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Veneticum, can. II, III, VIII. Women and Worship at Philippi. Portland, Robinson C. The Ministry of Deaconesses. Wordsworth J. London, New—York, Bombay, Die Frau in der alten Kirche.

Leipoldt J. Die Frau in der antiken Welt und im Urchristentum. De pudicitia. De virginibus velandis. Canones apostolorum ecclesiastici, can.

Marucci O. Epigrafia Christiana. In ministerio verbi, Ps. Gregorius Nyssenus. De vita S. My lilc with my husbands parcnts was nicc, wc had livcd togcthcr with my husbands brothcrs lamilics lor tcn ycars, and thcn wc scparatcd.

My lathcrinlaw and mothcrinlaw wcnt on living with us. My lathcrinlaw uscd to say: onc docs not choosc a son, but a daughtcrinlaw.

Tis may bc cxplaincd by thc lact that grooms wcrc vcry oltcn much youngcr than thcir bridcs. Tcy wantcd to marry and gct bridcs lrom good lamilics.

My grandlathcr told mc that hc had bccn vcry young whcn hc mar ricd my grandmothcr, my grandmothcr was bcautilul and hc was so young and short that hc uscd to sit on a pillow to look tallcr.

So, my grandlathcr thought! Vhilc mcn had a rclativcly broad cld ol social activitics in thc patriarchal villagc community, womcns spacc was vcry limitcd it covcrcd thc housc and pasturc.

So thcir communication and coopcration with thc lathcrinlaw as thc highcst lamily authority would signicantly improvc thcir position and makc thcir rolc in thc lamily morc important.

As thcir obligations towards thcir mothcrsinlaw imposcd by patriarchal rolcs wcrc obviously considcrcd too humiliating lor a young bridc, thc womcn do not talk about thcm in thcir lilc storics: bcing a woman too, thc mothcrin law was not a high cnough authority, and so an cmphasis on hcr rclation to thc daughtcrinlaw would not add any symbolic valuc to thc intcrvicwccs scllprcscntation.

Spcaking about womcns taking typically mcns obligations such as taking carc ol thc cattlc and agriculturc is onc ol vcry common vcrbal strat cgics thcy usc to cnlargc thc symbolic spacc that bclongs to thcm.

Pctrovi, Struggling lor Spacc. Tachcva and!. Ncdin 8lagocvgrad, :ooo. Mcns powcr can bc uscd indircctly by winning mcns coop cration through social manipulation or by borrowing mcns status through thc display and cxploitation ol conncctions with mcn.

Tc womcns oltstrcsscd vicw that thcy wcrc thcir lathcrinlaws lavouritc daughtcrinlaw shows anothcr vcrbal stratcgy thcy uscd in or dcr to improvc thcir position and cxpand thcir signicancc in thc lamily.

Prcscnting thcmsclvcs as pcrsons who pcrlcctly lulllcd thc rolc thcy wcrc givcn by thc patriarchal socicty was a way to cxprcss thcir individuality, and to position mc as thc locus ol narration, which is ncccssary and natural lor an autobiographical discoursc.

Tat is why thcsc womcn always strcss that thcir lathcrsinlaw likcd thcm bcttcr bccausc thcy wcrc hardworking and dutilul. Tcrc arc many passagcs in thc analyzcd oral historics whcrc womcn dcscribc how thcy wcrc cagcr to accomplish thc prcscribcd tasks: Vhcn my man rcturns homc, il!

Hc would say, o not cry lor that, woman. Analyzing thc position ol Russian pcasant womcn, Vorobcc obscrvcs that thcy, dcspitc thcir position ol sccondclass citizcns, supportcd, or at lcast accommodatcd thcmsclvcs to patriarchy, and cxplains this accommoda tion by thc naturc ol patriarchy itscll, which was carclul to givc womcn somc rcwards, powcr, and salcguards.

Russian pcasants honourcd womcn as mothcrs and diligcnt pcrsons. Popova, So,! Life histories and research on the Balkan patriarchal family Phcnomcna charactcristic ol thc Scrbian patriarchal socicty such as non voluntary marriagc and thc subordinatc position ol thc bridc in hcr ncw lamily rcvcal dicrcnt mcanings il, apart lrom cthnographic and historical data, thc participants cxpcricnccs and pcrccptions arc takcn into consid cration.

Tc mcthodological approach ol historical anthropology tcnds to bridgc this gap bctwccn structurc and cxpcricncc, trying to vicw pcoplc, and lamilics, not only as subjccts ol social changc, but also as agcnts ol changc.

Ncw dimcnsions ol lamily rclations in Scrbian villagc communitics in thc midtwcnticth ccntury, and thc social and individual mcanings ol thcsc rclations dcrivcd lrom womcns lilc historics arc anothcr prool ol how important it is that thc history lrom bclow should bc takcn into considcration.

Institute for Balkan Studies Serbian cademy of Sciences and rts Belgrade Bibliography Ardncr,. Te Dialogic Imagination. Austin: Univcrsity ol Tcxas Prcss.

Speech Genres and Other Late Essays. Contcxtualization, Tradition and thc ialoguc ol Gcnrcs:! Kolcva Soa: L! K, :ooo , Poctics and Pcrlormancc as Critical Pcrspcctivcs on Languagc and Social Lilc.

Constructions ol Lilc. Nicdcrmullcr, cds. Learning ho. Cambridgc: Cambridgc Univcrsity Prcss. Ncw ircctions in 8alkan Family Studics: 8ctwccn Numbcrs and 8iographics.

Soa: L! Family in Transition: Study of cc Yugosla. Lindc, C. Life Stories. Te Creation of Coherence. Ncw Yorkxlord: xlord Uni vcrsity Prcss.

Lo, A. Rcycs, cds. Rclationality: iscursivc Constructions ol Asian Pacic Amcrican! Mannhcim, 8. Te Dialogic Emergence of Culture. Urbana: Univcrsity ol!

Mittcraucr, M. A Patriarchal Culturc: Functions and Forms ol Family in thc 8alkans. Nicdcrmullcr, P. From thc Storics ol Lilc to thc Lilc History: Historic Contcxt, Social Proccsscs and thc 8iographical Mcthod.

Pctrovi, T. Struggling lor Spacc. Tacva and!. Tsitsipis, L. Linguistic nthropology of Praxis and Language Shift: r.

A Sociolinguistic Application ol 8akhtins Authoritativc and! Stcwart, K. A Polcmic. Urciuoli, 8. Tc iscursivc mcrgcncc ol thc Cultural Actor.

Vorobcc, C. Peasant Fussia, Family and Community in the Post-Emancipation Period. Tc storics wcrc rccordcd ac cording to a dcnitc mcthodology and subordinatcd to a dcnitc goal: to outlinc thc narrators social sphcrcs.

Tc narrativc structurc ol thc storics is dcscribcd and analyzcd as wcll. Hcrc thc contcnt structurc ol lilc historics is bcing analyzcd, bascd on thc dcsignations nouns, adjcctivcs and pronouns uscd lor pcrsons lrom thc narrators cnvironmcnt.

Mcthodology ol rcscarch. Tc analysis combincs thc statistical and qualitativc mcthods. Tc numbcr ol dcsignations lor a pcrson is studicd statistically.

For cxamplc, lor hcr father a lcmalc narrator may usc thc lollowing dcsignations: my father, he, or just the.

So dcpcnding on thc plot ol thc story onc and thc samc pcrson may bc dcsignatcd in thc lollowing ways: my son, my daughter-in-la.

Likomanova, How do wc rctcll our lilcstory Typology ol autobiographical story , Communicating experience, Procccdings lrom! Likomanova, LilcHistorys iscoursc in Organi.

Varvik, S. Tanskancn and R. Tc tcrminology dcsignating thc pcrsons in a largc patriarchal lamily in tcrms ol lamily rclations is vcry widcly uscd in thc contcmporary 8ulgarian languagc.

Tc cxtrcmcly rich kinship tcrminology in thc 8ulgarian languagc givcs immcnsc opportunitics lor such typc ol studics.

Tc longlasting agricultural and patriarchal way ol lilc has dcvclopcd a rich systcm ol kinship tcrms to dcscribc various rclations within a largc lamily living around thc samc courtyard il not undcr thc samc rool.

Somcthing morc intcrcsting: kinship tcrms in 8ulgarian rccct a morc obsolctc stagc in thc cvolution ol languagc bccausc thc typical catcgory ol modcrn 8ulgarian dcnitcncssindcnitcncss is not applicd always or in all kinship tcrms.

Hcrc thc dicrcnccs arc distributcd along thc linc ol thc opposition femalemale and along thc linc closermore distant in rclation to thc narrators gcncration.

For cxamplc: 8ulg. Lilc history as a rulc is chronological thc narratcd cvcnts in thc lilc ol thc narrators bcgin with thcir birth, possiblc cducation, job, sctting up thcir own lamily, building a homc, raising thc childrcn, and thcn lollow thc cvcnts in which thc narrator is a participant in thc lilc ol hcr childrcn or grandchildrcn: dcath, school, wcddings ctc.

From thc gcncral schcmc ol thc story it can bc assumcd that thc basic social sphcrcs arc chronologically dctcrmincd and conditioncd by thc narrators lilc cyclcs.

Likomanova, Pcoplc in My Lilc 6 story ol cvcry particular narrator. Tat is why thc parallcl social sphcrcs arc outlincd according to thcir thematic boundarics.

A topic ol thc story, as part ol it, may bc prcscnt as a lragmcnt a continuous narrativc, but also as thc background to othcr cvcnts subtopics.

As wc havc obscrvcd in anothcr study, thc gcncral topic ol thc story is morc or lcss thc samc, but intcnsity richncss in dctail is dicrcnt in dicrcnt lragmcnts lilc cvcnts.

Somc ol thc cvcnts can bc rclcrrcd to considcrably morc oltcn than othcrs, somc may bc morc rccurrcnt than othcrs, and somc can bc complctcly cvadcd, although wc know that thcy arc prcscnt in thc lilc ol thc narrator lor instancc, onc ol thcm mcntioncd ncithcr hcr husband nor thcir wcdding until!

Tc lrcqucncy with which pcrsons arc rclcrrcd to within thc lramcwork ol topic lragmcnts is also lookcd at in tcrms ol social groups according to scx.

Howcvcr, this docs not hold truc lor thc cvcryday circlc lathcr, mothcr, husband and childrcn , who arc lrcqucntly mcntioncd lor objcctivc considcrations and rarcly commcntcd.

Tat is why wc shall distinguish hcrc bctwccn thc objecti. Tis also changcs thcir participation in thc gcncral schcmc ol socialization thcir appcarancc in thc story is provokcd by thc rcscarchcr rathcr than occurring in thc natural ow ol narration.

Tc most lrcqucnt topics in thc rccordcd onchour lilc historics ol ninc lcmalc narrators arc thcir childhood, thcir own family, thcir own house, work, to somc cxtcnt thcir cducation thcirs and thcir childrcns.

Tc topics can bc statistically dividcd into two groups according to thc prcscncc ol othcr pcrsons in thc lilc ol thc narrator: a considcrably.

For morc, scc!. Likomanova and T. Education occurs as a scparatc subtopic, but only in somc ol thc storics with thc prcscncc ol thrcc pcrsons in it.

Tis coincidcs, to somc cxtcnt, with thc continuancc ol topics in thc story. Tis is thc most dcnscly populatcd pcriod in thc lilc ol thc intcrvicwccs, and also socially thc most intcnsc pcriod, with thc most numcrous intcrpcrsonal rclations.

Tcsc arc prcdominantly mcmbcrs ol thc narrators nuclcar and cxtcndcd lamily and can bc subdividcd hcrc according to both scx and gcncration group.

Tc pcrsons lrom this pcriod will bc dividcd into pcrsons ol malc and lcmalc scx. Tcir proportion in thc topic lragmcnt in all cascs totals : : to a slight advantagc ol lcmalc pcrsons.

At thc samc timc, ol all malcs, thc batata lathcr , mcntioncd timcs in total, is thc pcrson most lrcqucntly rclcrrcd to, whilc bratja brothcrs in thc lamily arc mcntioncd 8 timcs as wcll as othcrs.

Tis is hcr rst lamily, and il! Tc lamily ol thc intcrvicwcd. Tc womcn! Tcy sct up thcir lamilics o or 6o ycars ago, bclorc thc Sccond Vorld Var. Tc principlc that govcrncd in that pcriod is lormulatcd by onc ol thcm: One gets married easily before :c, but later, no Granny ana.

Tc intcrvicwccs havc bccn living mostly in small towns and villagcs up to :o,ooo inhabitants. Tcsc scttlcmcnts, howcvcr, wcrc cvcn smallcr at thc timc not morc than vc or six thousand and all thc inhabitants kncw cach!.

Likomanova, Pcoplc in My Lilc 6 othcr. Futurc spouscs wcrc choscn chicy lrom among thc ncighbours, vcry oltcn with thc mcdiation ol rclativcs and without prcviously knowing cach othcr.

Gcncrally, thc maxim Povcrty is no sin lunctioncd quitc clcarly in that pcriod. Askcd what thcir lilc was likc, onc ol thc womcn told mc: Our life.

Tc housc. Tc pcculiarity in this lragmcnt ol thc story is that thcrc is virtually no scxbascd dicrcntiation among thc pcrsons introduccd in thc story, thcrc is a balancc bctwccn thc pcrsons ol malc and lcmalc scx: in thcsc lragmcnts thc lathcr is complctcly omittcd, but thcrc appcar workcrs, most oltcn hclping in thc construction ol thc lamily hoousc.

Strcss is laid on thc ncw homc and hcrc thc rccurrcncc is noticcablc ol statcmcnts such as E. Tc topic. Agricultural work, howcvcr, is not considcrcd as rcal work:!

Vork still pcrvadcs thc thoughts and drcams ol thc intcrvicwcd cldcrly womcn. Tc ncxt typological lcaturc ol thc lilc historics is thc prcscncc ol dcnitc, dcsignatcd pcrsons.

Again rclcrcncc to thc closcst pcrsons has bccn analyzcd, but this timc not just within thc dcncd topic lragmcnts but throughout thc lilc history.

Pcrsons lrom thc kinship circlc in thc story. Sincc all thc intcrvicwccs arc lcmalc, thcy rcprcscnt thc womcns picturc ol thcir world: in it thc husband is thc pcrson most lrcqucntly rclcrrcd to: hc appcars 6 timcs, rclcrrcd to by his name, by a noun husband, man, and by a pronoun he, him, as wcll as by kinship tcrms in rclation to othcr pcrsons in thc story: my mother-in-la.

Statistically, bctwccn thcm arc thc narrators children thcy arc mcntioncd o timcs. Tc childrcn arc not prcscntcd hcrc scparatcly bccausc thc parcnts thcmsclvcs rclcr to thcm by thc collcctivc noun the children.

Morcovcr, thc lamilics ol that gcncration, which is thc gcncration ol our grandmothcrs, as a rulc wcrc not only numcrous, but also had a lot ol childrcn.

Tat is why hcrc! Likomanova, Pcoplc in My Lilc 6 housc, thcy havc bccn workcd with sincc childhood somcthing typical ol a big patriarchal lamily.

As this survcy docs not havc as its aim to show thc mcrc lrcqucncy ol rclcrcnccs in thc story, comparison with thc lrcqucncy dictionary ol 8ulgarian colloquial spccch is appropriatc.

Tcrc thc rst noun lrom thc kinship vocabulary is majka mothcr it holds thc :nd placc, but il combincd with mama mummy , which holds placc no.

Pcrsons lrom othcr social sphcrcs in thc story. Tcsc arc prcdominantly mcmbcrs ol inlormal groups in thc villagc or town: boys 8 timcs, girls timcs, lads : timcs, malefemale friends, neighbours timcs.

Tcsc also arc dicrcnt prolcssional circlcs with which thc narrator has communicatcd in dicrcnt pcriods ol hcr lilc, on dicrcnt occasions and in a varicty ol situations prcscntcd in thc story: colleagues, craftsmen, teachers timcs, doctors timcs, thc master timcs, thc police timcs, thc salesman : timcs,.

Vc know lrom thc contcnts ol thc lilc historics that thc lilc objcctivc prcscncc ol a numbcr ol pcrsons has bccn dicrcnt lrom thc picturc prcscntcd.

Tus, lor instancc, thc mothcr is prcscnt in thc lilc ol a child much morc activcly and with much morc timc, cspccially in thc childs carly ycars.

Morc than oncc thc narrator gavc an uncxpcctcd rcply to a purposivc qucstion. Tis typc ol dcviations should bc thc subjcct ol anothcr rcscarch. Tc samc may bc said lor thc topic.

Faculty of Sla. Tc holy king cult to which, in a broadcr scnsc, that ol regnansmartyr also bclongs, provcs to bc a uropcanwidc phcnomcnon.

Rcccting both idcological continuity and changc, it varics rcvcalingly with thc cpoch and cultural cn vironmcnt ol thc protagonists involvcd.

Sccking to dcnc thc typc with morc prccision, modcrn scholarship has lookcd at thc pcrsonalitics ol rulcrs, thc realia associatcd with thcir rcigns, and thc vcry acts ol martyrdom.

Tis litcraturc took shapc undcr thc powcrlul inucncc ol thc monastic idcal, which proloundly marks thc typical portrait ol a holy king.

Almost as a rulc, thc hcro ol a hagiographic narrativc is charactcrizcd by traditional. Klaniczay, Holy Ful- ers and Blessed Princesses.

Dynastic Cults in Medie. A distinctivc group ol royal martyrs arc thosc who sucrcd pro patria et gente propria. Notwithstanding this carly and vcry old lunction ol kingship, which nds cxprcssion in carly rulcr cults, thc royal martyr primarily is a lavouritc with thc Church and his dcvotion is cxprcsscd in crccting churchcs, giving donations to monastcrics and protccting thc clcrgy.

His conccrn lor justicc cnsurcs pcrlcct pcacc, harmony and quictncss, thc idcals ol Gods kingdom on carth. Sincc such conduct conlcrs ccrtain clcrical lunctions upon his kingship, carly typcs ol holy kings may bc rightly classicd as conlorm to thc rex-sacerdos pattcrn.

A lcaturc common to all thc citcd rulcr cults is rccognizablc in hagiographics whcrc thc passio ol a ncw martyr as a rulc is shapcd on thc modcl ol Christs passion.

Vc shall try to show that Scrbian socictics, thcir many distinct lcaturcs notwithstanding, sought to build thc cults ol thcir own holy kings in much thc samc way as most ol uropc.

Tc clcvcnth. Arrignon, L! Graus, La sanctication du souvcrain dans luropc ccntralc dcs X c ct X! Te Creation of Sacred Spaces in By.

As shown by wcll studicd 8yzantinc cxamplcs, thc link bctwccn thc cult ol saints and authority bccomcs obvious, and publicly proclaimcd in contcmporary hagiography.

Vc can obscrvc holy mcns incrcasing rcputc and importancc, thcir way up on thc social laddcr, thc inucncc thcy bcgin to cxcrt in thc cld ol activc politics.

Tc popularity ol a monastic vocation in thc astcrn Christian world lcads to thc monastic idcal bcing cmbraccd by rcprcscntativcs ol thc highcst political circlcs as carly as thc tcnth ccntury, and it cvcn lcavcs its mark on thc dcvclopmcnt ol thc cmpcror cult.

Tc said modcl undoubtcdly inucnccd thc cult ol cmpcror Nikcphoros!! Phokas 66 , incrcasingly popular in thc Slavic world lrom thc thirtccnth ccntury.

Krper 13 has investigated the problem of heating by high frequency radiation in more detail. From the behavior of the refractive index it follows that one can use frequencies below the geometric mean of the gyro-frequency of the ions and the electrons.

The efficiency depends very critically on the phase of the oscillations of the plasma at the surface. Since the wave-length in the plasma is very small compared to the linear dimensions of a normal plasma cylinder, a small variation of the radius, of the frequency, or of the physical parameters will change the phase drastically.

Thus, averages over all phases have to be taken into account. The input impedance of the heating coils varies in the same manner with the physical parameters and therefore it is not possible to use the customary high frequency methods for matching the generator to the coil.

Variational methods are to be used to find the optimum matching. Configurations in Mag neto hydrostatic Equilibrium. The aim of these investigations is to find the properties of exact solutions, of appropriate general character, of the equation of magnetohydrostatic equilibrium.

This equation expresses the exact balance of the gas pressure gradient or pressure difference by the magnetic volume or surface force given by the vector product of the electric current density and the magnetic field intensity.

The majority of those investigations pertain to the case of surface currents and to ring-shaped toroidal configurations of the plasma surrounded by a vacuum.

The special case of axial symmetry and circular cross section was discussed with potential theory methods in the properties of the solution with ex-.

Jrgens 15 extended the analysis to the more general case of non-circular meridianal cross section, using a stream function related to the magnetic flux, and indicated the locations of the singularities, outside the torus, which correspond to electric currents in exterior conductors.

Kippenhahn 16 established necessary and sufficient differential geometrical conditions for the surface of a plasma which must be fulfilled if the plasma is to be in equilibrium with a surrounding magnetic vacuum field and discussed, in particular, the case of azimuthdependent circular cross sections and currents spiralling around the torus surface.

In all these cases it was found that a component of the electric current parallel to the generating circle is necessary for equilibrium.

An attempt, made by Meyer and Schmidt,17 to prove this property to be true for still more general cases, revealed, however, that, in fact, solutions can be constructed, of torus-like geometry but with neither axial symmetry nor circular cross section, which are characterized by electric currents flowing everywhere with equal surface density along closed lines of meridianal character, but not in meridianal planes.

The cross section appears to have at least two maxima along the generating circle. If there are only a few maxima, the relative variation of the cross section along the generating circle appears to be fairly large; if, in contrast, there are many extrema, the surface must have a rippled structure at least on the " inner " side as seen from the centre of the aperture of the torus.

The magnetic lines of force, in this case, are everywhere perpendicular to the current if there is no magnetic field in the plasma. Axially symmetric solutions with volume currents have also been considered, using the stream-function method.

In addition to the analytic treatment by means of a special coordinate system, a simple model of the surface currents andfieldshas been constructed, using paper strips of suitable shapes, folded and joined together in a special way; this model is a true analogue to the physical situation for the case of vanishing magnetic field in the plasma, and it allows one to survey existing solutions and their general properties rather easily.

Stability Problems. In , general conditions for the stability of hydromagnetic configurations were investigated in Gttingen, by Hain, Lst and Schlter,20 on lines.

For the special case of cylindrical symmetry the stability of certain specific configurations has been treated by Hain et al. More general cases for the current distributions and for the coaxial magnetic field are still being investigated.

Since the emphasis in this work is to compare the properties of various current distributions, no regard is being taken of the possible stabilizing influence of external conductors.

The stability of a linear discharge in an exterior longitudinal magnetic field with surface currents has been investigated theoretically by Jordan22 in Aachen.

Of the work done by Hain, Lst and de Vries,21 a first paper by Hain and Lst 23 has been completed which contains the discussion of the more special case.

To study the problem of the so-called exchange stability, Meyer 24 has extended an investigation by Kruskal and Schwarzschild 34 in such a manner that a plasma with gravity and horizontal magnetic field is supported by a vacuum magnetic field, which is also horizontal but is skew to the inner one.

With the approximation used by Kruskal and Schwarzschild the unstable perturbations found by them can be stabilized. The stabilization depends on the angle between the two fields and on their relative strengths.

The calculations are extended to the case of large wave-length. It is shown that here unstable perturbations with very large wave-length exist for arbitrary angles and strengths of the magnetic field.

Particle Losses by Drift Motions. Since the macroscopic equations of plasma physics give information only on the net balance of mass, momentum and energy, their discussion must be supplemented by studying, from the microscopic point of view, the motion and, in particular, the containment of individual charged particles in suitable electromagnetic fields.

This can be done with the help of methods analogous to those developed earlier in connection with the theory of aurorae and of cosmic radiation.

For axially symmetric magnetic fields, Lst and Schlter25 derived an integral for the azimuthal component of the velocity which shows that this component depends only on the meridianal component of the magnetic field.

It may be seen, in addition, that it is not affected by a meridianal electric field as produced, e.

Also, the influence of an azimuthal electric field as, e. This leads by the energy integral to the existence of so-called forbidden regions which show that all particles within a certain range of initial conditions can, indeed, be contained in suchfieldswith a suitable.

For the simplest cases of toroidal symmetry, the structure of the forbidden regions and the geometrical properties of a number of individual trajectories have been studied by Fisser and Kippenhahn.

The magnitude of this drift has been calculated using the approximation method of Alfvn and by numerical solutions of the equations of motion.

A comparison of the results indicates the range of validity of the approximation. The constancy " adiabatic invariance " of the magnetic moment M or of the angular momentum of the gyrating motion of a charged particle in a magnetic field has been the subject of an investigation of Hertweck and Schlter,28 who established that, for a homogeneous field varying in time, the relative variation of M goes to zero at least exponentially with the rate of change of the magnetic field strength.

Fisser and Kippenhahn 26 have developed methods by which the properties of given trajectories in relation to the geometry of the allowed and the forbidden regions can be surveyed easily.

These methods can also be used to discuss problems of particle loss. The authors have applied these methods to the special case of the magnetic field of an ideal circular ring current.

Magnetohydrodynamic Shock Waves. In connection with the theory of controlled fusion, as well as in that of the acceleration of cosmic rays in cosmic magneticfields,the structure of hydromagnetic shock waves, in particular their thickness as compared to the kinetic mean path and the gyro-radius, is of importance.

For this reason, the special case of a stationary plane wave, propagating in the absence of collisions with unchanging form and speed perpendicular to a magnetic field, in a completely ionized gas plasma of " zero " temperature, has been investigated rigorously by Davis, Lst and Schlter.

The macroscopic equations for this case are identical with the microscopic ones and both ions and electrons have the same velocity U x and the same particle flux F in the direction of propagation x.

If one includes in the equations of motion the terms arising from the inertia of the current-carrying particles, one finds that B x is determined by the second order differential equation of a one-dimensional,.

Thus, the oscillatory character of the solutions is obvious, and the wave-length turns out to be of the order of the geometric mean of the gyro-radii of the ions and the electrons when moving with the velocity of the wave.

Numerical integration of the differential equation has been carried out for a systematic array of values of the parameters. For the limiting case of an oscillatory wave train when the frequency goes to zero, one gets solitary waves with Mach numbers between 1 and 2.

In the complete absence of collisions, all particle trajectories are symmetrical about their extrema and no stationary shock waves can be found. But if a few collisions are admitted, both the trajectories and the variation of with x become asymmetrical.

It appears that a shock will start with a wave that is almost a solitary wave followed by some kind of wave train, and that after the particles have travelled a distance of the order of a mean-free path there will be a fairly smooth flow of gas of higher temperature.

Thus the total shock thickness will be of the order of a few mean-free paths while its detailed structure should be related to the waves found here.

In the limit in which the time between collisions goes to infinity, the only solutions connecting regions of different properties must be non-stationary solutions; thus the stationary waves treated in this work are completely inadequate for the discussion of such cases.

The case of non-zero temperature, both with isotropic and non-isotropic pressure in the plane perpendicular to the magnetic field, has been studied by the same authors and Hain,32 using mainly the macro1J2.

For the first case, the results do not seem to differ essentially from those obtained for the case of zero pressure. The second case is still being studied; for this, new equations have been derived by discussing suitable moments of the Boltzmann equation.

The investigations of Davis, Hain, Lst and Schluter 33 on the structure of hydromagnetic shock waves with non-zero pressure isotropic perpendicular but not parallel to the magnetic field have been completed.

The results are very similar to the case of zero pressure. To get shock waves, dissipative mechanisms such as viscosity, heat conduction, electrical resistivity and gyro-relaxation were taken into account.

A discussion showed that the last two are the most important mechanisms. The dissipation has the consequence that a solitary wave, which one obtains under certain initial conditions and which is symmetrical without dissipation, is somewhat asymmetrical.

This solitary wave is followed by a train of waves with decreasing amplitude until finally the homogeneous subsonic solution is reached.

The whole thickness of this region will be of the order of the mean-free path and may be very large compared to the thickness of the solitary wave.

That concludes my very incomplete and brief survey of the work that has been done, mainly in the last two years, in the Federal Republic of Germany.

You will have noticed that hitherto there has been very much duplication of effort, but I should like to say that I share very much the satisfaction that has been expressed by earlier speakers that now the period of duplication and non-communication has apparently come to an end and that international cooperation gives better promise for the future of physics.

Funfer, H Herold, G. Lehner, H Tuczek and C. Andelfinger, Neutronenemission stromstarker DeutenumEntladungen, Z Naturforsch. L Biermann and A. Schluter, Zur Thorie quasistationarer thermonuklearer Prozesse, Z.

Biermann, ber den Mechanismus der Ionisation in der Sonnenkorona , Naturwiss. Elwert, ber die Ionisations- und Rekombmationsprozesse in einem Plasma und die Ionisations formel der Sonnenkorona, Z.

Naturforsch, 7a, Knorr, ber den Ionisationszustand und die Ausstrahlung von Fremdgasen eines Wasserstoff-Plasmas, to appear in Z.

Schmidt and W. Stodiek, to appear in Z. Boose et al, Nature, , Schmidt, to appear m Z. Grossmann-Doerth, personal communication.

Korper, Schwingung eines Plasmazyhnders in einem ausseren Magnetfeld, Z. Naturforsch, 12a, Schluter, Der Gyro-Relaxahons-Effekt, Z.

Naturforsch , 72a, Korper, to appear in Z. Biermann, K. Ham, K. Jorgens and R. Lust, Axialsymmetnsche Losungen der magnetohydrostatischen Gleichung mit Oberflachenstromen, Z.

Jorgens, Axialsymmetnsche Losungen der magnetohydrostatischen Gleichung mit Oberflachenstromen II, to appear in Z.

Kippenhahn, Plasma-Konflguralionen mit Oberflachenstromen, die von einem Magnetfeld im Gleichgewicht gehalten werden, to appear in Z Naturforsch.

Meyer and H. Schmidt, Torusartige Plasmakonfigurahonen ohne Gesamtstrom durch ihren Querschnitt im Gleichgewicht mit einem Magnerfeld, Z.

Naturforsch , in press. Lust and A. Schluter, Axialsymmetnsche magnetohydrodynamische Gleichgewichtshonflguralionen, Z. Schluter, Kraftfreie Magnetfelder II, Z.

Naturforsch , 12a, Ham, R. Lust and A Schluter, Zur Stabihtat eines Plasmas, Z. Lust and H. Jordan and K. Schmdler, On the Stabilization of a Pinched Plasma Column by Axial Magnetic Fields, p.

Ham and R Lust, Zur Stbihtat zylindersymmetnscher Plasmakonfigurationen mit Volumenstromen, Z Naturforsch, m press. R Lust and A Schluter, Die Bewegung geladener Teilchen m rotationssymmetnschen Magnetfeldern, Z Naturforsch , 12a, F Hertweck and A Schluter, Die " adiabahsche Invananz " des magnetischen Bahnmomentes geladener Teilchen, Z Naturforsch , 12a, L Davis, R Lust and A Schluter The Structure of Hydromagnehc Shock Waves, Part I Non linear Hydro magnetic Waves m a Cold Plasma, to appear in Z Natur forsch 30 R Lust, Magneto-hydrodynamische Stosswellen in emem Plasma unendhcher Leitfahigkeit, Z Naturforsch, 8a 31 R Lust, Stationare magneto-hydrodynamische Stosswellen behebiger Starke, Z Naturforsch , 10a, 32 L Davis, Ham, R Lust and A Schluter, The Structure of Hydromagnehc Shock Waves, Parts II and III, to be published 33 L Davis, Ham, R Lust and A Schluter, to appear in Z Naturforsch M D Kruskal and M Schwarzschild, Proc Roy Soc London , A , The second and more important difference is the following: The fission chain reaction is regulated by assembling the correct amounts of active materials and absorbers.

If the correct amount is exceeded, the energy release rises in a rather slow manner due to the action of delayed neutrons. In contrast, the main regulating feature in a fusion reaction is the temperature.

When a certain ignition temperature has been exceeded, the reaction itself raises the temperature and this leads to an exceedingly rapid acceleration of further energy release.

Slow energy release is possible only at low densities ; but this raises further problems. It is a great pleasure to discuss with you the topic of the day and I should like to begin by expressing the same sentiments with which the previous speaker finished his paper.

It is wonderful that over a large and important area of research we can now all talk and work together freely. I hope that this spirit of cooperation will endure, that it will be generally exercised throughout the world in this field and that it will be extended also to other fields.

It is remarkable how closely parallel the developments in the different countries are and this, of course, is due to the fact that we all live in the same world and obey the same laws of nature.

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