail, otherwise the field due to the wire will affect the compass needle and an incorrect reading will be obtained.

Theory

The galvanometer is oriented so that the plane of the coil is vertical and aligned along parallel to the horizontal component BH of the Earth's magnetic field (i.e. parallel to the local "magnetic meridian"). When an electric current flows through the galvanometer coil, a second magnetic field B is created. At the center of the coil, where the compass needle is located, the coil's field is perpendicular to the plane of the coil. The magnitude of the coil's field is:

where I is the current in amperes, n is the number of turns of the coil and r is the radius of the coil. These two perpendicular magnetic fields add vectorially, and the compass needle points along the direction of their resultant BH+B. The current in the coil causes the compass needle to rotate by an angle θ:

From tangent law, B = BH tan θ, i.e.

or

or I = K tan θ, where K is called the Reduction Factor of the tangent galvanometer.

One problem with the tangent galvanometer is that its resolution degrades at both high currents and low currents. The maximum resolution is obtained when the value of θ is 45°. When the value of θ is close to 0° or 90°, a large percentage change in the current will only move the needle a few degrees. [9]

Geomagnetic field measurement

A tangent galvanometer can also be used to measure the magnitude of the horizontal component of the geomagnetic field. When used in this way, a low-voltage power source, such as a battery, is connected in series with a rheostat, the galvanometer, and an ammeter. The galvanometer is first aligned so that the coil is parallel to the geomagnetic field, whose direction is indicated by the compass when there is no current through the coils. The battery is then connected and the rheostat is adjusted until the compass needle deflects 45 degrees from the geomagnetic field, indicating that the magnitude of the magnetic field at the center of the coil is the same as that of the horizontal component of the geomagnetic field. This field strength can be calculated from the current as measured by the ammeter, the number of turns of the coil, and the radius of the coils.

Astatic galvanometer

Unlike the tangent galvanometer, the astatic galvanometer does not use the Earth's magnetic field for measurement, so it does not need to be oriented with respect to the Earth's field, making it easier to use. Developed by Leopoldo Nobili in 1825, [10] it consists of two magnetized needles parallel to each other but with the magnetic poles reversed. These needles are suspended by a single silk thread. [11] The lower needle is inside a vertical current sensing coil of wire and is deflected by the magnetic field created by the passing current, as in the tangent galvanometer above. The purpose of the second needle is to cancel the dipole moment of the first needle, so the suspended armature has no net magnetic dipole moment, and thus is not affected by the earth's magnetic field. The needle's rotation is opposed by the torsional elasticity of the suspension thread, which is proportional to the angle.

Mirror galvanometer

To achieve higher sensitivity to detect extremely small currents, the mirror galvanometer substitutes a lightweight mirror for the pointer. It consists of horizontal magnets suspended from a fine fiber, inside a vertical coil of wire, with a mirror attached to the magnets. A beam of light reflected from the mirror falls on a graduated scale across the room, acting as a long mass-less pointer. The mirror galvanometer was used as the receiver in the first trans-Atlantic submarine telegraph cables in the 1850s, to detect the extremely faint pulses of current after their thousand-mile journey under the Atlantic. In a device called an oscillograph, the moving beam of light is used, to produce graphs of current versus time, by recording measurements on photographic film. The string galvanometer is a type of mirror galvanometer so sensitive that it was used to make the first electrocardiogram of the electrical activity of the human heart.

Ballistic galvanometer

A ballistic galvanometer is a type of sensitive galvanometer for measuring the quantity of charge discharged through it. It is an integrator, by virtue of the long time constant of its response, unlike a current-measuring galvanometer. The moving part has a large moment of inertia that gives it an oscillation period long enough to make the integrated measurement. It can be either of the moving coil or moving magnet type; commonly it is a mirror galvanometer.

See also

Related Research Articles

Ammeter

An ammeter is a measuring instrument used to measure the current in a circuit. Electric currents are measured in Amperes (A), hence the name. The ammeter is usually connected in series with the circuit in which the current is to be measured. An ammeter usually has low resistance so that it does not cause a significant voltage drop in the circuit being measured.

Electromagnetic coil

An electromagnetic coil is an electrical conductor such as a wire in the shape of a coil, spiral or helix. Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in devices such as electric motors, generators, inductors, electromagnets, transformers, and sensor coils. Either an electric current is passed through the wire of the coil to generate a magnetic field, or conversely, an external time-varying magnetic field through the interior of the coil generates an EMF (voltage) in the conductor.

Pressure measurement Analysis of force applied by a fluid on a surface

Pressure measurement is the analysis of an applied force by a fluid on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure and display pressure in an integral unit are called pressure meters or pressure gauges or vacuum gauges. A manometer is a good example, as it uses the surface area and weight of a column of liquid to both measure and indicate pressure. Likewise the widely used Bourdon gauge is a mechanical device, which both measures and indicates and is probably the best known type of gauge.

Voltmeter Instrument used for measuring voltage

A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.

Magnetic field Spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.

Ohmmeter Tool for measuring electrical resistance

An ohmmeter is an electrical instrument that measures electrical resistance. Multimeters also function as ohmmeters when in resistance-measuring mode.

Multimeter Electronic measuring instrument that combines several measurement functions in one unit

A multimeter is a measuring instrument that can measure multiple electrical properties. A typical multimeter can measure voltage, resistance, and current, in which case it is also known as a volt-ohm-milliammeter (VOM).

Magnet Material or object that produces a magnetic field

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets.

Mirror galvanometer

A mirror galvanometer is an ammeter that indicates it has sensed an electric current by deflecting a light beam with a mirror. The beam of light projected on a scale acts as a long massless pointer. In 1826, Johann Christian Poggendorff developed the mirror galvanometer for detecting electric currents. The apparatus is also known as a spot galvanometer after the spot of light produced in some models.

Torsion spring Type of spring

A torsion spring is a spring that works by twisting its end along its axis; that is, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a torque in the opposite direction, proportional to the amount (angle) it is twisted. There are various types:

Chart recorder

A chart recorder is an electromechanical device that records an electrical or mechanical input trend onto a piece of paper. Chart recorders may record several inputs using different color pens and may record onto strip charts or circular charts. Chart recorders may be entirely mechanical with clockwork mechanisms, electro-mechanical with an electrical clockwork mechanism for driving the chart, or entirely electronic with no mechanical components at all.

Wattmeter

The wattmeter is an instrument for measuring the electric active power in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio frequency power; other types are required for radio frequency measurements.

Syphon recorder

The syphon or siphon recorder is an obsolete electromechanical device used as a receiver for submarine telegraph cables invented by William Thomson, 1st Baron Kelvin in 1867. It automatically records an incoming telegraph message as a wiggling ink line on a roll of paper tape. Later a trained telegrapher would read the tape, translating the pulses representing the "dots" and "dashes" of the Morse code to characters of the text message.

Current clamp Tool for measuring electrical current

In electrical and electronic engineering, a current clamp, also known as current probe, is an electrical device with jaws which open to allow clamping around an electrical conductor. This allows measurement of the current in a conductor without the need to make physical contact with it, or to disconnect it for insertion through the probe.

Electrostatic voltmeter

Electrostatic voltmeter can refer to an electrostatic charge meter, known also as surface DC voltmeter, or to a voltmeter to measure large electrical potentials, traditionally called electrostatic voltmeter.

Megohmmeter

A Megohmmeter or insulation resistance tester is a special type of ohmmeter used to measure the electrical resistance of insulators. Insulating components, for example cable jackets, must be tested for their insulation strength at the time of commissioning and as part of maintenance of high voltage electrical equipment and installations.

Ballistic galvanometer

A ballistic galvanometer is a type of sensitive galvanometer; commonly a mirror galvanometer. Unlike a current-measuring galvanometer, the moving part has a large moment of inertia, thus giving it a long oscillation period. It is really an integrator measuring the quantity of charge discharged through it. It can be either of the moving coil or moving magnet type.

Air core gauge

An air core gauge is a specific type of rotary actuator in an analog display gauge that allows an indicator to rotate a full 360 degrees. It is used in gauges and displays, most commonly automotive instrument clusters.

Frequency meter Meter that displays the frequency of an electronic signal

A frequency meter is an instrument that displays the frequency of a periodic electrical signal. Various types of mechanical frequency meters were used in the past, but since the 1970s these have almost universally been replaced by digital frequency counters.

Deflection yoke part of a cathode ray tube which moves the electron beam around

A deflection yoke is a kind of magnetic lens, used in cathode ray tubes to scan the electron beam both vertically and horizontally over the whole screen.

References

  1. Schiffer, Michael Brian. (2008)"Electromagnetism Revealed," Power Struggles: Scientific Authority and the Creation of Practical Electricity Before Edison. Page 24.
  2. "Schweigger Multiplier – 1820". Maglab. National High Magnetic Field Laboratory. Retrieved 17 October 2017.
  3. Lindley, David, Degrees Kelvin: A Tale of Genius, Invention, and Tragedy, pp. 132–133, Joseph Henry Press, 2004 ISBN   0309167825
  4. Keithley, Joseph F. (1999). The story of electrical and magnetic measurements: from 500 B.C. to the 1940s. John Wiley and Sons. pp. 196–198. ISBN   0-7803-1193-0.
  5. Weschler Instruments (20 February 2020). "The taut-band analog meter" . Retrieved 25 April 2020.
  6. http://www.dictionarycentral.com/definition/taut-band-meter.html
  7. Pouillet (1837). "Mémoire sur la pile de Volta et sur la loi générale de l'intensité que prennent les courrants, soit qu'ils proviennent d'un seul élément, soit qu'ils proviennent d'une pile à grande ou à petite tension" [Memoir on the Voltaic pile [i.e., battery] and on the general law of the intensity that currents assume, whether they come from a single element or they come from a pile of high or low voltage]. Comptes rendus (in French). 4: 267–279.
  8. Greenslade Jr., Thomas B. "Tangent Galvanometer". Kenyon College. Retrieved 26 April 2016.
  9. "Theory". GALVANOMETER. Retrieved 5 April 2017.
  10. Nobili, Leopoldo (1825). "Sur un nouveau galvanomètre présenté à l'Académie des Sciences" [On a new galvanometer presented at the Academy of Sciences]. Bibliothèque universelle (in French). 29: 119–125.
  11. Greenslade, Thomas B. Jr. "Instruments for Natural Philosophy — Astatic Galvanometer". Kenyon College. Retrieved 6 November 2019.