scholarly journals XVI.—Additional Note on the Motion of a Heavy Body along the Circumference of a Circle

1871 ◽  
Vol 26 (2) ◽  
pp. 449-457
Author(s):  
Edward Sang
Keyword(s):  
Present Note ◽  
Circular Arc ◽  
Heavy Body ◽  
Additional Note ◽  
Convenient Formula ◽  
Fourth Volume

In the twenty-fourth volume of the Society's Transactions, a very convenient formula is given for computing the time of oscillation in a circular arc; and the investigation of that formula is conducted by an appeal to the actual phenomena. It is defective in so far that it contemplates chiefly the time of oscillation over the whole arc, and does not enable us conveniently to compute the time in which a part of that arc is described.The object of the present note is to supply that defect, and to present the whole subject in a new aspect remarkable alike for its generality and for its simplicity.

scholarly journals VII.—On the Motion of a Heavy Body along the Circumference of a Circle

1865 ◽  
Vol 24 (1) ◽  
pp. 59-71
Author(s):  
Edward Sang
Keyword(s):  
Royal Society ◽  
Elliptic Functions ◽  
The Other ◽  
Philosophical Magazine ◽  
Circular Arc ◽  
Heavy Body ◽  
Great Ease ◽  
Fourth Volume ◽  
The Common ◽  
The One

In the year 1861 I laid before the Royal Society of Edinburgh a theorem concerning the time of descent in a circular arc, by help of which that time can be computed with great ease and rapidity. A concise statement of it is printed in the fourth volume of the Society's Proceedings at page 419.The theorem in question was arrived at by the comparison of two formulæ, the one being the common series and the other an expression given in the “Edinburgh Philosophical Magazine” for November 1828, by a writer under the signature J. W. L. Each of these series is reached by a long train of transformations, developments, and integrations, which require great familiarity with the most advanced branches of the infinitesimal calculus; yet the theorem which results from their comparison has an aspect of extreme simplicity, and seems as if surely it might be attained to by a much shorter and less rugged road. For that reason I did not, at the time, give an account of the manner in which it was arrived at, intending to seek out a better proof. On comparing it with what is known in the theory of elliptic functions, its resemblance to the beautiful theorem of Halle became obvious; but then the coefficients in Halle's formulæ are necessarily less than unit, whereas for this theorem they are required to be greater than unit.

5. On the Motion of a Heavy Body along the circumference of a Circle

1866 ◽  
Vol 5 ◽  
pp. 408-409
Author(s):  
Edward Sang
Keyword(s):  
Philosophical Magazine ◽  
Circular Arc ◽  
Heavy Body ◽  
Fourth Volume ◽  
As If

This paper contains a demonstration of the theorem given in the fourth volume of the proceedings at p. 419.The theorem in question was arrived at by the comparison of the well-known formula for the time of descent in a circular arc, with another formula given in the “Edinburgh Philosophical Magazine” for November 1828, by a writer under the signature T. W. L. Each of these series is reached by a long train of transformations, developments, and integrations, which require great familiarity with the most advanced branches of the higher calculus. Yet the theorem which results from their comparison has an aspect of extreme simplicity, and seems as if it could be reached by an easier road.

3. Additional Note on the Motion of a Heavy Body along the Circumference of a Circle

1872 ◽  
Vol 7 ◽  
pp. 361-365
Author(s):  
E Sang
Keyword(s):  
Great Care ◽  
Heavy Body ◽  
Additional Note ◽  
The Law ◽  
Great Simplicity

AbstractIn the course of physical inquiries we meet with many problems having the appearance of great simplicity, and yet presenting to the analyst difficulties of the highest order. The law of the motion of a heavy body along the circumference of a circle is one of these.One particular case of this motion, viz., the case of the swinging of a clock-pendulum, is of paramount importance, and has been investigated with very great care. In this case our attention is directed principally to the computation of the time of an entire oscillation, since it is this which determines the beating of the clock.

scholarly journals 5. Additional Note on a Problem of Arrangement

1882 ◽  
Vol 11 ◽  
pp. 187-190
Author(s):  
Thomas Muir
Keyword(s):  
Royal Society ◽  
Present Note ◽  
Short Paper ◽  
Third Place ◽  
The Third ◽  
Additional Note

The present note is a continuation of a short paper which appeared in the Proceedings of the Royal Society of Edinburgh for session 1876–77. The problem in question is that referred to in Professor Tait's “Memoir on Knots,” viz.:—To find the number of possible arrangements of a set of n things, subject to the conditions that the first be not in the last or first place, the second not in the first or second place, the third not in the second or third place, and so on.

The Centre of Shear for Sections Bounded by Two Circular Arcs

1954 ◽  
Vol 58 (518) ◽  
pp. 138-139
Author(s):  
L. G. Whitehead ◽  
L. A. McQuillin
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Present Note ◽  
Structural Data ◽  
Limited Range ◽  
Data Sheet ◽  
Relative Influence ◽  
Circular Arc ◽  
Torsion Function ◽  
Circular Arcs

In two recent notes Jacobs and Duncan considered the St. Venant torsion and flexure problems for beams of aerofoil cross section and have given methods for determining the centre of shear once the torsion function for the section has been found. The purpose of the present note is to give results for the location of the centre of shear for a limited range of cross sections bounded by two circular arcs for which the torsion function has long been known. The calculations shed some light on the relative influence of camber and thickness on the location of the centre of shear and are compared with the well known results for thin circular arc sections illustrated in the Structural Data Sheet 00.06.04.

Editorial Introduction

2020 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Editors of the JIOWS
Keyword(s):  
Nineteenth Century ◽  
Indian Ocean ◽  
Western Indian Ocean ◽  
Late Nineteenth Century ◽  
Fourth Volume ◽  
History Of ◽  
The Indian Ocean ◽  
Complex Relationships ◽  
Indian Ocean World ◽  
Shed Light

The editors are proud to present the first issue of the fourth volume of the Journal of Indian Ocean World Studies. This issue contains three articles, by James Francis Warren (Murdoch University), Kelsey McFaul (University of California, Santa Cruz), and Marek Pawelczak (University of Warsaw), respectively. Warren’s and McFaul’s articles take different approaches to the growing body of work that discusses pirates in the Indian Ocean World, past and present. Warren’s article is historical, exploring the life and times of Julano Taupan in the nineteenth-century Philippines. He invites us to question the meaning of the word ‘pirate’ and the several ways in which Taupan’s life has been interpreted by different European colonists and by anti-colonial movements from the mid-nineteenth century to the present day. McFaul’s article, meanwhile, takes a literary approach to discuss the much more recent phenomenon of Somali Piracy, which reached its apex in the last decade. Its contribution is to analyse the works of authors based in the region, challenging paradigms that have mostly been developed from analysis of works written in the West. Finally, Pawelczak’s article is a legal history of British jurisdiction in mid-late nineteenth-century Zanzibar. It examines one of the facets that underpinned European influence in the western Indian Ocean World before the establishment of colonial rule. In sum, this issue uses two key threads to shed light on the complex relationships between European and other Western powers and the Indian Ocean World.

Kazimir Malevich: Economy as the Fifth Dimension

2019 ◽  
Vol 29 (6) ◽  
pp. 215-228
Keyword(s):  
Karl Marx ◽  
Dialectical Materialism ◽  
Economic Base ◽  
Surplus Value ◽  
Bourgeois Society ◽  
Fifth Dimension ◽  
Fourth Volume ◽  
Contemporary Painting ◽  
New Criterion ◽  
The Impact

This paper deals with the impact that Karl Marx"s Das Kapital (and especially its fourth volume, the theory of Surplus Value) had on the category of economy in Kazimir Malevich"s output. In a series of texts, Malevich proclaims economy the new criterion of art and the Black Square its embodiment in contemporary painting. While the author was analyzing Marx"s views on labor and human nature, echoes of them turned up in Malevich"s manifestos and philosophical essays where the artist pondered the idea of the liberation of creative exaltation. The article others an interpretation of the creative process itself from the standpoint of economy, which for Malevich provided an opportunity to lay down the foundation for a new kind of art that was consistent with the prevailing ideology. The author points out that while Malevich was in Vitebsk he studied Marx"s works with idea of incorporating economic studies into art: his speculations on the relationships between the ideological superstructure and the practical, economic base were written in the manner of Marxist philosophy and provided the basis for his main essays, The World as Non-Objectivity (1923) and Suprematism: Thee World as Non-Objectivity or Eternal Rest (1923-1924). They defined the new art as an independent ideological superstructure positioned “outside of other contents and ideologies.” Parallel to that, the author examines the correspondence between Malevich"s theory of the surplus element and Marxist doctrines on surplus value. It is also shown that Malevich hoped to prove that, as in dialectical materialism, his new surplus element opens the way to a new artistic structure that is emerging from the womb of the old system in the same way that communism comes about as a kind of heterogeneous body from within the underpinnings of bourgeois society.

The Common Law in Colonial America

2018 ◽  
Author(s):  
William E. Nelson
Keyword(s):  
New York ◽  
Colonial America ◽  
Main Theme ◽  
Revolutionary Movement ◽  
American Colonies ◽  
American Law ◽  
Fourth Volume ◽  
The Law ◽  
Substantive Law ◽  
The Revolution

This volume begins where volumes 2 and 3 ended. The main theme of the four-volume project is that the law of America’s thirteen colonies differed profoundly when they first were founded, but had developed into a common American law by the time of the Revolution. This fourth volume focuses on what was common to the law of Britain’s thirteen North American colonies in the mid-eighteenth century, although it also takes important differences into account. The first five chapters examine procedural and substantive law in colonies and conclude that, except in North Carolina and northern New York, the legal system functioned effectively in the interests both of Great Britain and of colonial localities. The next three chapters examine changes in law and the constitution beginning with the Zenger case in 1735—changes that ultimately culminated in independence. These chapters show how lawyers became leading figures in what gradually became a revolutionary movement. It also shows how lawyers used legal and constitutional ideology in the interests, sometimes of an economic character, of their clients. The book thereby engages prior scholarship, especially that of Bernard Bailyn and John Phillip Reid, to show how ideas and constitutional values possessed independent causal significance in leading up to the Revolution but also served to protect institutional structures and socioeconomic interests that likewise possessed causal significance.

The Folly of the Cross

2018 ◽  
Author(s):  
Richard Viladesau
Keyword(s):  
Early Modern ◽  
Early Modern Period ◽  
Theology Of The Cross ◽  
The Enlightenment ◽  
Modern Period ◽  
The Arts ◽  
Modern Thought ◽  
Fourth Volume ◽  
The Cross ◽  
Satisfaction Model

This work surveys the ways in which theologians, artists, and composers of the early modern period dealt with the passion and death of Christ. The fourth volume in a series, it locates the theology of the cross in the context of modern thought, beginning with the Enlightenment, which challenged traditional Christian notions of salvation and of Christ himself. It shows how new models of salvation were proposed by liberal theology, replacing the older “satisfaction” model with theories of Christ as bringer of God’s spirit and as social revolutionary. It shows how the arts during this period both preserved the classical tradition and responded to innovations in theology and in style.

scholarly journals Ductile failure analysis of epoxy resin plates containing multiple circular arc cracks by means of the equivalent material concept

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
M. Pourseifi ◽  
A. S. Rahimi
Keyword(s):  
Ductile Failure ◽  
Equivalent Material ◽  
Circular Arc ◽  
Equivalent Material Concept ◽  
Crack Tips ◽  
Fracture Tests ◽  
Polymeric Samples ◽  
Cracked Specimens ◽  
Brittle Fracture Criterion ◽  
Material Concept

AbstractDuctile failure of polymeric samples weakened by circular arc cracks is studied theoretically and experimentally in this research. Various arrangements of cracks with different arc angles are considered in the specimens such that crack tips experienced the mixed mode I/II loading conditions. Fracture tests are conducted on the multi-cracked specimens and their fracture loads are achieved. To provide the results, the equivalent material concept (EMC) is used in conjunction of dislocation method and a brittle fracture criterion such that there is no necessity for performing complex and time-consuming elastic-plastic damage analyses. Theoretical and experimental stress intensity factors are computed and compared with each other by employing the fracture curves which demonstrate the appropriate efficiency of proposed method to predict the tests results.

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