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.

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.

On the effect of surrounding media on voltaic ignition

1851 ◽  
Vol 5 ◽  
pp. 783-784
Keyword(s):  
Platinum Wire ◽  
Philosophical Magazine ◽  
The Wire ◽  
The Difference ◽  
Different Gases

The author refers to some experiments of his published in the Philosophical Magazine for December 1845, and in the Bakerian Lecture for 1847, relating to the difference of ignition generated in a platinum wire heated by the voltaic current, when the wire is immersed in atmospheres of different gases. In the present paper these experiments are continued, the current being passed through two platinum wires both in the same voltaic circuit, but immersed in atmospheres of different gases. It appears from these experiments that the heat generated in the wire is less in hydrogen and its compounds than in other gases; and that when the wires and their atmospheres of gas are immersed in given quantities of water, the water surrounding the hydrogenous gases is less heated than that surrounding those which contain no hydrogen.

X-ray microanalysis of thin specimens in the transmission electron microscope at voltages up to 1000 Kv.

1978 ◽  
Vol 36 (1) ◽  
pp. 540-541
Author(s):  
G. Cliff ◽  
M.J. Nasir ◽  
G.W. Lorimer ◽  
N. Ridley
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Weight Fraction ◽  
Present Series ◽  
Constant Independent ◽  
X Ray ◽  
Transmission Electron ◽  
Series Of Experiments ◽  
Image Position ◽  
X Ray Absorption

In a specimen which is transmission thin to 100 kV electrons - a sample in which X-ray absorption is so insignificant that it can be neglected and where fluorescence effects can generally be ignored (1,2) - a ratio of characteristic X-ray intensities, I1/I2 can be converted into a weight fraction ratio, C1/C2, using the equationwhere k12 is, at a given voltage, a constant independent of composition or thickness, k12 values can be determined experimentally from thin standards (3) or calculated (4,6). Both experimental and calculated k12 values have been obtained for K(11<Z>19),kα(Z>19) and some Lα radiation (3,6) at 100 kV. The object of the present series of experiments was to experimentally determine k12 values at voltages between 200 and 1000 kV and to compare these with calculated values.The experiments were carried out on an AEI-EM7 HVEM fitted with an energy dispersive X-ray detector.

The role of differential phase contrast in electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 176-177
Author(s):  
E.M. Waddell ◽  
J.N. Chapman ◽  
R.P. Ferrier
Keyword(s):  
Phase Contrast ◽  
Practical Method ◽  
Position Vector ◽  
Differential Phase ◽  
Pure Phase ◽  
Differential Phase Contrast ◽  
The Difference ◽  
Image Position ◽  
First Moment

Dekkers and de Lang (1977) have discussed a practical method of realising differential phase contrast in a STEM. The method involves taking the difference signal from two semi-circular detectors placed symmetrically about the optic axis and subtending the same angle (2α) at the specimen as that of the cone of illumination. Such a system, or an obvious generalisation of it, namely a quadrant detector, has the characteristic of responding to the gradient of the phase of the specimen transmittance. In this paper we shall compare the performance of this type of system with that of a first moment detector (Waddell et al.1977).For a first moment detector the response function R(k) is of the form R(k) = ck where c is a constant, k is a position vector in the detector plane and the vector nature of R(k)indicates that two signals are produced. This type of system would produce an image signal given bywhere the specimen transmittance is given by a (r) exp (iϕ (r), r is a position vector in object space, ro the position of the probe, ⊛ represents a convolution integral and it has been assumed that we have a coherent probe, with a complex disturbance of the form b(r-ro) exp (iζ (r-ro)). Thus the image signal for a pure phase object imaged in a STEM using a first moment detector is b2 ⊛ ▽ø. Note that this puts no restrictions on the magnitude of the variation of the phase function, but does assume an infinite detector.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 540-541
Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov
Keyword(s):  
Reciprocal Lattice ◽  
Unit Cell ◽  
Reciprocal Lattice Vector ◽  
Unit Cell Parameters ◽  
Lattice Vector ◽  
Cell Parameters ◽  
Accuracy Of Measurements ◽  
The Difference ◽  
Image Position ◽  
Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

A quantitative evaluation of some factors affecting the non-fatty solids of cow's milk

1960 ◽  
Vol 27 (1) ◽  
pp. 19-32 ◽  
Author(s):  
W. H. Alexander ◽  
F. B. Leech
Keyword(s):  
Cell Count ◽  
Residual Effect ◽  
Clinical Mastitis ◽  
High Cell ◽  
Factors Affecting ◽  
Stage Of Lactation ◽  
Cell Counts ◽  
Satisfactory Analysis ◽  
The Difference ◽  
Image Position

SummaryTen farms in the county of Durham took part in a field study of the effects of feeding and of udder disease on the level of non-fatty solids (s.n.f.) in milk. Statistical analysis of the resulting data showed that age, pregnancy, season of the year, and total cell count affected the percentage of s.n.f. and that these effects were additive and independent of each other. No effect associated with nutritional changes could be demonstrated.The principal effects of the factors, each one freed from effects of other factors, were as follows:Herds in which s.n.f. had been consistently low over a period of years were compared with herds in which s.n.f. had been satisfactory. Analysis of the data showed that about 70% of the difference in s.n.f. between these groups could be accounted for by differences in age of cow, stage of lactation, cell count and breed.There was some evidence of a residual effect following clinical mastitis that could not be accounted for by residual high cell counts.The within-cow regression of s.n.f. on log cell count calculated from the Durham data and from van Rensburg's data was on both occasions negative.The implications of these findings are discussed, particularly in relation to advisory work.

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

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.

Merciful heavens? A question in Aeschylus' Agamemnon

1974 ◽  
Vol 94 ◽  
pp. 100-113 ◽  
Author(s):  
Maurice Pope
Keyword(s):  
Oral Tradition ◽  
Correct Reading ◽  
The Difference ◽  
Image Position

In discussions of Aeschylus' theology one of the passages most often quoted is the so-called ‘hymn to Zeus’ in the first chorus of the Agamemnon (Ag. 160–83). Fraenkel in his commentary goes so far as to call it ‘the corner-stone not only of this play but of the whole trilogy’. The passage concludes with two lines which in all modern editions are read as a statement, though our oldest manuscript, the Medicean, writes them as a question. Textually the difference is merely one of accent, but the difference of accent carries with it a reversal of meaning. As a statement the lines mean that the gods are something to be grateful for, that there is some χάρις or kindness associated with them. Taken as a question they deny this. Clearly then it is of great importance for the interpretation of Aeschylus to decide which is the correct reading.The lines in question, written without accents, areOur oldest manuscript, M, as I have said, writes ποῦ with an accent. So does our next oldest, the manuscript 468 of the Biblioteca di San Marco, generally known as V. If this reading stems uncorrupted from the time when accents were first applied to the text of Aeschylus and if at that time the oral tradition of the poet's words was not yet dead, then it will not be destitute of authority. But the thread is far too tenuous to bear any weight of proof.Equally there can be no argument from authority on the side of reading the lines as a statement. For though Triclinius and the closely associated manuscript F write που without an accent as an enclitic, this is as likely as not to be due to simple conjecture.

The fractional parts of an additive form

1972 ◽  
Vol 72 (2) ◽  
pp. 209-212 ◽  
Author(s):  
R. J. Cook
Keyword(s):  
Quadratic Form ◽  
Analogous Result ◽  
The Difference ◽  
Image Position ◽  
Forms Of Higher Degree ◽  
Additive Form ◽  
Real Quadratic

Heilbronn (6) proved that for every ε ≥ 0 and N ≥ 1 and every real θ there is an integer x such that,where C(ε) depends only on ε and ∥α∥ is the difference between α and the nearest integer, taken positively. Danicic(1) obtained an analogous result for the fractional parts of nkθ, the proof of this is more readily accessible in Davenport(4). Danicic(2) also obtained an estimate for the fractional parts of a real quadratic form in n variables, and in order to extend this result to forms of higher degree it is desirable to first obtain results for additive forms.

Sign in / Sign up

Export Citation Format

Share Document