scholarly journals V. On the figure requisite to maintain the equilibrium of a homo­geneous fluid mass that revolves upon an axis

1824 ◽  
Vol 114 ◽  
pp. 85-150 ◽  
Keyword(s):  
Direct Analysis ◽  
The Body ◽  
Homogeneous Fluid ◽  
Material Body ◽  
Synthetic Process ◽  
Fluid Mass ◽  
The Earth ◽  
Figure Of The Earth ◽  
Fluid Body ◽  
Direct Investigation

The theory of the figure of the earth, as delivered in the Philosophice Naturalis Principia Mathematica , is liable to some objections. In determining the ratio of the axes, the illustri­ous author assumes that the terrestrial meridian is an ellipse, having the greatest diameter in the plane of the equator. M'Laurin afterwards proved, by a most elegant synthetic process of reasoning, that a homogeneous fluid body, possessed of such a figure as Newton supposed, will fulfil all the conditions of equilibrium arising from the attraction of the particles, and a centrifugal force of rotation. In this manner the assumption of Newton was verified; but the theory was still left imperfect, since it is necessary to deter­mine, by a direct investigation, all the figures of a fluid mass that are consistent with the laws of equilibrium, rather than to show that the same laws will be fulfilled in particular in­stances. We are indebted to Legendre for the first demon­stration that a homogeneous fluid body, revolving about an axis, cannot be in equilibrio by the attraction of its particles, unless it have the figure of an oblate elliptical spheroid. The researches of Legendre were rendered more general by Laplace, who gave a complete theory of the figure of the planets, distinguished by that depth and elegance which is so much admired in all his writings. It is assumed, however by the eminent geometers we have mentioned, that the figure of the fluid mass is but little different from a sphere which is a restriction not essential to the problem, but introduced for the sake of overcoming some of the difficulties of the investigation. In the following Paper, the figure of a homo­geneous fluid body, that revolves about an axis, and is in equilibrio by the attraction of its particles, is deduced by a direct analysis in which no arbitrary supposition is admitted. 1. It is necessary to begin this research, with laying down some general properties of the attractions of bodies ; and we cannot better accomplish this end, than by considering the function, which is the sum of all the molecules of a body divided by their respective distances from the attracted point. Conceive any material body to be divided into an indefinitely great number of molecules, one of which is represented by d m ; and having drawn three planes intersecting at right angles within the body, let x,y, z , denote the co-ordinates that determine the position of d m , and a, b, c, those that determine the attracted point: then, if we put r = √ a 2 + b 2 + c 2 f = √( a — x ) 2 + ( b — y ) 2 + ( c — z ) 2 ; r will be the distance of the attracted point from the origin of the co-ordinates, and f that of d m from the attracted point.

scholarly journals On the figure requisite to maintain the equilibrium of a homogeneous fluid mass that revolves upon an axis

1833 ◽  
Vol 2 ◽  
pp. 206-207
Keyword(s):  
Direct Analysis ◽  
Homogeneous Fluid ◽  
Mutual Attraction ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
Fluid Mass

The author enumerates the various steps by which Sir Isaac Newton, M c Laurin, and Laplace have carried the theory of the equilibrium of a revolving fluid very near to perfection, but he observes that they have generally supposed the spheroid to differ but little from a sphere; and he proceeds in the present paper to investigate the figure “by a direct analysis, in which no arbitrary supposition is admitted.” Mr. Ivory thinks it necessary to distinguish carefully two separate cases; the first is when the particles of the fluid do not attract one another, and the second when the particles are endued with attractive powers. These, he says, are plainly two cases that are essentially different from one another; for in the first, a stratum added induces no other change than an increase of pressure caused by the action of the accelerating forces at the surface; but in the second, besides the pressure, a new force is introduced, arising from the mutual attraction between the matter of the stratum and the fluid mass to which it is added.

scholarly journals Researches on physical geology.—Part I. The figure and primitive formation of the earth

1851 ◽  
Vol 5 ◽  
pp. 659-659
Keyword(s):  
Chemical Changes ◽  
Fluid Mass ◽  
General Properties ◽  
The Earth ◽  
Figure Of The Earth ◽  
Ellipsoid Of Revolution ◽  
The Law ◽  
Physical Geology ◽  
Analytical Expressions ◽  
Different Parts

The author’s investigations of the figure of the earth proceed on the hypothesis of its having originally been a heterogeneous fluid mass, possessing only such general properties as those which have been established for fluids; and independently of the supposition, with which the theory has generally been complicated, that the vo­lume of the entire mass, and the law of the density of the fluid, have suffered no change in consequence of the solidification of a part of that fluid. Assuming the figure of the mass to be an ellipsoid of revolution, the author obtains general analytical expressions for its ellipticity, and for the variation of gravity at its surface. He gives a general sketch of the consequences that may result from the im­proved hypothesis of the primitive figure of the earth, to physical geology, that is, to the changes occurring upon the external crust of the earth during the process of its solidification, resulting both from calorific and chemical changes taking place among its different parts, and giving rise to a process of circulation throughout the fluid por­tions of the mass. The present memoir is only the first of a series which the author announces it is his intention to communicate to the Society on the same subject.

scholarly journals Patrystyczna interpretacja Rdz 2, 7: „Pan Bóg ulepił człowieka z prochu ziemi i tchnął w jego nozdrza tchnienie życia”

Vox Patrum ◽  
2016 ◽  
Vol 65 ◽  
pp. 141-154
Author(s):  
Bogdan Czyżewski
Keyword(s):  
Holy Spirit ◽  
Essential Elements ◽  
The Body ◽  
Material Body ◽  
Early Christian ◽  
The Earth ◽  
The Holy Spirit ◽  
The Creation ◽  
The Moment ◽  
Natural Decomposition

The article aims at the presentation of the exegesis of Gen 2:7 made by some early Christian writers. Their interpretation contains three essential elements. Fathers start with pointing out the matter as a material from which God created man. Although the human body undergoes natural decomposition, it is not be­cause of the material from which it is built, but because of its frailty due to sin. Fathers also pay attention to the soul, which has its source in what Genesis calls the breath of God. However, it did not exist before the creation of the material body, as proclaimed by Origen, but was created along with the body. The soul animates the body putting it in motion. Although man was formed from the dust of the earth by the hands of God, he should be seen as a spiritual being. Whereas the soul is created, the body has been formed and this clearly differentiates the two. Due to the greatness and grandeur of man, he cannot be reduced to animal being, as it has a rational soul that animates his body. Finally, the third thread in connec­tion with the exegesis of the Gen 2:7 indicates the union of the body and the soul at the moment of creation. It occurred at the time when God breathed into man’s nostrils and put in some part of his grace. This does not mean, however, that the nature of God has changed into the soul of man. Not only did the first man receive the breath of God – everyone gets a second breath, the Holy Spirit, which leads to the creation of a new humanity.

Deformations of celestial bodies

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Stress ◽  
Internal Structure ◽  
External Force ◽  
Continuous Media ◽  
The Body ◽  
Stress Strain ◽  
Gravitational Effects ◽  
The Earth ◽  
Figure Of The Earth ◽  
Celestial Bodies

This chapter studies various gravitational effects arising from the non-sphericity of celestial bodies. It first considers the quadrupole expansion of the potential, as well as the causes of the non-sphericity of the bodies. Finally, it turns to the figure of the Earth. To calculate the proper potential of the Earth, it attempts to determine its deformation due to a perturbing potential. Doing this accurately requires knowledge of the internal structure of the Earth and use of the techniques of the mechanics of continuous media. In this approach, the internal stress–strain relationships of a body are described by various phenomenological parameters and it becomes possible to study the response of the body (deformation, oscillations, etc.) to the field of an external force.

Researches in physical geology.—Third series. On the phenomena of precession and nutation, assuming the interior of the earth to be a heterogeneous fluid

1843 ◽  
Vol 4 ◽  
pp. 129-130
Keyword(s):  
Past History ◽  
Direct Action ◽  
Analytical Investigation ◽  
Actual State ◽  
Solid Shell ◽  
Homogeneous Fluid ◽  
Fluid Mass ◽  
The Earth ◽  
External Shell ◽  
Rotatory Motion

Having, in his last memoir, completed the investigation of the amount of precession and nutation, on the hypothesis of the earth’s consisting of a homogeneous fluid mass, contained in a homogeneous solid shell, the author here extends the inquiry to the case in which both the interior fluid and external shell are considered as heterogeneous. After giving the details of his analytical investigation, he remarks, that he commenced the inquiry in the expectation that the solution of this problem would lead to results different from those previously obtained on the hypothesis of the earth’s entire solidity. Phis expectation was founded on the great difference existing between the direct action of a force on a solid, and that on a fluid mass, in its tendency to produce a rotatory motion; for, in fact, the disturbing forces of the sun and moon do not tend to produce directly any motion in the interior fluid, in which the rotatory motion causing precession and nutation is produced indirectly by the effect of the same forces on the position of the solid shell. A modification is thus produced in the effects of the centrifugal force, which exactly compensates for the want of any direct effect from the action of the disturbing forces; acompensation which the author considers as scarcely less curious than many others already recognized in the solar system and by which, amidst many conflicting causes, its harmony and permanence are so beautifully and wonderfully preserved. The solution of the problem obtained by the author destroys the force of an argument, which might have been urged against the hypothesis of central fluidity, founded on the presumed improbability of our being able to account for the phenomena of precession and nutation on this hypothesis, as satisfactorily as on that of internal solidity. The object, however, of physical researches of this kind is not merely to determine the actual state of the globe, but also to trace its past history through that succession of ages, in which the matter composing it has probably passed gradually through all the stages between a simple elementary state and that in which it has become adapted to the habitation of man. In this point of view the author conceives the problem he proposes is not without value as demonstrating an important fact in the history of the earth presuming its solidification to have begun at the surface; namely the permanence of the inclination of its axis of rotation, from the epoch of the first formation of an exterior crust. This permanence has frequently been insisted on, and is highly important as connected with the speculations of the author on the causes of that change of temperature which has probably taken place in the higher latitudes: all previous proofs of this fact having rested on the assumption of the earth s entire solidity; an assumption which, whatever may be the actual state of our planet, can never be admitted as applicable to it at all past epochs of time, at which it may have been the habitation of animate beings.

scholarly journals X. Researches in physical geology.—second series

1840 ◽  
Vol 130 ◽  
pp. 193-208 ◽  
Keyword(s):  
Tangent Plane ◽  
Solid Shell ◽  
The Moon ◽  
Homogeneous Fluid ◽  
Disturbing Force ◽  
Fluid Mass ◽  
Axis Of Rotation ◽  
The Earth ◽  
Internal Fluid ◽  
Physical Geology

On Precession and Nutaion, assuming the Interior of the Earth to be fluid and heterogeneous. Having in my last memoir completed the investigation of the amount of Precession and Nutation on the hypothesis of the earth’s consisting of a homogeneous fluid mass contained in a homogeneous solid shell, I shall now extend the investigation to the case in which both the interior fluid and exterior shell are considered heterogeneous. 1. When accelerating forces X, Y, Z act on any point x, y, z of a heterogeneous fluid mass, of which no part of the surface is free, and of which the density at the point x, y, z is ϧ, we have for the conditions of equilibrium (I.) X( d Y/ dz - d Z/ dy ) + Y ( d Z/ dx - d X/ dz ) + Z ( d X/ dy - d Y/ dx ) = 0. (II.) ϧ = constant throughout each surface of equal pressure. Now the forces which act on the internal fluid of the earth are (1.) The mutual attraction of the different particles of the fluid mass: (2.) The attraction of the solid shell on the fluid mass: (3.) The disturbing force of the sun: (4.) The disturbing force of the moon: The centrifugal force, the planes of rotation being parallel to the tangent plane at B' (fig. 2. First Series, Art. 8.): This may be separated into two parts, viz. (5.) The resolved part on any point acting in a direction perpendicular to the axis of rotation; and (6.) The resolved part parallel to the axis of rotation.

‘Man Is Ill Because He Is Badly Constructed’: Artaud, Klossowski and Deleuze in Search for the Earth Inside

2011 ◽  
Vol 5 (1) ◽  
pp. 18-34 ◽  
Author(s):  
Rick Dolphijn
Keyword(s):  
Performance Art ◽  
Holy Spirit ◽  
The Body ◽  
Deleuze And Guattari ◽  
The Earth ◽  
The Holy Spirit ◽  
Life Itself ◽  
Body Without Organs ◽  
Ways Of Thinking ◽  
And Performance

Starting with Antonin Artaud's radio play To Have Done With The Judgement Of God, this article analyses the ways in which Artaud's idea of the body without organs links up with various of his writings on the body and bodily theatre and with Deleuze and Guattari's later development of his ideas. Using Klossowski (or Klossowski's Nietzsche) to explain how the dominance of dialogue equals the dominance of God, I go on to examine how the Son (the facialised body), the Father (Language) and the Holy Spirit (Subjectification), need to be warded off in order to revitalize the body, reuniting it with ‘the earth’ it has been separated from. Artaud's writings on Balinese dancing and the Tarahumaran people pave the way for the new body to appear. Reconstructing the body through bodily practices, through religion and above all through art, as Deleuze and Guattari suggest, we are introduced not only to new ways of thinking theatre and performance art, but to life itself.

‘A pinch of unseen, unguarded dust’: The World and Self in Thomas Hardy's Poems

2018 ◽  
Vol 8 (1) ◽  
pp. 49-66
Author(s):  
Monika Szuba
Keyword(s):  
The Body ◽  
The Self ◽  
Phenomenological Philosophy ◽  
The Earth ◽  
The World ◽  
The Universe ◽  
Recurrent Theme ◽  
Body Subject

The essay discusses selected poems from Thomas Hardy's vast body of poetry, focusing on representations of the self and the world. Employing Maurice Merleau-Ponty's concepts such as the body-subject, wild being, flesh, and reversibility, the essay offers an analysis of Hardy's poems in the light of phenomenological philosophy. It argues that far from demonstrating ‘cosmic indifference’, Hardy's poetry offers a sympathetic vision of interrelations governing the universe. The attunement with voices of the Earth foregrounded in the poems enables the self's entanglement in the flesh of the world, a chiasmatic intertwining of beings inserted between the leaves of the world. The relation of the self with the world is established through the act of perception, mainly visual and aural, when the body becomes intertwined with the world, thus resulting in a powerful welding. Such moments of vision are brief and elusive, which enhances a sense of transitoriness, and, yet, they are also timeless as the self becomes immersed in the experience. As time is a recurrent theme in Hardy's poetry, this essay discusses it in the context of dwelling, the provisionality of which is demonstrated in the prevalent sense of temporality, marked by seasons and birdsong, which underline the rhythms of the world.

The figure of the Earth derived by triangulation methods

1929 ◽  
Vol s5-18 (103) ◽  
pp. 53-59 ◽  
Author(s):  
W. Bowie
Keyword(s):  
The Earth ◽  
Figure Of The Earth
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