scholarly journals III. Further experiments on the vapour densities of potassium and sodium

1879 ◽  
Vol 29 (196-199) ◽  
pp. 490-493 ◽  
Keyword(s):  
Considerable Error ◽  
Exact Determination ◽  
The Way

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.

scholarly journals Statistical error in counting experiments

1935 ◽  
Vol 149 (868) ◽  
pp. 467-486 ◽  
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.

scholarly journals Proposal for a new method of determining the longitude, by an absolute altitude of the moon

1843 ◽  
Vol 4 ◽  
pp. 52-52
Keyword(s):  
Great Difficulty ◽  
New Method ◽  
The Moon ◽  
Single Observation ◽  
Exact Determination ◽  
Absolute Altitude ◽  
The Way

The method employed by the author for determining the longitude by the observation of an absolute altitude of the moon, was pro­posed, many years ago by Pingré and Lemmonier; and the princi­pal difficulty which stood in the way of its adoption, was its re­quiring the exact determination of the moon’s declination reduced to the place of observation. This difficulty the author professes to have removed by supposing two meridians for which the altitudes are to be calculated: and the only remaining requisite is the accu­rate determination of the latitude, which presents no great difficulty, either on land or at sea. Examples are given of the practical work­ing of this method; showing that if the latitude of a place of obser­vation be obtained within a few seconds, the longitude will be found by means of a single observation of the altitude of the moon.

scholarly journals Universal Synthesizer of Mueller Matrices Based on the Symmetry Properties of the Enpolarizing Ellipsoid

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 983
Author(s):  
José J. Gil ◽  
Ignacio San José
Keyword(s):  
Mathematical Structure ◽  
Mueller Matrix ◽  
Morphological Properties ◽  
Nondestructive Analysis ◽  
Structural Decomposition ◽  
Symmetry Properties ◽  
Mueller Matrices ◽  
Scattering Measurement ◽  
The Way

Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others. For each given scattering measurement configuration, absolute Mueller polarimeters provide the most complete polarimetric information, intricately encoded in the 16 parameters of the corresponding Mueller matrix. Thus, the determination of the mathematical structure of the polarimetric information contained in a Mueller matrix constitutes a topic of great interest. In this work, besides a structural decomposition that makes explicit the role played by the diattenuation-polarizance of a general depolarizing medium, a universal synthesizer of Muller matrices is developed. This is based on the concept of an enpolarizing ellipsoid, whose symmetry features are directly linked to the way in which the polarimetric information is organized.

TO THE CALCULATION OF LENGTH OF GEOPHYSICAL OBJECTS OF HYPERBOLIC OUTLINE

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.

On the Inadequacy of existing Data for determining the Rate of Mortality among Select Lives

1854 ◽  
Vol 4 (1) ◽  
pp. 1-9
Author(s):  
William Spens
Keyword(s):  
First Year ◽  
Sufficient Data ◽  
Existing Data ◽  
Selection Of ◽  
The Way

I. While so much improvement has recently taken place in the arrangement and construction of various tables for facilitating calculations founded on existing data, very little has been done in the way of investigating and correcting the data themselves; and it is feared that the question of the rate of mortality among select lives is still involved in the greatest doubt and obscurity.II. It is not proposed in the present paper to go farther than to show that the rate of mortality, during the first year of selection, of select assured lives is so materially different from what it has hitherto been represented, as to lead to the inference that the data from which the erroneous deduction has been made cannot be true data for the ascertainment of the value of selection. To investigate the rate of mortality of select lives at separate ages, I conceive to be of the utmost importance for the elucidation of truth, and the proper direction of sanatory inquiries; but I do not consider that sufficient data at present exist for the determination of this, and these can only be obtained by a united inquiry. I shall be very happy if the present observations have any effect in hastening such an investigation, which sooner or later must be entered upon.

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

1907 ◽  
Vol 80 (535) ◽  
pp. 26-27 ◽  
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.

Study on Calculation of Rock Pressure and Determination of Depth for Shallow Asymmetric Tunnel

2011 ◽  
Vol 261-263 ◽  
pp. 1034-1038 ◽  
Author(s):  
Xiao Jun Zhou
Keyword(s):  
Rock Pressure ◽  
Calculation Method ◽  
Tunnel Structure ◽  
The Way

The method to calculate rock pressure for shallow asymmetric tunnel is analyzed by means of taking a mountainous tunnel with semicircular crown and straight sidewall as the object in this paper. The calculation method of tunnel rock pressure has been presented with consideration of both tunnel structure size and its overburden depth. Finally the way to determine the shallow or profound depth of asymmetric tunnel is also obtained.

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