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title: "Multi-parametric surface plasmon resonance"
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Multi-parametric surface plasmon resonance (MP-SPR) is based on surface plasmon resonance (SPR), an established real-time label-free method for biomolecular interaction analysis, but it uses a different optical setup, a goniometric SPR configuration. While MP-SPR provides same kinetic information as SPR (equilibrium constant, dissociation constant, association constant), it provides also structural information (refractive index, layer thickness). Hence, MP-SPR measures both surface interactions and nanolayer properties.
== History ==
The goniometric SPR method was researched alongside focused beam SPR and Otto configurations at VTT Technical Research Centre of Finland since 1980s by Janusz Sadowski. The goniometric SPR optics was commercialized by Biofons Oy for use in point-of-care applications. Introduction of additional measurement laser wavelengths and first thin film analyses were performed in 2011 giving way to MP-SPR method.
== Principle ==
The MP-SPR optical setup measures at multiple wavelengths simultaneously (similarly to spectroscopic SPR), but instead of measuring at a fixed angle, it rather scans across a wide range of θ angles (for instance 40 degrees). This results in measurements of full SPR curves at multiple wavelengths providing additional information about structure and dynamic conformation of the film.
== Measured values ==
The measured full SPR curves (x-axis: angle, y-axis: reflected light intensity) can be transcribed into sensograms (x-axis: time, y-axis: selected parameter such as peak minimum, light intensity, peak width). The sensograms can be fitted using binding models to obtain kinetic parameters including on- and off-rates and affinity. The full SPR curves are used to fit Fresnel equations to obtain thickness and refractive index of the layers. Also due to the ability of scanning the whole SPR curve, MP-SPR is able to separate bulk effect and analyte binding from each other using parameters of the curve.
While QCM-D measures wet mass, MP-SPR and other optical methods measure dry mass, which enables analysis of water content of nanocellulose films.
== Applications ==
The method has been used in life sciences, material sciences and biosensor development.
In life sciences, the main applications focus on pharmaceutical development including small-molecule, antibody or nanoparticle interactions with target with a biomembrane or with a living cell monolayer. As first in the world, MP-SPR is able to separate transcellular and paracellular drug uptake in real-time and label-free for targeted drug delivery.
In biosensor development, MP-SPR is used for assay development for point-of-care applications. Typical developed biosensors include electrochemical printed biosensors, ELISA and SERS.
In material sciences, MP-SPR is used for optimization of thin solid films from Ångströms to 100 nanometers (graphene, metals, oxides), soft materials up to microns (nanocellulose, polyelectrolyte) including nanoparticles. Applications including thin film solar cells, barrier coatings including anti-reflective coatings, antimicrobial surfaces, self-cleaning glass, plasmonic metamaterials, electro-switching surfaces, layer-by-layer assembly, and graphene.
== References ==

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The ozone monitoring instrument (OMI) is a nadir-viewing visual and ultraviolet spectrometer aboard the NASA Aura spacecraft, which is part of the satellite constellation A-Train. In this group of satellites Aura flies in formation about 15 minutes behind Aqua satellite, both of which orbit the Earth in a polar Sun-synchronous pattern, and which provides nearly global coverage in one day. Aura satellite was launched on July 15, 2004, and OMI has collected data since August 9, 2004.
From a technical point of view, OMI instrument use hyperspectral imaging to observe solar-backscatter radiation to the space with an spectral range that covers the visible and ultraviolet. Its spectral capabilities were designed to achieve specific requirements of total ozone amounts retrievals in terms of accuracy and precision. Also its characteristics provide accurate radiometric and wavelength self calibration over the long-term project requirements.
== OMI project ==
The OMI project is a cooperation between the Netherlands Agency for Aerospace Programmes (NIVR), the Finnish Meteorological Institute (FMI) and the National Aeronautics and Space Agency (NASA).
The OMI project was carried out under the direction of the NIVR and financed by the Dutch Ministries of Economic Affairs, Transport and Public Works and the Ministry of Education and Science. The instrument was built by Dutch Space in co-operation with Netherlands Organisation for Applied Scientific Research Science and Industry and Netherlands Institute for Space Research. The Finnish industry supplied the electronics. The scientific part of the OMI project is managed by KNMI (principal investigator Prof. Dr. P. F. Levelt now at the Delft University of Technology), in close co-operation with NASA and the Finnish Meteorological Institute.
== Scientific objectives and atmospheric monitoring ==
One of the scientific objectives of OMI is to measure trace gases: ozone (O3), nitrogen dioxide (NO2), sulfur dioxide (SO2), formaldehyde (HCHO), BrO, and OClO. However, OMI sensors can distinguish between aerosol types, such as smoke, dust, and sulfates, and can measure cloud pressure and cloud coverage, which provide data to derive tropospheric ozone. In that regard OMI follows in the heritage of TOMS, SBUV, GOME, SCIAMACHY, and GOMOS. On top of that, OMI aims to detect emissions in volcanic eruptions with up to at least 100 times more sensitivity than TOMS. The Ozone Monitoring Instrument has been proved an useful platform to monitor other traces gases like Glyoxal, variables like surface UV radiation, or total column estimations like the water vapor, NO2 and Ozone. Has been uses in operational services by European Centre for Medium-range Weather Forecasts (ECMWF), the US National Oceanic and Atmospheric Administration (NOAA) for ozone and air quality forecasts, and the Volcanic Ash Advisory Centers (VAACs) for the rerouting of aircraft in case of a volcanic eruption.
== Instrument Information ==
The instrument observes Earth's backscattered radiation and uses two imaging grating spectrometers, and each grating spectrometer is coupled to a CCD detector with 780x576 (spectral x spatial) pixels. The instrument can operate in two different modes: the normal operational mode where a single pixel in the observation has an spatial resolution 13x24 km2 at nadir (straight down), and the zoom mode where this resolution is increased to 13x12 km2.
=== Spectral Information ===
OMI measurements cover a spectral region of 264–504 nm (nanometers) with a spectral resolution between 0.42 nm and 0.63 nm and a nominal ground footprint of 13 × 24 km2 at nadir. This spectral coverage is divided in three different channels two of them in the ultraviolet range, and one in the visible spectrum. Note that the ground pixel size of the UV-1 channel is twice as large in the swath direction compared to the other two channels, this optical design of the UV channel were done to reduce straylight in this wavelength range.
=== Orbital Information ===
The Aura satellite orbits at an altitude of 705 km in a sun-synchronous polar orbit with an exact 16-day repeat cycle and with a local equator crossing time of 13. 45 ( 1:45 P.M.) on the ascending node. The orbital inclination is 98.1 degrees, providing latitudinal coverage from 82° N to 82° S. It is a wide-field-imaging spectrometer with a 114° across-track viewing angle range that provides a 2600 km wide swath, enabling measurements with a daily global coverage.
=== Calibration and Validation ===
The discussion of the calibration and validation processes began before the launch of Aura Satellite. Once the instrument was in orbit the information of these calibration was published, showing specific details of the absolute radiometric calibration, the bi-directional scattering distribution function (BSDF) calibration and the spectral calibration carried on. Note also that the instrument is equipped with an internal white light source for detector calibration purposes. The validation, which aim to assess the inherent uncertainties in satellite data products of the instrument together with retrieval algorithms used for each data product, was carried on continuously since the launch of Aura satellite. The validation include products like: total ozone column, NO2, ozone vertical profiles.
=== In-flight performance ===
One important aspect of satellite instruments for scientific measurements is the evolution of the performance during the life-cycle of the sensors, as well as, the continuous evaluation of the quality of the data products. In the case of an instrument like OMI the main aspects to consider are: the radiometric and spectral stability, the row anomaly, and detector degradation. In the first aspect: the radiometric degradation of OMI ranges from ~2% in the UV channels to ~0.5% in the VIS channel, which is much lower than any other similar satellite instrument. Regarding the wavelength calibration of the instrument it remains stable to 0.005–0.020 nm which indicates a high wavelength stability. It was detected a row anomaly due, probably, to a partial cover of the instrument, warning flags were included in the raw products to avoid the use of these specific rows and keep the quality of the retrieval products. Further information of the long-term calibration indicated in 2017 that the instrument will be able to provide useful science data for another 5 to 10 years.

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== Scientific relevance ==
The OMI project has been monitoring the atmospheric composition and providing measurements widely used in the field of atmospheric chemistry research. The fact that it has been operational for more than a decade makes it also useful for trend monitoring. The reference describing the first 14 years of the OMI details the research data products provided by NASA, KNMI, FMI and SAO, also according to these authors, beyond the initial goals, OMI has been important due the high-resolution NO2 and SO2 measurements (OMI is the first instrument that is able to obtain daily global coverage combined with such spatial resolution), and the fact that top-down studies allowed for source attribution analyses.
=== Awards ===
The International Team of the Ozone Monitoring Instrument has received several awards for its contributions to a better understanding of the Earth system:
USGS 2018 Pecora Award The Pecora award is annual to recognize individuals or teams using remote sensing in the field of Earth Science. It consider not only the scientific role but also its role informing decision makers and supporting natural or human-induced disaster responses.
2021 AMS Special Award A broad description of this award to OMI International Team is given as an AMS video.
=== Contributions to scientific research ===
Assessment of the Montreal Protocol: the instrument has proved stability to provide long-term data record for monitoring the ozone layer, which is the particular interest to evaluate the possible recovery of the ozone depletion in the southern hemisphere.
Global concentrations of trace gases: the OMI data show a steady decline in concentrations of NO2 in the United States, Europe, and Japan, whereas in China, first strong increases were observed, followed by decreases after 2014.
Absorbing aerosol that can cause warming: OMI can provide information as from its ultraviolet (UV) channel it is possible to derive such absorbing capacity.
Long-term data record of tropospheric ozone has been established: Tropospheric ozone assessment is important as it is the third main anthropogenic greenhouse gas, and the fraction of ozone in the troposphere can be derived from the OMI data, either by itself alone or in combination with other instruments
OMI formaldehyde retrievals indicate increases of this trace gas over India and China, and a downward trend over the Amazonian forest, spatially correlated with areas affected by deforestation
OMI has been the first satellite instrument to be used for daily monitoring of volcanic emissions
OMI satellite products of Ozone total column has been used for data assimilation en IFS model by ECMWF
== References ==
== External links ==
OMI webpage at NASA.gov
OMI webpage at KNMI.nl
Tropospheric Emission Monitoring Internet Service (TEMIS)
https://docserver.gesdisc.eosdis.nasa.gov/repository/Mission/OMI/3.3_ScienceDataProductDocumentation/3.3.2_ProductRequirements_Designs/README.OMI_DUG.pdf

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A pH meter is a scientific instrument that measures the hydrogen-ion activity in water-based solutions, indicating its acidity or alkalinity expressed as pH. The pH meter measures the difference in electrical potential between a pH electrode and a reference electrode, and so the pH meter is sometimes referred to as a "potentiometric pH meter". The difference in electrical potential relates to the acidity or pH of the solution. Testing of pH via pH meters (pH-metry) is used in many applications ranging from laboratory experimentation to quality control.
== Applications ==
The rate and outcome of chemical reactions taking place in water often depends on the acidity of the water, and it is therefore useful to know the acidity of the water, typically measured by means of a pH meter. Knowledge of pH is useful or critical in many situations, including chemical laboratory analyses. pH meters are used for soil measurements in agriculture, water quality for municipal water supplies, swimming pools, environmental remediation; brewing of wine or beer; manufacturing, healthcare and clinical applications such as blood chemistry; and many other applications.
Advances in the instrumentation and in detection have expanded the number of applications in which pH measurements can be conducted. The devices have been miniaturized, enabling direct measurement of pH inside of living cells. In addition to measuring the pH of liquids, specially designed electrodes are available to measure the pH of semi-solid substances, such as foods. These have tips suitable for piercing semi-solids, have electrode materials compatible with ingredients in food, and are resistant to clogging.
== Design and use ==
=== Principle of operation ===
Potentiometric pH meters measure the voltage between two electrodes and display the result converted into the corresponding pH value. They comprise a simple electronic amplifier and a pair of electrodes, or alternatively a combination electrode, and some form of display calibrated in pH units. It usually has a glass electrode and a reference electrode, or a combination electrode. The electrodes, or probes, are inserted into the solution to be tested. pH meters may also be based on the antimony electrode (typically used for rough conditions) or the quinhydrone electrode.
In order to accurately measure the potential difference between the two sides of the glass membrane reference electrode, typically a silver chloride electrode or calomel electrode are required on each side of the membrane. Their purpose is to measure changes in the potential on their respective side. One is built into the glass electrode. The other, which makes contact with the test solution through a porous plug, may be a separate reference electrode or may be built into a combination electrode. The resulting voltage will be the potential difference between the two sides of the glass membrane possibly offset by some difference between the two reference electrodes, that can be compensated for. The article on the glass electrode has a good description and figure.
The design of the electrodes is the key part: These are rod-like structures usually made of glass, with a bulb containing the sensor at the bottom. The glass electrode for measuring the pH has a glass bulb specifically designed to be selective to hydrogen-ion concentration. On immersion in the solution to be tested, hydrogen ions in the test solution exchange for other positively charged ions on the glass bulb, creating an electrochemical potential across the bulb. The electronic amplifier detects the difference in electrical potential between the two electrodes generated in the measurement and converts the potential difference to pH units. The magnitude of the electrochemical potential across the glass bulb is linearly related to the pH according to the Nernst equation.
The reference electrode is insensitive to the pH of the solution, being composed of a metallic conductor, which connects to the display. This conductor is immersed in an electrolyte solution, typically potassium chloride, which comes into contact with the test solution through a porous ceramic membrane. The display consists of a voltmeter, which displays voltage in units of pH.
On immersion of the glass electrode and the reference electrode in the test solution, an electrical circuit is completed, in which there is a potential difference created and detected by the voltmeter. The circuit can be thought of as going from the conductive element of the reference electrode to the surrounding potassium-chloride solution, through the ceramic membrane to the test solution, the hydrogen-ion-selective glass of the glass electrode, to the solution inside the glass electrode, to the silver of the glass electrode, and finally the voltmeter of the display device. The voltage varies from test solution to test solution depending on the potential difference created by the difference in hydrogen-ion concentrations on each side of the glass membrane between the test solution and the solution inside the glass electrode. All other potential differences in the circuit do not vary with pH and are corrected for by means of the calibration.
For simplicity, many pH meters use a combination probe, constructed with the glass electrode and the reference electrode contained within a single probe. A detailed description of combination electrodes is given in the article on glass electrodes.
The pH meter is calibrated with solutions of known pH, typically before each use, to ensure accuracy of measurement. To measure the pH of a solution, the electrodes are used as probes, which are dipped into the test solutions and held there sufficiently long for the hydrogen ions in the test solution to equilibrate with the ions on the surface of the bulb on the glass electrode. This equilibration provides a stable pH measurement.

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=== pH electrode and reference electrode design ===
Details of the fabrication and resulting microstructure of the glass membrane of the pH electrode are maintained as trade secrets by the manufacturers. However, certain aspects of design are published. Glass is a solid electrolyte, for which alkali-metal ions can carry current. The pH-sensitive glass membrane is generally spherical to simplify the manufacture of a uniform membrane. These membranes are up to 0.4 millimeters in thickness, thicker than original designs, so as to render the probes durable. The glass has silicate chemical functionality on its surface, which provides binding sites for alkali-metal ions and hydrogen ions from the solutions. This provides an ion-exchange capacity in the range of 10−6 to 10−8 mol/cm2. Selectivity for hydrogen ions (H+) arises from a balance of ionic charge, volume requirements versus other ions, and the coordination number of other ions. Electrode manufacturers have developed compositions that suitably balance these factors, most notably lithium glass.
The silver chloride electrode is most commonly used as a reference electrode in pH meters, although some designs use the saturated calomel electrode. The silver chloride electrode is simple to manufacture and provides high reproducibility. The reference electrode usually consists of a platinum wire that has contact with a silver/silver chloride mixture, which is immersed in a potassium chloride solution. There is a ceramic plug, which serves as a contact to the test solution, providing low resistance while preventing mixing of the two solutions.
With these electrode designs, the voltmeter is detecting potential differences of ±1400 millivolts. The electrodes are further designed to rapidly equilibrate with test solutions to facilitate ease of use. The equilibration times are typically less than one second, although equilibration times increase as the electrodes age.
=== Maintenance ===
Because of the sensitivity of the electrodes to contaminants, cleanliness of the probes is essential for accuracy and precision. Probes are generally kept moist when not in use with a medium appropriate for the particular probe, which is typically an aqueous solution available from probe manufacturers. Probe manufacturers provide instructions for cleaning and maintaining their probe designs. For illustration, one maker of laboratory-grade pH gives cleaning instructions for specific contaminants: general cleaning (15-minute soak in a solution of bleach and detergent), salt (hydrochloric acid solution followed by sodium hydroxide and water), grease (detergent or methanol), clogged reference junction (KCl solution), protein deposits (pepsin and HCl, 1% solution), and air bubbles.
=== Calibration and operation ===
The German Institute for Standardization publishes a standard for pH measurement using pH meters, DIN 19263.
Very precise measurements necessitate that the pH meter is calibrated before each measurement. More typically calibration is performed once per day of operation. Calibration is needed because the glass electrode does not give reproducible electrostatic potentials over longer periods of time.
Consistent with principles of good laboratory practice, calibration is performed with at least two standard buffer solutions that span the range of pH values to be measured. For general purposes, buffers at pH 4.00 and pH 10.00 are suitable. The pH meter has one calibration control to set the meter reading equal to the value of the first standard buffer and a second control to adjust the meter reading to the value of the second buffer. A third control allows the temperature to be set. Standard buffer sachets, available from a variety of suppliers, usually document the temperature dependence of the buffer control. More precise measurements sometimes require calibration at three different pH values. Some pH meters provide built-in temperature-coefficient correction, with temperature thermocouples in the electrode probes. The calibration process correlates the voltage produced by the probe (approximately 0.06 volts per pH unit) with the pH scale. Good laboratory practice dictates that, after each measurement, the probes are rinsed with distilled water or deionized water to remove any traces of the solution being measured, blotted with a scientific wipe to absorb any remaining water, which could dilute the sample and thus alter the reading, and then immersed in a storage solution suitable for the particular probe type.
== Types of pH meters ==
In general there are three major categories of pH meters. Benchtop pH meters are often used in laboratories and are used to measure samples which are brought to the pH meter for analysis. Portable, or field pH meters, are handheld pH meters that are used to take the pH of a sample in a field or production site. In-line or in situ pH meters, also called pH analyzers, are used to measure pH continuously in a process, and can stand-alone, or be connected to a higher level information system for process control.
pH meters range from simple and inexpensive pen-like devices to complex and expensive laboratory instruments with computer interfaces and several inputs for indicator and temperature measurements to be entered to adjust for the variation in pH caused by temperature. The output can be digital or analog, and the devices can be battery-powered or rely on line power. Some versions use telemetry to connect the electrodes to the voltmeter display device.
Specialty meters and probes are available for use in special applications, such as harsh environments and biological microenvironments. There are also holographic pH sensors, which allow pH measurement colorimetrically, making use of the variety of pH indicators that are available. Additionally, there are commercially available pH meters based on solid state electrodes, rather than conventional glass electrodes.
== History ==

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The concept of pH was defined in 1909 by S. P. L. Sørensen, and electrodes were used for pH measurement in the 1920s.
In October 1934, Arnold Orville Beckman registered the first patent for a complete chemical instrument for the measurement of pH, U.S. Patent No. 2,058,761, for his "acidimeter", later renamed the pH meter. Beckman developed the prototype as an assistant professor of chemistry at the California Institute of Technology, when asked to devise a quick and accurate method for measuring the acidity of lemon juice for the California Fruit Growers Exchange (Sunkist).
On April 8, 1935, Beckman's renamed National Technical Laboratories focused on the manufacture of scientific instruments, with the Arthur H. Thomas Company as a distributor for its pH meter. In its first full year of sales, 1936, the company sold 444 pH meters for $60,000 in sales. In years to come, the company sold millions of the units. In 2004 the Beckman pH meter was designated an ACS National Historic Chemical Landmark in recognition of its significance as the first commercially successful electronic pH meter.
The Radiometer Corporation of Denmark was founded in 1935, and began marketing a pH meter for medical use around 1936, but "the development of automatic pH-meters for industrial purposes was neglected. Instead American instrument makers successfully developed industrial pH-meters with a wide variety of applications, such as in breweries, paper works, alum works, and water treatment systems."
In the 1940s the electrodes for pH meters were often difficult to make, or unreliable due to brittle glass. Dr. Werner Ingold began to industrialize the production of single-rod measuring cells, a combination of measurement and reference electrode in one construction unit, which led to broader acceptance in a wide range of industries including pharmaceutical production.
Beckman marketed a portable "Pocket pH Meter" as early as 1956, but it did not have a digital read-out.
In the 1970s Jenco Electronics of Taiwan designed and manufactured the first portable digital pH meter. This meter was sold under the label of the Cole-Parmer Corporation.
== Building a pH meter ==
Specialized manufacturing is required for the electrodes, and details of their design and construction are typically trade secrets. However, with purchase of suitable electrodes, a standard multimeter can be used to complete the construction of the pH meter. However, commercial suppliers offer voltmeter displays that simplify use, including calibration and temperature compensation.
== See also ==
Antimony electrode
Ion-selective electrodes
ISFET pH electrode
Potentiometry
Quinhydrone electrode
Saturated calomel electrode
Silver chloride electrode
Standard hydrogen electrode
== References ==
== External links ==
Introduction to pH measurement – Overview of pH and pH measurement at the Omega Engineering website
What is pH meter? – Overview
Development of the Beckman pH Meter – National Historic Chemical Landmark of the American Chemical Society
pH Measurement Handbook - A publication of the Thermo-Scientific Co.
Monograph: pH measurement – Everything from A - Z by Metrohm AG

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PQube is a registered trademark of Power Standards Lab for an electronic measuring instrument that records power quality and electric energy on the electric power grid.
== Applications ==
PQube instruments are widely used to gather data for academic research, and at United States Department of Energy National Laboratories and state energy regulators. U.S. federal government agencies use PQubes to detect power quality issues – for example, the Federal Aviation Administration tracks disturbances at radar control centers.
Each PQube instrument is traceable to the National Institute of Standards and Technology, so often these instruments are used in international academic and research environments.
PQubes are a key element in many smart grid projects, recording power disturbance and power flow data to examine efficiency and reliability effects.
== Information on the Web ==
Approximately 50 PQubes, located in approximately 40 countries, have been designated by their owners as free public sources of information at http://map.pqube.com . The site is updated approximately every 2 minutes with worldwide power quality and energy recordings.
Data from these PQubes can be used, for example, for developing and testing power quality algorithms.
Available data include daily, weekly, and monthly files in GIF and Microsoft Excel CSV format. Voltage and current oscillographs are recorded during every power disturbance and these worldwide locations, and are freely available. Data from each worldwide site is updated approximately once per minute.
== References ==
== External links ==
Data from the PSL PQube, Power Standards Lab

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A Particle mass analyser (PMA) is an instrument for classifying aerosol particles according to their mass-to-charge ratio using opposing electrical and centrifugal forces. This allows the classifier to select particles of a specified mass-to-charge ratio independent of particle shape.
It one of the three types of monodisperse aerosol classifier, the others being the differential mobility analyser (DMA, for electrical mobility size), and the aerodynamic aerosol classifier (AAC, for relaxation time, or aerodynamic diameter). The corresponding three quantities are related by the expression τ = mB, where τ is relaxation time, m is mass and B is mobility.
Further work improved the technique by engineering the centrifugal force to match the electrostatic force across the whole classification region, thus increasing the throughput.
== References ==

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A Polarograph is a chemical analysis instrument used to record automatic voltage-intensity curves.
The Polarograph uses an electrolytic cell consisting of an electrode or microelectrode small area, generally of the mercury drop type, which is a very fine capillary tube through which mercury flows slowly, which comes in the form of small droplets, which fall on the same surface of a much broader element, which is the other electrode . When one applies a variable voltage in this cell, the electrode's large area remains unchanged, while the microelectrode undergoes a change of potential, ( i.e. is polarized). It also has a potentiometer coupled to the motor that moves the recording paper so that a certain voltage variation corresponds to a constant length of recording paper, and a galvanometer suitable for measuring the intensity of the electric current, whose response is transmitted to the actuator that moves the needle of the recorder. The technique used is called polarography. The Czech chemist and Nobel Prize winner Jaroslav Heyrovský invented it.
== References ==

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The post office box was a Wheatstone bridge–style testing device with pegs and spring arms to close electrical circuits and measure properties of the circuit under test.
== Resistance measurement ==
The boxes were used in the United Kingdom by engineers from then General Post Office, who were responsible for UK telecommunications to trace electrical faults, i.e. to determine where a break occurred in a cable which could be several miles in length. It works on the principle of Wheatstone bridge to identify the resistance of wire connected and then by using wire resistivity and cross section calculating length of wire and thus determining where the cable had broken.
Post office boxes were common pieces of scientific apparatus in the UK O-Level and A-Level schools public examination physics syllabus in the 1960s.
== Construction ==
A typical post office box is in a wooden box with a hinged lid and a metal or bakelite panel showing circuit connections. Coils of wire are wound non-inductively, mounted in the body of the box, and have a negligible temperature coefficient.
Pairs of ratio arms are each 5 10 20 ohms. Resistance arms contains a number of coils from 1 to 5000 ohms with a plug for infinite resistance.
== See also ==
Electronics portal
== References ==

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A probe tip is an instrument used in scanning probe microscopes (SPMs) to scan the surface of a sample and make nano-scale images of surfaces and structures. The probe tip is mounted on the end of a cantilever and can be as sharp as a single atom. In microscopy, probe tip geometry (length, width, shape, aspect ratio, and tip apex radius) and the composition (material properties) of both the tip and the surface being probed directly affect resolution and imaging quality. Tip size and shape are extremely important in monitoring and detecting interactions between surfaces. SPMs can precisely measure electrostatic forces, magnetic forces, chemical bonding, Van der Waals forces, and capillary forces. SPMs can also reveal the morphology and topography of a surface.
The use of probe-based tools began with the invention of scanning tunneling microscopy (STM) and atomic force microscopy (AFM), collectively called scanning probe microscopy (SPM) by Gerd Binnig and Heinrich Rohrer at the IBM Zurich research laboratory in 1982. It opened a new era for probing the nano-scale world of individual atoms and molecules as well as studying surface science, due to their unprecedented capability to characterize the mechanical, chemical, magnetic, and optical functionalities of various samples at nanometer-scale resolution in a vacuum, ambient, or fluid environment.
The increasing demand for sub-nanometer probe tips is attributable to their robustness and versatility. Applications of sub-nanometer probe tips exist in the fields of nanolithography, nanoelectronics, biosensor, electrochemistry, semiconductor, micromachining and biological studies.
== History and development ==
Increasingly sharp probe tips have been of interest to researchers for applications in the material, life, and biological sciences, as they can map surface structure and material properties at molecular or atomic dimensions. The history of the probe tip can be traced back to 1859 with a predecessor of the modern gramophone, called the phonautograph. During the later development of the gramophone, the hog's hair used in the phonautograph was replaced with a needle used to reproduce sound. In 1940, a pantograph was built utilizing a shielded probe and adjustable tip. A stylus was free moving allowing it to slide vertically in contact with the paper. In 1948, a circuit was employed in the probe tip to measure peak voltage, creating what may be considered the first scanning tunneling microscope (STM). The fabrication of electrochemically etched sharp tungsten, copper, nickel and molybdenum tips were reported by Muller in 1937. A revolution in sharp tips then occurred, producing a variety of tips with different shapes, sizes, and aspect ratios. They composed of tungsten wire, silicon, diamond and carbon nanotubes with Si-based circuit technologies. This allowed the production of tips for numerous applications in the broad spectrum of nanotechnological fields.
Following the development of STM, atomic force microscopy (AFM) was developed by Gerd Binnig, Calvin F. Quate, and Christoph Gerber in 1986. Their instrument used a broken piece of diamond as the tip with a hand-cut gold foil cantilever. Focused ion and electron beam techniques for the fabrication of strong, stable, reproducible Si3N4 pyramidal tips with 1.0 μm length and 0.1 μm diameter were reported by Russell in 1992. Significant advancement also came through the introduction of micro-fabrication methods for the creation of precise conical or pyramidal silicon and silicon nitride tips. Numerous research experiments were conducted to explore fabrication of comparatively less expensive and more robust tungsten tips, focusing on a need to attain less than 50 nm radius of curvature.
A new era in the field of fabrication of probe tips was reached when the carbon nanotube, an approximately 1 nm cylindrical shell of graphene, was introduced. The use of single wall carbon nanotubes makes the tips more flexible and less vulnerable to breaking or crushing during imaging. Probe tips made from carbon nano-tubes can be used to obtain high-resolution images of both soft and weakly adsorbed biomolecules like DNA on surfaces with molecular resolution.
Multifunctional hydrogel nano-probe techniques also advanced tip fabrication and resulted in increased applicability for inorganic and biological samples in both air and liquid. The biggest advantage of this mechanical method is that the tip can be made in different shapes, such as hemispherical, embedded spherical, pyramidal, and distorted pyramidal, with diameters ranging from 10 nm – 1000 nm. This covers applications including topography or functional imaging, force spectroscopy on soft matter, biological, chemical and physical sensors. Table 1. Summarizes various methods for fabricating probe tips, and the associated materials and applications.
== Tunneling current and force measurement principle ==
The tip itself does not have any working principle for imaging, but depending on the instrumentation, mode of application, and the nature of the sample under investigation, the probe's tip may follow different principles to image the surface of the sample. For example, when a tip is integrated with STM, it measures the tunneling current that arises from the interaction between the sample and the tip. In AFM, short-ranged force deflection during the raster scan by the tip across the surface is measured. A conductive tip is essential for the STM instrumentation whereas AFM can use conductive and non-conductive probe tip. Although the probe tip is used in various techniques with different principles, for STM and AFM coupled with probe tip is discussed in detail.
=== Conductive probe tip ===
As the name implies, STM utilizes the tunneling charge transfer principle from tip to surface or vice versa, thereby recording the current response. This concept originates from a particle in a box concept; if potential energy for a particle is small, the electron may be found outside of the potential well, which is a classically forbidden region. This phenomenon is called tunneling.
Expression derived from Schrödinger equation for transmission charge transfer probability is as follows:
T
=
16
ϵ
(
1
−
ϵ
)
−
2
k
{\displaystyle T=16\epsilon (1-\epsilon )^{-2k}}
where
ϵ
=
E
V
=
Kinetic energy/potential energy
{\displaystyle \epsilon ={\frac {E}{V}}={\text{Kinetic energy/potential energy}}}
k
=
2
π
2
m
E
h
{\displaystyle k=2\pi {\sqrt {\frac {2mE}{h}}}}
h
{\displaystyle h}
is the Planck constant

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=== Non-conductive probe tip ===
Non-conductive nanoscale tips are widely used for AFM measurements. For non-conducting tip, surface forces acting on the tip/cantilever are responsible for deflection or attraction of tip. These attractive or repulsive forces are used for surface topology, chemical specifications, magnetic and electronic properties. The distance-dependent forces between substrate surface and tip are responsible for imaging in AFM. These interactions include van der Waals forces, capillary forces, electrostatic forces, Casimir forces, and solvation forces. One unique repulsion force is Pauli Exclusion repulsive force, which is responsible for single-atom imaging as in references and Figures 10 & 11 (contact region in Fig. 1).
== Fabrication methods ==
Tip fabrication techniques fall into two broad classifications, mechanical and physicochemical. In the early stage of the development of probe tips, mechanical procedures were popular because of the ease of fabrication.
=== Mechanical methods ===
Reported mechanical methods in fabricating tips include cutting, grinding, and pulling.; an example would be cutting a wire at certain angles with a razor blade, wire cutter, or scissors. Another mechanical method for tip preparation is fragmentation of bulk pieces into small pointy pieces. Grinding a metal wire or rod into a sharp tip was also a method used. These mechanical procedures usually leave rugged surfaces with many tiny asperities protruding from the apex, which led to atomic resolution on flat surfaces. However, irregular shape and large macroscopic radius of curvature result in poor reproducibility and decreased stability especially for probing rough surfaces. Another main disadvantage of making probes by this method is that it creates many mini tips which lead to many different signals, yielding error in imaging. Cutting, grinding and pulling procedures can only be adapted for metallic tips like W, Ag, Pt, Ir, Pt-Ir and gold. Non-metallic tips cannot be fabricated by these methods.
In contrast, a sophisticated mechanical method for tip fabrication is based on the hydro-gel method. This method is based on a bottom-up strategy to make probe tips by a molecular self-assembly process. A cantilever is formed in a mould by curing the pre-polymer solution, then it is brought into contact with the mould of the tip which also contains the pre-polymer solution. The polymer is cured with ultraviolet light which helps to provide a firm attachment of the cantilever to the probe. This fabrication method is shown in Fig. 2.
=== Physio-chemical procedures ===
Physiochemical procedures are fabrication methods of choice, which yield extremely sharp and symmetric tips, with more reproducibility compared to mechanical fabrication-based tips. Among physicochemical methods, the electrochemical etching method is one of the most popular methods. Etching is a two or more step procedure. The "zone electropolishing" is the second step which further sharpens the tip in a very controlled manner. Other physicochemical methods include chemical vapor deposition and electron beam deposition onto pre-existing tips. Other tip fabrication methods include field ion microscopy and ion milling. In field ion microscopy techniques, consecutive field evaporation of single atoms yields specific atomic configuration at the probe tip, which yields very high resolution.
==== Fabrication through etching ====
Electrochemical etching is one of the most widely accepted metallic probe tip fabrication methods. Three commonly used electrochemical etching methods for tungsten tip fabrication are single lamella drop-off methods, double lamella drop-off method, and submerged method. Various cone shape tips can be fabricated by this method by minor changes in the experimental setup. A DC potential is applied between the tip and a metallic electrode (usually W wire) immersed in solution (Figure 3 a-c); electrochemical reactions at cathode and anode in basic solutions (2M KOH or 2M NaOH) are usually used. The overall etching process involved is as follows:
Anode;
W
(
s
)
+
8
OH
−
⟶
WO
4
+
4
H
2
O
+
6
e
−
(
E
=
1
⋅
05
V
)
{\displaystyle {\ce {W (s) + 8OH- -> WO4 + 4H2O + 6e- (E= 1.05V)}}}
Cathode:
6
H
2
O
+
6
e
−
⟶
3
H
2
+
6
OH
−
(
E
=
−
2
⋅
48
V
)
{\displaystyle {\ce {6H2O + 6e- -> 3H2 + 6OH- (E=-2.48V)}}}
Overall:
W
(
s
)
+
2
OH
−
⟶
WO
4
2
−
+
2
H
2
O
(
l
)
+
6
e
−
+
3
H
2
(
g
)
(
E
=
−
1
⋅
43
V
)
{\displaystyle {\ce {W (s) + 2OH- -> WO4^2- + 2H2O (l) + 6e- + 3H2 (g) (E= -1.43V)}}}
Here, all the potentials are reported vs. SHE.
The schematics of the fabrication method of probe tip production through the electrochemical etching method is shown in Fig. 3.
In the electrochemical etching process, W is etched at the liquid, solid, and air interface; this is due to surface tension, as shown in Fig. 3. Etching is called static if the W wire is kept stationary. Once the tip is etched, the lower part falls due to the lower tensile strength than the weight of the lower part of the wire. The irregular shape is produced by the shifting of the meniscus. However, slow etching rates can produce regular tips when the current flows slowly through the electrochemical cells. Dynamic etching involves slowly pulling up the wire from the solution, or sometimes the wire is moved up and down (oscillating wire) producing smooth tips.
==== Submerged method ====
In this method, a metal wire is vertically etched, reducing the diameter from 0.25 mm ~ 20 nm. A schematic diagram for probe tip fabrication with submerged electrochemical etching method is illustrated in Fig 4. These tips can be used for high-quality STM images.

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==== Lamella method ====
In the double lamella method, the lower part of the metal is etched away, and the upper part of the tip is not etched further. Further etching of the upper part of the wire is prevented by covering it with a polymer coating. This method is usually limited to laboratory fabrication. The double lamella method schematic is shown in Fig. 5.
=== Single atom tip preparation ===
Transitional metals like Cu, Au and Ag adsorb single molecules linearly on their surface due to weak van der Waals forces. This linear projection of single molecules allows interactions of the terminal atoms of the tip with the atoms of the substrate, resulting in Pauli repulsion for single molecule or atom mapping studies. Gaseous deposition on the tip is carried out in an ultrahigh vacuum (5 × 10−8 mbar) chamber at a low temperature (10K). Depositions of Xe, Kr, NO, CH4 or CO on tip have been successfully prepared and used for imaging studies. However, these tips preparations rely on the attachment of single atoms or molecules on the tip and the resulting atomic structure of the tip is not known exactly. The probability of attachment of simple molecules on metal surfaces is very tedious and required great skill; as such, this method is not widely used.
=== Chemical vapor deposition (CVD) ===
Sharp tips used in SPM are fragile, and prone to wear and tear under high working loads. Diamond is considered the best option to address this issue. Diamond tips for SPMs are fabricated by fracturing, grinding and polishing bulk diamond, resulting in a considerable loss of diamond. One alternative is depositing a thin diamond film on Silicone tips by CVD. In CVD, diamond is deposited directly on silicon or W cantilevers. A is shown in Fig. 6. In this method, the flow of methane and hydrogen gas is controlled to maintain an internal pressure of 40 Torr inside the chamber. CH4 and H2 dissociate at 2100 °C with the help of the Ta filament, and nucleation sites are created on the tip of the cantilever. Once CVD is complete, the flow of CH4 is stopped and the chamber is cooled under the flow of H2. A schematic diagram of a CVD setup used for diamond tip fabrication for AFM application is shown in Fig. 6.
=== Reactive ion etching (RIE) fabrication ===
A groove or structure is made on a substrate to form a template. The desired material is then deposited in that template. Once the tip is formed, the template is etched off, leaving the tip and cantilever. Fig. 7 illustrates diamond tip fabrication on silicon wafers using this method.
=== Focused ion beam (FIB) milling ===
FIB milling is a sharpening method for probe tips in SPM. A blunt tip is first fabricated by other etching methods, such as CVD, or the use of a pyramid mold for pyramidal tips. This tip is then sharpened by FIB milling as shown in Fig. 8. The diameter of the focused ion beam, which directly affects the tip's final diameter, is controlled through a programmable aperture.
=== Glue ===
This method is used to attach carbon nanotubes to a cantilever or blunt tip. A strong adhesive (such as soft acrylic glue) is used to bind CNT with the silicon cantilever. CNT is robust, stiff and increases the durability of probe tips, and can be used for both contact and tapping mode.
== Cleaning procedures ==
Electrochemically etched tips are usually covered with contaminants on their surfaces which cannot be removed simply by rinsing in water, acetone or ethanol. Some oxide layers on metallic tips, especially on tungsten, need to be removed by post-fabrication treatment.
=== Annealing ===
To clean W sharp tips, it is highly desirable to remove contaminant and the oxide layer. In this method a tip is heated in an UHV chamber at elevated temperature which desorb the contaminated layer. The reaction details are shown below.
2WO3 + W → 3WO2 ↑
WO2 → W (sublimation at
∽
{\displaystyle \backsim }
1075K)
At elevated temperature, trioxides of W are converted to WO2 which sublimates around 1075K, and cleaned metallic W surfaces are left behind. An additional advantage provided by annealing is the healing of crystallographic defects produced by fabrication, and the process also smoothens the tip surface.
=== HF chemical cleaning ===
In the HF cleaning method, a freshly prepared tip is dipped in 15% concentrated hydrofluoric acid for 10 to 30 seconds, which dissolves the oxides of W.
=== Ion milling ===
In this method, argon ions are directed at the tip surface to remove the contaminant layer by sputtering. The tip is rotated in a flux of argon ions at a certain angle, in a way that allows the beam to target the apex. The bombardment of ions at the tip depletes the contaminants and also results in a reduction of the radius of the tip. The bombardment time needs to be finely tuned with respect to the shape of the tip. Sometimes, short annealing is required after ion milling.
=== Self-sputtering ===
This method is very similar to ion milling, but in this procedure, the UHV chamber is filled with neon at a pressure of 10−4 mbar. When a negative voltage is applied on the tip, a strong electric field (produced by tip under negative potential) will ionize the neon gas, and these positively charged ions are accelerated back to the tip, where they cause sputtering. The sputtering removes contaminants and some atoms from the tip which, like ion milling, reduces the apex radius. By changing the field strength, one can tune the radius of the tip to 20 nm.

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== Coating ==
The surface of silicon-based tips cannot be easily controlled because they usually carry the silanol group. The Si surface is hydrophilic and can be contaminated easily by the environment. Another disadvantage of Si tips is the wear and tear of the tip. It is important to coat the Si tip to prevent tip deterioration, and the tip coating may also enhance image quality. To coat a tip, an adhesive layer is pasted (usually chromium layer on 5 nm thick titanium) and then gold is deposited by vapor deposition (40-100 nm or less). Sometimes, the coating layer reduces the tunnelling current detection capability of probe tips.
== Characterization ==
The most important aspect of a probe tip is imaging the surfaces efficiently at nanometre dimensions. Some concerns involving credibility of the imaging or measurement of the sample arise when the shape of the tip is not determined accurately. For example, when an unknown tip is used to measure a linewidth pattern or other high aspect ratio feature of a surface, there may remain some confusion when determining the contribution of the tip and of the sample in the acquired image. Consequently, it is important to fully and accurately characterize the tips. Probe tips can be characterized for their shape, size, sharpness, bluntness, aspect ratio, radius of curvature, geometry and composition using many advanced instrumental techniques. For example, electron field emission measurement, scanning electron microscopy (SEM), transmission electron microscopy (TEM), scanning tunnelling spectroscopy as well as more easily accessible optical microscope. In some cases, optical microscopy cannot provide exact measurements for small tips in nanoscale due to the resolution limitation of the optical microscopy.
=== Electron field emission current measurement ===
In the electron field emission current measurement method, a high voltage is applied between the tip and another electrode, followed by measuring field emission current employing Fowler-Nordheim curves
[
log
10
⁡
(
1
/
V
2
)
v
s
.
(
1
/
V
)
]
{\displaystyle [\log _{10}(1/V^{2})vs.(1/V)]}
. Large fields-emission current measurements may indicate that the tip is sharp, and low field-emission current indicates that the tip is blunt, molten or mechanically damaged. A minimum voltage is essential to facilitate the release of electrons from the surface of the tip which in turn indirectly is used to obtain the tip curvature. Although this method has several advantages, a disadvantage is that the high electric field required for producing strong electric force can melt the apex of the tip, or might change the crystallographic tip nature.
=== Scanning electron microscopy and transmission electron microscopy ===
The size and shape of the tip can be obtained by scanning electron microscopy and transmission electron microscopy measurements. In addition, transmission electron microscopy (TEM) images are helpful to detect any layer of insulating materials on the surface of the tip as well as to estimate the size of the layer. These oxides are formed gradually on the surface of tip soon after fabrication, due to the oxidation of the metallic tip by reacting with the O2 present in the surrounding atmosphere. Scanning electron microscopy (SEM) has a resolution limitation of below 4 nm, so TEM may be needed to observe even a single atom theoretically and practically. Tip grain down to 1-3 nm, thin polycrystalline oxides, or carbon or graphite layers at the tip apex, are routinely measured using TEM. The orientation of tip crystal, which is the angle between the tip plane in the single-crystal and the tip normal, can be estimated.
=== Optical microscopy ===
In the past, optical microscopes were the only method used to investigate whether the tip is bent, through microscale imaging at many microscales. This is because the resolution limitation of an optical microscope is about 200 nm. Imaging software, including ImageJ, allows determination of the curvature, and aspect ratio of the tip. One drawback of this method is that it renders an image of tip, which is an object due to the uncertainty in the nanoscale dimension. This problem can be resolved by taking images of the tip multiple times, followed by combining them into an image by confocal microscope with some fluorescent material coating on the tip. It is also a time-consuming process due to the necessity of monitoring the wear or damage or degradation of the tip by collision with the surface during scanning the surface after each scan.
=== Scanning tunneling spectroscopy ===
The scanning tunneling spectroscopy (STS) is spectroscopic form of STM. Spectroscopic data based on curvature is obtained to analyze the existence of any oxides or impurities on the tip. This is done by monitoring the linearity of the curve, which represents metallic tunnel junction. Generally, the curve is non-linear; hence, the tip has a gap-like shape around zero bias voltage for oxidized or impure tip, whereas the opposite is observed for sharp pure un-oxidized tip.
=== Auger electron spectroscopy, X-ray photoelectron spectroscopy ===
In Auger electron spectroscopy (AES), any oxides present on the tip surface are sputtered out during in-depth analysis with argon ion beam generated by differentially pumped ion pump, followed by comparing the sputtering rate of the oxide with experimental sputtering yields. These Auger measurements may estimate the nature of oxides because of the surface contamination. Composition can also be revealed, and in some cases, thickness of the oxide layer down to 1-3 nm can be estimated. X-ray photoelectron spectroscopy also performs similar characterization for the chemical and surface composition, by providing information on the binding energy of the surface elements.
Overall, the aforementioned characterization methods of tips can be categorized into three major classes. They are as follows:

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Imaging tip using microscopy is used to take image of tip with microscopy, except scanning probe microscopy (SPM) e.g. scanning tunnelling microscopy (STM), atomic force microscopy (AFM) are reported.
Using known tip characterizer is when the shape of tip is deduced by taking an image of a sample of known measurement, which is known as tip characterizer.
Blind method is where tip characterizer of either known or unknown measurement is used.
== Applications ==
Probes tips have a wide variety of applications in different fields of science and technology. One of the major areas where probe tips are used is for application in SPM i.e., STM and AFM. For example, carbon nanotube tips in conjunction with AFM provides an excellent tool for surface characterization in the nanometer realm. CNT tips are also used in tapping-mode Scanning Force Microscopy (SFM), which is a technique where a tip taps a surface by a cantilever driven near resonant frequency of the cantilever. The CNT probe tips fabricated using CVD technique can be used for imaging of biological macromolecules, semiconductor and chemical structure. For example, it is possible to obtain an intermittent AFM contact image of IgM macromolecules with excellent resolution using a single CNT tip. Individual CNT tips can be used for high resolution imaging of protein molecules.
In another application, multiwall carbon nanotube (MWCNT) and single wall carbon nanotube (SWCNT) tips were used to image amyloid β (1-40) derived protofibrils and fibrils by tapping mode AFM. Functionalized probes can be used in Chemical Force Microscopy (CFM) to measure intermolecular forces and map chemical functionality. Functionalized SWCNT probes can be used for chemically sensitive imaging with high lateral resolution and to study binding energy in chemical and biological system. Probe tips that have been functionalized with either hydrophobic or hydrophilic molecules can be used to measure the adhesive interaction between hydrophobic-hydrophobic, hydrophobic-hydrophilic, and hydrophilic-hydrophilic molecules. From these adhesive interactions the friction image of patterned sample surface can be found. Probe tips used in force microscopy can provide imaging of structure and dynamics of adsorbate at the nanometer scale. Self-assembled functionalized organic thiols on the surface of Au coated Si3N4 probe tips have been used to study the interaction between molecular groups. Again, carbon nanotube probe tips in conjunction with AFM can be used for probing crevices that occur in microelectronic circuits with improved lateral resolution. Functionality modified probe tips have been to measure the binding force between single protein-ligand pairs. Probe tips have been used as a tapping mode technique to provide information about the elastic properties of materials. Probe tips are also used in the mass spectrometer. Enzymatically active probe tips have been used for the enzymatic degradation of analytes. They have also been used as devices to introduce samples into the mass spectrophotometer. For example, trypsin-activated gold (Au/trypsin) probe tips can be used for the peptide mapping of the hen egg lysozyme.
Atomically sharp probe tips can be used for imaging a single atom in a molecule. An example of visualizing single atoms in water cluster can be seen in Fig. 10. By visualizing single atoms in molecules present on a surface, scientists can determine bond length, bond order and discrepancies, if any, in conjugation which was previously thought to be impossible in experimental work. Fig. 9 shows the experimentally determined bond order in a poly-aromatic compound, which was thought to be very hard in the past.
== References ==

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In fluid mechanics (specifically rheology), a rheoscope is an instrument for detecting or measuring the viscosity of a fluid.
In the study of blood flow, a rheoscope is used to observe and measure the deformation of blood cells subject to different levels of fluid shear stress.
== References ==
Stein, Jess, ed. (1980). The Random House college dictionary. Random House. p. 1132. ISBN 0-394-43600-8.

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A scale of chords may be used to set or read an angle in the absence of a protractor. To draw an angle, compasses describe an arc from origin with a radius taken from the 60 mark. The required angle is copied from the scale by the compasses, and an arc of this radius drawn from the sixty mark so it intersects the first arc. The line drawn from this point to the origin will be at the target angle.
== Mathematics ==
A chord is a line drawn between two points on the circumference of a circle. Look at the centre point of this line. For a circle of radius r, each half will be
r
sin
⁡
θ
2
{\displaystyle r\sin {\tfrac {\theta }{2}}}
so the chord will be
2
r
sin
⁡
θ
2
{\displaystyle 2r\sin {\tfrac {\theta }{2}}}
. The line of chords scale represents each of these values linearly on a scale running from 0 to 60.
== Availability ==
It appears on Gunter's scale and the Foster Serle dialing scales. The commercial company Stanley marketed a metal version (Stanley 60R Line of Chords Rule) in 2015.
== See also ==
Ptolemy's table of chords
== References ==
Notes
Bibliography
Agrawal, Basant (1964). Engineering Drawing. Tata McGraw-Hill Education. ISBN 1259083136. {{cite book}}: ISBN / Date incompatibility (help)