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 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.

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.

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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