scholarly journals XXIII. Theorems on the attraction of ellipsoids for certain laws of force other than the inverse square

1895 ◽  
Vol 186 ◽  
pp. 897-950 ◽  
Keyword(s):  
Radius Vector ◽  
Internal Point ◽  
Ellipsoidal Shell ◽  
Direction Cosines ◽  
The Law

1. To find the potential at an internal point P of a thin ellipsoidal shell bounded by similar concentric ellipsoids, the law of force being the inverse k th power of the distance. Let ( x, y, z ) be the coordinates of P; ( l, m, n ) the direction cosines of a radius vector drawn from P to any point Q on the surface; and let PQ = r . Let ( a, b, c ) be the semi-axes of the ellipsoids, and ( α, β, γ ) their squared reciprocals. Then from the equation of the ellipsoid ( αl 2 + βm 2 + γn 2 ) r 2 + 2 ( αlx + βmy + γnz )r - (1 - αx 2 - βy 2 - γz 2 ) = 0.

A nomogram for the law of direction-cosines

1942 ◽  
Vol 26 (179) ◽  
pp. 272-273
Author(s):  
S. I. Tomkeieff
Keyword(s):  
Line Passing ◽  
Direction Cosines ◽  
The Law

If α, β, and γ are the three angles between a line passing through the origin and the three rectangular co-ordinate axes, then the equation connecting them is as follows:cos2α+cos2β+cos2γ = 1.This is the law of direction-cosines of a line. Substituting (cos 2α+1)/2 for cos2α, &c., we get:cos 2α+cos 2β+cos 2γ = −1.

scholarly journals VII. Theorems on the attraction of ellipsoids for certain laws of force other than the inverse square

1895 ◽  
Vol 58 (347-352) ◽  
pp. 215-217 ◽  
Keyword(s):  
Ellipsoidal Shell ◽  
The Law ◽  
In The Beginning

The object of the author is to find finite expressions for the potentials of an ellipsoidal shell, and of a solid ellipsoid when the law of force is the inverse κ th power of the distance, κ being positive or negative. It is shown in the beginning of the paper that the two cases in which κ is an even integer and an odd integer require different treatment.

scholarly journals Continuos Parameterization of the Median Surface of an Ellipsoidal Shell and Its Geometric Parameters

2020 ◽  
pp. 5-12
Author(s):  
Natalya Gureeva ◽  
Anatoliy Nikolaev ◽  
Mikhail Klochkov
Keyword(s):  
Vertical Plane ◽  
Arbitrary Point ◽  
Radius Vector ◽  
Median Surface ◽  
Coordinate Plane ◽  
Parametric Function ◽  
Engineering Structures ◽  
Ellipsoidal Shell ◽  
Ellipsoidal Surface ◽  
Intersection Points

When analyzing the stress-strain state of thin-walled structural elements that have the shape of an ellipsoid, it becomes necessary to calculate the geometric characteristics of the ellipsoidal surface. When using the canonical ellipsoid equation, regions of uncertainty appear in the Cartesian coordinate system at the intersection points of the ellipsoid surface with the horizontal coordinate plane. To exclude these areas of uncertainty, we propose an expression of the radius vector of an ellipsoidal surface whose projections are functions of two parametric representations in mutually perpendicular planes. One of the planes is the vertical plane XOZ, and the other plane is the plane perpendicular to the axis O at the point with the x coordinate. The parameter T of the ellipse obtained from the intersection of the ellipsoid with the XOZ plane was chosen as the argument of the first parametric function. The argument of the second parametric function t is the parameter of an ellipse formed as a result of the intersection of an ellipsoidal surface with a plane perpendicular to the abscissa axis at a distance of x from the origin. The proposed representation of the ellipsoidal surface allowed us to exclude uncertainties at the intersection points of the ellipsoid with the HOWE coordinate plane. By differentiating the proposed radius-vector expression at an arbitrary point on an ellipsoidal surface, we obtain relations for the basis vectors of an arbitrary point and their derivatives represented by components in the same local basis. These relations are necessary for the development of algorithms for numerical analysis of deformation processes of engineering structures that have ellipsoidal surfaces.

scholarly journals Islamic Law from the Internal Point of View

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Haider A. Hamoudi
Keyword(s):  
Islamic Law ◽  
Legal Rule ◽  
Point Of View ◽  
Internal Point ◽  
Legal Rules ◽  
Internal View ◽  
Historical Method ◽  
Making Sense ◽  
Points Of View ◽  
The Law

Haider Hamoudi notes the different perspectives lawyers and historians employ in making sense of the law. Invoking H.L.A. Hart’s famous distinction between “internal” and “external” points of view with respect to law and legal rules, Hamoudi describes lawyers as primarily adopting the former, and historians, the latter point of view. This is not to suggest that lawyers do not take history into consideration, but rather to mean that when they do, their focus is results oriented in that they use history to understand the ultimate endpoint, the contemporaneous meaning of a legal rule or institution. Hamoudi observes two consequences emanating from lawyers’ adoption of the internal view that puts lawyers somewhat at odds with the demands of historical method and meaning. While deliberately omitting discussion on the normative desirability of either method, Hamoudi concludes by observing value in merely pointing out the differences between the internal and external viewpoints of law and history, respectively, to help expose “our own biases and assumptions.”

scholarly journals On the Attractions of Spherical and Ellipsoidal Shells

1913 ◽  
Vol 32 ◽  
pp. 91-100
Author(s):  
A. Gray
Keyword(s):  
General Problem ◽  
Thin Shell ◽  
Process Integration ◽  
Volume Density ◽  
Internal Point ◽  
Philosophical Magazine ◽  
Ellipsoidal Shell ◽  
Short Account

So far as I am aware, the methods, described below, of finding the attraction of a uniform shell of matter on a particle placed at external or an internal point, are new. They are particular applications of a method of finding the attraction of a thin shell uniform volume density bounded by similar and similarly situated ellipsoidal surfaces (what some have called a homothetic shell, and Thomson and Tait an elliptic homceoidœ) which I explained a paper, on the attraction of ellipsoidal shells and of solid ellipsoids, which was published in the Philosophical Magazine for April 1907. I give here also a short account of the more general problem with some additional notes and remarks. The solution depends on a geometrical theorem of some interest which occurred me in thinking over the problem of the ellipsoidal shell, and its solution by Poisson by a laborious and somewhat difficult process integration (Me'moires de I'Institut, t. xv., 1835).

scholarly journals The Rule of Law and Legal-Process Reasons in Attorney Advising

2018 ◽  
Author(s):  
W. Bradley Wendel
Keyword(s):  
Attorney General ◽  
Point Of View ◽  
Internal Point ◽  
Legal Ethics ◽  
Rigorous Approach ◽  
High Profile ◽  
Purposive Activity ◽  
The Law ◽  
Open Question ◽  
Torture Memos

This is an intervention in long-standing debates in the philosophy of law and the theory of professional ethics. In jurisprudential terms, it elaborates on H.L.A. Hart’s concept of the internal point of view, which is the perspective of one who views the law as creating obligations, not merely affecting one’s prudential calculations. In other words, Hart’s idea is that the law must be capable of normativity. Hart limited this conceptual requirement to judges, who are obligated to take the internal point of view, leaving a deeply important open question concerning the attitude that citizens and their advisors must take with respect to the law. The argument in this Article is that it is a constitutive principle of the professional obligations of lawyers that they regard the law from the internal point of view. From this obligation flow further, more specific duties of good faith in interpretation of the law. The Article therefore connects scholarship on the nature of law with more practical questions concerning the duties of lawyers advising clients. It provides an analytically rigorous approach to evaluating the conduct of lawyers in high-profile scandals such the Panama Papers revelations, the so-called torture memos prepared by lawyers in the Bush Administration, and Acting Attorney General Rod Rosenstein’s memo explaining the firing of FBI Director James Comey. The position defended here differs from both the Nineteenth Century "wise counselor" conception of lawyer professionalism and the standard conception of legal ethics as "zealous advocacy within the bounds of the law." It is in some ways an elaboration on some of my previous scholarship on legal ethics and interpretation of law, but is grounded much more explicitly not only in Hart's notion of the internal point of view but - perhaps surprisingly - also in Lon Fuller's insight that law is a purposive activity characterized by giving reasons of a certain type in justification of one's actions.

The Compton Effect in Wave Mechanics

1927 ◽  
Vol 23 (5) ◽  
pp. 500-507 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Hamiltonian Function ◽  
Compton Effect ◽  
Relativity Theory ◽  
Hamiltonian Equation ◽  
Wave Mechanics ◽  
Matrix Mechanics ◽  
Principle Of Relativity ◽  
Direction Cosines ◽  
The Law ◽  
Image Position

The problem of the scattering of radiation by a free electron has been treated by the author on the basis of Heisenberg's matrix mechanics, which was first modified to be in agreement with the principle of relativity. The main point of this modification is that, whereas in the non-relativity theory one deals with matrices whose elements vary with the time according to the law eiwt, in the relativity theory the elements of the matrices must vary according to the law eiwt′ where t′ = t − (l1x1 + l2x2 + l3x3)/c if they are to determine correctly the radiation emitted in the direction specified by the direction cosines (l1, l2, l3), x1x2 and x3 being the coordinates of the electron at the time t. These matrices were obtained by writing the Hamiltonian equation of the system in the formwhere W′ is a variable canonically conjugate to t′ and H′ commutes with t′, and then using H′ as an ordinary Hamiltonian function of a dynamical, system that has W′ for its energy and t′ for its time variable.

Ideologies in Law Time: The Oxford History of the Laws of England

2013 ◽  
Vol 38 (03) ◽  
pp. 746-764
Author(s):  
Janet McLean
Keyword(s):  
Public Sphere ◽  
Review Essay ◽  
Common Law ◽  
Point Of View ◽  
Internal Point ◽  
The Public ◽  
History Of ◽  
The Common ◽  
The Law ◽  
The Public Sphere

In the introduction to the newOxford History of the Laws of England 1820–1914, the authors suggest that their task is to tell the “history of the law itself.” This review essay examines what can be learned from a history told from law's internal point of view rather than through the perspectives of other disciplines, such as economics or philosophy. It considers whether and how the common law responded to industrialization and laissez-faire ideology, the influence of salient philosophical movements—such as utilitarianism—on statutory change, and how all history is an exercise in ideology. In considering the public sphere, it suggests that this work should form the inspiration for further inquiry.

Ethical Challenges: Less About Moral Wrongdoing and More About Communication Breakdown

2015 ◽  
Vol 20 (3) ◽  
pp. 72-84 ◽  
Author(s):  
Paula Leslie ◽  
Mary Casper
Keyword(s):  
Ethical Challenges ◽  
Speech Language Pathology ◽  
Thickened Liquids ◽  
Communication Breakdown ◽  
Professional Duty ◽  
Language Pathology ◽  
The Law ◽  
Personal Case

“My patient refuses thickened liquids, should I discharge them from my caseload?” A version of this question appears at least weekly on the American Speech-Language-Hearing Association's Community pages. People talk of respecting the patient's right to be non-compliant with speech-language pathology recommendations. We challenge use of the word “respect” and calling a patient “non-compliant” in the same sentence: does use of the latter term preclude the former? In this article we will share our reflections on why we are interested in these so called “ethical challenges” from a personal case level to what our professional duty requires of us. Our proposal is that the problems that we encounter are less to do with ethical or moral puzzles and usually due to inadequate communication. We will outline resources that clinicians may use to support their work from what seems to be a straightforward case to those that are mired in complexity. And we will tackle fears and facts regarding litigation and the law.

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