Mathematical Notes by Professor Tait (2.) On the Equipotential Surfaces for a Straight Wire

1875 ◽  
Vol 8 ◽  
pp. 443-443
Keyword(s):  
Natural Philosophy ◽  
Line Density ◽  
Straight Wire ◽  
Equipotential Surfaces ◽  
The Wire ◽  
Image Position

Some results given in Vol. I. of Thomson and Tait's Natural Philosophy may be much more simply obtained by calculating the potential of a wire rather than its attraction. That potential is easily found aswhere c is the length of the wire, ρ its line density, r1 and r2 the distances of its ends from the point at which the potential is to be found.

scholarly journals XIV.—On Torsional Oscillations of Wires

1900 ◽  
Vol 39 (2) ◽  
pp. 425-455
Author(s):  
W. Peddie
Keyword(s):  
Philosophical Magazine ◽  
Torsional Oscillations ◽  
Series Of Experiments ◽  
The Wire ◽  
The Difference ◽  
Image Position

This paper is in continuation of two others, on the same subject, previously communicated to the Society. In the First Paper (Philosophical Magazine, July 1894) it was shown that the formulawhere n, a, and b are constants in any one experiment, represents with accuracy the relation between y, the range of oscillation, and x, the number of oscillations which have taken place since torsion was first applied and the wire was left to itself, so that the oscillations gradually diminished. The apparatus employed, and the method of observation used, were identical with those described in the Second Paper above referred to. The wire which was experimented upon was the same as that used on the previous occasions. Its length, as given in the First and Second Papers, was 89·1 cm. A measurement made on the date 19.10.1897, in the course of the last series of experiments described in the present paper, showed that the length had become 89*3 cm. This increase was doubtless due to the fact that the heavy lead oscillator had been left attached to the wire during the whole of the intervening period. On the date given, it was also found that, with the same oscillator as was used in the experiments first described, ten oscillations were performed in 81 seconds, when the range was large, while 79 seconds were occupied when the range was small. This observation verified the result stated in the First Paper, that the period slightly increases as the range increases. It also showed that the wire was practically in the same condition as it was at first, in so far as elastic qualities are concerned; for the corresponding periods were only slightly less in earlier experiments, the difference being largely accounted for by the slight increase of length of the wire.

7. On a Singular Case of Rectification in Lines of the Fourth Order

1872 ◽  
Vol 7 ◽  
pp. 613-615
Author(s):  
Edward Sang
Keyword(s):  
Fourth Order ◽  
General Equation ◽  
Singular Case ◽  
Straight Wire ◽  
Image Position

The class of curves resulting from the formulaare of considerable interest as occurring in various mechanical inquiries. When a straight wire, whose effective breadth and thickness are as two to one, is fixed at one end and made to vibrate, its free end describes a curve of which the general equation isin which k is constant for the particular variety of curve. When the curve becomes a parabola, and when k = 0, it takes the form above mentioned; these phases were exhibited by me in 1832. Again, when a system of toothed wheels is deduced from a straight rack, having a curve of sines for its outline, the points of contact describe a curve of this class, as is shown in my treatise on the teeth of wheels.

scholarly journals 34. Meteor mass distribution from underdense-trail echoes

1968 ◽  
Vol 33 ◽  
pp. 362-372 ◽  
Author(s):  
M. Šimek ◽  
B.A. McIntosh
Keyword(s):  
High Power ◽  
Statistical Error ◽  
Total Sample ◽  
Logarithmic Scale ◽  
Line Density ◽  
A Value ◽  
Electron Line ◽  
The Mean ◽  
Image Position

The amplitude of meteor echoes is recorded on a logarithmic scale by a high-power radar equipment (λ = 9·2 m, PT=3 MW, G = 5·6) at Springhill Meteor Observatory near Ottawa. The smallest amplitude measured corresponds to a pulse power of 10−12 W, which represents a minimum electron line density of about 7 × 1011 el/m or a radio magnitude of + 10.Distribution curves of number of echoes as a function of echo power have been obtained from some 50 samples of 500 meteors each, at various times of day on about 1 day per month. The slopes showed little variation throughout the year. The statistical error in the slope value for any one sample was small, ~ 2–3%. However, determination of the mass index s from these slopes involves several problems. On the basis of simplest theory we have obtained for the sporadic background, with no definite seasonal or diurnal variation.During shower periods, lower values of s were obtained. For the 1966 Leonids, s for the shower was determined by estimating the percentage of shower meteors in the total sample. A value s = 1·7 ± 0·1 was obtained as the mean of 6 samples. It is not known to what extent the height-ceiling effect influences the observation of this shower.

scholarly journals XVIII.—On Torsional Oscillations of Wires

1897 ◽  
Vol 38 (3) ◽  
pp. 611-630
Author(s):  
W. Peddie
Keyword(s):  
Previous Treatment ◽  
Philosophical Magazine ◽  
Torsional Oscillations ◽  
The Wire ◽  
The Law ◽  
Image Position

About two years ago I communicated to this Society a paper on the above subject, which was printed in the Philosophical Magazine (1894). The object of the investigations therein discussed was the determination of the law of decrease of torsional oscillations when the range of oscillation was large in comparison with the palpable limits of elasticity. An equation of the formwhere y represents the range of oscillation, and x represents the number of oscillations which have taken place since the commencement of the observations in any one experiment, was found to give an exceedingly close representation of the results. The values of the quantities n, a, and b depend on the magnitude of the initial oscillation, and on the previous treatment of the wire. It was also found that, when the oscillations were allowed to die away to a sufficient extent, the value of n tended to diminish. The oscillations were practically isochronous.

A Study on Wire Sweep in Encapsulation of Semiconductor Chips Using Simulated Experiments

1995 ◽  
Vol 117 (3) ◽  
pp. 178-184 ◽  
Author(s):  
Sejin Han ◽  
K. K. Wang
Keyword(s):  
General Shape ◽  
Homogeneous Fluid ◽  
Dead Weight ◽  
Transfer Molding ◽  
Straight Wire ◽  
Semiconductor Chip ◽  
Series Of Experiments ◽  
The Wire ◽  
Semiconductor Chips ◽  
Made In

An effort has been made in this study to develop a model which can predict wire sweep during semiconductor chip encapsulation with transfer molding. The calculation of wire sweep during encapsulation depends on many factors. In this study, a step-by-step approach has been used considering one factor at a time. As the first step, the wire deformation has been measured and calculated under a known dead-weight loading. The next step has been to measure and calculate the deformation of a single straight wire attached to the mid-plane of a rectangular cavity due to the flow of a clear and homogeneous fluid. Finally, the wire deformation due to the flow has been measured and calculated when a wire of general shape is attached to a leadframe. The effect of bubble on the wire-sweep has been analyzed qualitatively. Through this series of experiments, a first step in the development of model for the prediction of wire sweep during chip encapsulation has been made.

2. On the Curves produced by Reflection from a Polished Revolving Wire

1878 ◽  
Vol 9 ◽  
pp. 302-302
Author(s):  
Edward Sang
Keyword(s):  
Fixed Point ◽  
Curved Surface ◽  
Third Order ◽  
Straight Wire ◽  
The Third ◽  
Straight Line ◽  
Plane Passing ◽  
The Subject ◽  
The Wire

When a polished thin straight wire turns on a fixed point in space, the point at which light coming from a fixed source is reflected, moves in a curved surface. In this paper the motion of the wire was supposed to be restricted to the plane passing through the eye and the source of light. The curve was shown to be of the third order, having a straight line as a symptote both ways, and to depend for its form upon a characterising angle. The interest of the subject lay chiefly in the remarkable transformations of the curve.

Turbulence Measurements With Symmetrically Bent V-Shaped Hot-Wires. Part 2: Measuring Velocity Components and Turbulent Shear Stresses

1988 ◽  
Vol 110 (3) ◽  
pp. 270-274 ◽  
Author(s):  
M. Hishida ◽  
Y. Nagano
Keyword(s):  
Flow Field ◽  
Velocity Component ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Wall Surface ◽  
Hot Wire ◽  
Turbulence Measurements ◽  
Straight Wire ◽  
Hot Wires ◽  
The Wire

An analysis of the response of a V-shaped hot-wire to velocity component fluctuations is presented. A V-shaped hot-wire works in the same manner as a conventional inclined straight wire. The great differences are: the V-shaped wire is less sensitive to the w component of velocity; the V-shaped wire can be supported just like a cantilever, and thus the wire may be brought closer to the wall until it touches the wall surface, whereas an inclined straight wire is kept away from the wall by the supports, and a probe body distorts the flow field.

scholarly journals 74. The distribution of meteor masses

1957 ◽  
Vol 4 ◽  
pp. 392-393
Author(s):  
I. C. Browne ◽  
K. Bullough ◽  
S. Evans ◽  
T. R. Kaiser
Keyword(s):  
Mass Distribution ◽  
Ionization Process ◽  
Line Density ◽  
Simple Theories ◽  
Electron Line ◽  
Statistical Studies ◽  
Meteor Trails ◽  
Image Position

Kaiser (1953) [1] has shown how it is possible, from statistical studies of radio echoes from meteor trails, to obtain values of the exponent s in the assumed equation for the number of meteors n(α) of line density α where αm is the maximum electron line density (number of electrons per cm.) produced in the trail of a meteor. If the simple theories of the meteor ionization process are correct, αm is proportional to the meteor mass m, so that from radio echo studies it should be possible to obtain a measure of the meteor mass distribution: where n(m) is the number of meteors with mass in the range from m to m + dm.

Complex potential equations I. A technique for solution

1976 ◽  
Vol 80 (1) ◽  
pp. 165-187 ◽  
Author(s):  
C. B. Collins
Keyword(s):  
Differential Equation ◽  
Close Association ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
Novel Technique ◽  
Linear Partial Differential Equations ◽  
Classical Differential Geometry ◽  
Equipotential Surfaces ◽  
Geometric Technique ◽  
Image Position

AbstractThis work amalgamates and solves certain problems arising in differential equation theory and in classical differential geometry.It describes a novel technique for solving systems of non-linear partial differential equations of the formwhere f(γ) and g(γ) are arbitrarily assigned functions. The circumstances are determined under which compatible solutions exist, not only when γ is real, but also when γ is complex, and all of the corresponding solutions are found. This is done by using a geometric technique that incorporates the equipotential surfaces of constant γ. In general, these surfaces are imaginary, and a fairly extensive treatment of such surfaces in (complexified) 3-dimensional Euclidean space is included. A close association is discovered between the set of equipotential surfaces and the class of surfaces of constant radii of principal normal curvature.

Hydrodynamic theory of magnetic fields due to electron currents in a straight wire

2013 ◽  
Vol 26 (3) ◽  
pp. 438-449
Author(s):  
Benjamin B. Dayton
Keyword(s):  
Magnetic Field ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Hydrodynamic Theory ◽  
Return Flow ◽  
Straight Wire ◽  
Conduction Electrons ◽  
Positive Ions ◽  
The Wire

In previous articles in this journal, the author presented hydrodynamic models of the electron as a sink and the positron as a source for the continuous flow of a primordial incompressible ideal fluid from sources to sinks in ordinary three-dimensional space generating the electrostatic field. The return flow from a sink to a source occurs through a wormhole tube (called an ether string) in four-dimensional space-time. It was assumed that the finite core of a primitive electron and the core of a primitive positron would be trapped at the boundary surface of the cylindrical core of a linear vortex in the fluid. The interaction between the flow component into the electron sink and the vortex field would wind the ether string linking the electron and positron cores into a helix (called an ether spring) located at the surface of the vortex core. Loosely bound electrons in metal atoms can migrate through the lattice of a metal crystal while still remaining linked by an ether spring to the positron in the proton in the original atomic nucleus. When a piece of metal is broken into two or more parts, some of the free electrons in each part may remain linked to protons in another part. These electrons are referred to as externally linked conduction electrons. When such electrons are induced to move along a straight wire, a magnetic field is generated around the wire. The magnetic field is due to regions of vorticity in the primordial fluid around the wire. These regions result from a criss-crossing of fixed and moving ether springs. The fixed ether springs link conduction electrons in metal objects outside the wire to positive ions in the wire. The axes of ether springs linked to the moving conduction electrons in the wire are straight and inclined forward through a small Lorentz angle so that they cross over the fixed straight ether springs linked to positive ions in the wire. It can be shown that the overlapping ether springs produce regions with a vorticity with vorticity vectors tangent to circles centered on the straight wire axis. Alternating currents will cause these regions of vorticity to move outward away from the wire corresponding to radio waves.

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