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Logarithmic scale

A logarithmic scale is a nonlinear scale used for a large range of positive multiples of some quantity. Common uses include earthquake strength, sound loudness, light intensity, pH of solutions, it is based on orders of magnitude, rather than a standard linear scale, so the value represented by each equidistant mark on the scale is the value at the previous mark multiplied by a constant. Logarithmic scales are used in slide rules for multiplying or dividing numbers by adding or subtracting lengths on the scales; the following are examples of used logarithmic scales, where a larger quantity results in a higher value: Richter magnitude scale and moment magnitude scale for strength of earthquakes and movement in the earth sound level, with units bel and decibel neper for amplitude and power quantities frequency level, with units cent, minor second, major second, octave for the relative pitch of notes in music logit for odds in statistics Palermo Technical Impact Hazard Scale logarithmic timeline counting f-stops for ratios of photographic exposure the rule of'nines' used for rating low probabilities entropy in thermodynamics information in information theory particle-size-distribution curves of soilThe following are examples of used logarithmic scales, where a larger quantity results in a lower value: pH for acidity stellar magnitude scale for brightness of stars Krumbein scale for particle size in geology absorbance of light by transparent samplesSome of our senses operate in a logarithmic fashion, which makes logarithmic scales for these input quantities appropriate.

In particular our sense of hearing perceives equal ratios of frequencies as equal differences in pitch. In addition, studies of young children in an isolated tribe have shown logarithmic scales to be the most natural display of numbers in some cultures, it can be used for geographical purposes like for measuring the speed of earthquakes. The top left graph is linear in the X and Y axis, the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y axis of the bottom left graph, the Y axis ranges from 0.1 to 1,000. The top right graph uses a log-10 scale for just the X axis, the bottom right graph uses a log-10 scale for both the X axis and the Y axis. Presentation of data on a logarithmic scale can be helpful when the data: covers a large range of values, since the use of the logarithms of the values rather than the actual values reduces a wide range to a more manageable size. A slide rule has logarithmic scales, nomograms employ logarithmic scales; the geometric mean of two numbers is midway between the numbers.

Before the advent of computer graphics, logarithmic graph paper was a used scientific tool. If both the vertical and horizontal axes of a plot are scaled logarithmically, the plot is referred to as a log–log plot. If only the ordinate or abscissa is scaled logarithmically, the plot is referred to as a semi-logarithmic plot. A logarithmic unit is a unit that can be used to express a quantity on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type; the choice of unit indicates the type of quantity and the base of the logarithm. Examples of logarithmic units include units of data storage capacity, of information and information entropy, signal level. Logarithmic frequency quantities are used for music pitch intervals. Other logarithmic scale units include the Richter magnitude scale point. Bit, byte hartley nat shannon bel, decibel neper decade, savart octave, semitone, cent The two definitions of a decibel are equivalent, because a ratio of power quantities is equal to the square of the corresponding ratio of root-power quantities.

The motivation behind the concept of logarithmic units is that defining a quantity on a logarithmic scale in terms of a logarithm to a specific base amounts to making a choice of a unit of measurement for that quantity, one that corresponds to the specific logarithm base, selected. Due to the identity log b ⁡ a = log c ⁡ a log c ⁡ b, the logarithms of any given number a to two different bases differ only by the constant factor logc b; this constant factor can be considered to represent the conversion factor for converting a numerical representation of the pure logarithmic quantity Log from one arbitrary unit of measurement to another, since Log ⁡ = =. For example, Boltzmann's standard definition of entropy S = k ln W can be written more as just S = Log, where "Log" here denotes the indefinite logarithm, we let k =; this identity works be

Paul Madden (diplomat)

Paul Damian Madden is a British diplomat, High Commissioner to Singapore and to Australia, Ambassador to Japan since January 2017. Madden was educated at The King's School, Ottery St Mary, Gonville and Caius College, where he gained a BA degree in economic geography, he has a Master of Business Administration degree from Durham University. He is a Fellow of the Royal Geographical Society. Madden began his career in the Department of Trade and Industry where he was Private Secretary to the Minister 1984–86, he studied Japanese at the School of Oriental and African Studies, University of London, at Kamakura, Japan, before joining the Diplomatic Service. He served at the Embassy in Tokyo 1988–92, at the Foreign and Commonwealth Office, dealing with EU enlargement and Environmental issues, 1992–96, at the Embassy in Washington, D. C. 1996–2000. He was Deputy High Commissioner in Singapore 2000–03, Assistant Director of Information at the FCO 2003–04, Managing Director at UK Trade & Investment 2004–06.

He was British High Commissioner in Singapore 2007–11 and High Commissioner to Australia 2011–15. Madden was appointed Companion of the Order of St Michael and St George in the 2013 Birthday Honours. In April 2016 Madden was appointed British Ambassador to Japan in succession to Tim Hitchens, he took up his appointment in January 2017 as planned. Madden, Paul. Raffles: lessons in business leadership. Singapore: WhosWho Publishing. MADDEN, Paul Damian, Who's Who 2013, A & C Black, 2013.

Oliver Lambart, 1st Baron Lambart

Oliver Lambart, 1st Lord Lambart, Baron of Cavan was a military commander and an MP in the Irish House of Commons. He was Governor of Connaught in 1601, he was invested as a Privy Counsellor in 1603. He was an English MP, for Southampton 1597, he is buried in Westminster Abbey. Fighting the Spanish Lambert took part in the Dutch campaign under his commander Francis Vere: he was wounded in the assault on Steenwijk which led to its capture in 1592. On 20 June 1596, Effingham sacked the harbour of Cádiz; the Spanish scuttled their Indies fleet including a cargo of 12 million ducats. The force occupied the city until 5 July. Lambart was knighted for his part in the looting. During the Nine Years' War Lambart served in Essex's Irish campaign of 1599, he commanded the 200 Foot at County Wexford. On 6 January 1615, he retook Dunyvaig Castle, with the assistance of Sir John Campbell of Calder, he was in 1613 elected one of two MPs for County Cavan, sitting from 1613 to 1615. He was created Baron of Cavan, County Cavan shortly before his death.

His son was 1st Earl of Cavan. ThePeerage.com