On exact determination of small radiation frequency shifts using a Fabry–Perot interferometer

In one former communication “On the Vapour Densities of Potassium and Sodium,” we pointed out the chief obstacles which lay in the way of an exact determination of these constants. Having overcome the chief manipulative difficulties in connexion with the method we described, there still remained the problem for solution as to how far the use of iron bottles in our experiments might affect the results. If the iron retained the metals or allowed their vapours to diffuse with rapidity through it, a considerable error might be produced without its being easily detected.

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TO THE CALCULATION OF LENGTH OF GEOPHYSICAL OBJECTS OF HYPERBOLIC OUTLINE

Prirodoobustrojstvo ◽

10.26897/1997-6011-2021-4-85-89 ◽

2021 ◽

pp. 85-89

Author(s):

K. N. ANAKHAEV ◽

◽

B. KH. AMSHOKOV ◽

K. K. ANAKHAEV

Keyword(s):

Water Management ◽

Applied Research ◽

Free Fall ◽

Linear Interpolation ◽

Close Approximation ◽

Tabular Data ◽

Exact Determination ◽

Complex Dependence ◽

Incomplete Elliptic Integrals

Hyperbolic curves are used in various theoretical and practical studies, including in the field of water management and environmental construction when calculating various geophysical objects with hyperbolic outlines (surfaces of coastal slopes, sliding lines of landslide massifs, directing dams, spillway surfaces of watersheds, water free fall trajectories, etc.). The exact determination of the length of the hyperbola arc is represented by a rather complex dependence based on “unbreakable” incomplete elliptic integrals, which makes it difficult to carry out analytical calculations and involves the use of tabular data with a time-consuming cross and non-linear interpolation of them, etc. Elementary dependencies are proposed to determine the length of the hyperbola arc, which give a very close approximation (up to 1%) to exact values. The obtained calculated analytical dependencies for determining the length of the hyperbola arc are recommended for practical use in theoretical and applied research in various fi elds of science and technology.

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On the surface-tension of liquids investigated by the method of jet vibration

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1907.0070 ◽

1907 ◽

Vol 80 (535) ◽

pp. 26-27 ◽

Cited By ~ 2

Keyword(s):

Surface Tension ◽

Cross Section ◽

Wave Length ◽

Standing Waves ◽

Exact Determination ◽

Relative Measurements

1. According to Lord Rayleigh’s theory of jet-vibrations, measurement of the length of the standing waves and the velocity and cross-section of a jet, together with the density of the liquid, affords the necessary constants for the calculation of the surface-tension. Notwithstanding the great fundamental advantages of this method, it has only been used in very few cases, and only for relative measurements of the surface-tension. The explanation hereof is to be found in the great difficulties connected with the adequate exact determination of the wave-length, and cross-section or velocity of the jet. As none of the methods in use for the measurement of these quantities could be taken as satisfactory, the main object of this investigation has been to work out really good methods for them.

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Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

Canadian Geotechnical Journal ◽

10.1139/t83-005 ◽

1983 ◽

Vol 20 (1) ◽

pp. 47-54 ◽

Cited By ~ 10

Author(s):

V. Silvestri ◽

C. Tabib

Keyword(s):

Plane Strain ◽

Half Plane ◽

Inclination Angle ◽

Complex Variable ◽

Earth Pressure ◽

Exact Distributions ◽

Exact Determination ◽

Upper Half Plane ◽

Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

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Statistical error in counting experiments

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1935.0076 ◽

1935 ◽

Vol 149 (868) ◽

pp. 467-486 ◽

Cited By ~ 83

Keyword(s):

Finite Number ◽

Statistical Error ◽

Single Particles ◽

Exact Determination ◽

Statistical Laws ◽

The Way

Experiments in which single particles are studied with the aid of counters would, in principle, lead to an exact determination of the statistical laws governing the behaviour of these particles if the number of counted particles were infinitely large. With a finite number of counts, however, a finite statistical error will always remain. This error depends upon the number of counts and upon the way in which one makes use of the counter readings to calculate the parameters entering into the statistical laws. The purpose of the following investigation is to show for some typical cases which way of calculating has to be adopted in order to make the error a minimum.

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