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102-591: The International Tree-Ring Data Bank ( ITRDB ) is a data repository for tree ring measurements that has been maintained since 1990 by the United States' National Oceanic and Atmospheric Administration Paleoclimatology Program and World Data Center for Paleoclimatology. The ITRDB was initially established by Hal Fritts through the Laboratory of Tree-Ring Research at the University of Arizona , with

204-539: A 2 t 3 k v ρ 1 3 ( c 4 + c 1 e − a 1 t + c 2 e − a 2 t ) 2 3 {\displaystyle \Delta L(t)=-{\frac {c_{1}e^{-a_{1}t}+c_{2}e^{-a_{2}t}}{3k_{v}\rho ^{\frac {1}{3}}\left(c_{4}+c_{1}e^{-a_{1}t}+c_{2}e^{-a_{2}t}\right)^{\frac {2}{3}}}}} where c 1 , c 2 , and c 4 are some coefficients,

306-535: A 1 and a 2 are positive constants. The formula is useful for correct approximation of samples data before data normalization procedure. The typical forms of the function Δ L ( t ) of annual growth of wood ring are shown in the figures. Dendrochronology allows specimens of once-living material to be accurately dated to a specific year. Dates are often represented as estimated calendar years B.P. , for before present, where "present" refers to 1 January 1950. Timber core samples are sampled and used to measure

408-491: A German professor of forest pathology, wrote a series of papers on the anatomy and ecology of tree rings. In 1892, the Russian physicist Fedor Nikiforovich Shvedov  [ ro ; ru ; uk ] (1841–1905) wrote that he had used patterns found in tree rings to predict droughts in 1882 and 1891. During the first half of the twentieth century, the astronomer A. E. Douglass founded the Laboratory of Tree-Ring Research at

510-550: A broader syllabus and more interest in applications; but William Whewell found the programme unacceptable. A controversy Babbage had with Richard Jones lasted for six years. He never did give a lecture. It was during this period that Babbage tried to enter politics. Simon Schaffer writes that his views of the 1830s included disestablishment of the Church of England , a broader political franchise , and inclusion of manufacturers as stakeholders. He twice stood for Parliament as

612-531: A candidate for the borough of Finsbury . In 1832 he came in third among five candidates, missing out by some 500 votes in the two-member constituency when two other reformist candidates, Thomas Wakley and Christopher Temple, split the vote. In his memoirs Babbage related how this election brought him the friendship of Samuel Rogers : his brother Henry Rogers wished to support Babbage again, but died within days. In 1834 Babbage finished last among four. In 1832, Babbage, Herschel and Ivory were appointed Knights of

714-708: A conventional resident don , and inattentive to his teaching responsibilities, he wrote three topical books during this period of his life. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1832. Babbage was out of sympathy with colleagues: George Biddell Airy , his predecessor as Lucasian Professor of Mathematics at Trinity College, Cambridge, thought an issue should be made of his lack of interest in lecturing. Babbage planned to lecture in 1831 on political economy . Babbage's reforming direction looked to see university education more inclusive, universities doing more for research,

816-550: A degree without examination in 1814. He had defended a thesis that was considered blasphemous in the preliminary public disputation, but it is not known whether this fact is related to his not sitting the examination. Considering his reputation, Babbage quickly made progress. He lectured to the Royal Institution on astronomy in 1815, and was elected a Fellow of the Royal Society in 1816. After graduation, on

918-470: A divine legislator. In this book, Babbage dealt with relating interpretations between science and religion; on the one hand, he insisted that "there exists no fatal collision between the words of Scripture and the facts of nature;" on the other hand, he wrote that the Book of Genesis was not meant to be read literally in relation to scientific terms. Against those who said these were in conflict, he wrote "that

1020-504: A fast and lifelong friendship with Herschel and with Babbage, who was then quite young. I would ask any fair-minded mathematician to read Babbage's Ninth Bridgewater Treatise and compare it with the works of his contemporaries in England; and then ask himself whence came the peculiar conception of the nature of miracle which underlies Babbage's ideas of Singular Points on Curves (Chap, viii) – from European Theology or Hindu Metaphysic? Oh! how

1122-401: A gradual replacement of wooden panels by canvas as the support for paintings, which means the technique is less often applicable to later paintings. In addition, many panel paintings were transferred onto canvas or other supports during the nineteenth and twentieth centuries. The dating of buildings with wooden structures and components is also done by dendrochronology; dendroarchaeology is

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1224-585: A grant from the US National Science Foundation , following the First International Workshop on Dendrochronology in 1974. The ITRDB accepts all tree ring data with sufficient metadata to be uploaded, but its founding focus was on tree ring measurements intended for climatic studies . Specific information is required for uploading data to the database, such as the raw tree ring measurements, an indication of

1326-659: A later visit to Piedmont . In April 1828 he was in Rome , and relying on Herschel to manage the difference engine project, when he heard that he had become a professor at Cambridge, a position he had three times failed to obtain (in 1820, 1823 and 1826). Babbage was instrumental in founding the Royal Astronomical Society in 1820, initially known as the Astronomical Society of London. Its original aims were to reduce astronomical calculations to

1428-625: A life-threatening fever. For a short time, he attended King Edward VI Grammar School in Totnes , South Devon, but his health forced him back to private tutors for a time. Babbage then joined the 30-student Holmwood Academy , in Baker Street, Enfield , Middlesex , under the Reverend Stephen Freeman. The academy had a library that prompted Babbage's love of mathematics. He studied with two more private tutors after leaving

1530-508: A meeting hosted by John Chapman to campaign against the Booksellers Association, still a cartel . It has been written that "what Arthur Young was to agriculture, Charles Babbage was to the factory visit and machinery". Babbage's theories are said to have influenced the layout of the 1851 Great Exhibition , and his views had a strong effect on his contemporary George Julius Poulett Scrope . Karl Marx argued that

1632-401: A more standard form, and to circulate data. These directions were closely connected with Babbage's ideas on computation, and in 1824 he won its Gold Medal , cited "for his invention of an engine for calculating mathematical and astronomical tables ". Babbage's motivation to overcome errors in tables by mechanisation had been a commonplace since Dionysius Lardner wrote about it in 1834 in

1734-512: A much greater number have been analysed. A portrait of Mary, Queen of Scots in the National Portrait Gallery, London was believed to be an eighteenth-century copy. However, dendrochronology revealed that the wood dated from the second half of the sixteenth century. It is now regarded as an original sixteenth-century painting by an unknown artist. On the other hand, dendrochronology was applied to four paintings depicting

1836-525: A prominent figure in the ideating of computing. Parts of his incomplete mechanisms are on display in the Science Museum in London. In 1991, a functioning difference engine was constructed from the original plans. Built to tolerances achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked. Babbage's birthplace is disputed, but according to

1938-503: A reference for subsequent European naturalists. In the U.S., Alexander Catlin Twining (1801–1884) suggested in 1833 that patterns among tree rings could be used to synchronize the dendrochronology of various trees and thereby to reconstruct past climates across entire regions. The English polymath Charles Babbage proposed using dendrochronology to date the remains of trees in peat bogs or even in geological strata (1835, 1838). During

2040-480: A relative internal chronology, they cannot be dendro-matched with the main Holocene absolute chronology. However, 14C analyses performed at high resolution on overlapped absolute and floating tree-rings series enable one to link them almost absolutely and hence to extend the calibration on annual tree rings until ≈13 900 cal yr BP." Herbchronology is the analysis of annual growth rings (or simply annual rings) in

2142-597: A section against another chronology (tree-ring history) whose dates are known. A fully anchored and cross-matched chronology for oak and pine in central Europe extends back 12,460 years, and an oak chronology goes back 7,429 years in Ireland and 6,939 years in England . Comparison of radiocarbon and dendrochronological ages supports the consistency of these two independent dendrochronological sequences. Another fully anchored chronology that extends back 8,500 years exists for

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2244-424: A small part of the radius of the trunk. Consequently, dating studies usually result in a terminus post quem (earliest possible) date, and a tentative date for the arrival of a seasoned raw panel using assumptions as to these factors. As a result of establishing numerous sequences, it was possible to date 85–90% of the 250 paintings from the fourteenth to seventeenth century analysed between 1971 and 1982; by now

2346-464: A student, Babbage was also a member of other societies such as The Ghost Club , concerned with investigating supernatural phenomena, and the Extractors Club, dedicated to liberating its members from the madhouse, should any be committed to one. In 1812, Babbage transferred to Peterhouse, Cambridge . He was the top mathematician there, but did not graduate with honours. He instead received

2448-402: A translation from French of the lectures of Sylvestre Lacroix , which was then the state-of-the-art calculus textbook. Reference to Lagrange in calculus terms marks out the application of what are now called formal power series . British mathematicians had used them from about 1730 to 1760. As re-introduced, they were not simply applied as notations in differential calculus . They opened up

2550-888: A uniform rate that was put into effect with the introduction of the Uniform Fourpenny Post supplanted by the Uniform Penny Post in 1839 and 1840. Colby was another of the founding group of the Society. He was also in charge of the Survey of Ireland . Herschel and Babbage were present at a celebrated operation of that survey, the remeasuring of the Lough Foyle baseline. The Analytical Society had initially been no more than an undergraduate provocation. During this period it had some more substantial achievements. In 1816, Babbage, Herschel and Peacock published

2652-417: A wide ring, while a drought year may result in a very narrow one. Direct reading of tree ring chronologies is a complex science, for several reasons. First, contrary to the single-ring-per-year paradigm, alternating poor and favorable conditions, such as mid-summer droughts, can result in several rings forming in a given year. In addition, particular tree species may present "missing rings", and this influences

2754-531: Is a Divine energy which overrides what we familiarly call the laws of nature." He alluded to the limits of human experience, expressing: "all that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that

2856-636: Is a term used to designate a layer of deformed, collapsed tracheids and traumatic parenchyma cells in tree ring analysis. They are formed when air temperature falls below freezing during a period of cambial activity. They can be used in dendrochronology to indicate years that are colder than usual. Dates from dendrochronology can be used as a calibration and check of radiocarbon dating . This can be done by checking radiocarbon dates against long master sequences, with Californian bristle-cone pines in Arizona being used to develop this method of calibration as

2958-496: Is also used as a check in radiocarbon dating to calibrate radiocarbon ages . New growth in trees occurs in a layer of cells near the bark. A tree's growth rate changes in a predictable pattern throughout the year in response to seasonal climate changes, resulting in visible growth rings. Each ring marks a complete cycle of seasons , or one year, in the tree's life. As of 2023, securely dated tree-ring data for Germany and Ireland are available going back 13,910 years. A new method

3060-531: Is an inherent assumption in Frederick Winslow Taylor 's scientific management . Mary Everest Boole claimed that there was profound influence – via her uncle George Everest – of Indian thought in general and Indian logic , in particular, on Babbage and on her husband George Boole , as well as on Augustus De Morgan : Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on

3162-427: Is based on measuring variations in oxygen isotopes in each ring, and this 'isotope dendrochronology' can yield results on samples which are not suitable for traditional dendrochronology due to too few or too similar rings. Some regions have "floating sequences", with gaps which mean that earlier periods can only be approximately dated. As of 2024, only three areas have continuous sequences going back to prehistoric times,

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3264-409: Is more uniform (complacent). In addition, some genera of trees are more suitable than others for this type of analysis. For instance, the bristlecone pine is exceptionally long-lived and slow growing, and has been used extensively for chronologies; still-living and dead specimens of this species provide tree-ring patterns going back thousands of years, in some regions more than 10,000 years. Currently,

3366-493: Is that skilled workers typically spend parts of their time performing tasks that are below their skill level. If the labour process can be divided among several workers, labour costs may be cut by assigning only high-skill tasks to high-cost workers, restricting other tasks to lower-paid workers. He also pointed out that training or apprenticeship can be taken as fixed costs; but that returns to scale are available by his approach of standardisation of tasks, therefore again favouring

3468-426: Is the science of determining past climates from trees primarily from the properties of the annual tree rings. Other properties of the annual rings, such as maximum latewood density (MXD) have been shown to be better proxies than simple ring width. Using tree rings, scientists have estimated many local climates for hundreds to thousands of years previous. Dendrochronology has become important to art historians in

3570-449: Is width of annual ring, t is time (in years), ρ is density of wood, k v is some coefficient, M ( t ) is function of mass growth of the tree. Ignoring the natural sinusoidal oscillations in tree mass, the formula for the changes in the annual ring width is: Δ L ( t ) = − c 1 e − a 1 t + c 2 e −

3672-472: The Edinburgh Review (under Babbage's guidance). The context of these developments is still debated. Babbage's own account of the origin of the difference engine begins with the Astronomical Society's wish to improve The Nautical Almanac . Babbage and Herschel were asked to oversee a trial project, to recalculate some part of those tables. With the results to hand, discrepancies were found. This

3774-578: The Oxford Dictionary of National Biography he was most likely born at 44 Crosby Row, Walworth Road , London, England. A blue plaque on the junction of Larcom Street and Walworth Road commemorates the event. His date of birth was given in his obituary in The Times as 26 December 1792; but then a nephew wrote to say that Babbage was born one year earlier, in 1791. The parish register of St. Mary's , Newington , London, shows that Babbage

3876-696: The Royal Guelphic Order , however they were not subsequently made knights bachelor to entitle them to the prefix Sir , which often came with appointments to that foreign order (though Herschel was later created a baronet ). Babbage now emerged as a polemicist . One of his biographers notes that all his books contain a "campaigning element". His Reflections on the Decline of Science and some of its Causes (1830) stands out, however, for its sharp attacks. It aimed to improve British science, and more particularly to oust Davies Gilbert as President of

3978-702: The Statistical Society followed. Babbage was its public face, backed by Richard Jones and Robert Malthus . Babbage published On the Economy of Machinery and Manufactures (1832), on the organisation of industrial production . It was an influential early work of operational research . John Rennie the Younger in addressing the Institution of Civil Engineers on manufacturing in 1846 mentioned mostly surveys in encyclopaedias, and Babbage's book

4080-471: The University of Arizona . Douglass sought to better understand cycles of sunspot activity and reasoned that changes in solar activity would affect climate patterns on earth, which would subsequently be recorded by tree-ring growth patterns ( i.e. , sunspots → climate → tree rings). Horizontal cross sections cut through the trunk of a tree can reveal growth rings, also referred to as tree rings or annual rings . Growth rings result from new growth in

4182-417: The University of Edinburgh , with the recommendation of Pierre Simon Laplace ; the post went to William Wallace . With Herschel, Babbage worked on the electrodynamics of Arago's rotations , publishing in 1825. Their explanations were only transitional, being picked up and broadened by Michael Faraday . The phenomena are now part of the theory of eddy currents , and Babbage and Herschel missed some of

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4284-550: The Vistula region via ports of the Hanseatic League . Oak panels were used in a number of northern countries such as England , France and Germany . Wooden supports other than oak were rarely used by Netherlandish painters. Since panels of seasoned wood were used, an uncertain number of years has to be allowed for seasoning when estimating dates. Panels were trimmed of the outer rings, and often each panel only uses

4386-493: The exponential map ). But via Herschel he was influenced by Arbogast's ideas in the matter of iteration , i.e. composing a function with itself, possibly many times. Writing in a major paper on functional equations in the Philosophical Transactions (1815/6), Babbage said his starting point was work of Gaspard Monge . From 1828 to 1839, Babbage was Lucasian Professor of Mathematics at Cambridge. Not

4488-444: The factory system . His view of human capital was restricted to minimising the time period for recovery of training costs. Another aspect of the work was its detailed breakdown of the cost structure of book publishing. Babbage took the unpopular line, from the publishers' perspective, of exposing the trade's profitability. He went as far as to name the organisers of the trade's restrictive practices. Twenty years later he attended

4590-413: The otolith bones. Charles Babbage This is an accepted version of this page Charles Babbage KH FRS ( / ˈ b æ b ɪ dʒ / ; 26 December 1791 – 18 October 1871) was an English polymath . A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered by some to be " father of

4692-438: The vascular cambium , a layer of cells near the bark that botanists classify as a lateral meristem ; this growth in diameter is known as secondary growth . Visible rings result from the change in growth speed through the seasons of the year; thus, critical for the title method, one ring generally marks the passage of one year in the life of the tree. Removal of the bark of the tree in a particular area may cause deformation of

4794-837: The Almighty which afterwards so much disgusted me in my youthful years. Rejecting the Athanasian Creed as a "direct contradiction in terms", in his youth he looked to Samuel Clarke 's works on religion, of which Being and Attributes of God (1704) exerted a particularly strong influence on him. Later in life, Babbage concluded that "the true value of the Christian religion rested, not on speculative [theology] ... but ... upon those doctrines of kindness and benevolence which that religion claims and enforces, not merely in favour of man himself but of every creature susceptible of pain or of happiness." In his autobiography Passages from

4896-642: The Creator ever open to our examination, we possess a firm basis on which to raise the superstructure of an enlightened creed. The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles ... The works of the Creator, ever present to our senses, give a living and perpetual testimony of his power and goodness far surpassing any evidence transmitted through human testimony. The testimony of man becomes fainter at every stage of transmission, whilst each new inquiry into

4998-567: The English clergy of that day hated Babbage's book! Babbage was raised in the Protestant form of the Christian faith, his family having inculcated in him an orthodox form of worship. He explained: My excellent mother taught me the usual forms of my daily and nightly prayer; and neither in my father nor my mother was there any mixture of bigotry and intolerance on the one hand, nor on the other of that unbecoming and familiar mode of addressing

5100-455: The Life of a Philosopher (1864), Babbage wrote a whole chapter on the topic of religion, where he identified three sources of divine knowledge: He stated, on the basis of the design argument , that studying the works of nature had been the more appealing evidence, and the one which led him to actively profess the existence of God . Advocating for natural theology, he wrote: In the works of

5202-551: The Royal Society, which Babbage wished to reform. It was written out of pique, when Babbage hoped to become the junior secretary of the Royal Society, as Herschel was the senior, but failed because of his antagonism to Humphry Davy . Michael Faraday had a reply written, by Gerrit Moll , as On the Alleged Decline of Science in England (1831). On the front of the Royal Society Babbage had no impact, with

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5304-526: The Whitmore sisters. He made a home in Marylebone in London and established a large family. On his father's death in 1827, Babbage inherited a large estate (value around £100,000, equivalent to £10.9 million or $ 15 million today), making him independently wealthy. After his wife's death in the same year he spent time travelling. In Italy he met Leopold II, Grand Duke of Tuscany , foreshadowing

5406-690: The academy. The first was a clergyman near Cambridge ; through him Babbage encountered Charles Simeon and his evangelical followers, but the tuition was not what he needed. He was brought home, to study at the Totnes school: this was at age 16 or 17. The second was an Oxford tutor, under whom Babbage reached a level in Classics sufficient to be accepted by the University of Cambridge. Babbage arrived at Trinity College, Cambridge , in October 1810. He

5508-467: The barb that both Babbage and Brewster had received public money. In the debate of the period on statistics ( qua data collection) and what is now statistical inference , the BAAS in its Statistical Section (which owed something also to Whewell ) opted for data collection. This Section was the sixth, established in 1833 with Babbage as chairman and John Elliot Drinkwater as secretary. The foundation of

5610-691: The bland election of the Duke of Sussex to succeed Gilbert the same year. As a broad manifesto, on the other hand, his Decline led promptly to the formation in 1831 of the British Association for the Advancement of Science (BAAS). The Mechanics' Magazine in 1831 identified as Declinarians the followers of Babbage. In an unsympathetic tone it pointed out David Brewster writing in the Quarterly Review as another leader; with

5712-701: The bristlecone pine in the Southwest US ( White Mountains of California). The dendrochronological equation defines the law of growth of tree rings. The equation was proposed by Russian biophysicist Alexandr N. Tetearing in his work "Theory of populations" in the form: Δ L ( t ) = 1 k v ρ 1 3 d ( M 1 3 ( t ) ) d t , {\displaystyle \Delta L(t)={\frac {1}{k_{v}\,\rho ^{\frac {1}{3}}}}\,{\frac {d\left(M^{\frac {1}{3}}(t)\right)}{dt}},} where Δ L

5814-921: The clues to unification of electromagnetic theory , staying close to Ampère's force law . Babbage purchased the actuarial tables of George Barrett , who died in 1821 leaving unpublished work, and surveyed the field in 1826 in Comparative View of the Various Institutions for the Assurance of Lives . This interest followed a project to set up an insurance company, prompted by Francis Baily and mooted in 1824, but not carried out. Babbage did calculate actuarial tables for that scheme, using Equitable Society mortality data from 1762 onwards. During this whole period, Babbage depended awkwardly on his father's support, given his father's attitude to his early marriage, of 1814: he and Edward Ryan wedded

5916-599: The computer ". He is credited with inventing the first mechanical computer , the Difference Engine , that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in his Analytical Engine , programmed using a principle openly borrowed from the Jacquard loom . Babbage had a broad range of interests in addition to his work on computers covered in his 1832 book Economy of Manufactures and Machinery . He

6018-475: The concept of a trade . John Ruskin went further, to oppose completely what manufacturing in Babbage's sense stood for. Babbage also affected the economic thinking of John Stuart Mill . George Holyoake saw Babbage's detailed discussion of profit sharing as substantive, in the tradition of Robert Owen and Charles Fourier , if requiring the attentions of a benevolent captain of industry , and ignored at

6120-519: The contradiction they have imagined can have no real existence, and that whilst the testimony of Moses remains unimpeached, we may also be permitted to confide in the testimony of our senses." The Ninth Bridgewater Treatise was quoted extensively in Vestiges of the Natural History of Creation . The parallel with Babbage's computing machines is made explicit, as allowing plausibility to

6222-404: The database software Tellervo, which is based on the new standard format whilst being able to import lots of different data formats. The desktop application can be attached to measurement devices and works with the database server that is installed separately. Bard et al write in 2023: "The oldest tree-ring series are known as floating since, while their constituent rings can be counted to create

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6324-491: The dating of panel paintings . However, unlike analysis of samples from buildings, which are typically sent to a laboratory, wooden supports for paintings usually have to be measured in a museum conservation department, which places limitations on the techniques that can be used. In addition to dating, dendrochronology can also provide information as to the source of the panel. Many Early Netherlandish paintings have turned out to be painted on panels of "Baltic oak" shipped from

6426-623: The effects on tree rings of defoliation caused by insect infestations. By 1882, this observation was already appearing in forestry textbooks. In the 1870s, the Dutch astronomer Jacobus Kapteyn (1851–1922) was using crossdating to reconstruct the climates of the Netherlands and Germany. In 1881, the Swiss-Austrian forester Arthur von Seckendorff -Gudent (1845–1886) was using crossdating. From 1869 to 1901, Robert Hartig (1839–1901),

6528-460: The fields of functional equations (including the difference equations fundamental to the difference engine) and operator ( D-module ) methods for differential equations . The analogy of difference and differential equations was notationally changing Δ to D, as a "finite" difference becomes "infinitesimal". These symbolic directions became popular, as operational calculus , and pushed to the point of diminishing returns. The Cauchy concept of limit

6630-577: The first part of the book. The second part considered the "domestic and political economy" of manufactures. The book sold well, and quickly went to a fourth edition (1836). Babbage represented his work as largely a result of actual observations in factories, British and abroad. It was not, in its first edition, intended to address deeper questions of political economy; the second (late 1832) did, with three further chapters including one on piece rate . The book also contained ideas on rational design in factories, and profit sharing . In Economy of Machinery

6732-563: The foothills of the Northern Alps , the southwestern United States and the British Isles. Miyake events , which are major spikes in cosmic rays at known dates, are visible in trees rings and can fix the dating of a floating sequence. The Greek botanist Theophrastus (c. 371 – c. 287 BC) first mentioned that the wood of trees has rings. In his Trattato della Pittura (Treatise on Painting), Leonardo da Vinci (1452–1519)

6834-405: The history of building technology. Many prehistoric forms of buildings used "posts" that were whole young tree trunks; where the bottom of the post has survived in the ground these can be especially useful for dating. Examples: There are many different file formats used to store tree ring width data. Effort for standardisation was made with the development of TRiDaS. Further development led to

6936-426: The isotopes of carbon and oxygen in their spines ( acanthochronology ). These are used for dating in a manner similar to dendrochronology, and such techniques are used in combination with dendrochronology, to plug gaps and to extend the range of the seasonal data available to archaeologists and paleoclimatologists . A similar technique is used to estimate the age of fish stocks through the analysis of growth rings in

7038-552: The latter half of the nineteenth century, the scientific study of tree rings and the application of dendrochronology began. In 1859, the German-American Jacob Kuechler (1823–1893) used crossdating to examine oaks ( Quercus stellata ) in order to study the record of climate in western Texas. In 1866, the German botanist, entomologist, and forester Julius Theodor Christian Ratzeburg (1801–1871) observed

7140-458: The longevity of the trees (up to c.4900 years) in addition to the use of dead samples meant a long, unbroken tree ring sequence could be developed (dating back to c.  6700 BC ). Additional studies of European oak trees, such as the master sequence in Germany that dates back to c.  8500 BC , can also be used to back up and further calibrate radiocarbon dates. Dendroclimatology

7242-601: The mathematical atmosphere of 1830–65. What share had it in generating the Vector Analysis and the mathematics by which investigations in physical science are now conducted? In 1837, responding to the series of eight Bridgewater Treatises , Babbage published his Ninth Bridgewater Treatise , under the title On the Power, Wisdom and Goodness of God, as manifested in the Creation . In this work Babbage weighed in on

7344-432: The maximum span for fully anchored chronology is a little over 11,000 years B.P. IntCal20 is the 2020 "Radiocarbon Age Calibration Curve", which provides a calibrated carbon 14 dated sequence going back 55,000 years. The most recent part, going back 13,900 years, is based on tree rings. European chronologies derived from wooden structures initially found it difficult to bridge the gap in the fourteenth century when there

7446-490: The other hand, he applied for positions unsuccessfully, and had little in the way of a career. In 1816 he was a candidate for a teaching job at Haileybury College ; he had recommendations from James Ivory and John Playfair , but lost out to Henry Walter . In 1819, Babbage and Herschel visited Paris and the Society of Arcueil , meeting leading French mathematicians and physicists. That year Babbage applied to be professor at

7548-499: The precise age of samples, especially those that are too recent for radiocarbon dating , which always produces a range rather than an exact date. However, for a precise date of the death of the tree a full sample to the edge is needed, which most trimmed timber will not provide. It also gives data on the timing of events and rates of change in the environment (most prominently climate) and also in wood found in archaeology or works of art and architecture, such as old panel paintings . It

7650-462: The rings as the plant overgrows the scar. The rings are more visible in trees which have grown in temperate zones , where the seasons differ more markedly. The inner portion of a growth ring forms early in the growing season, when growth is comparatively rapid (hence the wood is less dense) and is known as "early wood" (or "spring wood", or "late-spring wood" ); the outer portion is the "late wood" (sometimes termed "summer wood", often being produced in

7752-454: The same locale, in overlapping fashion, chronologies can be built up—both for entire geographical regions and for sub-regions. Moreover, wood from ancient structures with known chronologies can be matched to the tree-ring data (a technique called 'cross-dating'), and the age of the wood can thereby be determined precisely. Dendrochronologists originally carried out cross-dating by visual inspection; more recently, they have harnessed computers to do

7854-482: The same subject, that of Christ expelling the money-lenders from the Temple . The results showed that the age of the wood was too late for any of them to have been painted by Hieronymus Bosch . While dendrochronology has become an important tool for dating oak panels, it is not effective in dating the poplar panels often used by Italian painters because of the erratic growth rings in poplar. The sixteenth century saw

7956-445: The secondary root xylem of perennial herbaceous plants . Similar seasonal patterns also occur in ice cores and in varves (layers of sediment deposition in a lake, river, or sea bed). The deposition pattern in the core will vary for a frozen-over lake versus an ice-free lake, and with the fineness of the sediment. Sclerochronology is the study of algae deposits. Some columnar cacti also exhibit similar seasonal patterns in

8058-536: The selection of trees for study of long time-spans. For instance, missing rings are rare in oak and elm trees. Critical to the science, trees from the same region tend to develop the same patterns of ring widths for a given period of chronological study. Researchers can compare and match these patterns ring-for-ring with patterns from trees which have grown at the same time in the same geographical zone (and therefore under similar climatic conditions). When one can match these tree-ring patterns across successive trees in

8160-408: The side of uniformitarianism in a current debate. He preferred the conception of creation in which a God-given natural law dominated, removing the need for continuous "contrivance". The book is a work of natural theology , and incorporates extracts from related correspondence of Herschel with Charles Lyell . Babbage put forward the thesis that God had the omnipotence and foresight to create as

8262-455: The source of ships as well as smaller artifacts made from wood, but which were transported long distances, such as panels for paintings and ship timbers. Miyake events , such as the ones in 774–775 and 993–994 , can provide fixed reference points in an unknown time sequence as they are due to cosmic radiation. As they appear as spikes in carbon 14 in tree rings for that year all round the world, they can be used to date historical events to

8364-415: The source of the productivity of the factory system was exactly the combination of the division of labour with machinery, building on Adam Smith , Babbage and Ure. Where Marx picked up on Babbage and disagreed with Smith was on the motivation for division of labour by the manufacturer: as Babbage did, he wrote that it was for the sake of profitability , rather than productivity, and identified an impact on

8466-400: The summer, though sometimes in the autumn) and is denser. Many trees in temperate zones produce one growth-ring each year, with the newest adjacent to the bark. Hence, for the entire period of a tree's life, a year-by-year record or ring pattern builds up that reflects the age of the tree and the climatic conditions in which the tree grew. Adequate moisture and a long growing season result in

8568-413: The task, applying statistical techniques to assess the matching. To eliminate individual variations in tree-ring growth, dendrochronologists take the smoothed average of the tree-ring widths of multiple tree-samples to build up a 'ring history', a process termed replication. A tree-ring history whose beginning- and end-dates are not known is called a 'floating chronology'. It can be anchored by cross-matching

8670-477: The term for the application of dendrochronology in archaeology. While archaeologists can date wood and when it was felled, it may be difficult to definitively determine the age of a building or structure in which the wood was used; the wood could have been reused from an older structure, may have been felled and left for many years before use, or could have been used to replace a damaged piece of wood. The dating of building via dendrochronology thus requires knowledge of

8772-432: The theory that transmutation of species could be pre-programmed. Jonar Ganeri, author of Indian Logic , believes Babbage may have been influenced by Indian thought; one possible route would be through Henry Thomas Colebrooke . Mary Everest Boole argues that Babbage was introduced to Indian thought in the 1820s by her uncle George Everest: Some time about 1825, [Everest] came to England for two or three years, and made

8874-451: The time. Charles Babbage's Saturday night soirées , held from 1828 into the 1840s, were important gathering places for prominent scientists, authors and aristocracy. Babbage is credited with importing the "scientific soirée" from France with his well-attended Saturday evening soirées . Works by Babbage and Ure were published in French translation in 1830; On the Economy of Machinery

8976-406: The type of measurement (full ring widths, earlywood, latewood), and the location. However, the types of data and the rules for accuracy and precision of the primary data, tree-ring width measurements, are decided by the dendrochronologists who are contributing the data, rather than by NOAA or any other governing organization. Tree ring#Growth rings Dendrochronology is useful for determining

9078-405: The width of annual growth rings; by taking samples from different sites within a particular region, researchers can build a comprehensive historical sequence. The techniques of dendrochronology are more consistent in areas where trees grew in marginal conditions such as aridity or semi-aridity where the ring growth is more sensitive to the environment, rather than in humid areas where tree-ring growth

9180-433: The works of the Almighty gives to us more exalted views of his wisdom, his goodness, and his power. Like Samuel Vince , Babbage also wrote a defence of the belief in divine miracles . Against objections previously posed by David Hume , Babbage advocated for the belief of divine agency, stating "we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there

9282-533: The year. For example, wooden houses in the Viking site at L'Anse aux Meadows in Newfoundland were dated by finding the layer with the 993 spike, which showed that the wood is from a tree felled in 1021. Researchers at the University of Bern have provided exact dating of a floating sequence in a Neolithic settlement in northern Greece by tying it to a spike in cosmogenic radiocarbon in 5259 BC. Frost ring

9384-581: Was baptised on 6 January 1792, supporting a birth year of 1791. Babbage was one of four children of Benjamin Babbage and Betsy Plumleigh Teape. His father was a banking partner of William Praed in founding Praed's & Co. of Fleet Street , London, in 1801. In 1808, the Babbage family moved into the old Rowdens house in East Teignmouth . Around the age of eight, Babbage was sent to a country school in Alphington near Exeter to recover from

9486-521: Was a building hiatus, which coincided with the Black Death . However, there do exist unbroken chronologies dating back to prehistoric times, for example the Danish chronology dating back to 352 BC. Given a sample of wood, the variation of the tree-ring growths not only provides a match by year, but can also match location because climate varies from place to place. This makes it possible to determine

9588-480: Was already self-taught in some parts of contemporary mathematics; he had read Robert Woodhouse , Joseph Louis Lagrange , and Maria Gaetana Agnesi . As a result, he was disappointed in the standard mathematical instruction available at the university. Babbage, John Herschel , George Peacock , and several other friends formed the Analytical Society in 1812; they were also close to Edward Ryan . As

9690-444: Was an important figure in the social scene in London, and is credited with importing the "scientific soirée" from France with his well-attended Saturday evening soirées . His varied work in other fields has led him to be described as "pre-eminent" among the many polymaths of his century. Babbage, who died before the complete successful engineering of many of his designs, including his Difference Engine and Analytical Engine, remained

9792-435: Was described what is now called the "Babbage principle". It pointed out commercial advantages available with more careful division of labour . As Babbage himself noted, it had already appeared in the work of Melchiorre Gioia in 1815. The term was introduced in 1974 by Harry Braverman . Related formulations are the "principle of multiples" of Philip Sargant Florence , and the "balance of processes". What Babbage remarked

9894-647: Was first an article in the Encyclopædia Metropolitana , the form in which Rennie noted it, in the company of related works by John Farey Jr. , Peter Barlow and Andrew Ure . From An essay on the general principles which regulate the application of machinery to manufactures and the mechanical arts (1827), which became the Encyclopædia Metropolitana article of 1829, Babbage developed the schematic classification of machines that, combined with discussion of factories, made up

9996-539: Was in 1821 or 1822, and was the occasion on which Babbage formulated his idea for mechanical computation. The issue of the Nautical Almanac is now described as a legacy of a polarisation in British science caused by attitudes to Sir Joseph Banks , who had died in 1820. Babbage studied the requirements to establish a modern postal system , with his friend Thomas Frederick Colby , concluding there should be

10098-437: Was kept at bay. Woodhouse had already founded this second "British Lagrangian School" with its treatment of Taylor series as formal. In this context function composition is complicated to express, because the chain rule is not simply applied to second and higher derivatives. This matter was known to Woodhouse by 1803, who took from Louis François Antoine Arbogast what is now called Faà di Bruno's formula . In essence it

10200-405: Was known to Abraham De Moivre (1697). Herschel found the method impressive, Babbage knew of it, and it was later noted by Ada Lovelace as compatible with the analytical engine. In the period to 1820 Babbage worked intensively on functional equations in general, and resisted both conventional finite differences and Arbogast's approach (in which Δ and D were related by the simple additive case of

10302-412: Was the first person to mention that trees form rings annually and that their thickness is determined by the conditions under which they grew. In 1737, French investigators Henri-Louis Duhamel du Monceau and Georges-Louis Leclerc de Buffon examined the effect of growing conditions on the shape of tree rings. They found that in 1709, a severe winter produced a distinctly dark tree ring, which served as

10404-423: Was translated in 1833 into French by Édouard Biot , and into German the same year by Gottfried Friedenberg. The French engineer and writer on industrial organisation Léon Lalanne was influenced by Babbage, but also by the economist Claude Lucien Bergery , in reducing the issues to "technology". William Jevons connected Babbage's "economy of labour" with his own labour experiments of 1870. The Babbage principle

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