Still from The Death of Empedocles (1986), dir. Straub and Huillet.
Jean-Marie Straub and Danièle Huillet. A retrospective at the Museum of Modern Art, organized by Joshua Siegel.
Ted Fendt (ed.). Jean-Marie Straub and Danièle Huillet. With essays by Claudia Plummer, John Gianvito and others. Austrian Film Museum, 2016.
Jean-Marie Straub and Danièle Huillet. Writings (edited and translated by Sally Shafto, with Katherine Pickard). Sequence Press, 2016.
Jean-Marie Straub and Danièle Huillet: Films and Their Sites. An exhibition at Miguel Abreu Gallery, organized by Jean-Louis Raymond.
Of our grand nature intimated from afar.
Of gods to some obnoxious servitude.
That I would treat all things as you treat them.
Abuses holy things as stock in trade.
Over their fifty-year career, which lasted from their marriage in 1959 until Huillet's death in 2006, Straub and Huillet gave themselves many "cardinal rules." They took tremendous care to respect anything over which they might have control—the spaces they shot in, the voices they recorded, the texts they adapted, the actors they cast—and they spoke equally often of respecting the moviegoers who watched their films. Most commercial movies were crude devices for eking money out of browbeaten viewers—"abusing holy things as stock in trade"—and their own work was, to them, a brave resolve to "[cleave] to sun and ether": to give their audiences the freedom they thought most films withheld. Their films can be thrilling purgatives, a vision of what the movies could look like cleared of anything lazy or complacent or pat. But they also suggest how the parameters set by respect—by the determination not to exploit—can restrict in their own way.
Huillet was born in Paris in 1936, three years after Straub's birth in Alsace-Lorraine and four years before both of their home cities came under German occupation. By 1954, Straub was living in Paris and hoping to make a film about Bach that would give central attention to the composer's wife and her writings; in the scholar Claudia Pummer's uninflected telling of the young couple's meeting, "[Straub] asked [Huillet] if she would help him write the script." When Straub fled France in 1958 under threat of imprisonment for dodging the draft during the Algerian War, Huillet took turns hitchhiking with him through Germany and raising money for "the Bach film" in Paris. A year later, they married and settled in Munich. There they shot much of Machorka-Muff (1963) and Not Reconciled (1965), their first two films, both Heinrich Böll adaptations filmed in grim black-and-white and set in hotels, restaurants, and hideous concrete developments where ex-Nazis continued to circulate.
A new traveling retrospective of this exacting couple's films—organized by MoMA's Joshua Siegel and accompanied by a critical volume edited by Ted Fendt, as well as an exhaustive collection of the pair's writings published by Sequence Press and an exhibition of their papers and film stills at the Miguel Abreu gallery—surveys everything they made together from those two movies on. It is a daunting body of work: seventeen features and exactly as many shorts, all adaptations or studies of plays, novels, operas, pieces of music, and works of art from their idiosyncratic personal canon. Chronicle of Anna Magdalena Bach, which the couple finally funded after finishing Not Reconciled, was followed by an adaptation of the lesser-known Corneille play Othon, and then, after several other projects, by a staging of Schoenberg's Moses and Aaron. The couple made two essay films about Cezanne, multiple versions of The Death of Empedocles, adaptations of unfinished works by Kafka and Brecht, and a film in which shots of rural villages are overlaid with a reading of two texts on peasant revolt by Friedrich Engels and the Egyptian political theorist Mahmoud Hussein. Some of these movies have storylines and protagonists; others, like the Bach and Cezanne films, are nonfiction studies of specific pieces of music or works of art. Since the death of his wife in 2006, Straub has finished over a dozen more movies, returning to the couple's old textual sources (Corneille, Brecht) and adding some of his own (Dante, Montaigne).
Straub and Huillet considered over-dubbed sound, studio sets, and illusionistic cuts phony and cheap, but they praised filmmakers who used those devices particularly cannily.
At every turn they strove for precision, to a degree that could seem either heroic or pedantic. Working on Class Relations (1984), their adaptation of Kafka's Amerika, Huillet politely asked their subtitle translator to remove a "but" from one sentence because the word had been added to Kafka's manuscript by Max Brod. In the editing room, as shown in the Portuguese director Pedro Costa's loving documentary Where Does Your Hidden Smile Lie? (2001), they quarreled for hours over whether to include a half-frame more or less in a shot. No sound, movement, or rhythmic pause could be cut short for the sake of dramatic momentum, just as no illusion of spatial or temporal continuity could be kept at the expense of shortening a line of birdsong or a rustle of wind in the trees. "No need to assassinate the bird," Huillet mumbled.
Stories like these have given Straub and Huillet a kind of fearsome allure for generations of younger directors dissatisfied with conventional filmmaking. Here were two filmmakers who managed to keep themselves immune to the movie industry's pressures and fads, who held themselves to impractically high standards even when doing so meant running through film stock at a rate most producers would find unacceptable. Starting as early as the 1980s, some of their uncompromising methods and stylistic habits were taken up by a range of European filmmakers, including Costa and the couple's friend and near-contemporary Harun Farocki. More recently, they've been embraced by a cluster of American independent filmmakers that includes Gianvito, the architect of the 2012 omnibus film Far from Afghanistan, and Fendt himself.
depends precisely on things that cannot be reproduced—the incarnation of Corneille's language in each character at every moment, the noise, the air, and the wind, and the effort that the actors make and the risks they take, like tightrope walkers, from one end to the other with long texts difficult to record live—in other words at the same time as the image: in perfect synchrony.
Statements like these can make Straub and Huillet sound like hopeless aesthetes. Other claims of Straub's—like his outburst in a 2001 interview that because of "where we're at," with "no alternatives," the only "political cinema is the one that ends with saying: 'sickle and hammer, cannons, cannons, dynamite!'"—make the couple come off as hotheaded anti-authoritarians. Their actual political commitments are harder to pin down. They presented all their extreme aesthetic choices as acts of defiance against vague hegemonic authorities, but they tended to discuss their politics only in cryptic sayings, such as that there is "no political film without morality . . . theology . . . [or] mysticism." Their attitude toward Marxism was something like that of mystics to organized religion: they took what language and ideas they wanted from competing parties and schools without subscribing to any one.
A political film must remind people that we don't live in "the best of all possible worlds" . . . and that the present time, stolen from us in the name of progress, is going by and is irreplaceable . . . that they are ransacking human feelings like they ransack the planet . . . We should make people feel that the price is too high, that the only thing worth defending is precisely the passing moment, that they should by no circumstances take flight into the future.
Precisely who is "ransacking human feelings" or stealing people's time is unspecified, but it's not clear that Straub would consider that question relevant. Why take the trouble to identify your enemies when you don't believe in political progress, or when you can't conceive of political engagement directed at the future as anything but "taking flight"?
Straub goes on to quote the saying by Charles Péguy that he and Huillet inscribed at the top of the script of Anna Magdalena Bach: "To make a revolution also means to put back into place things that are very ancient but forgotten." The future, for them, was largely off-limits; visions of progress were pipe dreams or misleading advertisements. To the extent that they had a political project, it was oddly resigned. They gravitated toward serious, browbeaten, or defeated characters. Moses and Aaron (1973) opens with a dedication to the Red Army member Holger Meins, who died during a hunger strike in prison, and The Death of Empedocles ends just before the event in its title, which occurred, according to Diogenes Laërtius, when the exiled philosopher threw himself into Mount Etna.
The couple's reluctance to participate in political struggles among defined parties with concrete goals kept them from making agitprop films, which Straub thought strong-armed already beleaguered viewers into staying put. ("If we can afford to hoarsen our own voice, you have no right to do it to people whose voice is already hoarse for other reasons.") It led them to throw themselves into the work of getting things just right on set, which in turn encouraged them to keep up decades-long collaborations. Their association with the Teatro Francesca di Bartolo—a municipal theater company based in the small Tuscan town of Buti and made up partly of working-class actors from the region—produced some of their best movies, including the last film they made together, the Pavese adaptation These Encounters of Theirs (2005).
Straub and Huillet's suspicion of any farsighted political activity seemed to force them into a narrow but particularly intense, even seductive engagement with whatever they filmed.
At times Straub and Huillet's suspicion of any farsighted political activity seemed to force them into a narrow but particularly intense, even seductive engagement with whatever they filmed. According to the scholar Barton Byg, Huillet was once asked whether her films were "built on a strict system, based on renunciation." "I hope not only that," she replied. "I hope that one can feel sensuality and pleasure at the same time. Can sense the fragrance of things." The shots that show a meadow brightening and dimming as the sun passes behind a cluster of clouds in The Death of Empedocles; the exhilarating joyride around the Place de la Bastille in Too Early, Too Late; the way the couple's great cinematographer William Lubtchansky managed to soften his subject's skin tones with golden shades of sunlight—these are pleasures that a more flexible and less hardworking pair of directors wouldn't have been able to hit upon.
But there is something wrongheaded about the couple's insistence that their primary political task was to "give people the liberty to get up and leave." Their talk of "respecting the space" can be exasperating, as can be Huillet's concern that they not "assassinate the bird" in their editing, and Pummer's contention that "Straub-Huillet's understanding of materialism . . . is deeply grounded in the belief that the medium of film can be entrusted with the task of recording, showing and revealing while the filmmaker steps back to allow viewers to see for themselves." No interesting filmmaker has ever "stepped back" and turned down the job of "showing and revealing" things. Nor did Straub and Huillet, although they sometimes claimed to.
Where Pummer sees an admirable refusal not to bully the viewer, it's also possible to see a kind of unwillingness on Straub and Huillet's part to dirty their hands, to engage openly in the sorts of deceptions and elisions and selective modifications movies depend on to generate their energy and life. How can it be that cutting a passage of birdsong short, overdubbing a soundtrack, or moving the camera through a peripheral sightline constitutes a serious offense to a moviegoer's freedom of imagination, whereas refusing to allow spontaneous human interactions into one's movies does not? Considering what startling and majestic images they often produced, Straub and Huillet are two of the rare filmmakers you wish had been more willing to coerce, manipulate, and deceive you than they were.
Opening glimpses reveal the cruel world hasn't stripped these aging hipsters of their faith in the promise of love.


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Home Conservative Do we want Scotland to leave the UK or should we keep...
Do we want Scotland to leave the UK or should we keep our neighbour close?
Max Anderson, Jack Kane and Isabella Jewell
Should Scotland break away from the UK? In 2014, Scotland took the voting booths to answer this exact question, with 55% of the Scottish population deciding to remain part of the UK. In 2019, we now ask, is another referendum needed?
Nicola sturgeon has called for a referendum again. In recent weeks, the calls for the another vote have grown, with her telling Andrew Marr recently 'I'm putting legislation through the Scottish Parliament right now, to put the rules and regulations in place' ready for the 'Indyref2'.
Many have asked what is the point of another referendum. This is down to the massive elephant in the room that seems to absorb everything in British politics at the moment, Brexit.
Scotland is very much at odds with what Parliament are doing, with 62% of the population voting to remain. The highlight of their dissatisfaction with parliament's recent actions can be shown by Boris Johnson's recent visit to Scotland, in which he was met by a wave of boo's while greeting Nicola Sturgeon.
With Nicola Sturgeon's rhetoric backed up by 'pro-independence marches all over Scotland', the question has certainly moved to the centre of British politics once again. So with that being said, should Scotland leave the UK?
The question our editors face therefore is not whether or not there should be a Scottish referendum, but whether or not it would be good for Scotland to leave for both Scotland and England, or should Parliament do everything in their power to keep Scotland part of the UK.
Scottish Independence is a Scottish matter: Westminster imperialism has gone on too long – Labour Article
The Labour stance on Scottish Independence is complex. In a move which contradicts the manifesto, as well as the stance of scottish Labour MSPs, John McDonnell announced at the Edinburgh Fringe that "the Scottish parliament will come to a considered view and they will submit that to the government and the English parliament itself. If the Scottish people decide they want a referendum, that's for them." In summary; he believes the question of a second independence referendum isn't for the english parliament to decide and impose on the Scots. Jeremy Corbyn further reinforced this stance in a later interview, taking the pragmatic view that "it's not up to parliament to block it but it's up to parliament to make a point whether it is a good idea or not. I do not think it is a good idea."
The problem of this sudden change of tact, is the implications for the unity of the Labour party – Scottish Labour MSPs responded with the statement, "Labour's position on Scotland's future is a decision for Scottish Labour, which the UK party must accept." Whilst I fully accept the anger of the MSPs following this sudden change of stance, I am inclined to believe that the greater injustice would be the english Government in Westminster refusing a referendum to Scotland, despite recent polls revealing that support for independence has reached 52%… a figure which won the Brexit referendum. It would be a dangerous act of hypocrisy, the implications of which would entrench existing divides.
One only needs to look at what's happening in Catalonia to realise that independence movements can escalate into violence. Of course, Scotland has remained peaceful during its countless campaigns and requests for independence referendums, however frustration is building. Only a few days ago, on the 13th October, the SNP leadership faced calls in Aberdeen to enact a 'plan B', in which they 'do a Catalonia' and begin independence negotiations without the constitutional approval of London. The independence movement is far from diminishing in Scotland, and my worry is that another imperialist rejection of a referendum from Westminster could be the straw that breaks the camel's back.
The 'B word' makes the question of Scottish independence even more urgent, of course I'm talking about Brexit *sigh*. In the 2016 brexit referendum, Scotland voted overwhelmingly to remain, with every single one of Scotland's 32 local authority areas rejecting brexit, in total 62 per cent of those who voted. The idea that Brexit, something that Scotland utterly rejected as a unified nation, could be forced upon them, is quite outrageous. Especially as Scotland is not mentioned once in the latest withdrawal agreement. The imposition of Brexit on Scotland would only be another reason to escalate the independence movement, as such, the only way to diffuse tensions is to offer a referendum.
Many in Scotland propose leaving the UK to remain in the EU, the only problem being that this might not be so easy. EU entry requirements could make the maintenance of scottish currency, tax policies, and membership of the UK single market rather difficult. The question of borders would also be problematic, as we have seen in the case of Ireland.
However, some have drawn parallels with the case of Denmark, given the similarity of population size and resources. They suggest that if it worked for the danes, it can work for the scots, Scotland would simply have to wean itself off the UK's economy and begin restructuring its own economy.
Overall, I side with Jeremy Corbyn's stance on Scottish independence; it isn't something that the UK government should ban, it's a question for the Scots. Brexit has catalysed the issue, with the support of independence skyrocketing. It is time to let Scotland propose a referendum if they reach an agreement to do so in Holyrood; questions over the possibility to reenter the EU are problems that Scotland should be left to consider.
Wise words to the Scottish movement, but let's take a break from referendum for a second? – a Liberal response
Miss Jewell proposes some very sensible words of wisdom to Scottish and English MP's. A Catalonia type situation is the last thing this country needs or wants. The UK is so divided already, to create a bigger gap between Parliament and Scotland is the last thing needed right now and I think Miss Jewell is wise to point this out. We must to a point allow Scotland to dictate their own fate.
This being said, I think we need to slow Scotland down a bit. Running off into the sunset with a piece of paper which says independence might of worked for America all that time ago, but I don't think it will have such a happy ending. The UK is already going through a massive constitutional shift, which was caused by a referendum. I firstly worry about MP's being so eager to give the power back to the people in the form of a referendum. The British politically system was not built to have referendums of course.
I think we need to slow the process down, and allow for British politics to settle first. Before we move onto decide any more massive constitutional changes, we must sort out the ones we currently face, and that is another warning I think Miss Jewell missed out.
Scotland and Sturgeon must stop being cry babies. Scotland must accept the UK's decision – a Conservative response
Miss Jewell writes "The Labour stance on Scottish Independence is complex. In a move which contradicts the manifesto." It appears Miss Jewell might be secretly wanting to help my Conservative party and my cause. Why should we trust a crazy Corbyn led government who have an extremely complex and unnecessary position on Scotland? It beats me.
What does agitate me on the issue of Scotland is quotes like this. "I am inclined to believe that the greater injustice would be the English Government in Westminster refusing a referendum to Scotland, despite recent polls revealing that support for independence has reached 52%." If we allowed government policy to be dictated by recent polls, then no governance would get done. The Scottish independence vote was a once in a generation vote and Scotland must accept this Brexit or not.
"The idea that Brexit, something that Scotland utterly rejected as a unified nation, could be forced upon them, is quite outrageous." It is my understanding that Scotland is part of the United Kingdom and that the UK overall voted to leave the EU. Scotland must stop thinking of itself as a special state who receive dispensation just because. The referendum result was clear and as Scotland is part of our glorious union they must accept the electorate's decision to leave.
Just on the issues of the Economy and Security, Scottish independence is a bad move – Conservative article
In 2014 Scotland spoke and elected to stay in the United Kingdom. Five years on the call for Scottish independence is still being heard especially with Brexit completely changing the political landscape. Nicola Sturgeon is using Brexit as a rally cry to fight again for Scottish independence. I believe that she is blinded by her nationalism and I will argue why Scotland is far better off in the glorious United Kingdom.
Economically, Scottish Independence in 2020 will be extremely dangerous especially with Scotland being heavily dependent on oil revenues. In 2001 Scotland's oil revenues was "in excess of £9 Billion to the economy." Yet post the Scottish referendum oil prices slumped with "the revenue had gone from £9bn to a mere £60m." As an independent country this could have had a catastrophic effect and with oil prices staying low, Scotland will seriously struggle without being part of the UK.
Scotland would also severely struggle outside of the United Kingdom due to its outrageously high deficit. "Scotland's deficit is higher than the UK average an estimated 7 per cent of GDP, as opposed to the UK's 2 per cent." The reason why is due to the SNP's terrible spending habits resulting in Scottish public spending being "13.6% higher per head than the UK average and revenue collected being 2.6% lower." There is a gap of nearly £2000 between public spending and tax revenue which is highly worrying. So if we cannot trust the SNP with the deficit, then why should we trust them with what would be the most politically and economical difficult time in Scotland's history.
The SNP would be in charge of keeping Scotland's economy afloat while trying to enter the European Union. Scotland would have to adopt the Euro as well as join the Schengen and yet with all of this, the EU would have to force Scotland into strong austerity measure due to its eye-watering deficit of 7%. This is due to the EU's "excessive deficit procedure" for countries over 3%. So if Scotland choose to leave it would have to adopt dangerous levels of Austerity due the poor policies of the SNP.
Furthermore, we haven't even talked about the benefits Scotland receives due to being part of the UK. Scotland's home market trade "with the rest of UK is worth £48.9billion-a-year to Scotland's economy. It makes up 60 per cent of all exports, dwarfing trade with the EU." Scotland would be worsening ties and creating trade barriers with its biggest trading partner. This is an insensible thing to do especially with us seeing how difficult trade talks are in relation to Brexit. In addition, the people of Scotland all benefit from being part of the UK due to Scotland only generating 8% of all the UK taxes, but "benefits from 9.3%of the UK's public spending." All of this would disappear with an independent Scotland.
My final point is on Security. With Scotland being part of our glorious union we are entitled to keep them safe with our nuclear deterrent. The SNP's policy on Trident is to get rid of it in order to save cash and that is not surprising with their horrendous deficit. However, I believe this is wrong. Our Nuclear deterrent is vital in this crazy world for the protection and security of our land. By leaving the UK Scotland will lose this and I do not want to see Scotland lose this deterrent. Scotland is safer in the UK as well as economically far better off in the UK.
Mr Kane makes a strong argument for Scotland to remain, and I buy it – a Liberal response
Although Mr Kane's rhetoric is perhaps a bit distasteful for many to hear including me, I do think he makes an excellent overall point – Scotland should not leave and I agree with him. I do worry just as Mr Kane does that Scotland would struggle on its own. My article says very similar things to Mr Kane, but I put my hands up and concede Mr Kane's article which is backed up by a wave of fact really does almost makes my semi-irrelevant.
I think in a time of where feeling trumps fact, and indeed post-truth itself means taking fact and creating your own truth infused with passion, Scotland should be rational and take note of these facts.
If we give the people another vote, they will vote with passion not fact. They may make a choice which they seriously regret, just like Brexit. I think purely for our neighbours sake, we can't allow Scotland to leave just yet.
The so called United Kingdom is far from 'glorious' – a Labour response
Mr Kane's argument does provide a thorough examination of Scotland's economy, he is correct in the belief that independence is not an easy option, although I do wonder why he is a supporter of Brexit if the Economy is his major preoccupation…
My main problem with Mr Kane's argument is the recurring use of language which idolises the UK: 'the glorious United Kingdom' our 'glorious union'… I don't know where Mr Kane has been for the last three years, but 'glorious' and 'union' are the antonyms of the UK at the moment. It seems like he's wearing the rose-tinted glasses of leave campaigners who evoke – and embellish – past centuries of Great Britain, making reference to those lovely World Wars and the entirely benevolent British Empire.
Mr Kane's argument is worryingly England-centred; he seems to believe it the divine right of Westminster to dictate to Scotland their own future. Don't worry Nicola, when Brexit happens at least we'll be united in our downfall!
More seriously, Mr Kane does make some solid assertions. Yes, the economic future of Scotland would be complex if they leave the United Kingdom, but surely they have the right to decide for themselves whether to impart on an economic disaster with the rest of the Unite Kingdom, or if they'd prefer to take the other unknown path of independence.
Brexit has 'completely changed the political landscape', and as such Scotland should have the right to decide between two uncertain outcomes; remaining in the UK with Brexit, or leaving in the attempt to re-join the EU.
Staying works best for both parties as unfortunate as that is for Scotland – Liberal Article
There are three reasons as to why I and Liberals think the UK should stay together, and not see Scotland venture out on its own. I think it is of vital importance that the UK keeps Scotland close for many economic reasons. I believe that Scotland will suffer some of the same fate as Britain but worse as they will not be accepted into the European Union under any circumstance. Finally, I do not want to see our Northern brethren leave in a time of crisis.
If another Scottish referendum does occur in 2020 as Nicola Sturgeon hopes for, and Scotland decides to leave, I do wish the best for them and if that is what the people of Scotland want them we must accept their decision. However, for Scotland it would be a tough rebirth for their country to deal with.
Most small countries would look to the EU for economic support through the benefits of their trade across the continent and beyond and their strong institutions from beaucracy to legal matters whilst the pound will remain their currency. However, this seemingly crucial aspect for Scotland to have a successful break away from the UK, would be blocked by Spain.
Spain, just as they were back during the first Scottish independence referendum, are incredibly concerned about this issue. They do not want to see countries break away from their big brother and go it alone. This is because there 'are still "hesitations" about Scottish independence in Spain, which is concerned about Catalonia breaking away'. Spain will not want Scotland to be a beacon of light for Catalonia to have for them to break away from Spain, and be successful.
Now there are more reasons than this for a Scotland to remain in the UK. For many Scots they will be well aware of the advantages of the UK, but why should the UK want to keep Scotland. This question has not been examined in the same way.
Scotland's economy is providing a nice boost to the UK at the moment with GDP growing 'slightly stronger in Scotland than the UK average'. Having "resources and share risks across Scotland, England, Wales and Northern Ireland" has protected the UK from major economic collapse, and the diversity itself provides strength for both the UK and Scotland. It also allows businesses to connect more easily and hit a bigger population to sell products. In addition, if Scotland leaves the UK, this will ultimately mean the UK will lose 'North Sea oil.'
I think seeing Scotland break from the UK would be economically challenging for both sides, but more importantly I don't want to see the UK break up. If it is the wish of Scotland to leave, I wish them the best in the near future. However, I personally and rationally think the UK should keep Britain, Wales, Scotland and Northern Ireland, and we should move together, not drift apart.
Scotland must decide between two different unions: The United Kingdom or the European Union – a Labour response
I applaud the sentiment of Mr Anderson's argument; in a moment of division and polarised politics, unity is important for the UK. The problem lies, I believe, in the failure to recognise that it is not the place of the UK to dictate what happens to Scotland.
Brexit has changed the game, no longer is it just a question of unity for the Scots, rather a choice between 'united isolation' in the UK, whereby Scotland's economy will take huge blows, or the short term trauma of leaving the UK for the long term benefit of EU membership. Unlike Mr Anderson, I do not believe it impossible that the EU would accept Scotland; the fact – as I underlined in my article – that Scotland has shown its commitment to the European project would earn deep sympathy. Furthermore, as Mr Anderson has argued, Scotland's economy is stable, another prerequisite for joining the EU. It is important to ask oneself, why should Scotland be dragged out of a union that they cherish? The figures do highlight which union the Scots favour at the moment…
The Catalonia situation is worrying, and I do understand Mr Anderson's hesitations, however it should not be a reason to deny Scotland the power to make a choice regarding their own future. Allowing a democratic process in Scotland would serve as a stark contrast to the behaviour of Spain, which has responded to the Catalan independence movement by imprisoning those who disagree with the status quo – hardly in keeping with the European value of democracy…
Scotland is better in the United Kingdom and Mr Anderson knows it – a Conservative response
I am happy again to report that Mr Anderson for the second week running has written an article that I agree with, though I must critique him one issue.
My only problem is when Mr Anderson writes "whilst the pound will remain their currency." The key part of Scotland joining the EU is that it must agree to be part of Schengen while also accepting the euro. Very few Scots want this and with them accepting the Euro they must accept serve spending cuts due to their horrendous deficit. It would economically be wrong to inflict this pain onto Scotland, especially due to Scotland being so heavily reliant on oil revenues which have drastically shrunk in recent years.
However, with my critique over Mr Anderson does write that "resources and share risks across Scotland, England, Wales and Northern Ireland has protected the UK from major economic collapse." I could not agree more. We are safer and stronger as a union and as a collective rather than many independent countries. Our combined economies have made and will make economic life for us far easier than if we were split into two countries.
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You are here: Home / Blog / Don't Let Them See Your Dirty Laundry
Don't Let Them See Your Dirty Laundry
December 18, 2018 By Melinda Eitzen
What if there was a way to divorce where all your dirty laundry was not aired out publicly? What if there was a way to divorce where we could honor what we had, but move on to more fulfilling lives. What if there was a way to divorce that shielded the children? What if there was a way to divorce that allowed for a creative settlement that addressed both of our goals and concerns? What if there was a way to divorce that allowed us to behave with dignity and respect while divorcing? There is a way- the Collaborative Way.
The Texas Family Code has a statute that allows for a collaborative divorce instead of a litigated divorce.
The Collaborative Divorce Process
The Collaborative process is a noncourt more amicable process. It is designed to help people with serious disagreements resolve those disagreements in a private confidential setting. It includes a child specialist to bring the voice of the children to the parents.
It includes a financial neutral to help with budgeting and forward forecasting. It uses nontraditional negotiation techniques to increase the size of the pie and to truly understand and attempt to meet as many of both client's concerns and goals.
It also involves a neutral mental health professional to help us to deal with the normal emotion that gets in the way of the deal like anger, sadness and fear and to keep us on track. The neutral mental health professional also helps the divorcing couple to put together a parenting plan. The parenting plan includes the parenting time for each parent including holiday time. The parenting time also addresses decision making regarding the children.
It can even include special concerns such as what about how the parents might introduce future love interest to the children. To find out more go to www.collaborativedivorcetexas.com.


Ever since I worked for a startup building educational kids apps in China, I've been tossing around a few ideas about writing one of my own. I may be biased as an engineer, but one of the main areas I perceive to be lacking both in the classroom and the app store is our ability to teach math. Mathpx is my new experiment to rethink the way we teach the very fundamentals of arithmetic.
When I was an undergraduate in electrical engineering at the University of Michigan, I took quite a few math-heavy courses, and I quickly discovered the obvious fact that you're a lot better off in a class when you understand the fundamentals as opposed to just regurgitating formulas.
Some of my first rigorous math classes really made me realize how much I hadn't understood of the basics in grade school. I had breezed through the Nevada public school system answering questions like "What is pi?" with "3.14" without realizing that was only the tip of the ice berg.
With Mathpx, I wanted to help kids get a solid foundation in the most basic concepts possible. Based on my own grade school experiences and my observations volunteering in classrooms, I realized that I had to take it way back.
Enough has been said elsewhere about education systems' reliance on memorization and testing, but the way we teach math doesn't just encourage memorization, it prevents anything deeper from day one.
Why do we teach our children subtraction in the first grade but wait years to introduce the concept of negative numbers? 2 - 1 is something a toddler should be able to calculate, but change the order to -1 + 2 and that's taboo until middle school, and 2 - 1 = x has to remain hidden for even longer.
Each of these problems are fundamentally the same thing, but with our grade school they require a leap in understanding to progress. Why not just teach the fundamentals at the start?
With the fairly recent rise of tablets, we're just getting started with what teachers can do when they're not limited to counting apples on their hands and writing problems on the board. I scrapped all of this and tried to rethink what the connections to basic arithmetic really are, and this is what I came up with.
In Mathpx, players count out the answers to basic arithmetic problems by dragging balls around the screen. The written form of the problem sits right above and automatically updates, making the connection to pencil-and-paper math intuitive.
Pressing the equals button racks up all number balls, so it's easy to see if the two sides of the equation are equal or not.
Let's make the jump to subtraction. Subtraction works the same way, but it shows numbers being subtracted as blue balls instead of red. Now when the player presses the equals button, positives and negatives visually cancel out, and the remaining values rack up.
With this visualization of math, why hold out on negatives for the next few years? Here is the easy jump to negatives.
Mathpx is designed to evoke a visualization of math that fits nicely with everything from counting to arithmetic with positives and negatives to algebra, because really, it's all one concept.
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text:
\section{Introduction}

Non-relativistic treatments of the Sunyaev-Zel'dovich effect usually employ
the Kompaneets equation~\cite{komp57} to determine the distortion of the
Cosmic Microwave Background (CMB) spectrum.
The Kompaneets equation does not, however, include relativistic effects, which
may be important for hot clusters where $k_{B}T_{e} \gtrsim 10 \mbox{\rm \,keV}$.
For this reason, and because of the low optical depth of typical clusters,
relativistic treatments of the Sunyaev-Zel'dovich effect usually employ
a multiple scattering description of the
Comptonization process~\cite{wright79,fabbri81,taylor89,loeb91,reph95}.
Including
relativistic effects in this procedure gives a complicated expression
for the spectral distortion, which is best handled by numerical
techniques (see, for example,~\cite{reph95}).

In this paper, we show how the Kompaneets equation may be extended to
include relativistic effects in a self-consistent manner,
allowing the Sunyaev-Zel'dovich effect in
hot clusters to be described on the basis of a Kompaneets type equation.
The extension of the Kompaneets equation can be carried out to
arbitrary orders in relativistic effects,
although we shall only consider the lowest order corrections here. The
resulting equation conserves photons at every order, and we demonstrate
that it is consistent with earlier calculations of the energy transfer rate
between the plasma and a Planck distribution of photons~\cite{woodward70}.

We then consider the application of the generalised Kompaneets equation
to the calculation of the Sunyaev-Zel'dovich effect in hot clusters.
Simple analytic forms are given for the spectral distortions in the
limit of small optical depth, including relativistic effects to
second-order. These are
in excellent agreement with Rephaeli's (1995) numerical calculations,
which were based on the multiple scattering approach (truncated at one
scattering). This lends further support to Fabbri's observation
that the Boltzmann equation can be applied to describe the Sunyaev-Zel'dovich
effect in optically thin clusters~\cite{fabbri81}, despite claims to the
contrary~\cite{wright79}.

The relativistic corrections to the Sunyaev-Zel'dovich effect are of
importance in the calculation of the Hubble constant $H_{0}$ by
the Sunyaev-Zel'dovich route in hot clusters (see, for
example,~\cite{las97} for a recent review of the Sunyaev-Zel'dovich route
of determining $H_{0}$, and~\cite{saun96} for recent observations).
In the Rayleigh-Jeans region, we find that
relativistic effects lead to a small decrease in the Sunyaev-Zel'dovich effect,
and hence a small reduction in the hitherto determined values of $H_{0}$, in
agreement with the conclusions in~\cite{reph97}.

We employ natural units, $c=\hbar=1$, except in the discussion of the
Sunyaev-Zel'dovich effect in Section~\ref{sz_sec_sun_zel}.

\section{Extending the Kompaneets Equation}
\label{sz_sec_komp}

In this paper we shall not consider effects due to the peculiar motion of the
cluster (such effects give rise to a kinetic correction to the
Sunyaev-Zel'dovich effect). For a comoving cluster, the CMB photon distribution
function is isotropic and may be denoted $n(\omega)$, where $\omega$ is the
photon energy. The electrons are assumed to be in thermal equilibrium at
temperature $T_{e}$, and are described by an isotropic distribution
function $f(E)$, where $E$ is the photon energy.
The Boltzmann equation
describing the evolution of $n(\omega)$ may be written as~\cite{buchler76}
\begin{equation}
\frac{\partial n(\omega)}{\partial t} = -2 \int \frac{d^{\,3} p}{(2\pi)^{3}}
d^{\,3} p' d^{\,3} k' \,W \Bigl[n(\omega)\bigl(1+ n(\omega')\bigr)f(E) -
n(\omega')\left(1+n(\omega)\right)f(E') \Bigr],
\label{sz_eq_1}
\end{equation}
where $W$ is the invariant transition amplitude for Compton
scattering of a photon of 4-momentum $k^{\mu}$
by an electron (of charge $e$ and mass $m$) with
4-momentum $p^{\mu}$, to a photon momentum $k^{\prime\mu}$ and an
electron momentum $p^{\prime\mu}$~\cite{ber-quan}:
\begin{eqnarray}
W &=& \frac{(e^{2}/4\pi)^{2} \bar{X}}{2\omega\omega' E E'}
\delta^{4}(p+k-p'-k') \label{sz_eq_2} \\
\bar{X} &\equiv& 4m^{4} \left(\frac{1}{\kappa} + \frac{1}{\kappa'}\right)^{2} -
4m^{2} \left(\frac{1}{\kappa} + \frac{1}{\kappa'}\right) -
\left(\frac{\kappa}{\kappa'} + \frac{\kappa'}{\kappa}\right),\label{sz_eq_2b}
\end{eqnarray}
with $\kappa \equiv -2p^{\mu}k_{\mu}$ and $\kappa'\equiv
2p^{\mu}k^{\prime}_{\mu}$. In equation~\eqref{sz_eq_1},
we have assumed that electron
degeneracy effects may be ignored.

The electrons are described by a relativistic Fermi distribution. Since we
are ignoring degeneracy effects, we have
\begin{equation}
f(E)\approx \et{-(E-\mu)/k_{B}T_{e}}.
\end{equation}
Substituting this form for $f(E)$ into equation~\eqref{sz_eq_1},
and expanding the
term in brackets in the integrand in powers of $\Delta x$, where
\begin{eqnarray}
x & \equiv & \frac{\omega}{k_{B}T_{e}} \\
\Delta x &\equiv & \frac{\omega'-\omega}{k_{B}T_{e}},
\end{eqnarray}
gives a Fokker-Planck expansion
\begin{eqnarray}
\lefteqn{\frac{\partial n(x)}{\partial t} = 2
\left(\frac{\partial n}{\partial x} + n(1+n)\right) I_{1}
+ 2 \left(\frac{\partial^{2}n}{\partial x^{2}} +
2(1+n)\frac{\partial n}{\partial x} + n(1+n) \right) I_{2} }
\nonumber \\
& & \hspace{1.6cm} \mbox{} + 2\left(\frac{\partial^{3}n}{\partial x^{3}}+3(1+n)
\frac{\partial^{2}n}{\partial x^{2}} + 3 (1+n)
\frac{\partial n}{\partial x} + n(1+n) \right) I_{3}
\nonumber \\
& & \hspace{-1.5cm} \mbox{} + 2\left(\frac{\partial^{4} n}
{\partial x^{4}} + 4(1+n)
\frac{\partial^{3} n}{\partial x^{3}} + 6(1+n)
\frac{\partial^{2} n}{\partial x^{2}} + 4(1+n)
\frac{\partial n}{\partial x} + n(1+n) \right) I_{4} + \cdots,
\label{sz_eq_3}
\end{eqnarray}
where
\begin{equation}
I_{n} \equiv
\frac{1}{n!}\int \frac{d^{\,3} p}{(2\pi)^{3}} d^{\,3} p' d^{\,3} k' \,W f(E)
(\Delta x)^{n},
\label{sz_eq_4}
\end{equation}
which does not depend on $n(\omega)$.

The calculation of the $I_{n}$ may be performed by
expanding the integrand in powers of $p/m$ and $\omega/m$. The factor
$f(E)$ is handled by the expansion
\begin{equation}
f(E) \approx \et{(\mu-m)/k_{B}T_{e}} \et{-u}
\Bigl(1+\case{1}{2} \theta_{\!e} u^{2} + \tfrac{1}{8}\theta_{\!e}^{2}u^{3}(u-4) + \cdots\Bigr),
\label{sz_eq_8}
\end{equation}
where
\begin{eqnarray}
u &\equiv& \frac{p^{2}}{2mk_{B}T_{e}} \\
\theta_{\!e} &\equiv& \frac{k_{B}T_{e}}{m},
\label{sz_eq_9}
\end{eqnarray}
and the chemical potential $\mu$ may be eliminated by introducing the
electron number density $N_{e}$, which evaluates to
\begin{equation}
N_{e} = \frac{m\sqrt{2m}}{\pi^{2}} \Gamma(3/2)
(k_{B}T_{e})^{\mbox{\scriptsize $\frac{3}{2}$}} \et{(\mu-m)/k_{B}T_{e}}
\left(1 + \frac{15}{8} \theta_{\!e} + \frac{105}{128} \theta_{\!e}^{2} + \mbox{O}(\theta_{\!e}^{3})
\right).
\label{sz_eq_10}
\end{equation}
Note that equation~\eqref{sz_eq_10} is an asymptotic expansion about $\theta_{\!e}=0$
of the result
\begin{equation}
N_{e} = \frac{m^{3}}{\pi^{2}} \theta_{\!e} K_{2} (1/\theta_{\!e}) \et{\mu/k_{B}T_{e}},
\end{equation}
where $K_{2}(x)$ is a modified Bessel function, which suggests that our
series expansions of the $I_{n}$ will only be asymptotic series.
The calculations of the $I_{n}$ are ideally suited to symbolic computer
algebra packages (we use Maple).
Expressing the results in terms of $\theta_{\!e}$, $x$, and the Thomson
cross section $\sigma_{T}$, we find
\begin{eqnarray}
I_{1} & = & \case{1}{2} \sigma_{T} N_{e} \theta_{\!e} x \left( (4-x) +
\theta_{\!e}(10 - \tfrac{47}{2}
x + \tfrac{21}{5}x^{2} ) \right) + \mbox{O}(\theta_{\!e}^{3})
\nonumber \\
I_{2} & = & \case{1}{2} \sigma_{T} N_{e} \theta_{\!e} x^{2} \left(1 + \theta_{\!e}(\tfrac{47}{2}
-\tfrac{63}{5} x + \tfrac{7}{10} x^{2} ) \right) + \mbox{O}(\theta_{\!e}^{3})
\nonumber \\
I_{3} & = & \case{1}{2} \sigma_{T} N_{e} \theta_{\!e} x^{3} \left(\tfrac{7}{5}(6-x) \theta_{\!e}
\right) + \mbox{O}(\theta_{\!e}^{3}) \nonumber \\
I_{4} & = &\case{1}{2} \sigma_{T} N_{e} \theta_{\!e} x^{4} (7\theta_{\!e} ) + \mbox{O}(\theta_{\!e}^{3}).
\label{sz_eq_is}
\end{eqnarray}
For $n>4$, $I_{n}$ is third-order or higher in $\theta_{\!e}$.
For CMB photons passing through a cluster at
redshift $z$, we have $\bar{x}\simeq 6.2\times 10^{-4}(1+z)/k_{B}T_{e}$,
where $\bar{x}$ is the average of $x$ over a Planck distribution and
$k_{B}T_{e}$ expressed in $\mbox{\rm \,eV}$. The electron temperature is typically
$\lesssim 10\mbox{\rm \,keV}$, so that $x\ll 1$.

Substituting these expansions for the $I_{n}$ into the
series~\eqref{sz_eq_3}, we develop an expansion of $\partial n/\partial t$
in $\theta_{\!e}$. In this paper, we shall only be
concerned with the lowest order relativistic corrections, and start by
retaining all terms up to $\mbox{O}(\theta_{\!e}^{2})$. To include all such terms
consistently, it is necessary to retain only the first four terms in the
series~\eqref{sz_eq_3}. A lengthy calculation gives the result
\begin{equation}
\frac{\partial n(x)}{\partial t} = \sigma_{T} N_{e}\theta_{\!e}
\frac{1}{x^{2}}\frac{\partial}
{\partial x} \left(x^{2} j(x)\right),
\label{sz_eq_phcons}
\end{equation}
where the current $j(x)$ is given by
\begin{eqnarray}
j(x) & = & x^2\Biggl[\left(\frac{\partial n}{\partial x} +
n(1+n)\right)
+ \theta_{\!e} \Biggl[ \frac{5}{2} \left(\frac{\partial n}{\partial x} + n(1+n)
\right) + \frac{21}{5} x \frac{\partial}{\partial x}\left(\frac{\partial n}
{\partial x} + n(1+n)\right)  \nonumber \\
& & \mbox{} + \frac{7}{10} x^2
\left( \frac{\partial^{3} n}{\partial x^{3}} +
2\frac{\partial^{2} n}{\partial x^{2}}(1+2n) + \frac{\partial n}{\partial x}
\left(1-2\frac{\partial n}{\partial x}\right)
\right) \Biggr]+ \mbox{O}(\theta_{\!e}^{2}) \Biggr].
\label{sz_eq_cur}
\end{eqnarray}
The zero-order term in equation~\eqref{sz_eq_cur} is just that term
which usually
appears in the Kompaneets equation~\cite{komp57}. The $\mbox{O}(\theta_{\!e})$ term is
the lowest-order relativistic correction to the current. The form
of equation~\eqref{sz_eq_phcons} ensures conservation of the total
number of photons, which is true for each order in $\theta_{\!e}$. A similar
expression has been derived independently by Stebbins (1997) using
non-covariant methods, although he only considers the lowest-order terms
in $\omega/m$.

This derivation makes it clear that trying to include relativistic terms
in the framework of the usual Kompaneets equation~\cite{komp57},
although it would seem natural to retain only terms in $I_{1}$ and $I_{2}$,
would be incorrect, since it would
not obey photon conservation. To be specific, if only $I_{1}$ and $I_{2}$ are
retained, then photon conservation requires that the current be given by
\begin{equation}
j(x) = 2 \frac{I_{2}}{\sigma_{T}N_{e}\theta_{\!e}}
\left(\frac{\partial n}{\partial x} + n(1+n)\right),
\end{equation}
and consistency with the expansion of the Boltzmann equation~\eqref{sz_eq_3}
requires that
\begin{equation}
I_{1} = \frac{\partial I_{2}}{\partial x} + 2\frac{I_{2}}{x} - I_{2}.
\label{sz_eq_cons}
\end{equation}
Calculating $I_{2}$ to $\mbox{O}(\theta_{\!e}^{2})$ in the limit of
small $x$, gives the current $j'(x)$ (in the limit of small $x$) where
\begin{equation}
j'(x) = x^2 \left(\frac{\partial n}{\partial x} + n(1+n) \right) \left(
1 + \frac{47}{2} \theta_{\!e} \right),
\label{sz_eq_wrong}
\end{equation}
which amounts to a relativistic correction to the cross section appearing
in the usual Kompaneets equation. This result is incorrect, since the
approach is not self-consistent to the order that the answer is quoted.
To see this, one need only calculate $I_{1}$ using equation~\eqref{sz_eq_cons}
and the expression for $I_{2}$ from equation~\eqref{sz_eq_is}. The expression
for $I_{1}$ obtained by this procedure only agrees with the direct
calculation equation~\eqref{sz_eq_is} to $\mbox{O}(\theta_{\!e})$,
not to $\mbox{O}(\theta_{\!e}^{2})$.
One obtains a better approximation to the true
current (eq.~\eqref{sz_eq_cur}) by calculating $I_{1}$ directly and then
using equation~\eqref{sz_eq_cons} to calculate an effective value of
$I_{2}$, which may
then be used to deduce the current. This procedure reproduces the first term
in the $\mbox{O}(\theta_{\!e})$ correction in $j(x)$, in the limit of small $x$, and
is similar to that employed by Fabbri~(1981) in obtaining his
equation (11).
However, it is only the full expression equation~\eqref{sz_eq_cur} which is
consistent with the original Boltzmann equation~\eqref{sz_eq_1} to
$\mbox{O}(\theta_{\!e}^{2})$.

\section{Rate of Energy Transfer}

As a check on the consistency of equation~\eqref{sz_eq_cur} with
existing results
in the literature, we calculate the energy transfer rate between the
electrons and a Planck distribution of photons at temperature $T_{r}$.

Multiplying the continuity equation~\eqref{sz_eq_phcons} by $x^{3}$ and
integrating, we find
\begin{equation}
\frac{\partial}{\partial t} \int_{0}^{\infty} x^{3} n(x) \, dx =
- \sigma_{T} N_{e}\theta_{\!e} \int_{0}^{\infty} x^{2} j(x) \, dx.
\label{sz_eq_etrans_i}
\end{equation}
The left-hand side of equation~\eqref{sz_eq_etrans_i} is proportional to the
rate at which the
photons are gaining energy per unit volume, denoted $dE/dt$.
Substituting a Planck distribution for $n(\omega)$ in
equation~\eqref{sz_eq_cur} and integrating gives the result
\begin{equation}
\frac{dE_{r}}{dt} = 4E_{r}N_{e} \sigma_{T} (\theta_{\!e}-\theta_{\!r})
\left(1+ \frac{5}{2} \theta_{\!e} - 21\frac{\zeta(6)}{\zeta(4)} \theta_{\!r} +
\mbox{O}(\theta^{2}) \right),
\label{sz_eq_etrans}
\end{equation}
where
\begin{equation}
\theta_{\!r} \equiv \frac{k_{B}T_{r}}{m},
\end{equation}
and $\zeta(x)$ is the Riemann Zeta function.

This result may be compared with a direct evaluation of the energy transfer,
obtained by multiplying the transition rate $W$ by the
energy transfer $\omega'-\omega$, and integrating over all collisions:
\begin{equation}
\frac{dE_{r}}{dt} = 4 \int \frac{d^{\,3} k}{(2\pi)^{3}} \frac{d^{\,3} k'}
{(2\pi)^{3}}
d^{\,3} p\, d^{\,3} p' \, W f(E) n(\omega)[1+ n(\omega')] (\omega'-\omega).
\label{sz_eq_17}
\end{equation}
The integral may be evaluated by a consistent expansion of the integrand.
A lengthy calculation gives the result~\eqref{sz_eq_etrans}, which also
agrees with the non-covariant calculation of Woodward~(1970) (who
gives higher-order corrections also). Note that if we had considered only
$I_{1}$ and $I_{2}$, then using $j'(x)$ given by equation~\eqref{sz_eq_wrong},
we would have obtained (in the limit of small $\theta_{\!r}$)
\begin{equation}
\frac{dE_{r}}{dt} = 4E_{r}N_{e}\sigma_{T} (\theta_{\!e}-\theta_{\!r})\left(
1 + \frac{47}{2}\theta_{\!e} + \mbox{O}(\theta_{\!e}^{2}) \right),
\end{equation}
which grossly overestimates the importance of the relativistic corrections.

\section{The Sunyaev-Zel'dovich Effect}
\label{sz_sec_sun_zel}

In this section we apply the generalised Kompaneets equation (to
first-order in relativistic corrections) to the
calculation of the Sunyaev-Zel'dovich effect in optically thin clusters.
We consider higher-order effects in the next section.

Following the standard assumptions, we assume that the optical depth
is sufficiently small that the spectral distortions are small. In this limit,
we may solve equation~\eqref{sz_eq_phcons} iteratively.
The lowest order solution is obtained by substituting the initial photon
distribution $n_{0}(x)$ into the current (eq.~\eqref{sz_eq_cur}).
The integral over time is then trivial, and
may be replaced by an integral along the line of sight through the cluster,
giving
\begin{equation}
\Delta n(x) = \frac{y}{x^{2}} \frac{\partial}{\partial x} \left(x^{2} j(x)
\right),
\label{sz_eq_z1}
\end{equation}
where $j(x)$ is evaluated with $n_{0}(x)$, and
\begin{equation}
y \equiv \sigma_{T} \int N_{e} \theta_{\!e} \, dl,
\label{sz_eq_z2}
\end{equation}
where the integral is taken along the line of sight through the cluster.

For the CMB we take the initial (undistorted) photon distribution to be
Planckian with temperature $T_{0}$:
\begin{equation}
n_{0}(x) = \frac{1}{\et{\alpha x} - 1},
\label{sz_eq_z3}
\end{equation}
where $\alpha \equiv T_{e}/T_{0}$ is the (large) ratio of electron temperature
to the CMB temperature. Evaluating equation~\eqref{sz_eq_z1} in the limit of
large $\alpha$, we find the following fractional distortion:
\begin{eqnarray}
\frac{\Delta n(X)}{n(X)} & = & \frac{yX\et{X}}{\et{X}-1} \Biggl[
X\coth(\case{1}{2} X) - 4 + \theta_{\!e} \Bigl[
-10 + \frac{47}{2} X \coth(\case{1}{2} X) - \frac{42}{5} X^2 \coth^{2}(\case{1}{2} X)
\nonumber
\\
&& \mbox{} + \frac{7}{10} X^3 \coth^{3}(\case{1}{2} X) +
 \frac{7X^{2}}{5\sinh^{2}(\case{1}{2} X)}
\left(X \coth(\case{1}{2} X) - 3\right) \Bigr] \Biggr],
\label{sz_eq_z4}
\end{eqnarray}
correct to first-order in relativistic effects, where
\begin{equation}
X \equiv \frac{\hbar\omega}{k_{B} T_{0}}.
\end{equation}
The first two terms in square brackets in equation~\eqref{sz_eq_z4} give the
usual non-relativistic Sunyaev-Zel'dovich expression, while the terms
proportional to $\theta_{\!e}$ are the lowest order relativistic correction.
Equation~\eqref{sz_eq_z4} agrees with the result in Stebbins (1997).
In the Rayleigh-Jeans limit (small $X$), we find
\begin{equation}
\frac{\Delta n(X)}{n(X)} \simeq -2 y
\left(1- \frac{17}{10} \theta_{\!e} + \mbox{O}(\theta_{\!e}^{2})\right).
\end{equation}

\begin{figure}[t!]
\begin{center}
\begin{picture}(340,210)

\put(-5,235){\hbox{\epsfig{figure=adc_sz_fig1.ps,angle=-90,width=12cm}}}
\put(165,73){\makebox(0,0)[t]{\normalsize $X$}}
\put(24,125){\makebox(0,0)[r]{\normalsize $\theta_{\!e}\Delta I/y$}}
\put(160,108){\makebox(0,0)[t]{\small $5$}}
\put(160,138){\makebox(0,0)[t]{\small $10$}}
\put(211,175){\makebox(0,0)[t]{\small $15$}}
\end{picture}
\end{center}
\caption{\sl{The intensity change $\theta_{\!e}\Delta I/y$
(in units of $2(k_{B}T_{0})^{3}
/(hc)^{2}$) plotted against $X$ for three values
of $k_{B}T_{e}$ (in $\mbox{\rm \,keV}$).
The solid curves are calculated using the first-order
correction to the Kompaneets equation, while the dashed lines are
calculated from the usual Kompaneets expression.}}
\label{sz_fig_1}
\end{figure}

In Figure~\ref{sz_fig_1} we plot the change in spectral intensity
$\theta_{\!e}\Delta I/y$ as a function of $X$, where
\begin{equation}
\Delta I = \frac{X^{3}}{\et{X}-1} \frac{\Delta n}{n}.
\end{equation}
Also plotted in Figure~\ref{sz_fig_1} are the non-relativistic predictions
made with the standard Kompaneets equation.
The curves in Figure~\ref{sz_fig_1} are for $k_{B}T_{e} = 5$, $10$, and
$15\mbox{\rm \,keV}$, which are the same as the parameters used
by Rephaeli~(1995) in his Figure 1. His calculations, which
were based on the multiple scattering formalism~\cite{wright79}
and required a numerical analysis, give results in excellent agreement
with ours, which only require the use of the simple expression~\eqref{sz_eq_4}.
This suggests that there is no problem in principle with applying the Boltzmann
equation to the problem of Comptonization in clusters even though the
optical depth may be very small. Similar conclusions were reached by
Fabbri~(1981), but his demonstration was restricted to low
temperature clusters where relativistic effects are not important.

It is clear from Figure~\ref{sz_fig_1} that for $X \lesssim 8$, the relativistic
corrections lead to a reduction in the magnitude of the intensity change,
compared to the non-relativistic prediction. This in turn leads to
a reduction in the inferred value of the Hubble constant determined by the
Sunyaev-Zel'dovich route.

\begin{figure}[t!]
\begin{center}
\begin{picture}(340,210)

\put(-5,235){\hbox{\epsfig{figure=adc_sz_fig2.ps,angle=-90,width=12cm}}}
\put(271,184){\makebox(0,0)[b]{\normalsize $X$}}
\put(24,105){\makebox(0,0)[r]{\normalsize $\Delta T_{\mbox{\scriptsize RJ}}/T_{0
}$}}
\put(65,145){\makebox(0,0)[r]{\small $5$}}
\put(65,112){\makebox(0,0)[r]{\small $10$}}
\put(68,50){\makebox(0,0)[l]{\small $15$}}

\end{picture}
\end{center}
\caption{\sl{The fractional change $\Delta T_{\mbox{\scriptsize RJ}} / T_{0}$
in the Rayleigh-Jeans brightness temperature plotted against $X$ for three
values of $k_{B}T_{e}$ (in $\mbox{\rm \,keV}$). The solid curves are
calculated using the first-order
correction to the Kompaneets equation, while the dashed lines are
calculated from the usual Kompaneets expression.}}
\label{sz_fig_2}
\end{figure}

In Figure~\ref{sz_fig_2} we plot the fractional change in the Rayleigh-Jeans
brightness temperature $\Delta T_{\mbox{\scriptsize RJ}}/T_{0}$ (divided
by $y/\theta_{\!e}$), where
\begin{equation}
\frac{\Delta T_{\mbox{\scriptsize RJ}}}{T_{0}} = \frac{X}{\et{X}-1}
\frac{\Delta n}{n},
\end{equation}
for the same $\theta_{\!e}$ as in Figure~\ref{sz_fig_1}. The
relativistic corrections to the change in the Rayleigh-Jeans brightness
temperature are significant even at low frequency, unlike the corrections
to the intensity, where relativistic corrections are small in the
Rayleigh-Jeans part of the spectrum.

\section{Higher-order Effects}

We have found that for $k_{B}T_{e} \gtrsim 10 \mbox{\rm \,keV}$ the second-order
relativistic effects make a significant contribution to the
spectral distortion, while third-order effects are only significant for
$k_{B}T_{e} \gtrsim 15 \mbox{\rm \,keV}$.

These calculations require a straightforward extension of the method
of Section~\ref{sz_sec_komp} to include terms at $\mbox{O}(\theta_{\!e}^{3})$ (for
second-order relativistic effects). For the calculation to $\mbox{O}(\theta_{\!e}^{3})$,
it is necessary to retain the first six
terms of the series~\eqref{sz_eq_3}, and to calculate $I_{1}$ through $I_{6}$
to $\mbox{O}(\theta_{\!e}^{3})$. The first iteration
of equation~\eqref{sz_eq_phcons} for $T_{e} \gg T_{0}$
gives the following next order (in $\theta_{\!e}$) correction to $\Delta n/n$:
\begin{eqnarray}
\left(\frac{\Delta n(X)}{n(X)}\right)^{\!(2)} &=&
\theta_{\!e}^{2} \frac{yX\et{X}}{\et{X}-1} \Bigl[-\frac{15}{2} + \frac{1023}{8}
X\coth(\case{1}{2} X) - \frac{868}{5} X^{2} \coth^{2}(\case{1}{2} X)
\nonumber
\\
&& \mbox{} \hspace{-1.5cm} + \frac{329}{5}
X^{3}\coth^{3}(\case{1}{2} X) - \frac{44}{5} X^{4} \coth^{4}(\case{1}{2} X) +
\frac{11}{30} X^{5} \coth^{5}(\case{1}{2} X)
\nonumber \\
&& \hspace{-3.5cm}\mbox{} + \frac{X^{2}}{30 \sinh^{2}(\case{1}{2} X)}
\left( -2604 + 3948 X\coth(\case{1}{2} X)
- 1452 X^{2} \coth^{2}(\case{1}{2} X) + 143
X^{3} \coth^{3}(\case{1}{2} X) \right)
\nonumber\\
&& \mbox{} \hspace{2.3cm} + \frac{X^{4}}{60\sinh^{4}(\case{1}{2} X)}
\left( -528 + 187 X\coth(\case{1}{2} X) \right) \Bigr].
\label{sz_eq_s_1}
\end{eqnarray}
In the Rayleigh-Jeans limit, we find
\begin{equation}
\frac{\Delta n(X)}{n(X)} \simeq -2y \left( 1- \frac{17}{10} \theta_{\!e} +
\frac{123}{40} \theta_{\!e}^{2} + \mbox{O}(\theta_{\!e}^{3}) \right).
\label{sz_eq_s_2}
\end{equation}

\begin{figure}[t!]
\begin{center}
\begin{picture}(340,210)

\put(-5,235){\hbox{\epsfig{figure=adc_sz_fig3.ps,angle=-90,width=12cm}}}
\put(168,80){\makebox(0,0)[t]{\normalsize $X$}}
\put(24,135){\makebox(0,0)[r]{\normalsize $\theta_{\!e}\Delta I/y$}}
\put(160,119){\makebox(0,0)[t]{\small $5$}}
\put(160,150){\makebox(0,0)[t]{\small $10$}}
\put(160,180){\makebox(0,0)[t]{\small $15$}}

\end{picture}
\end{center}
\caption{\sl{The intensity change $\theta_{\!e}\Delta I/y$
(in units of $2(k_{B}T_{0})^{3}
/(hc)^{2}$) plotted against $X$ for three values
of $k_{B}T_{e}$ (in $\mbox{\rm \,keV}$).
The solid curves are calculated using the second-order
correction to the Kompaneets equation, while the dashed lines are
calculated from the first-order correction. The points are the results
of a Monte-Carlo evaluation of the Boltzmann collision integral.}}
\label{sz_fig_3}
\end{figure}

In Figure~\ref{sz_fig_3} we compare the spectrum of $\Delta I$ calculated
with equation~\eqref{sz_eq_z4} to the spectrum with the
correction~\eqref{sz_eq_s_1} included, for $k_{B}T_{e} = 5$, $10$ and
$15\mbox{\rm \,keV}$ ($\theta_{\!e} \approx 0.01$,
$0.02$ and $0.03$ respectively). In each case, the
second-order relativistic effects are not significant in the Rayleigh-Jeans
part of the spectrum. This is to be expected from inspection
of equation~\eqref{sz_eq_s_2}, where the $\theta_{\!e}^{2}$ term is
clearly insignificant for the values of $\theta_{\!e}$ considered.
For $k_{B}T_{e}=5\mbox{\rm \,keV}$, the second-order effects are
insignificant over the entire spectrum. However, for $k_{B}T_{e} \gtrsim
10\mbox{\rm \,keV}$, the second-order effects make a significant contribution to
the relativistic correction to the Kompaneets based prediction outside the
Rayleigh-Jeans region. We have verified that the
third-order corrections are negligible over the entire spectrum for
$k_{B}T_{e} \simeq 10\mbox{\rm \,keV}$.
This is confirmed by a comparison of the curves in Figure~\ref{sz_fig_3}
with the points which are the results of a direct Monte-Carlo
evaluation of the Boltzmann collision integral with $n(\omega)$
given by the Planck distribution $n_{0}(x)$~\cite{gull97}. The
second-order effects should be included in the analysis of high frequency data
for hot clusters. The magnitude of the second-order
correction to the Sunyaev-Zel'dovich result for the rather mild
values of $\theta_{\!e}$ considered here, is symptomatic of the asymptotic nature of
the series expansion of $\partial n/\partial t$ in $\theta_{\!e}$.
However, for the majority of clusters
considered in Sunyaev-Zel'dovich analyses, the inclusion of the first
two relativistic corrections should be sufficient, particularly for
experiments working in the Rayleigh-Jeans region of the spectrum.

\subsection{The Crossover Frequency}

\begin{figure}[t!]
\begin{center}
\begin{picture}(340,210)

\put(-5,245){\hbox{\epsfig{figure=adc_sz_fig4.ps,angle=-90,width=12cm}}}
\put(163,10){\makebox(0,0)[t]{\normalsize $k_{B}T_{e}/\mbox{\rm \,keV}$}}
\put(28,130){\makebox(0,0)[r]{\normalsize $X_{0}$}}
\end{picture}
\end{center}
\caption{\sl{The crossover frequency $X_{0}$ plotted against $k_{B}T_{e}$.
The solid line is calculated with the inclusion of third-order corrections
to the Kompaneets equation. The upper dotted line is a linear fit to the solid
line with $X_{0}=3.83(1+1.13\theta_{\!e})$, while the lower dotted line is the
linear fit given in~\cite{reph95}: $X_{0} = 3.83(1+\theta_{\!e})$.}}
\label{sz_fig_4}
\end{figure}

The accurate determination of the crossover frequency $X_{0}$
(where the thermal component of the spectral distortion vanishes)
is essential for reliable
subtraction of the kinematic contribution to the Sunyaev-Zel'dovich
effect~\cite{reph95}.
In Figure~\ref{sz_fig_4} we plot the crossover frequency as a function of
$k_{B}T_{e}$, with the first three relativistic corrections included.
For $k_{B}T_{e} \lesssim 20\mbox{\rm \,keV}$ we find that $X_{0}$ is well approximated by
the linear relation
\begin{equation}
X_{0} \simeq 3.83(1+1.13\theta_{\!e}).
\label{sz_eq_s_3}
\end{equation}
For comparison, Rephaeli~(1995),
found $X_{0}$ to be approximated by $X_{0}\simeq 3.83(1+\theta_{\!e})$
in the interval $k_{B}T_{e} = 1 \mbox{--} 50\mbox{\rm \,keV}$, while Fabbri~(1981)
found $X_{0}\simeq 3.83(1+1.1\theta_{\!e})$ for $k_{B}T_{e} \lesssim 150\mbox{\rm \,keV}$.
It is clear that our calculation favours Fabbri's expression.
For $k_{B}T_{e} \gtrsim 20\mbox{\rm \,keV}$, $X_{0}$ calculated with the first three
relativistic corrections departs from the linear prediction~\eqref{sz_eq_s_3}.
However, we do not regard this as indicative of a breakdown of the linear
approximation, since it is clear from Figure~\ref{sz_fig_3}
that the inclusion of higher-order terms may have a significant effect on the
value of the crossover frequency.

\section{Conclusion}

We have shown how the Kompaneets equation may be generalised to include
relativistic effects in a self-consistent manner. The resulting equation
guarantees photon conservation at each order and is in agreement
with direct calculations
of the energy transfer rate between the plasma and a Planckian
distribution of photons.

We have applied this formalism to the calculation of the Sunyaev-Zel'dovich
effect in optically thin clusters. We presented simple analytic expressions
for the first two relativistic corrections to the usual Kompaneets based
expression for the spectral distortion, which are in excellent agreement
with the numerical calculations of Rephaeli~(1995) for electron
temperatures $\lesssim 10\mbox{\rm \,keV}$.
This provides further evidence that the
low optical depth of clusters does not forbid the application of the
Boltzmann equation to the calculation of the Sunyaev-Zel'dovich
effect~\cite{fabbri81}.
The asymptotic nature of the expansion of $\partial n/\partial t$ in $\theta_{\!e}$
requires the inclusion of higher-order corrections
to calculate the effect in hotter clusters in the Wien region of the spectrum.
While the calculation of higher-order corrections is not problematic,
the bad convergence properties of the series means that ultimately one must
resort to a numerical calculation of the
collision integral~\cite{corman70} (or employ the multiple scattering
formalism~\cite{wright79}) to calculate the effect in very hot clusters.

Our calculations support the conclusions reached in~\cite{reph97}, that
including relativistic effects leads to a small decrease in the value of the
Hubble constant, inferred from combined X-ray and Sunyaev-Zel'dovich
information. For a cluster temperature of $\simeq 8\mbox{\rm \,keV}$, the reduction in
$H_{0}$ due to relativistic effects is $\simeq 5$ percent for measurements made
in the Rayleigh-Jeans region.

\acknowledgements

We would like to express our gratitude to Drs N. Itoh, Y. Kohyama and
S. Nozawa, whose preprint~\cite{itoh97} stimulated this research, and to
Drs S. Gull and A. Garrett for allowing us to quote the (unpublished) results
of a Monte-Carlo simulation.

redpajama_set_name: RedPajamaArXiv


text:
linkgo.io
=========

The landing site of linkgo.io.
github profile: https://github.com/linkgo

License for Pure CSS
--------------------

This software is free to use under the Yahoo! Inc. BSD license.
See the [LICENSE file][] for license text and copyright information.

[LICENSE file]: https://github.com/yahoo/pure-site/blob/master/LICENSE.md

redpajama_set_name: RedPajamaGithub


text:
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text:
Les glaceres dels Pirineus són la resta de les masses de gel que cobrien la serralada durant l'era glacial. Són les glaceres més meridionals d'Europa i, tot i que es troben distribuïdes pels dos vessants pirinencs, són més grans al vessant sud. Totes són glaceres de muntanya en la seva última fase. Només es conserven els circs glaceres i, en alguns casos, petites llengües que no descendeixen fins a la vall.

Queden 19 glaceres als Pirineus, de les quals només 10 poden ser considerades glaceres pròpiament dites, ja que 9 d'aquestes són geleres, és a dir, masses de gel permanent de certa grandària però sense moviment propi, que és la característica definitòria d'un glacera.

Foren cartografiades per primera vegada pel geògraf francès i alemany Franz Schrader, que va estudiar les glaceres pirinenques a la fi del  fent mesuraments de cada una d'elles. En aquell temps les glaceres de la serralada ocupaven 1.779 hectàrees. Avui ocupen unes 600 hectàrees en dos vessants.

Vessant sud
Tan sols la part central del vessant sud dels Pirineus compta amb glaceres. Es concentren a la capçalera de les valls de Tena, Ordesa i Benasc. L'orientació habitual d'aquestes glaceres és la nord i només es presenten a partir dels 2.700 metres d'altitud, generalment envoltades per circs rocosos de més de 3.000 metres. Les glaceres i geleres del vessant sud amb una superfície de més d'1 hectàrea (10.000 metres quadrats) són:

Massís del Besiberri
 Glacera del Besiberri - 6 ha (2008)

Vall de Benasc
 Glacera d'Aneto - 85 ha (2007)
 Glacera de la Maladeta - 33 ha (2007)
 Glacera de Barrancs - 8 ha (2007)
 Glacera de Corones - 1,3 ha (2007)
 Glacera de Tempestats - 10 ha (2007)
 Glacera d'Alba - 3 ha (1990)
 Glacera de Salenques - 1,2 ha (1990)

Massís de Posets
 Glacera de Posets - 2 ha (2007)
 Glacera de Llardana - 9 ha (2007)
 Glacera de la Paul - 6 ha (2007)

Massís de Perdiguero
 Glacera de Literola - 1,5 ha

Massís del Mont Perdut-Gabarnie
 Glacera del Mont Perdut - 32 ha
 Glacera del Cilindro - 6 ha

Massís de Vinyamala
 Glacera del Clot de la Hount - 2 ha
 Glacera de Labaza - 9 ha

Massís dels Pics de l'Inferno

 Glacera de l'Inferno - 6 ha (2004)
 Glacera de Frondellas - 7 ha (1991)
 Glacera de la Brecha Latour - 4 ha (1996)

Massís de la Munia
 Glacera de Robiñera - 5 ha (1990)

Vessant nord
Al igual que al vessant sud, al vessant nord de la serralada les glaceres es concentren a l'àrea central de la carena muntanyosa. Apareixen a partir dels 2.800 metres d'altitud. En aquest vessant hi ha l'única glacera pròpiament dita de tots els Pirineus, la glacera d'Ossoue, a la cara nord del Massís de Vinyamala. Les glaceres i geleres del vessant nord amb una superfície de més d'una hectàrea són:

Massís de Vinyama
 Glacera d'Ossoue - 46 ha (2007)
 Glacera de Las Néous - 8 ha (2007)
 Glacera d'Oulettes - 13,5 ha (2007)
 Glacera del Petit Vignemale 3,5 ha (2007)

Massís de Mont Perdut-Gavarnie
 Glacera de Gabiétous - 8 ha (2007)
 Glacera de Taillon - 12 ha (2007)
 Glacera de Pailla - 8,5 ha (2007)

Massís de La Munia
 Glacera de Munia - 4 ha (2007)
 Glacera de Barroude - 5 ha (2001)

Massís del Perdiguero
 Glacera de Gourgs Blancs - 2,5 ha (2006)
 Glacera de la Baque - 13,5 ha (2007)
 Glacera del Portillon d'Oô - 4 ha (2007)
 Glacera de Boum - 7 ha (2007)

Mont Valier
 Glacera de Mont Valier - 1,5 ha (2004)

Estat actual
Totes les glaceres del Pirineu es troben en recessió des de fa dos segles. Es calcula que el 1830 la superfície glacial dels dos vessants del Pirineu era d'unes 2.000 hectàrees (20 quilòmetres quadrats) i avui s'ha quedat reduïda a una quarta part. Les causes per les quals les glaceres pirinenques s'estan fonent es deuen fonamentalment a l'escalfament progressiu de la superfície de la Terra des del final de la Petita Edat de Gel. En les últimes dècades la velocitat de fusió ha augmentat i es preveu que l'any 2070 no quedin glaceres als Pirineus. Amb la desaparició d'aquestes glaceres es donaria per consumada la desglaciació a la península Ibèrica una vegada fosos els casquets de la Serralada Cantàbrica, el Sistema Central i Sierra Nevada en els segles precedents.

A causa del seu estat terminal les glaceres pirinenques són objecte d'especial atenció per part de les autoritats espanyoles i franceses. A Espanya van ser declarats el 1990 Monuments Naturals per les Corts de la Comunitat Autònoma d'Aragó. L'àrea protegida en el vessant espanyol és de 2.411 hectàrees que abasten la massa gelada de la glacera i les morrenes llaurades per aquests glaceres en temps passats.

Referències

redpajama_set_name: RedPajamaWikipedia


There are various types of Trusts which can be set up, each with their own benefits.
Fixed Trust – In this type of Trust the beneficiaries are named and the exact proportions of how much each will get is clearly stated.
Discretionary Trust – In this type of Trust the beneficiaries are named, but the Trustees are given the power to decide to whom and how much to give.
Interest in Possession Trust – In this type of Trust the beneficiary can use the asset whilst they are alive, however it is then passed onto another beneficiary when the 1st dies.
Protective Trust – In this type of Trust the beneficiary is simply paid the interest and income from the asset whilst the capital remains protected.
When appointing trustees to run your family trust it is important to make sure that you choose people who you feel will be able to conduct the affairs of the Trust properly and who will follow your wishes and perhaps equally importantly, people you can hold accountable if necessary, such as professionals who are insured and who are expected to meet high standards of competence.
A maximum of 4 trustees can be appointed, and whilst you may choose to only have 1, it is best practice to have at least 2 so that they can check on each others work.
Trustees can be a friend, relative or professional, however they cannot be a minor, or someone of unsound mind. Whilst professionals may charge for their services, it can be beneficial to have one on board, especially if you and the other Trustees do not have the financial or organisational skills required.
However, in some instances where an individual has very substantial assets or a firm view on ensuring assets are invested properly or for other personal reasons, a discretionary trust may be set up in a will or such trusts can also be established outside of a will and without wills and estate planning being the motivating factors.
to protect beneficiaries from creditors – with a discretionary trust no individual beneficiary has a set right to a specified proportion of trust assets so if a beneficiary becomes insolvent, the trust assets can be protected from a claim by the trustee in bankruptcy.
to ensure that trust assets are retained for beneficiaries who are children, or until adults reach specified ages, or specified events occur. In short to safeguard future generations.
enabling a high degree of flexibility to react to different events, needs and situations.
a means to lessen liability to pay Inheritance Tax.
As with any trust, as a matter of technicality, this will mean legal transfer of ownership to the trustees, so it's vital that the appointed trustee(s) are the right people to comply with your wishes.
A discretionary trust gives the appointed trustee (the person in charge of the trust) the power to decide how to use any income that is produced by the trust. Sometimes the powers in a discretionary trust stretch to allow the trustee to use the fund monies themselves, but generally speaking, their powers are limited to use of the income of the trust.
The trustees of a discretionary trust may, for example, be granted the power to decide how much income or capital is paid out, when it is to be paid and to who and when it should be paid and they have this flexible power over all the assets in the trust, be it property, shares or money.
By creating a Trust in your lifetime, you may be saving your loved ones from having to go through the legal procedures of Probate when you die. However, this would depend on what other assets you had at the date of your death.
If you need a solicitor for setting up a family trust, drafting a trust deed, issues on administering a trust or legal issues or problems with trustees, please do get in contact with us.
An experienced and approachable lawyer, Michael advises on all aspects of family trusts including drafting trust deeds, administration of trusts, legal disputes arising on family trusts. Michael is based in our Edgware Office but advises clients in North London and London generally on family trusts.


text:
10 cars you'll probably never see again
Andrew Newton
2016 Amelia Island preview
Events like Amelia Island gather all kinds of classics that are beautiful, historically significant, fast and often all three. This of course applies not just to the concours but to the auctions as well, where many of the cars on offer are not only gorgeous and valuable but also extremely rare. Strolling the auction previews in Amelia Island is a unique experience, whether you're shopping or just dreaming, because there are cars on offer there that you might just never see again unless you're the winning bidder. This year is no exception, and there are 10 in particular that are definitely not the kind of thing to come up for sale every day.
1964 Sabra GT Coupe
Bonhams
Presale estimate: $80,000 – $100,000
When you think of great car-building nations, Israel probably doesn't immediately spring to mind. Yet, an Israeli company called Autocars did build cars for over twenty years, and called their little sports car the Sabra. Having nothing to do with the delicious hummus we know and love today, the word Sabra means cactus and is also slang for someone born in Israel. The UK's Reliant was actually responsible for much of the Sabra's design and construction, while the engine was a 1.7-liter four out of the Ford Consul. 379 were built during the 1960s, with 144 of them coming to the United States. Apparently, the Sabra was particularly popular in Belgium, where over 80 Sabras were sold, and the example offered by Bonhams originally belonged to the wife of the Belgian Israeli Consulate General.
1964 Peel P50
The Isle of Man is another place not normally associated with car manufacturing, but a Manx company called Peel Engineering was actually responsible for the world's smallest production automobile. Designed as a city car that could carry one person (and not much else), the Peel P50 had a 4.5-hp two-stroke engine and a top speed of 37, but it could get up to 100 mpg and you could park it pretty much anywhere. Despite the P50's appeal, particularly to European urbanites, microcars were falling out of fashion by the 1960s and just 50 were built. According to RM Sotheby's, only 26 are thought to still exist, although production of new built-to-order P50s started again in 2010.
Presale estimate: $350,000 – $425,000
People who know a thing or two about Porsche's early history might remember that they built diesel tractors, but a much more obscure vehicle is the ill-fated Type 597 Jagdwagen, which basically translates to "hunter's car". When the German military was seeking a capable light duty vehicle, Porsche threw their hat into the ring against Borgward and Auto Union for a contract. The four-wheel drive, amphibious Jagdwagen featured Porsche/VW suspension and a single carb, air-cooled flat-four that was basically a detuned 356 motor. It was a capable little thing that could climb a steep 60 percent grade, but the German government went with a simpler, cheaper design from DKW instead. Porsche sold a few dozen to the public and moved on. 71 were built and, according to Gooding & Company, only about 15 still exist today. The example on offer at Amelia Island is one of the 16 Jerry Seinfeld cars, and while it's certainly not the prettiest, most significant or fastest, it's still one of the most interesting and rare Porsches that will be auctioned this coming weekend.
1932 Ruxton Model C
Along with the Cord L-29, the Ruxton was America's first front-wheel drive production car. Ruxton was a featured class at Pebble Beach in 2014 and 16 of them were present on the lawn. At first glance, then, it might have seemed that Ruxtons aren't all that rare, but those were 16 of the approximately 19 Ruxtons surviving today and 96 total that were originally constructed. By comparison, Cord made over 4,000 L-29s. Front-wheel drive allowed the Ruxton to sit considerably lower than other cars of the period, and several examples (including this one) were given a "rainbow" paint scheme by Joseph Urban that made the car appear even lower and longer than it already was.
1973 Porsche 917/30
Presale estimate: $5,000,000 – $7,000,000
After they won overall at Le Mans in 1970 and 1971 with the 12-cylinder 917K, Porsche decided to campaign the car in North America's Can-Am championship. In order to make it competitive with the then-dominant McLarens, though, Porsche turbocharged the flat-12 and fitted spider bodywork. The resulting 917/10 dominated Can-Am in the 1972 season. For 1973, Porsche further tweaked the design with the 917/30, and in qualifying trim the 917/30 could make over 1,500 hp. With Mark Donohue at the wheel, Porsche again dominated in 1973 and at the time Donohue called it the perfect racecar. The one on offer in Amelia Island, one of six built, was sold new in Australia and never raced in anger, but it is nevertheless one of the top cars from the Seinfeld collection.
1937 Bugatti Type 57SC Sports Tourer by Vanden Plas
Presale estimate: N/A
Any Bugatti Type 57 is rare, but even rarer is a supercharged example with one-off coachwork, a car that can truly be considered unique. The Bugatti offered by Bonhams wears coachwork by Vanden Plas, an English coachbuilder that spawned from the Brussels-based firm Van den Plas. The 57SC was one of the fastest cars in the world in its day and made a full 200 hp from its blown eight-cylinder motor. This one is fully documented and has long been owned by sympathetic collectors. Such collectors tend to keep cars like this for a long time, so chances of seeing this car come up again any time soon aren't high.
1935 MG PA Airline Coupe by Carbodies
At first glance, this car might look like a T-Series with a roof stuck on it, but it's actually a prewar PA with an aerodynamic coupe body by Carbodies. Just over 50 MG Airline Coupes were built, mostly on PA and PB chassis. According to Bonhams, 28 of them were PAs like this one, and only about a dozen of those survive today. While it lacks the open, wind in your hair feeling of an MG roadster, this car does at least have a sunroof and it would be a star at any MG gathering.
1959 OSCA Tipo S-273
Officine Specializzate Costruzione Automobili (OSCA) was established in the postwar years by the Maserati brothers. They had sold their shares in Maserati, so they weren't allowed to start another company using their own name. OSCAs were highly competitive in the small displacement classes and sometimes overall wins during the 1950s, and the car offered by Gooding & Company was sold to the famed Cunningham race team. It was driven by Denise McCluggage at Sebring in 1960 but unfortunately retired with cooling issues. It was then sold again and enjoyed considerable regional success in the early 1960s. Exceedingly rare, the car has since been restored and is race-ready.
1935 Riley MPH
Riley is one of the oldest names in sports cars, with roots going back to 1896. They made some of the more memorable British cars of the 1930s, and one of the more notable of those was the MPH, of which just 16 were built with many of those raced to considerable success. The one offered by Bonhams was sold new in Switzerland and raced by its first owner, who kept it until he died in the 1940s. It stayed in the family's garage and it was actually bought in 1963 by a young Bob Lutz, who kept it for almost 50 years.
1962 Kurtis Aguila
Frank Kurtis is largely known for building Indy and dirt track cars, but there were Kurtises that won in road racing too, during the 1950s. By the early 1960s, however, Kurtis designs' best days were over and this car offered by RM Sotheby's was one of his last. The idea was to take an Indy car and convert it into a sports car for road racing, but also make the fenders easily removable so it could race in open wheel competition as well. Powered by a 327 cubic inch Chevy V-8 with triple Stromberg carburetors, the car showed promise and was featured in a 1963 issue of Road & Track, but it simply couldn't compete with the quicker mid-engined sports cars that were starting to arrive on the racing scene. Today, though, it makes a tempting vintage racer, especially since you can race it as an open wheel machine as well as a sports car.
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