scholarly journals II. On the attractions of an extensive class of spheroids

1812 ◽  
Vol 102 ◽  
pp. 46-82 ◽  
Keyword(s):  
Integral Function ◽  
Attractive Force ◽  
General Description ◽  
Separate Paper ◽  
The Third ◽  
Algebraic Expressions ◽  
The Earth ◽  
Extensive Class ◽  
The Subject ◽  
Ingenious Method

In this discourse I propose to investigate the attractions of a very extensive class of spheroids, of which the general description is, that they have their radii expressed by rational and integral functions of three rectangular co-ordinates of a point in the surface of a sphere. Such spheroids may be characterized more precisely in the following manner: conceive a sphere of which the radius is unit, and three planes intersecting one another at right angles in the centre; from any point in the surface of the sphere draw three perpendicular co-ordinates to the fixed planes, and through the same point in the surface likewise draw a right line from the centre, and cut off from that line a part equal to any rational and integral function of the three co-ordinates: then will the extremity of the part so cut off be a point in the surface of a spheroid of the kind alluded to; and all the points in the same surface will be determined by making the like construction for every point in the surface of the sphere. The term of a rational and integral function is not to be strictly confined here to such functions only as consist of a finite number of terms; it may include infinite serieses, provided they are converging ones; and it may even be extended to any algebraic expressions that can be expanded into such serieses. This class of spheroids comprehends the sphere, the ellipsoid, both sorts of elliptical spheroids of revolution, and an infinite number of other figures, as well such as can be described by the revolving of curves about their axes, as others which cannot be so generated. In the second chapter of the third book of the Mécanique Céleste , Laplace has treated of the attractions of spheroids of every kind; and in particular he has given a very ingenious method for computing the attractive forces of that class which in their figures approach nearly to spheres. In studying that work, I discovered that the learned author had fallen into an error in the proof of his fundamental theorem; in consequence of which he has represented his method as applicable to all spheroids whatever, provided they do not differ much from spheres; whereas in truth, when the error of calculation is corrected, and the demonstration made rigorous, his analysis is confined exclusively to that particular kind, described above, which it is proposed to make the subject of this discourse. I have already treated of this matter in a separate paper, in which I have pointed out the source of Laplace’s mistake, and likewise have strictly demonstrated his method for the instances that properly fall within its scope. In farther considering the same subject, it occurred to me that the investigation in the second chapter of the third book of the Mécanique Céleste , however skilfully and ingeniously conceived, is nevertheless indirect, and is besides liable to another objection of still greater weight; it does not exhibit the several terms of the series for the attractive force in separate and independent expressions: it only points out in what manner they may be derived successively, one after another; in so much that the terms of the series near the beginning cannot be found without previously computing all the rest. This remark gave occasion to the following paper, in which it is my design to give a solution of the problem which is not chargeable with the imperfections just mentioned: the analysis is direct, and every term of the series for the attractive force is deduced immediately from the radius of the spheroid. As the ellipsoid, which comprehends both sorts of elliptical spheroids of revolution, falls within the class of figures here treated of, I have derived, as a corollary from my investigation, the formulas for the attractions of that figure which are required in the theory of the earth: this paper therefore will contain all that is useful on the subject of the attractions of spheroids, as far as our knowledge at present extends, deduced by one uniform mode of analysis.

Eratosthenes of Cyrene

Classics ◽  
2019 ◽  
Author(s):  
P. J. Finglass
Keyword(s):  
Literary Criticism ◽  
Second Best ◽  
The Third ◽  
The Earth ◽  
Mediterranean World ◽  
The Subject ◽  
Research Institute

Eratosthenes was one of the great scholars of Antiquity. Born in Cyrene in c. 285, he studied in Athens before becoming the third librarian at the great research institute founded by King Ptolemy I at Alexandria in Egypt. Rather than specializing in any one field, he produced scholarship in philology, geography, mathematics, philosophy, and chronography, as well as composed poetry. This breadth of learning was (remarkably) the subject of criticism: he was called “Beta” and the “Pentathlete,” which referred to being the second-best in every field. But his versatility did not preclude considerable achievement: most notably, he calculated the circumference of the earth and made other great intellectual advances in geography (where his influence on the later geographer Strabo was considerable) and literary criticism (where, for instance, he refused to believe that the places of Homer’s Odyssey could be mapped onto the actual Mediterranean world), as well as receiving praise for his poetry (from pseudo-Longinus). His works have not survived in full; the process of gathering and assessing his fragments is still ongoing.

scholarly journals On the precession of the equinoxes

1832 ◽  
Vol 1 ◽  
pp. 253-254
Keyword(s):  
The Sun ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
The Third ◽  
The Earth ◽  
Figure Of The Earth ◽  
The Subject

The Professor observes, that Sir Isaac Newton was the first mathematician who endeavoured to estimate the quantity of the precession from the attractive influence of the sun and moon on the spheroidal figure of the earth. His investigations relating to this subject evince the same transcendent abilities that are displayed in other parts of his Principia; but it is admitted, that, from a mistake in his process, his conclusion is erroneous. The investigations of other mathematicians in attempting the solu­tion of the same problem are arranged by the author under three general heads. The first arrive at wrong conclusions, in consequence of mistake in some part of their proceedings; the second obtain just conclusions, but rendered so by balance of opposite errors; the third approach as near the truth as the nature of the subject will admit, but, in the author’s estimation, are liable to the charge of obscurity and perplexity.

The Origin and Growth of the Cities of Southern Gaul to the Third Century A.D.: An Assessment of the Most Recent Archaeological Discoveries

1973 ◽  
Vol 63 ◽  
pp. 1-28 ◽  
Author(s):  
Paul-Albert Février
Keyword(s):  
Third Century ◽  
The Third ◽  
The Earth ◽  
The Alps ◽  
The Subject

There is scarcely a region of the Roman west which can claim, superficially, to be better known than southern Gaul. There can be no lover of antiquities who has not visited Arles or Nîmes, studied the arch of Orange or the Pont du Gard, devoted some interest to the monuments of Fréjus, the sculptures of Nîmes, or the mosaics of Vienne, not to mention the houses of Glanum or Vaison which have been recovered from the earth by the dedication of Henri Rolland and Canon Sautel. And yet many of these famous monuments have had to wait until very recent years before becoming the subject of detailed monographs: so, the trophy of the Alps, the arch of Orange, or the mausoleum of Glanum. Others, without having received exhaustive publication, have only in recent decades been properly dated (the amphitheatres of Arles and Nîmes) or adequately described: I am thinking of the Maison Carrée.

II. On the precession of the equinoxes

1807 ◽  
Vol 97 ◽  
pp. 57-82
Keyword(s):  
Natural Philosophy ◽  
The Other ◽  
The Sun ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
The Third ◽  
The Earth ◽  
Figure Of The Earth ◽  
The Subject ◽  
Theory Of Gravity

Perhaps the solution of no other problem, in natural philo­sophy, has so often baffled the attempts of mathematicians as that of determining the precession of the equinoxes, by the theory of gravity. The phenomenon itself was observed about one hundred and fifty years before the Christian æra, but Sir Isaac Newton was the first who endeavoured to estimate its magnitude by the true principles of motion, combined with the attractive influence of the sun and moon on the spheroidal figure of the earth. It has always been allowed, by those competent to judge, that his investigations relating to the subject evince the same transcendent abilities as are displayed in the other parts of his immortal work, the mathematical Principles of natural Philosophy, but, for more than half a century past, it has been justly asserted that he made a mistake in his process, which rendered his conclusions erro­neous. Since the detection of this error, some of the most eminent mathematicians in Europe have attempted solutions of the problem. Their success has been various; but their investi­gations may be arranged under three general heads. Under the first of these may be placed such as lead to a wrong conclusion, in consequence of a mistake committed in some part of the proceedings. The second head may be allotted to those in which the conclusions may be admitted as just, but rendered so by the counteraction of opposite errors. Such may be ranked under the third head as are conducted without error fatal to the conclusion, and in which the result is as near the truth as the subject seems to admit.

UPAYA MENINGKATKAN HASIL BELAJAR IPA MELALUI PENGGUNAAN VIDEO PEMBELAJARAN BAGI SISWA KELAS IV DI SDN 187/IV KOTA JAMBI

2015 ◽  
Vol 8 (2) ◽  
pp. 93
Author(s):  
Juniar Siregar
Keyword(s):  
Action Research ◽  
Research Method ◽  
Research Report ◽  
The Third ◽  
The Media ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research

This study presents a research report on improving students’ Learning results on IPA through Video. The objective was to find out whether students’ learning result improved when they are taught by using Video. It was conducted using classroom action research method. The subject of the study was the Grade IV students of SDN 187/IV Kota Jambi which is located on Jln. Adi Sucipto RT 05 Kecamatan Jambi Selatan, and the number of the students were 21 persons. The instruments used were test. In analyzing the data, the mean of the students’ score for the on fisrt sycle was 65,4 (42,85%) and the mean on cycle two was 68,5 (37,15%) and the mean of the third cycle was 81,4 (100%). Then it can be concluded that the use of video on learning IPA can improve the students’ learning result. It is suggested that teachers should use video as one of the media to improve students’ learning result on IPA.Keywords : IPA, students’ learning result, video

Enhaching Primary Students’ Science Learning Outcome Utilizing Visual Multimedia

2018 ◽  
Vol 1 (2) ◽  
pp. 109
Author(s):  
Nurmi Nurmi ◽  
Hadi Putra ◽  
Penti Nursida ◽  
Khoiro Mahbubah ◽  
Neni Hermita
Keyword(s):  
Learning Outcomes ◽  
Science Learning ◽  
Learning Outcome ◽  
Visual Media ◽  
Primary Students ◽  
Average Score ◽  
The Third ◽  
Third Grade Students ◽  
The Subject ◽  
3Rd Grade

This study aims to improve 3rd grade students’ science learning outcomes bylearning to use visual multimedia. This research method uses classroom actionresearch. The subject of this research was the third grade students of secondsemester of elementary school which conducted 30 students. Based on theresults of research by using visual media, it have been found that theimprovement learning outcome, seen from the initial average score before theaction of 3rd grade class students from 65.5 to 83.83. The results of this studyindicate that with the use of visual media can improve student learningoutcomes.

Biographical Studies of G.I. Gurdjieff

2016 ◽  
Vol 11 (1) ◽  
pp. 10-35
Author(s):  
Joseph Azize
Keyword(s):  
Comparative Research ◽  
Source Material ◽  
Future Studies ◽  
The Third ◽  
The Subject

The various published biographies and biographical notices of G.I. Gurdjieff (c.1865-1949) are of diverse style, quantity and content. While some have made considerable contributions to the subject, most attempts have reacted for or against Gurdjieff’s status as what might call an ‘Enlightened Master’. Little biographical writing on Gurdjieff has questioned the scope, reliability and prejudices of the sources. Further, possible resources have been neglected. The development in Gurdjieff’s ideas is often overlooked, his life is not sufficiently related to that development, and the lack of comparative research has failed to highlight Gurdjieff’s unique contributions. This article is structured in four parts. The first is an introduction, followed by an overview of existing biographical studies of Gurdjieff. The third part addresses bias in these studies, and this is followed by suggestions for future studies. It is concluded that fieldwork regarding the biography of Gurdjieff has been hampered by imperfect methodology. However, with better use of the source material, some of which has only recently been discovered, and a rigorous use of sources, a more balanced and nuanced picture of Gurdjieff’s life, and the development of his ideas and methods, should emerge.

IMPROVING STUDENTS’ ACHIEVEMENT IN WRITING RECOUNT TEXT THROUGH THINK PAIR SHARE

2013 ◽  
Vol 2 (1) ◽  
Author(s):  
Hotria Manik ◽  
Elia Masa Ginting
Keyword(s):  
Action Research ◽  
Quantitative Data ◽  
Qualitative Data ◽  
Writing Achievement ◽  
The Third ◽  
Post Test ◽  
Class Viii ◽  
The Subject ◽  
The Mean ◽  
Writing Tests

This study attempts to improve students’ writing achievement in recount text through Think-Pair-Share Strategy. This study was conducted by using classroom action research. The subject of the research was class VIII-1 SMPN 1 Pematangsiantar. The number of the students was 32 students, consisted of 5 males and twenty seven females. The research was conducted in two cycles and consisted of six meetings. The instruments for collecting data were writing tests as the quantitative data and diary notes, observation sheet, interview sheet and questionnaire sheet as qualitative data. Based on the writing score, students’ scores kept improving in every test. In analyzing the data, the mean of the students’ score for the first test as a pre-test was 57.84, for the second test as a post test I was 73.56, for the third test as a post test II was 77.56. Based on diary notes, observation sheet and questionnaire sheet, it was found that students were actively involved in writing process. The result of the research showed that Think-Pair-Share Strategy can improve students’ achievement in writing recount text.   Keywords: Think Pair Share, Writing, Recount text, Action research

THE EFFECT OF APPLYING DEMONSTRATION METHOD ON STUDENTS’ ACHIEVEMENT IN SPEAKING SKILL AT THE THIRD GRADE OF SMK PAB 3 MEDAN ESTATE

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Meryanti Napitupulu And Anni Holila Pulungan
Keyword(s):  
High School ◽  
Control Group ◽  
Vocational High School ◽  
Control Groups ◽  
Speaking Test ◽  
The Third ◽  
Speaking Skill ◽  
The Subject ◽  
And Control ◽  
Experimental Group

This study was conducted as an attempt to discover the effect of applying Demonstration Method on students’ achievement in speaking skill. It was an experimental research. The subject was students of Grade XII, Vocational High School (Sekolah Menengah Kejuruan: SMK), which consisted of 79 students. The research was divided into two groups: experimental and control groups. The instrument used to collect the data was speaking test. To obtain the reliability of the test, the writer applied Kuder Richardson 21 formula. The result of the reliability was 0.7, and it was found that the test was reliable. The data were analyzed by using t-test formula. The analysis showed that the scores of the students in the experimental group were significantly higher than the scores of the students in the control group at the level of significant m = 0.05 with the degree of freedom (df) 77, t-observed value 8.9 > t-table value 1.99. The findings indicate that using Demonstration Method significantly affected the students’ achievement in speaking skill. So, English teachers are suggested to use Demonstration Method in order to improve students’ achievement in speaking skill.

IMPROVING STUDENTS’ WRITING ACHIEVEMENT IN THE REPORT TEXT THROUGH FILM

2013 ◽  
Vol 2 (4) ◽  
Author(s):  
Esra N.F. Hutahaean And Tjut Ernidawati
Keyword(s):  
Action Research ◽  
Research Method ◽  
Writing Achievement ◽  
The Third ◽  
Total Percentage ◽  
The Subject ◽  
The Mean ◽  
Report Text

This research concerns on improving students’ writing achievement in the report text through film.  The objective was to find out the improvement of students’ writing achievement in writing the report text through film. This research was conducted by using action research method. The subject of the research was XI IPA grade students of SMA SWASWTA JOSUA Medan. The numbers of students were thirty one students. They were taught writing the report text through film. The instruments used were writing report text test, diary notes, interview sheets, questionnaire sheets and observation sheets. In analyzing data, the mean of students’ score for the first competency test was 43.1, for the second competency test was 64.8 and for the third competency test was 76.3 and the total percentage of improvement from the first competency test to the third competency test was 84.1%. The conclusion is that through watching film can improve the students’ writing achievement in the report text. It is suggested that teachers should apply watching film as one of media to improve students’ writing achievement in the report text.

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