Geographic Meridian Research Articles

Precyzyjne wyznaczanie geodezyjne w budowie obiektów inżynierskich z orientacją w określonym kierunku

In the construction practice, there are engineering structures, where some complex requirements in the process of their building have to be meet, e.g., their positioning, geographical orientation and geometric determination. The current publication examines the specificity of geodetic activities, regarding the orientating of the main construction axes of the foundation and the supporting structures of the terrestrial telecommunication antennas in a predetermined direction, for example, in the parallel direction to the geographical meridian. The focus is on the assessment of the accuracy and the choice of appropriate methods and equipment in order to create the required geodetic network, as well as to perform accurate setting out works. The combination of demands, namely for a specific geographic orientation and precise relative accuracy of the setting elements, implies a suitable transition from the ellipsoidal geodetic coordinates to the projection plane of the setting out project. In this connection, the influence of the meridian convergence on the accuracy of the planning setting out works is examined. A mathematical approach is proposed to assess the need of elimination of this factor, depending on the value of the constructional tolerance and the geographic location of the site.The necessary precision for determining the geodetic ellipsoidal coordinates by GNSS (Global Navigation Satellite System) measurements as well as the required accuracy of the planning and elevation setting out works are shown.Using different geodetic methods and tools, a preliminary accuracy assessment approach and the choice of the appropriate coordinate projection and height reference system is also proposed. The real data, which were obtained in different Earth’s locations by the explained methodology, are presented. The established geodetic networks provide orientation of the main construction axes of the bases of the terrestrial communication antennas in the parallel direction to the geodetic meridian with an azimuth standard error - МА = ± 2÷5' (minutеs) and allowable error in distances and eleventions of the setting out elements, respectively - MdS ≤ ±3 mm, Mdh ≤ ± 2 mm.

Increasing the accuracy of the vessel’s course orientation

The object of the study is the process of increasing the accuracy of measuring the vessel's course and course orientation by using the mathematical model of the gyrocompass in the on-board computer. On modern vessels, the gyrocompass is the main course measuring device. Its advantages lie in measuring the current course relative to the geographic meridian, its readings are not affected by magnetic anomalies, as was the case when using magnetic compasses, which led to a partial or complete loss of orientation of control objects. At the same time, gyrocompasses also have their drawbacks. The most significant of them is the inertial deviation of the sensitive element caused by the curvature of the Earth's surface, a change in course, acceleration or deceleration of the vessel. With the appearance of the moments of these forces, the axis of the gyrocompass leaves the equilibrium position and begins to make precessional movements. To reduce the inertial deviation, constructive solutions and recommendations to shipmasters regarding the consideration of deviational errors are used. Structural solutions lead to an increase in weight, complexity of the design, a decrease in reliability, and an increase in cost. The recommendations of regulatory documents regarding the consideration of the inertial deviation of the sensitive element of the gyrocompass are difficult to implement in practice, but they can be implemented in the on-board computer of the vessel control system by using a mathematical model of the sensitive element. The paper developed a method of increasing the accuracy of gyrocompass course measurement and the accuracy of course orientation by using an observation device built on the basis of a mathematical model of the gyrocompass in the on-board computer of the course control system. This makes it possible to estimate the useful component of course measurement and deviational errors from changes in speed and course, the curvature of the earth's surface. The useful component, without deviational errors, is used in the vessel's course control channel. The developed method can be used on vessels, provided it is integrated into the existing automated system of the on-board computer to solve the problem of monitoring the components of the gyrocompass measurement.

Determination of meridian position by a two-step ground gyrocompass in eesthetical rotor positioning

Contradiction between accuracy and time of definition of a plane of a geographical meridian has significantly weakened with appearance of automatic gyrocompasses and algorithmic methods of processing of the information from them. These methods allow us to expand the range of possible modes of gyrocompasses, including non-traditional. The article considers an automatic two-stage ground gyro compass operating in the mode of natural stopping of the rotor after its pulse acceleration by non-electrical means (squib , compressed air, etc.). The specified mode is attractive because it allows to identify uncontrolled harmful moment around the axis of suspension in one start and significantly reduce the measurement time. In order to further improve the device, it is proposed to abandon the measurement of the current value of the kinetic moment, and to identify the decay coefficient of the exponential function by observing the azimuthal motion of the sensitive element of the device. Moreover, the paper shows that it is possible not to measure the initial value of the kinetic momentum, replacing the measurement with identification of this parameter by observing the same azimuthal motion of the sensitive element. In this case there is no need to have on the sensitive element any nodes associated with the transmission of power and electrical signals, the sensitive element can be made as a purely mechanical element, carrying on itself a rotating rotor.
 For all considered variants of measurement (or identification) of parameters the machine simulation was carried out, which confirmed the performance of the proposed methodology.

Сравнительная распространенность и особенности течения неспецифического язвенного колита в странах одного географического меридиана: Украина — Тунис. Проверка гипотезы «Север — Юг»

Актуальность. Хронические воспалительные заболевания кишечника (неспецифический язвенный колит (НЯК) и болезнь Крона) относятся к тяжелым, неизлечимым страданиям, сопровождающимся в большинстве случаев потерей трудоспособности и ранней смертностью из-за их осложнений. Истинная распространенность этих заболеваний остается недостаточно изученной из-за статистической отчетности, построенной на обращаемости пациентов за медицинской помощью. Целью работы было проведение сравнительного анализа распространенности, особенностей течения и терапии НЯК в Украине и Тунисе, находящихся на одном географическом меридиане на расстоянии 1626 км. Результаты. При сравнении особенностей течения НЯК у жителей двух стран — Украины и Туниса, находящихся на одном гео­графическом меридиане и удаленных на расстояние более 1600 км, прослеживается градиентный фактор, установленный в пределах европейского континента. Это проявляется в том, что НЯК чаще страдает более молодое население Туниса (средний возраст (37,13 ± 1,24) года против (45,33 ± 1,65) года у жителей Украины); кроме того, среди больных НЯК жителей Туниса в 1,5 раза больше мужчин, чем женщин. Отмечается преобладание у пациентов Украины тотального поражения кишечника и тяжелого течения заболевания. Выводы. Таким образом, при анализе популяции пациентов с НЯК в Украине и Тунисе выявлено увеличение частоты встречаемости пациентов с НЯК в украинской популяции. Неспецифический язвенный колит у украинских пациентов имеет более распространенные формы и тяжелое течение, чем у больных из Туниса. Это связано с особенностями воздействия факторов внешней среды, генетической предрасположенностью, изменениями иммунитета и кишечного микробиома и подтверждает гипотезу «Север — Юг».

INDIRECT CONTROL GYROCOMPASS FOR LAND MOBILE VEHICLES

This work consists of two parts. The first part is a historical overview of the creation of two generations of marine and land gyrocompasses with direct and indirect control. During the review of pendulum or direct control gyrocompasses, using primary sources and authoritative secondary sources, the main practical and analytical developments that led to the creation of the first industrially applicable marine gyrocompass are highlighted. The review of non pendulum or indirect control gyrocompasses is largely an original study of the origins of their creation that is provided through an analysis of available patents taking into account the lack of other available early sources. There are distinguished the developments according to the patent of Narciss Ach (1906, Germany) where the scheme of the gyrocompass with indirect control probably appeared for the first time, the developments according to the patent of Preston R. Basset (1923, USA), where the scheme of proper tuning of indirect control gyrocompass appeared for the first time, and other developments as well. There are also considered the developments of a gyrocompass with electromagnetic correction by Pavel Koptyaev (1932, 1951-1954, USSR) and the main industrial developments of corrected gyrocompasses in the territory of the former USSR. The review also briefly indicates the main operational properties of marine and land gyrocompasses, including a new generation of gyrocompasses based on fiber-optic gyroscopes (FOG) and hemispherical resonator gyroscopes (HRG), attitude heading reference system (AHRS). The second part of this work reasonably follows from the first part, in which the gyrocompass with indirect control for land mobile vehicles based on a dynamically tuned gyroscope (DTG) on a platform stabilized in the horizon plane is studied. A general model of errors of such gyrocompass is determined, when the main axis of the gyroscope is brought into the plane of the true (geographical) meridian in the direction to the North and in the direction to the South. A hardware compensation scheme for the systematic errors of the gyrocompass is provided. A problem of determining and compensating for the gyroscope own drift relative to the horizontal axis of the suspension is solved through indirect measurements. The estimation of parameters of the indirect control gyrocompass is provided as a device of a navigation accuracy class

Comment on “The night when the auroral and equatorial ionospheres converged” by Martinis, C., J. Baumgardner, M. Mendillo, J. Wroten, A. Coster, and L. Paxton

AbstractIntense OI 630.0 nm emission depletions were detected over Mexico by an all‐sky imager during the main phase of the geomagnetic storm on 1 June 2013 (minimum Dst index: −119 nT). Those emission depletions were interpreted to be associated with equatorial plasma bubbles. If bubbles were responsible for those middle‐latitude emission depletions, they would have been extreme bubbles which extended over 40° magnetic latitudes and 7000 km in altitude at the magnetic equator. However, a few factors challenge this interpretation. First, the emission depletions detected over Mexico showed westward drift, whereas the equatorial ionosphere including bubbles drifted eastward on that night. Second, the middle‐latitude emission depletions were tilted westward with respect to the geographic meridian, but the westward tilt of bubbles was not identified. Third, the growth of bubbles was not evident when the middle‐latitude emission depletions grew. The westward tilt and westward propagation of the middle‐latitude emission depletions are consistent with the characteristics of medium‐scale traveling ionospheric disturbances (MSTIDs) observed over the United States on that night. Thus, the emission depletions over Mexico can be interpreted to be the signature of MSTIDs.

Method of determining the geographic meridian plane by ground-based pendulum gyrocompass in exponential acceleration mode of its rotor

A method of determining the position of the geographic meridian by threefold pendulum gyrocompass during the process of exponential acceleration of its rotor. Obtained an algorithm identifying the initial position of the rotor axis, which are based on the properties of the gyrocompass's motion solutions of differential equation and the equation itself. The results of simulations of the relevant data processing algorithms, these advantages of the proposed method compared to traditional.

ABOUT DETERMINING THE POSITION OF THE GEOGRAPHIC MERIDIAN THREE-STAGE PENDULUM GYROCOMPASS DURING ACCELERATION OF ITS ROTOR

The article considers three-stage pendulum gyrocompass ground with torsion suspension unmanaged sensor, equipped with high-precision digital angle sensor azimuthal position sensor and information processing unit. During processing of information isused an indirect method to get facts about initial deviations of dynamical systems.In the process of improving the instrument have revealed that a further increasing of accuracy due to the necessity to consider the following factors. During the measurement around the vertical axis of the sensor operates permanent uncontrolled moment due to operational reasons are different from measurement to measurement. Specified point shifts the center of oscillation of the azimuthal sensor, which is in accordance with the procedure identified azimuth northerly direction on a constant value. For self-compensation of this error have been proposed several methods based on measurements with different but fixed parameters of the device. However, these measures have extended more than twice the measurement process.In this article there is proposing to define the position of the geographic meridian based on the analysis of the azimuthal motion sensor gyro during acceleration of its rotor. The proposal can bring dual gain in reducing measurement time: at first, the rotor becomes "staff " rather than ballast gyro operation mode, as it was before; secondly, there is no need for special measures to combat harmful vertical moments, as the shift of the equilibrium caused by the action of the latter, is variable in time, which allows to determine the magnitude of harmful moment during a single measurement.

A Comparison of Equatorial Electrojet in Peru and East Brazil

The paper describes the characteristics of the equatorial electrojet at Huancayo (HUA, 12.1oS, 75.3oW, inclination 1.5oN, declination 1.0oE) in western side of South America, where the geomagnetic field is aligned almost along the geographic meridian, and at Itinga (ITI, 4.3oS, 47.oW, inclination 1.4oN, declination 19.3oW) in eastern part of South America, where the geomagnetic field is aligned about 19o west of the geographic meridian; although the mean intensity of the magnetic field in the two regions are almost of the same order. Further comparisons are made of the current at Itinga and at Tatuoca (TTB, 1.2oS, 48.5oW, inclination 7.8o N, declination 18.7oW), a low latitude station in the same longitude sector. The daily range of horizontal component of the geomagnetic field, H, is shown to be almost 16% higher at HUA compared to that at ITI. The daily variation of the eastward field, Y, showed a strong minimum of -40 nT around 13-14 hr LT at ITI whereas very low values were observed at HUA with a positive peak of about 4 nT around 11- 12 hr LT. The vertical field, Z, showed abnormally large negative values of -70 nT at TTB around 13 hr LT. The day-today fluctuations of midday and midnight values of X field were positively correlated between HUA and ITI with a high correlation coefficient of 0.78 and 0.88 respectively. Values of Y field were also significantly positively correlated between HUA and ITI for midnight hours (0.72), while no correlation was observed for the midday hours. The midnight values of X field at HUA, ITI and TTB showed significant (0.90 or greater) correlation with Dst index. Correlation values of about 0.7 were observed between Dst and midday values of X at ITI and TTB and to a lesser degree (0.4) at HUA.

Drift‐parallax determination of the altitude of traveling ionospheric disturbances observed with the Los Alamos radio‐beacon interferometer

From 1993 to 1997, the Los Alamos very long baseline interferometer was routinely employed to detect traveling ionospheric disturbances (TID) and inner plasmaspheric irregularities by measuring the change in the electrical phase of several satellite beacon signals that backlit the inner plasmasphere and ionosphere from geosynchronous orbit. The fortuitous placement of two satellite beacons nearly in the Los Alamos geographic meridian, in late 1995, permits us to infer the nominal altitude of each TID event by employing a novel parallax ranging technique. In the context of this paper, the nominal altitude of a TID refers to the altitude at which the slant‐path averaged, amplitude‐weighted phase perturbation existed along the lines of sight from the interferometer to the satellite. In this paper, we outline the method and present validation results.

Palaeomagnetism of middle Proterozoic (c. 1.25 Ga) dykes from central North Greenland

From a nunatak in central North Greenland (81.5°N, 44.7°W) nine sites of Middle Proterozoic basic dykes, cutting Archaean basement, were palaeomagnetically investigated. After AF and thermal cleaning the nine dyke sites and three adjacently baked gneiss sites give a stable characteristic remanent mean direction of D = 265°, I = 21.5° (N= 12, α95= 5.6°), the direction being confirmed by a detailed and positive baked contact test. The polarity of the dykes in the nunatak area is opposite to that of the Zig-Zag Dal Basalts and the Midsommersø Dolerites in eastern North Greenland some 200–300 km away, the volcanics of which are assumed to be of similar age (about 1.25 Ga). The remanent directions of the two sets of data are antiparallel within the 95 per cent significance level of confidence. When rotating Greenland 18° clockwise back to North America by the ‘Bullard fit’, the pole of the central North Greenland dolerites (NDL) falls at (14.3°N, 144.3°W). The reversed pole (14.3°S, 35.7°E) fits well on to the loop between 1.2 and 1.4 Ma on the apparent polar wander swath of Berger & York for cratonic North America. The palaeomagnetic results from the Middle Proterozoic basic dykes from central North Greenland thus strengthen previous palaeomagnetic results from the Midsommersø Dolerites and Zig-Zag Dal Basalts from the Peary Land Region in eastern North Greenland, suggesting that Greenland was part of the North American craton at least for the period between c. 1.3 and 1 Ma (and probably up to the end of Cretaceous time). The major geographical meridian of Greenland was orientated approximately E–W, and the palaeo-latitude of Greenland was about 10°–15°.

A paleomagnetic study of Rangitoto Island, Auckland, New Zealand

Abstract A paleomagnetic study has been made of 99 specimens from 11 sites in the recent basalt lavas of Rangitoto Island. The measured natural remanent magnetisation (NRM) had a formation mean direction of 1.9°0E, –62.1°, α95 = 2.6°; thermal cleaning changed the formation mean NRM direction only slightly to 0.2°E, –61.7°, α95= 1.8°. The densities, magnetisations, and magnetic susceptibilities measured for each site are recorded. Since Konigsberger's Qn ratio is large in every case, it follows that the aeromagnetic total force anomaly is symmetrical about the geographic meridian. Paleomagnetic declinations, at each site, when compared with historically recorded declinations of the geomagnetic field, confirm the dating results previously obtained by the l4C method; that is, Rangitoto was an active volcano between A.D. 850 and A.D. 1800, with a maximum of activity between A.D. 1200 and A.D. 1500. It is inferred that near Auckland the geomagnetic field has changed direction at approximately 2.87 × 10-2 deg/y...

Nighttime VHF scintillations at 23°N magnetic latitude and their association with equatorial F region irregularities

A study of postsunset VHF scintillations observed during recent solar maximum period (1980) at 23°N magnetic latitude, which is substantially beyond the daytime crest of the equatorial anomaly along 84.4°E geographic meridian, is carried out in order to examine their association with the irregularities of the equatorial F region. This is an extension of the study reported earlier from a chain of stations along the same meridian but covering a magnetic latitude belt of 3°‐21°N (Somayajulu et al, 1984). The characteristics and the occurrence pattern of scintillations observed at 23°N agree with the results reported upto 21°N. Also, the occurrence of scintillations at 23°N is found to be conditional to their prior occurrence at lower latitudes. This further confirms that the occurrence of nighttime scintillations up to 23°N magnetic latitude in the Indian zone are essentially controlled by the generation of equatorial F region irregularities. The study also provides evidence that the equatorial F region irregularities extend to altitudes in excess of 1300 km at least during equinoctial periods of high sunspot years and consequently cause scintillations in a wider latitudinal belt. The occurrence frequency of nighttime scientillations at 84°E, when compared with that of 93°E and 122°E longitudes for the same period of time, indicates strong longitudinal dependence, particularly in the Indian sector.

A model of theFregion abovehmaxF2

A simple Chapman model (scale height 100 km) of the ionosphere above the peak of the F region is found to be in good agreement with the few observed profiles of this region. The ratio of the above-peak electron content implied by the model to below-peak electron content is found to vary from about 2.8 to 4.0, also in good agreement with observations. The model is used in conjunction with electron density profiles observed from the ground to construct meridional cross sections along the 75°W geographic meridian.

Note on quiet-day vertical cross sections of the ionosphere along 75°W geographic meridian

Programs are now under way at several institutions for the systematic reduction of ionospheric vertical soundings to electron density profiles, N (h) curves, thereby making available for the first time adequate numerical data on electron densities throughout the lower ionosphere at many dates, times, and places (see Thomas [1959] for a complete bibliography of work in this field). In undertaking a similar program, the National Bureau of Standards has had two immediate objectives: to develop efficient methods by which hourly ionospheric soundings may be systematically reduced to N(h) profiles from a number of sounding stations, making these data available regularly to research workers; and to carry out a study of ionospheric morphology along a chain of stations stretching nearly from pole to pole along the 75°W geographic meridian. It is planned to combine these objectives by concentrating a systematic hourly reduction program on the 75th meridian stations. Already, stations at Fort Monmouth, New Jersey; Grand Bahama Island; St. Johns, Newfoundland (U. S. Army Signal Corps); and Puerto Rico (NBS), are preparing hourly virtual height data in the form required for N (h) analysis.

Time relationship of small magnetic disturbances in Arctic and Antarctic

Magnetograph records for February and March 1934 from Little America and College-Fairbanks (Alaska) were examined for conspicuous disturbance movements with respect to their parallelism in time of occurrence. The study, although based on only a few available records, is unique, in that the two stations lie in about the same geographical meridian and each is located in respective northern and southern auroral zones. It was found that the time difference between the occurrences at the two stations is often small (a matter of minutes or less).

Frequency Variation of the Intensity of Cosmic Radio Noise

THE intensity of cosmic radio noise (as received on horizontal half-wave dipole antennae one quarter wave-length above ground) has been measured at 25 Mc. and 110 Mc. by H. V. Cottony, W. Q. Crichlow, J. W. Herbstreit and J. R. Johler at the Central Radio Propagation Laboratory, National Bureau of Standards, using identical noise diode calibration methods. The use of similar antennae on the two frequencies ensured that comparable weights would be given the cosmic radio noise arriving from various directions in space. Results of these measurements are shown in the accompanying graph in terms of an external noise factor 1. Results are given on 110 Mc. for antennae oriented both normal to and parallel to the geographic meridian. These have somewhat different diurnal patterns which compare favourably with the calculated patterns obtained when the cosmic radio noise intensity contours obtained by Reber2, using highly directional antennae, are appropriately integrated over the two broad directivity patterns of the dipole antennae.

Chapters in the history of terrestrial magnetism

Chapter III—The discovery of the magnetic inclination1—It has been shown in Chapter II that the literature of the fourteenth century contains references to the fact that the direction of a suspended or pivoted magnetic needle is not, always and everywhere, that of the geographical meridian at the place of observation; that for nearly 200 years the existence of this variation was either denied, or doubted, or ascribed to irregularity in the magnetization of the needle or to faulty methods of observation; but that finally, about the middle of the fifteenth century, it was recognized as a general or world‐wide phenomenon. Thus was reached the conception of magnetic declination.

Hudson's strait and the oblique Meridian

In his illuminating and penetrating study of The Pseudo-Labrador and the Oblique Meridian, published in the second issue of Imago Mundi, H. Winter has afforded us the clue to what at first sight appears the inexplicably confused and faulty cartography of the northern and north-western shore-lines of the Atlantic Ocean during the sixteenth century. He proves conclusively that the oblique meridian placed by Reinel on his map of i5o4/5 is inserted to indicate the direction of the geographical meridian on that part of the map. The magnetic variation postulated is 224 ( two points ) to the west, and that this was the accepted figure for Cape Race on the New Land coast we know from the writings of Jean Alfonce and from the unpublished treatise on the Variation Compass which John Rotz (Ross) of Dieppe composed for Henry VIII in I542('). The present day variation at Cape Race (see fig. i) is about 280 W., but apart from the secular variation, the difference may be due to the error up to 30 likely to be present in the i6th century figure. That the figure used by the French fishermen on the Banks goes back to the voyages of the Corte Reals is made clear by H. Winter's paper, but the present writer must join issue with him when he remarks (p. 66): Why Pedro Reinel did not follow the course which to us seems simpler, of changing the position of the area in question on the map itself, remained a mystery. To have done so would have rendered the chart worthless to the seaman, to whom a sea-chart was a compass-chart, and its rhumb-lines compass-rhumrbs. Using a common compass the ship-master laid his course by the ruled lines on the map (as explained e.g. in Rotz' Boke of Ydrography), while it was with the common compass that he took his bearings on approaching the shore. What would he have made of this chart had it shown a coast trending along the N.W. rhumb where his compass showed one trending due north ? He had no isogonic chart, and even had he possessed so rare an instrument as a variation compass, to make the necessary frequent observations and calculations was beyond him. A point which needs constant emphasis is the disparity between the theoretical teachings of such men as Reinel, Faleiro, Nunez and Rotz on the one hand, and the practices and beliefs of the practical seamen on the other. How could the latter, who worked entirely by rule of thumb, be expected to grasp or disentangle the three-fold errors of the marine chart ? The chart was made and used on the assumption that the compass pointed to the geographical north (in despite of the variation); that lines pointing north were parallel (in despite of the convergence of the meridians); and that the course between two points a and b lay along the straight rhumb-line or compass-bearing a-b (in despite of the fact that a great circle is not a line of constant bearing). Many pilots of standing flatly refused to believe in the ' north-easting and north-westing of the needle ' as the variation was termed, and ascribed discrepancies to faulty ' touching,' i.e. magnetizing, of the needle with the lodestone. Others considered that the behaviour of a compass depended upon the meridian in which it was ' touched,' and for this they had some warrant, since (as H. Winter recognises) it was the practice of early compass-makers to attach the card to the needle in such a way as to allow for the variation at the place where the instrument was made. Since during the sixteenth century the European variation was everywhere east, this naturally exaggerated the faultiness of the compass in American waters where it was everywhere west. William Bourne's warning to pilots in his Navigating Manual of I573(2) 'not to meddle with the mending of the compass, or 'Whettynge of the side of the needle to make it stand due north,' is evidence of blundering attempts to put matters right, and the more skilful masters seem to have set their compasses for the particular voyage in hand. We read, for example(3), that Henry Hudson did so in i6io: He came to the Isles of Orkney and here he set the north-end of the needle and the north-end of the fly all one. Sufficient has been said to make clear that in the then state of nautical practice, the traditional method.

Chapters in the history of terrestrial magnetism

I—On the directive property of a magnet in the Earth's field and the origin of the nautical compass1—The science of Terrestrial Magnetism is based on the fact that a magnet, free to move about its center of gravity, tends to assume a position of relative rest in an approximately definite direction with respect to the geographical meridian and the vertical at the place of observation. That it should do so must be due to the existence of a field of force which is known as the terrestrial magnetic field [1], and the systematized knowledge of that field, of its variations in time and space, and of its relations with the subject‐matter of other branches of terrestrial and cosmical physics, constitutes the science of Terrestrial Magnetism.