Reference Circle Research Articles

Dispersion versus absorption (DISPA): Modulation broadening and instrumental distortions in electron paramagnetic resonance lineshapes

Plots of dispersion versus absorption (DISPA) in NMR have previously been shown to provide an extremely sensitive test for deviations from Lorentzian lineshape. In this paper, the experimental absorption derivative EPR spectrum of peroxylamine disulfonate (PADS) is digitized during field-sweep detection and numerically integrated to give an absorption spectrum, which is then numerically Hilbert transformed to yield a dispersion spectrum, and in turn a DISPA plot. The effect of field modulation is demonstrated both theoretically and experimentally to produce an EPR DISPA curve whose displacement outside its reference circle is directly related to the strength of the modulating field. The modulating field strength can thus be determined without external calibration, using a single DISPA plot. In addition, DISPA detection of small lineshape distortions resulting from field sweep at rates faster than are appropriate to the time constant of the phase-sensitive detector is demonstrated experimentally. Finally, the circular DISPA plot for PADS at high concentration readily illustrates the homogeneous nature of the line broadening, again from a single EPR spectrum. These results show that the DISPA technique can be used, even when only the absorption spectrum is experimentally available.

Roundness measurement using limacons

Most roundness measuring systems which find automatically the ‘reference circles’ to a profile have used, for convenience, a limacon figure as an approximation to a circle. However this figure has important geometrical properties relevant to normal roundness measurement and can be regarded as the bais of an analytical system rather than an instrumental convenience. This paper examines some of the implications of the limacon method under practical conditions by comparison with circular references. It includes a comparison of roundness measurements taken using limacon references according to minimum zone, minimum circumscribing, maximum inscribing and least squares criteria

Stochastic Characterization of Macro- and Microerrors of Journal Bearing Roundness

A new approach for the characterization of form error and surface roughness of round bearings is presented. The method employs the theory of random function excursions to describe the macro- and microerrors of the round surface in both radial and circumferential directions. The mathematical principle of the measuring technique is given, and it is shown that an accurate description of the roundness can be obtained from the knowledge of the intercept probabilities of the crest and valley excursions of the surface trace about a given reference circle. Based on the mathematical model, new indices for the characterization of journal bearing roundness are proposed. These indices are computed directly from data obtained from commercially available roundness measuring devices. A number of experiments were performed to justify the validity of the proposed roundness indices. Roundness measurements were carried out on a number of differently machined cylinders using a specially equipped measuring device (Talyrond 51) with a link to a hybrid computer EAI-690. The theoretically computed indices compared favorably with the measurements made on the actual round surfaces.

A method for aligning crystals in precession photography using monochromated radiation

Routine alignment procedures based on the position and shift of white radiation streaks in the zero-level Laue cone are unsuitable if monochromated radiation is used in precession photography. Correct orientation can be achieved using the following two step procedure: (1) Owing to misalignment of the crystal some reflections can be shifted off the trace of the zero-level Laue cone. This can result in an unequal distribution of reciprocal-lattice rows within the upper (or lower) semicircle along the horizontal (and/or vertical) diameter of a reference circle generated by a reciprocal-lattice plane truly parallel to the precession axis. The amount of angular rotation necessary to bring an equivalent number of rows into the two semicircles constituting the trace of the zero-level Laue cone is first measured. (2) Since an error of at most 2°20′ will remain after step 1 (for μ = 10°) the correct orientation is obtained by a series of sequential corrections continued until an equal intensity distribution is obtained from symmetry-related reflection spots.

The nonius horopter—II. An experimental report

Пpeдcтaвлeн aнaлиз пpoблeмы идeaльнoгo цeнтpa глaзa для pacхeтoв диcпapaтнocти, пpи cвoбoднoм и фикcиpoвaннoм пoлoжeнии глaзa нaблюдaтeля. Oпиcaн aппapaт, кoтopый пoзвoляeт пpoизвoдить нoниycныe измepeния нa фикcиpoвaнных и движyщихcя глaзaх. Двe cooтвeтcтвyющиe кpнвыe пoлyхeны пpи paзных paccтoяниях и экcцeнтpицитeтaх. Пpи мaлoм paccтoянии нaблюдeния (1 M) нoниyc-гopoптep лoжитcя внe cooтвeтcтвyющeгo кpyгa Vieth-Müller, пpи хeм pacхoждeниe yвeлихивaeтcя к пepифepии. Oднaкo, этo oтклoнeниe знaхитeльнo yмeньшaeтcя пpи yмeнышeнии кoнвepгeнции. Этo, пo-видимoмy, oзнaхaeт, хтo бинoкyляpнaя кoppecпoндeнция peopгaнизyeтcя в зaвиcимocти oт кoнвepгeнции. Бoлee тoгo, и ocoбeннo нa пepифepии, нoниyc движyщeгocя глaзa для нopмaльнoгo нaблюдaтeля в знaтитeльнoй cтeпeни oтлихaeтcя oт нoниyca нeпoдвижнoгo глaзa. Этo дaжe eщe бoлee oхeвиднo пpи aнизэйкoнии; пpивoдятcя нeкoтopыe cooбpaжeния для oбъяcнeния этoгo. Cooбщaeтcя o cpaвнитeльных измepeниях фpoнтaльнo-гeoдeзихecких и фpoнтaльнoгo гopизoнтa и oкaзaлocь, хтo кpивыe пoлyхeнныe для хapaктepиcтики пocлeднeгo нe oтлихнмы oт кpyгa Vieth-Müller. Haкoнeц, былo нaйдeнo, хтo нaдeжнocть нoниycных oцeнoк oбpaтнo пpoпopциoнaльнa cтeпeни кoнвepгeнции и этoт фaкт oбcyждaeтcя в cвязи c пpoблeмoй aocтpoты cтepeocкoпихecкoгo зpeния.

Paper 35: Some Aspects of Measurement of Roundness

This paper deals with the analysis of the extent to which the results obtained from the measurements of the same graph may vary while using different reference circles. The statistical characteristics of the graph were obtained experimentally, and the algorithms for circles were worked out. The analysis was carried out by the Monte-Carlo method on a digital computer.

An Analog Computer Realization of the Euclidean Tools

The compass and straightedge of Euclidean geometry offer many computational possibilities. Their analog computer realization as described here was developed for the study of the kinematics of machinery, but may be useful in several other areas. For the particular case discussed it was necessary to realize these tools without the use of special electronic devices and to make them available for simultaneous use at an arbitrary number of locations. Low operating frequencies were acceptable. The realization utilizes dynamic computing equipment to generate a reference circle or line, and simple logic in the utilization of the reference. The system may be extended to function generation and multiplication.

Further studies on the stellar orientation of nocturnally migrating birds

The discussion of the previously published experiments on the star-orientation of Lesser Whitethroats, Blackcaps, and Garden Warblers confirms the findings, that these nocturnal migrants, possessing an internal clock, rely on a spherical grid of two celestial coordinates. It still has to be analysed if these birds would refer to the azimuth and altitude of their stellar orientation pattern with the natural or an artificial horizon as the primitive circle. They also could make use of the second spherical grid with hour angle and declination, and the celestial equator as the circle of reference. There is no indication that the birds would rely on a star-compass alone. The system of orientation with two stellar coordinates is sufficient for nocturnal homing after displacements, as they were simulated in planetarium experiments. Some general remarks were made regarding migration orientation and homing abilities of displaced birds. In relation to this celestial orientation and the setting of the internal clock a possible establishment of a newly expanded species in a new geographical area is briefly discussed.

The Use of Stereographic Net for the Rapid Approximate Determination of Distance and Azimuth*

Abstract The distance and azimuth from a seismograph station to earthquake epicentres anywhere in the world may be determined simply and rapidly by means of a stereographic chart bearing a suitable family of reference circles. Base charts designed for this purpose are obtainable from the Dominion Observatory, Ottawa.

Feret‘s Statistical Diameter as a Measure of Particle Size

VARIOUS measures of the size of irregularly shaped particles as seen in profile under the microscope have been used, chosen according to their theoretical significance or practical ease of measurement. These include, using Heywood‘s notation1,2 : (i) the diameter of the circle of equal area, d ; (ii) the diameter of the circle of equal perimeter, D ; (iii) the length of line bisecting the profile area (Martin‘s statistical diameter3), M ; and (iv) the perpendicular distance between parallel tangents touching opposite sides of the profile (Feret‘s statistical diameter4), F. M and F are determined for randomly oriented particles, thus giving an average value over all possible orientations. d is usually regarded as the ideal measure of particles seen in profile, but is somewhat difficult to determine experimentally with precision. It is, however, common practice when sizing very small particles to estimate d visually by comparing them with standard reference circles on a Patterson and Cawood or similar type of eyepiece graticule5,6. M and F are convenient to measure in practice with aid of an eyepiece scale or filar micrometer, and have been extensively used by various Workers. D, or rather the ratio D/d, termed by Heywood1 the ‘contour ratio', and its reciprocal called the ‘degree of circularity' by Wadell7, have been used in discussing the shape and hydrodynamical properties of particles. For these purposes D has usually been determined by direct perimeter measurement of the projected images of particles. It does not appear to have been adopted intentionally in any work known to me as a direct single measure of particle size.

Gyrograms for Simple Harmonic Systems Subjected to External Forces

A graphical method is described for the approximate integration of equations of the form md2x/dt2+kx=f(t), which arise in several branches of physics and engineering. The graphs, named ``gyrograms,'' are an extension of the familiar ``reference circle'' used in representing simple harmonic motion. The method is applicable whenever f(t) can be adequately approximated by a step function having a few steps.

Group Velocity and Wave Mechanics

IF it be true that Nature is built up not of particles but of waves, it is obviously of great importance to gain clear ideas as to the characteristics of wave motion. In dealing with any oscillatory motion, Dr. Albert Campbell suggested several years ago the use of the term pulsatance (an alternative form sometimes used is pulsance) for 2πσ where σ is the frequency (Proc. Phys. Soc., vol. 31, p. 80; 1919). Thus the pulsatance is the number of vibrations in 2π units of time. I have found this term of very great service in teaching, as it economises time in discussion and space in writing or printing. Even the elementary student appreciates its value when he recognises that it corresponds to angular velocity in the reference circle in defining simple harmonic motion. Such a motion is represented by the equation y = A sin pt, where A is the amplitude and p the pulsatance.

The Little Circle of Reference

The Little Circle of Reference

Congestion de luxe—Do we want it?

AbstractLast month Daniel Turner wrote on the vicious circle of rapid transit and congestion math special reference to New York City. This month Mr. Dykstra discusses the same problem from the standpoint of Los Angeles' experience. And the east and the west have met, for without any collusion or conspiracy the two authors have arrived at wirtually the same conclusions.

The Prismatic Astrolabe1

IN the process of measuring the places of stars on the celestial sphere, or in the converse process of using these measured places to fix the position of the observer upon the earths surface, the astronomer has at his disposal two systems of reference lines or circles upon which to base his measurements. These are respectively the vertical great circles through his zenith and the small circles parallel to his horizon, the circles of equal altitude or equal zenith distance. Using the first system, his method is to time the transit of a star across a vertical circle, almost invariably the meridian circle passing through the north and south points. If, in addition to timing the transit, he measures the altitude, he gets a complete determination of the position of the star observed, and uses both sets of reference circles, the vertical circle for fixing the time of transit, and hence the right ascension of the star, and the horizontal circle for fixing the altitude of transit, and hence the star's declination. This is the ordinary observation carried out in the observatory with the transit circle or by the surveyor in the field with the theodolite. Another method of observation which gives the same quantities, though not in the same direct form, is by the use of an instrument adapted for the recording of transits across a horizontal circle of constant altitude. An instrument of this class is the almucantar, in which horizontality is secured by the device of floating the whole in a mercury bath, it being easily seen that if either the instrument or the bath is moved round, the telescope will maintain a constant angle with the horizontal, and the line of vision will therefore always intersect an almucantar or circle of equal altitude.

Our Astronomical Column

GALACTIC CO-ORDINATES.—An interesting article on the galactic circle as a plane of reference for star places is contributed to the February number of Scientia by Dr. A. C. D. Crommelin. Following a comparison of the more familiar systems of coordinates, it is explained that catalogues of stars giving positions with respect to a plane which is independent of the earth's motions would have the great advantage that they would not get out of date as our present catalogues do, as only small corrections for proper motion would be required. The most obvious circle of reference is that provided by the Galaxy, for almost ever) feature either of distribution or of motion of the various classes of stars is based on the Galaxy as a plane of symmetry. It is difficult to give precision to> the definition of the galactic circle, but from a consideration of eight determinations, Dr. Crommelin suggests that the adopted position of the north galactic pole, for the equinox of 1900, should be R.A. 12h. 42m. 37s., decl. +270.32′. It is further suggested that an actual star should be selected to mark the zero of galactic longitude, say a Cygni, which has an extremely small proper motion. The general adoption of some-such scheme has been widely advocated, and will doubtless sooner or later be realised.

Dr. S. C. Chandler

DR. S. C. CHANDLER, whose death we recorded with regret last week, was not the least conspicuous in that earnest band of American astronomers whose energy and resource have done so much to advance astronomical science. He began his scientific career in the United States Coast Survey, a school that has trained many brilliant observers, who, in positions of greater independence, have rendered valuable service. Dr. Chandler's claim to a place among the most famous of these rests upon three notable achievements. First, the invention and use of the Almacantar, an instrument in which the small circle perpendicular to the meridian passing through the pole is adopted as a fundamental circle of reference, and gravitational action round an imaginary vertical axis is substituted for the motion of rotation round the pivots of the horizontal axis in the case of a vertical circle. Secondly, for his valuable catalogues of variable stars, in which he systematised the results collected by many observers, thereby encouraging and facilitating further observations. His work in this direction was by no means confined to simple compilation. He was both an indefatigable observer and the fortunate discoverer of many interesting objects of this class, ever directing attention to a branch of astronomy that has proved both suggestive and fructiferous.