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Peter Barlow (mathematician)

Peter Barlow (mathematician) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Peter Barlow (mathematician) rather than just read about it. In short: Peter Barlow (13 October 1776 – 1 March 1862) was an English mathematician and physicist. Work in mathematics In 1801, Barlow was appointed assistant mathematics master at the Royal Military Academy, Woolwich, and retained this post until 1847.

Peter Barlow (mathematician) — main illustration
Peter Barlow (mathematician) — illustration

Key takeaways

  • Peter Barlow (mathematician) belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Peter Barlow (mathematician) to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Peter Barlow (mathematician) from memory before moving on to harder problems.

Reference excerpt

Peter Barlow (13 October 1776 – 1 March 1862) was an English mathematician and physicist.

Work in mathematics In 1801, Barlow was appointed assistant mathematics master at the Royal Military Academy, Woolwich, and retained this post until 1847. He contributed articles on mathematics to The Ladies' Diary as well as publishing books such as:

An Elementary Investigation of the Theory of Numbers (1811) A New Mathematical and Philosophical Dictionary (1814) New Mathematical Tables (1814) The latter became known as Barlow's Tables and gives squares, cubes, square roots, cube roots, and reciprocals of all integer numbers from 1 to 10,000. These tables were regularly reprinted until 1965, when computers rendered them obsolete. He contributed to Rees's Cyclopædia articles on Algebra, Analysis, Geometry and Strength of Materials. Barlow also contributed largely to the Encyclopædia Metropolitana.

Work in physics and engineering

In collaboration (1827–1832) with optician George Dollond, Barlow built an achromatic lens that utilized liquid carbon disulfide. (Achromatic lenses were important optical elements of improved telescopes.) After Joseph von Fraunhofer had developed improved glassmaking methods in Germany, Barlow in 1833 improved on Dollond's original design of an achromatic combination by joining flint glass and crown glass to form a doublet lens. Modern optical systems exhibit a vast variance of designs, but most of their elements are still of the flint/crown-doublet type. Modern astronomy and photography is familiar with a so-called Barlow lens, an optical element which is sometimes used to increase magnification, but can also improve achromatism. In 1823, he was made a fellow of the Royal Society. Two years later, he received its Copley Medal for his work on correcting the deviation in ship compasses caused by the presence of iron in the hull. Some of his magnetic research was done in collaboration with Samuel Hunter Christie. He conducted early experimental and observational studies on the origins of terrestrial magnetism. He is credited with Barlow's wheel (an early homopolar electric motor) and with Barlow's law (an incorrect formula of electrical conductance). Barlow investigated a suggestion made by André-Marie Ampère in 1820 that an electromagnetic telegraph could be made by deflecting a compass needle with an electric current. In 1824 Barlow proclaimed the idea impractical after he found that the effect on the compass seriously diminished "with only 200 feet of wire". Barlow, and other eminent scientists of the time who agreed with him, have subsequently been criticised for retarding the development of the telegraph. A decade passed between Ampère's paper being read at the Paris Academy of Sciences and William Ritchie building the first demonstration electromagnetic telegraph. In Barlow's defence, Ampère's design did not enclose the compass in a multiplying coil, as Ritchie's demonstrator did, so the effect would have been very weak at a distance. Steam locomotion received much attention at Barlow's hands and he sat on the railway commissions of 1836, 1839, 1842 and 1845. He also conducted several investigations for the newly formed Railway Inspectorate in the early 1840s.

Barlow made several contributions to the theory of strength of materials, including Essay on the strength and stress of timber (1817) which contains experimental data collected at Woolwich. The sixth edition (1867) of this work was prepared by Barlow's two sons after his death and contains a biography of their father. Barlow also applied his knowledge of materials to the design of bridges. His sons Peter W. Barlow and William Henry Barlow became notable civil engineers of the 19th century. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1832. Following his death in 1862 at his home in Charlton, he was buried in Charlton Cemetery.

See also 2147483647, Barlow commented on this Mersenne prime

References

External links

Barlow's Formula Calculator Biographical information

Illustrations

Peter Barlow (mathematician) illustration
Peter Barlow (mathematician): Essay on magnetic attractions, and on the laws of terrestrial and electro magnetism, 1824
Essay on magnetic attractions, and on the laws of terrestrial and electro magnetism, 1824
Peter Barlow (mathematician): Peter Barlow FRS – gravestone in Charlton Cemetery, London SE7
Peter Barlow FRS – gravestone in Charlton Cemetery, London SE7

Worked examples

Example 1 — a first encounter with Peter Barlow (mathematician)

Start with the simplest possible case. Write down what Peter Barlow (mathematician) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Peter Barlow (mathematician) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Peter Barlow (mathematician) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Peter Barlow (mathematician)

In research
Peter Barlow (mathematician) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Peter Barlow (mathematician) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Peter Barlow (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1776 births, 1862 deaths, 18th-century English people, so understanding it makes those chapters shorter.
In everyday life
Look for Peter Barlow (mathematician) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Peter Barlow (mathematician) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Peter Barlow (mathematician) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Peter Barlow (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter Barlow (mathematician) in simple terms?

Peter Barlow (13 October 1776 – 1 March 1862) was an English mathematician and physicist. Work in mathematics In 1801, Barlow was appointed assistant mathematics master at the Royal Military Academy, Woolwich, and retained this post until 1847.

Why does Peter Barlow (mathematician) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Peter Barlow (mathematician)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Peter Barlow (mathematician).

Tags

  • 1776 births
  • 1862 deaths
  • 18th-century English people
  • 19th-century English mathematicians
  • British fellows of the Royal Society
  • English scientists
  • Fellows of the American Academy of Arts and Sciences
  • Recipients of the Copley Medal
  • Scientists from Norwich

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