“The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good telescope, when a diaphragm bounded by a rectilinear contour is placed upon the object-glass, though sometimes tedious is never difficult. The expressions which it is necessary to integrate are always sines and cosines of multiples of the independent variable, and the only trouble consists in taking properly the limits of integration. Several cases of this problem have been completely worked out, and the result, in every instance, has been entirely in accordance with observation. These experiments… have seldom been made except by those whose immediate object was to illustrate the undulatory theory of light. There is however a case of a somewhat different kind; which in practice recurs perpetually, and which in theory requires for its complete investigation the value of a more difficult integral; I mean the usual case of an object-glass with a circular aperture. The desire of submitting to mathematical investigation every optical phænomenon of frequent occurrence has induced me to procure the computation of the numerical values of the integral that presents itself in this inquiry: and I now beg leave to lay before the Society the calculated table, with a few remarks upon its application.”

— George Biddell Airy

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good tel…" by George Biddell Airy?

George Biddell Airy 13

English mathematician and astronomer 1801–1892

Related quotes

“It seems as though the goal of my work has always been to dissolve myself completely into the sensations of the surroundings in order to then integrate this into a coherent painterly form.”

Ernst Ludwig Kirchner (1880–1938) German painter, sculptor, engraver and printmaker

Letter to Karl Ernst Osthaus, 23 December 1917; as quoted in Kirchner and the Berlin street, ed. Deborah Wye, Moma, New York, 2008, p. 36
1916 - 1919

“For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is therefore included in this simplest case. The next case in simplicity includes those manifoldnesses in which the line-element may be expressed as the fourth root of a quartic differential expression…. I restrict myself… to those manifoldnesses in which the line element is expressed as the square root of a quadric differential expression…. Manifoldnesses in which, as in the Plane and in Space, the line-element may be reduced to the form \sqrt{ \sum (dx)^2 }, are… only a particular case of the manifoldnesses to be here investigated; they require a special name, and therefore these manifoldnesses… I will call flat. In order now to review the true varieties of all the continua which may be represented in the assumed form, it is necessary to get rid of difficulties arising from the mode of representation, which is accomplished by choosing the variables in accordance with a certain principle.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“The methods of the Bernoullis and of Taylor, were held, at the time of their invention, to be most complete and exact. Several imperfections, however, belong to them. They do not apply to problems involving three or more properties; nor do they extend to cases involving differentials of a higher order than the first: for instance, they will not solve the problem, in which a curve is required, that with its radius of curvature and evolute shall contain the least area. Secondly, they do not extend to cases, in which the analytical expression contains, besides x, y, and their differentials, integral expressions; for instance, they will not solve the second case proposed in James Bernoulli's Programma if the Isoperimetrical condition be excluded; for then the arc s, an integral, since it =\int \! dx \sqrt(1+\frac{dy^2}{dx^2}), is not given. Thirdly, they do not extend to cases, in which the differential function, expressing the maximum should depend on a quantity, not given except under the form of a differential equation, and that not integrable; for instance, they will not solve the case of the curve of the quickest descent, in a resisting medium, the descending body being solicited by any forces whatever.”

Robert Woodhouse (1773–1827) English mathematician

A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

“David Ray Griffin has done admirable and painstaking research in reviewing the mysteries surrounding the 9/11 attacks. It is the most persuasive argument I have seen for further investigation [into] that historic and troubling event.”

Howard Zinn (1922–2010) author and historian

Comment on David Ray Griffin's book The New Pearl Harbor, quoted at 911Truth.org (13 August 2004) http://www.911truth.org/article.php?story=20040525224251221

“For common purposes we may without sensible error suppose the earth's motion equable and neglect the corrections, and then the rule for the parallax of right ascension will be this:
Sine lat. : rad. : : cotang. A : cotang. C, or rad : sine lat. : : tang. A : tang. C; then long. star \mp C = long. of λ.
Cosine C : cosine A : : semi transverse axis : z.
And cosine decl. cosine (ʘ - λ) :: z : x = parallax of right ascension.”

James Bradley (1693–1762) English astronomer; Astronomer Royal

Miscellaneous Works and Correspondence (1832), Demonstration of the Rules relating to the Apparent Motion of the Fixed Stars upon account of the Motion of Light.

“Convictions are variable; to be always consistent is to be sometimes dishonest.”

Ambrose Bierce (1842–1914) American editorialist, journalist, short story writer, fabulist, and satirist

Source: Epigrams, p. 367

“A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static.”

Buckminster Fuller (1895–1983) American architect, systems theorist, author, designer, inventor and futurist

Pattern Integrity 505.201 http://www.rwgrayprojects.com/synergetics/s05/p0400.html#505
1970s, Synergetics: Explorations in the Geometry of Thinking (1975), "Synergy" onwards

“The forms under which human love ends up being expressed are not governed by sex relations. They are governed by the objective love for humanity; that is to say love for humankind as an integral part of nature and of the universe.”

J. Posadas (1912–1981) Argentine Trotskyist (1912-1981)

Source: Childbearing in Space, 1978

“I have throughout introduced the Integral Calculus in connexion with the Differential Calculus…. Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction? The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold…”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Advertisement, pp.3-4
The Differential and Integral Calculus (1836)

“The process of poetry consists firstly in maintaining this vision in its integrity and secondly in expressing this vision in words.”

Herbert Read (1893–1968) English anarchist, poet, and critic of literature and art

Form in Modern Poetry(1932)

Help us to complete the source, original and additional information

George Biddell Airy 13

Related quotes

Related topics