Terrestrial Physics Research Articles

Cosmoclimatology: a new theory emerges

Data on cloud cover from satellites, compared with counts of galactic cosmic rays from a ground station, suggested that an increase in cosmic rays makes the world cloudier. This empirical finding introduced a novel connection between astronomical and terrestrial events, making weather on Earth subject to the cosmic-ray accelerators of supernova remnants in the Milky Way. The result was announced in 1996 at the COSPAR space science meeting in Birmingham and published as “Variation of cosmic-ray flux and global cloud coverage – a missing link in solar-climate relationships” (Svensmark and Friis-Christensen 1997). The title reflected a topical puzzle, that of how to reconcile abundant indications of the Sun’s influence on climate (e.g. Herschel 1801, Eddy 1976, Friis-Christensen and Lassen 1991), with the small 0.1% variations in the solar irradiance over a solar cycle measured by satellites. Clouds exert (on average) a strong cooling effect, and cosmic-ray counts vary with the strength of the solar magnetic field, which repels much of the influx of relativistic particles from the galaxy. The connection offers a mechanism for solardriven climate change much more powerful than changes in solar irradiance. During the past 10 years, considerations of the galactic and solar influence on climate have progressed so far, and have found such widespread applications, that one can begin to speak of a new paradigm of climate change. I call it cosmoclimatology and in this article I suggest that it is already at least as secure, scientifically speaking, as the prevailing paradigm of forcing by variable greenhouse gases. It has withstood many attempts to refute it and now has a grounding in experimental evidence for a mechanism by which cosmic rays can affect cloud cover. Cosmoclimatology already interacts creatively with current issues in solar–terrestrial physics and astrophysics and even with astrobiology, in questions about the origin and survival of life in a high-energy universe. All these themes are pursued in a forthcoming book (Svensmark and Calder 2007).

The change of solar shape in time and depth. Some consequences for space climate

During the last five years, studies of the Sun and Sun–Earth relationships have dramatically changed our view on solar terrestrial physics. We will here focus on new views on the solar interior. The internal non-homogeneous mass distribution and non-uniform angular velocity (function of the radial distance to the center and of the latitude) yield a complex outer shape. Beyond a “spherical” Sun is a new approach of solar-physics taking into account the gravitational energy which triggers the various layers. Such energy has been skipped in many ways up to now in theoretical models describing the solar output variability. In spite of many works on solar variations, there is not yet a consensus on the global experimental phenomenology. For instance, it is not yet known if this gravitational energy may explain faint observed irradiance variations, and the way the asphericity-luminosity parameter W acts on our stratosphere. Such issues must be solved to understand how the solar output variability may influence the Earth’s environment (helioclimatology). We will emphasize the key role of the subsurface layers (the leptocline, recently put in evidence by helioseismology) for a better prediction of the solar cycles. Regarding the solar core dynamics, the subject is of high priority for new investigations. We will conclude by giving some imprints on space-dedicated missions: GOLF-NG/DynaMICS in a joint effort with SDO (Solar Dynamics Observatory).

A “Large and Graceful Sinuosity”

In 1833 John Herschel published a graphical method for determining the orbits of double stars. He argued that his method, which depended on human judgment rather than mathematical analysis, gave better results than computation, given the uncertainty in the data. Herschel found that astronomy and terrestrial physics were especially suitable for graphical treatment, and he expected that graphs would soon become important in all areas of science. He argued with William Whewell and James D. Forbes over the process of induction, over the application of probability, and over the moral content of science. Graphs entered into all these debates; but because they constituted a method, not a metaphysics, they were acceptable to most practicing scientists and became increasingly popular throughout the nineteenth century.

James Alfred Van Allen

James Alfred Van Allen

Modeling the impact of the gravity wave source strength on the thermal structure of the middle atmosphere

The role of gravity wave (GW) forcing in the zonal mean circulation of the middle atmosphere (16–120 km) is investigated on the base of a two-dimensional, time-dependent, mechanistic model. The globally averaged prescribed profiles of O 3 and CO 2 are used to calculate net diabatic heating basing on the detailed non-LTE algorithm for cooling due to CO 2 15-μm bands [Fomichev, V.I., Kutepov, A.A., Akmaev, R.A., Shved, G.M., 1993. Parameterization of the 15 micron CO 2 band cooling in the middle atmosphere (15–115 km). Journal of Atmospheric and Terrestrial Physics 55, 7–18] and O 3 9.6-micron band [Fomichev, V.I., Shved, G.M., 1985. Parameterization of the radiative divergence in the 9.6 micron O 3 band. Journal of Atmospheric and Terrestrial Physics 47, 1037–1049]. The GW parameterization scheme has been developed to account for momentum deposition, heating, and turbulent heat transfer associated to the GW breaking. Motivated by possible changes in atmospheric GW climatology, we have investigated the sensitivity of the middle atmosphere structure to tropospheric GW source strength by prescribing the appropriate value of the vertical wave action flux at the lower boundary of the model domain. The results show, that the associated temperature response varies greatly with height, latitude, and season, and attains its maximum in the mesosphere and lower thermosphere (MLT) region primary due to the adiabatic effect caused by the corresponding changes in the vertical velocity field. Thus, the long-term variability of tropospheric GW source strength can produce substantial effect on MLT temperatures, which should be accounted for in the analysis of the observed climatological changes in the thermal structure of the middle atmosphere.

Bent Marshak waves

Radiation-driven heat waves (Marshak waves) are ubiquitous in astrophysics and terrestrial laser-driven high-energy density plasma physics experiments. Generally, the equations describing Marshak waves are so nonlinear, that solutions involving more than one spatial dimension require simulation. However, in this paper it is shown that one may analytically solve the problem of the two-dimensional nonlinear evolution of a Marshak wave, bounded by lossy walls, using an asymptotic expansion in a parameter related to the wall albedo and a simplification of the heat front equation of motion. Three parameters determine the nonlinear evolution: a modified Markshak diffusion constant, a smallness parameter related to the wall albedo, and the spacing of the walls. The final nonlinear solution shows that the Marshak wave will be both slowed and bent by the nonideal boundary. In the limit of a perfect boundary, the solution recovers the original diffusion-like solution of Marshak. The analytic solution will be compared to a limited set of simulation results and experimental data.

Auroral Plasma Acceleration Above Martian Magnetic Anomalies

Aurora is caused by the precipitation of energetic particles into a planetary atmosphere, the light intensity being roughly proportional to the precipitating particle energy flux. From auroral research in the terrestrial magnetosphere it is known that bright auroral displays, discrete aurora, result from an enhanced energy deposition caused by downward accelerated electrons. The process is commonly referred to as the auroral acceleration process. Discrete aurora is the visual manifestation of the structuring inherent in a highly magnetized plasma. A strong magnetic field limits the transverse (to the magnetic field) mobility of charged particles, effectively guiding the particle energy flux along magnetic field lines.The typical, slanted arc structure of the Earth’s discrete aurora not only visualizes the inclination of the Earth’s magnetic field, but also illustrates the confinement of the auroral acceleration process. The terrestrial magnetic field guides and confines the acceleration processes such that the preferred acceleration of particles is frequently along the magnetic field lines. Field-aligned plasma acceleration is therefore also the signature of strongly magnetized plasma.This paper discusses plasma acceleration characteristics in the night-side cavity of Mars. The acceleration is typical for strongly magnetized plasmas – field-aligned acceleration of ions and electrons. The observations map to regions at Mars of what appears to be sufficient magnetization to support magnetic field-aligned plasma acceleration – the localized crustal magnetizations at Mars (Acuña et al., 1999). Our findings are based on data from the ASPERA-3 experiment on ESA’s Mars Express, covering 57 orbits traversing the night-side/eclipse of Mars. There are indeed strong similarities between Mars and the Earth regarding the accelerated electron and ion distributions. Specifically acceleration above Mars near local midnight and acceleration above discrete aurora at the Earth – characterized by nearly monoenergetic downgoing electrons in conjunction with nearly monoenergetic upgoing ions. We describe a number of characteristic features in the accelerated plasma: The “inverted V” energy-time distribution, beam vs temperature distribution, altitude distribution, local time distribution and connection with magnetic anomalies. We also compute the electron energy flux and find that the energy flux is sufficient to cause weak to medium strong (up to several tens of kR 557.7 nm emissions) aurora at Mars.Monoenergetic counterstreaming accelerated ions and electrons is the signature of field-aligned electric currents and electric field acceleration. The topic is reasonably well understood in terrestrial magnetospheric physics, although some controversy still remains on details and the cause-effect relationships. We present a potential cause-effect relationship leading to auroral plasma acceleration in the nightside cavity of Mars – the downward acceleration of electrons supposedly manifesting itself as discrete aurora above Mars.

Laplace: the manHahnRoger, Pierre Simon Laplace, 1749–1827: A determined scientist. Harvard University Press, Cambridge, MA, 2005. pp. x+310, £21.95, €29.80, $35.00 (hardback).0-674-01892-3.

Roger Hahn, Pierre Simon Laplace, 1749–1827: A determined scientist. Harvard University Press, Cambridge, MA, 2005. pp. x+310, £21.95, €29.80, $35.00 (hardback). 0-674-01892-3. Although Laplace was, perhaps, the most important mathematical physicist between Newton and Maxwell and also a

Non-linear resonant wave–wave interaction (triad): Case studies based on rocket data and first application to satellite data

Gravity waves are well known to have significant influence on the circulation and thermal structure of the atmosphere by transporting energy and momentum. When reaching instability, gravity waves dissipate energy, causing the surrounding wind regime to be modified. Therefore, knowledge about the geographical location of sources of gravity waves (‘GWS’), their dynamical characteristics (e.g. wave spectral information) as well as their energy dissipation mechanisms and rates is essential. Besides pure wave breaking, other possibilities of energy transmission are possible. One prominent mechanism is the non-linear resonant wave–wave interaction (‘triad’). In this paper, an early case study performed by Widdel et al. [1994. Vertical velocities measured at Biscarrosse (44°N) and by EISCAT at Tromso (69.6°N) during DYANA campaign. Journal of Atmospheric and Terrestrial Physics 56, 1779–1796], to look for a possible triad within wind data obtained by the meteorological rocket based foil-chaff cloud technique during the DYANA campaign (DYnamics Adapted Network for the Atmosphere) in 1990, is reinvestigated. Their assumption of seeing a triad in the data is now proved. In addition the observed wave field is dynamically characterized. Energy dissipation rates and the acceleration of the zonal mean flux are estimated applying linear and non-linear theory, respectively. Furthermore, ozone data derived from the satellite-based ERS-2-GOME (Global Ozone Monitoring Experiment) instrument in January 2003 are assimilated into the 3D-chemical transport model ROSE (Research on Ozone in the Stratosphere and its Evolution) to yield synoptic and global coverage and to allow the tracing of dynamical processes. Regions of pronounced dynamical variability are identified and are supposed—at least occasionally—to generate gravity waves. Due to their relatively high vertical resolution, ozone measurements of the ENVISAT-GOMOS (Global Ozone Monitoring by Occultation of Stars) instrument are further used to look for possible indications of triad effects above these gravity wave sources (‘GWSs’).

Mantle unmixed; Aurora gets the goahead; Charon pinned down; Dark skies for a car park; Sirius B balances the Sun; Liverpool on the Honours List; Middle-sized black hole; Dark galaxy found

Sue Bowler, Editor This issue contains a very satifying example of a step forward in science, when conflicting data and ideas resolve themselves into a new and clearer picture thanks to advances in data collection, modelling and so on. The example is excellently described by George Helffrich in his Bullerwell Lecture, which elegantly explains how the emerging geophysical picture of a mantle mixing throughout its depth conflicts with the geochemical view of distinct regions, chemically isolated and unable to mingle. The lesson of this review is that different viewpoints allow observers to see different things. The geochemical picture defined characteristics of distinct parts of the mantle, without locating them, whereas the geophysical view showed where such isolated volumes of rock could not be, but can see only fuzzily what the different rocks might be. Together, however, they now have a vastly improved picture of around half the planet, and one that in turn provides a framework for future research in all aspects of the deep Earth. But this is also a lesson for scientists in general. One point of view, whether a fixed opinion or a limited collection of data, is not enough. Astronomers have in the past few years seen a comparable explosion of data, thanks again to improved data collection and handling methods, and to the larger observatories now available. The boost in this field has been the availability of multiwavelength data, so that astrophysicists can now examine objects such as gamma-ray bursters in full colour, as opposed to the monochrome views of the past, that used only a fraction of the electromagnetic spectrum. Planetary science, solar– terrestrial physics, and all branches of astrophysics are benefitting in the same way from this avalanche of data. Long may it continue – as long as the development of data storage and handling methods keeps pace, or we will all drown in data. EDITORIAL

A study into the effects of gravity wave activity on the diurnal tide and airglow emissions in the equatorial mesosphere and lower thermosphere using the Coupled Middle Atmosphere and Thermosphere (CMAT) general circulation model

Momentum deposition by gravity wave breaking is known to affect the amplitude and phase of the diurnal tide. Modelling studies of this interaction have produced some conflicting results and as yet, the exact nature of this interaction is not fully understood. In this study, the effects of parameterised gravity wave momentum deposition on the diurnal tide and subsequently on green line airglow from atomic oxygen during equinox are investigated using the Coupled Middle Atmosphere and Thermosphere (CMAT) general circulation model. The effects of gravity wave drag calculated by two different parameterisations, Meyer [1999. Gravity wave interactions with the diurnal propagating tide. Journal of Geophysical Research 104, 4223–4239] and Medvedev and Klaassen [2000. Parameterisation of gravity wave momentum deposition based on non-linear wave interactions: basic formulation and sensitivity tests. Journal of Atmospheric and Terrestrial Physics 62, 1015–1033], are compared in the low latitude MLT region between 70 and 120 km, where the amplitude of the diurnal tide and green line volume emission rates maximise. Results indicate that momentum sources from both gravity wave parameterisations act to reduce the mid-latitude zonal jets and advance the phase of the diurnal tide, such that the peak amplitude at a given height occurs at an earlier time of day. Gravity wave momentum deposition as parameterised by Meyer [1999. Gravity wave interactions with the diurnal propagating tide. Journal of Geophysical Research 104, 4223–4239] results in a reduction of the amplitude of the diurnal tide in the MLT region, whereas the tidal amplitude is increased when the Medvedev and Klaassen [2000. Parameterisation of gravity wave momentum deposition based on non-linear wave interactions: basic formulation and sensitivity tests. Journal of Atmospheric and Terrestrial Physics 62, 1015–1033] parameterisation is used. Both parameterisations affect the local time variability of the simulated airglow, and the magnitude of the peak emission rate. When using gravity wave momentum sources from the Medvedev and Klaassen [2000. Parameterisation of gravity wave momentum deposition based on non-linear wave interactions: basic formulation and sensitivity tests. Journal of Atmospheric and Terrestrial Physics 62, 1015–1033] parameterisation, the magnitude and morphology of CMAT tidal winds and O( 1S) 557.7 nm emission rates are in agreement with recent satellite observations.

High-resolution time changes in some indices and parameters of solar–terrestrial physics

Comparison of the daily values of indices and parameters of solar–terrestrial physics in 2001 is made in order to allocate the most important values for future forecasts of geomagnetic activity. Changes in the indices and parameters describing all sequences of active processes from the surface of the Sun to the magnetosphere of the Earth were considered. The validity of application of the Wolf numbers as characteristics of solar activity due to sunspots is confirmed. The most geoeffective parameters depend on the arrival of the interplanetary shock from coronal mass ejection to the Earth’s orbit and the presence of the southern component of the interplanetary magnetic field with intensity values less than−20 nT. If these parameters are known in real time, about 90% of magnetic storms with sudden commencement can be forecast within 8–10 h before the start of their negative influence on the Earth.

Science rationale for CAWSES (Climate and Weather of the Sun–Earth System): SCOSTEP’s interdisciplinary program for 2004–2008

An international program called Climate and Weather of the Sun–Earth System (CAWSES) has been developed by the Scientific COmmittee on Solar–TErrestrial Physics (SCOSTEP) for the study of integrated Sun–Earth system science to be conducted over the period 2004–2008. This program aims to significantly enhance our understanding of the space environment and its impacts on life and society. The main functions of CAWSES are: (a) to help coordinate international activities in observations, modeling and theory crucial to achieving this understanding; (b) to encourage involvement of scientists in both developed and developing countries in such efforts; and (c) to provide educational opportunities for students at all levels. Such multi-nation, multi-technique studies are absolutely essential for an understanding of the short term (space weather) and the long term (space climate) variability throughout the entire solar–terrestrial domain, for its societal applications and for tracking global changes in climate and ozone. The CAWSES program has been organized under four science Themes: (i) Solar Influence on Climate; (ii) Space Weather: Science and Applications; (iii) Atmospheric Coupling Processes; (iv) Space Climatology. Progress on some of these Themes can only be achieved through conducting carefully planned experimental campaigns with the data being assimilated in coupled physics based models. An end-to-end modeling capability is the ultimate goal of solar–terrestrial science. We hope these aspects will help us also in our Capacity Building efforts which is the fifth Theme under the CAWSES program – particularly in developing countries. In this paper, we will highlight some of the aspects of CAWSES science and attempt to discuss how different specialities in various research fields can be brought together with a well-defined purpose of understanding the interdependencies of the Sun–Earth system as a single entity.

High performance computing for self-gravitating systems

A peculiarity of astrophysics with respect to terrestrial physics is the unavoidable presence of self-gravity. This makes astrophysical simulations very hard to be done, because self-gravity induces, by mean of the fine grain structure superposed to the coarse grain, a multitude of space and time scales. In this report I give (i) a brief overview of the simulation problems to be faced in astrophysics and cosmology, with particular emphasis on the classic gravitational N-body problem and (ii) some results on the evolution of a typical example of intermediate N-body system, like a globular cluster moving in an external galactic field.

The importance of real-time data in solar–terrestrial physics

This concise review demonstrates that for further progress in studies of the solar–terrestrial environment, it is very important to make data from ground-based and satellite observations available in real time through the modern network technologies. Some of the old examples of the hand-drawn distribution of auroral forms and equivalent ionospheric currents are shown, and these are compared with output from the computer simulations using real-time data as input. It is cautioned that the solar wind provides the magnetosphere only with the boundary condition under which various types of magnetospheric disturbances, such as magnetospheric substorms, take place internally. It would, therefore, not be highly recommended to attempt to find a very high correlation between fine time-scale variations in the solar wind and those of geomagnetic indices. This paper also points out that it is imperative to combine real-time data from the solar wind, magnetosphere, ionosphere, and ground-based observations with computer simulations. The availability of real-time data changes not only the practical style of research but also the concept of solar–terrestrial physics.

Response of the Earth–ionosphere cavity resonator to the 11-year solar cycle in X-radiation

Global changes in the fundamental Earth's Schumann resonances (SR) have been identified on the time scale of the 11-year solar cycle (SC). The first multi-station, multi-field component, multi-mode experimental evidence for solar X-ray modulation of the Earth–ionosphere waveguide is presented. Long-term SR observations covering one solar minimum and two solar maxima, accumulated under different experimental conditions in Antarctica, Hungary and the United States, have been analyzed. The variations of both SR frequencies and quality ( Q ) factors display pronounced maxima during solar maxima #22 and #23, and corresponding minima during the solar minimum of 1996–1997. The observed variations are interpreted on the basis of the uniform extremely low frequency (ELF) mode theory and the presence of two characteristic ionospheric layers responsible for ELF propagation (Greifinger and Greifinger, 1978: Radio Science 13, 831–837; Mushtak and Williams, 2002: Journal of Atmospheric and Solar Terrestrial Physics 64, 1989–2001). The hundredfold changes in the solar X-ray flux dominate the variations in the conductivity profile within the upper characteristic ELF layer (the 90–100 km portion of the E-region), with a negligible effect on the lower characteristic layer (the 50–60 km portion of the D-region). The general increase/decrease of this conductivity by up to one order of magnitude over the solar cycle is responsible for changes in the wave phase velocity and, consequently, in the observed SR frequencies by several tenths of Hz. The change in the scale height of the conductivity profile by several tenths of percent modulates the reflection/dissipation effects within the upper characteristic layer and, therefore, the Q-factors of the resonator. The physical role of the X-radiation in influencing SR is also demonstrated on short ( ∼ 1 h ) time scales, when occasionally variations in X-radiation comparable to the 11-year solar cycle are experienced.

Equatorward expansion of the westward electrojet during magnetically disturbed periods

The auroral electrojet (AE) indices have widely been used in various fields of solar terrestrial physics since their introduction to the community. Recently, it has been reported that the AE indices do not, at times, properly monitor the auroral electrojets because as magnetic activity increases, they expand equatorward beyond the standard AE network, resulting in a serious underestimation of the auroral electrojet intensity. It is particularly the case during severe geomagnetic storms. To determine quantitatively the equatorial expansion of the auroral electrojets, we examined an extensive database obtained from the Alaska, International Monitor for Auroral Geomagnetic Effects (IMAGE), and Canadian Auroral Network for the OPEN Program Unified Study chain of magnetometers. These chains of magnetometers enable us to determine the latitude where the maximum current density of the auroral electrojet flows. It is generally understood that the center of the auroral electrojet tends to migrate equatorward with an increase in magnetic activity. We note, however, that there seems to be a lower limit particularly of the westward electrojet, ∼60° in corrected geomagnetic latitude, regardless of magnetic activity levels. The relative location of the westward electrojet with respect to the global auroral image taken from the Polar satellite is also examined. Contrary to the generally accepted notion, the auroral electrojets are found to be most intense not in the region of bright auroral luminosity but slightly poleward of it in less luminous region. The current center seems to be the region where both ionospheric conductivity and electric field become significantly high.

Necessary conditions for geosynchronous magnetopause crossings

The International Solar Terrestrial Physics database of the magnetic measurements on GOES and plasma measurements on Los Alamos National Laboratory (LANL) geosynchronous satellites is used for selection of 169 case events containing 638 geosynchronous magnetopause crossings (GMCs) in 1995 to 2001. The GMCs and magnetosheath intervals associated with them are identified using advanced methods that take into account (1) strong deviation of the magnetic field measured by GOES from the magnetospheric field, (2) high correlation between the GOES magnetic field and interplanetary magnetic field (IMF), and (3) substantial increase of the midenergy ion and electron fluxes measured by LANL. Accurate determination of the upstream solar wind conditions for the GMCs is performed using correlation of geomagnetic activity (Dst(SYM‐H) index) with the upstream solar wind pressure. The location of the GMCs and associated upstream solar wind conditions are ordered in an aberrated GSM coordinate system (aGSM) with X‐axis directed along the solar wind flow. In the selected data set of GMCs the solar wind total pressurePswvaries up to 100 nPa and the southward IMFBzreaches 60 nT. We study the conditions necessary for geosynchronous magnetopause crossings using scatterplots of the GMCs in the coordinate space ofPswversusBz. In such a representation the upstream solar wind conditions show a sharp envelope boundary beyond which no GMCs are observed. The boundary has two straight horizontal branches whereBzdoes not influence the magnetopause location. The first branch is located in the range ofPsw= 21 nPa for large positiveBzand is associated with a regime of pressure balance. The second branch asymptotically approaches the range ofPsw= 4.8 nPa under strong negativeBz, and it is associated with a regime in which theBzinfluence saturates. The intermediate region of the boundary ranges from moderate negative to moderate positive IMFBzand can be well approximated by a hyperbolic tangent function. We interpret the envelope boundary as a range of necessary upstream solar wind conditions required for the magnetopause to reach geosynchronous orbit at its closest approach to the Earth (its “perigee” location).

Introduction to space weather

The solar and interplanetary origin of space weather disturbances, as well as the related magnetospheric dynamics, will be presented. Besides the involved phenomenology in solar–terrestrial physics, some of the main effects of space weather variability concerning mankind in space and at the earth’s surface will also be discussed. The November 2003 event is shown as an example of the solar, interplanetary and magnetospheric aspects of a space weather storm.

Polarization singularities in the clear sky

Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima.It is not one of the least wonders of terrestrial physics, that the blue atmosphere which overhangs us, exhibits in the light which it polarises phenomena somewhat analogous to those of crystals with two axes of double refractionBrewster D 1863 Trans. R. Soc. Ed. 23 205–10