text:
Talk:Politics of Trinidad and Tobago

Untitled
This page shouldn't list the US ambassador to T&T, and the T&T ambassador to the US. Wiki isn't a US source book but a world one. Nobody outside the US is likely to have any interest in US-T&T diplomatic links. If they are there, so should T&T ambassdors to other countries. If they aren't there, the US one shouldn't be in isolation. JTD 16:04 Feb 16, 2003 (UTC)

Diplomatic representation in the US: chief of mission: Ambassador Michael A. ARNEAUD chancery: 1708 Massachusetts Avenue NW, Washington, DC 20036 telephone: [1] (202) 467-6490 FAX: [1] (202) 785-3130 consulate(s) general: Miami and New York Diplomatic representation from the US: chief of mission: Ambassador Edward E. SHUMAKER, III embassy: 15 Queen's Park West, Port-of-Spain mailing address: P. O. Box 752, Port-of-Spain telephone: [1] (809) 622-6372 through 6376, 6176 FAX: [1] (809) 628-5462

Link to US diplomatic link removed as per reason above.

 * I don't get it. This looks like encyclopaedic information to me. Perhaps it should be in a different article. I've moved it to a new article, probably badly named and it obviously needs to be fleshed out with actual discussion of the diplomatic links and so on, but it can always be sorted out later. -- Oliver P. 16:18 Feb 16, 2003 (UTC)

 * user:-- April and I talke about that awhile back (a year ago? longer?) and decided it aggravated the U.S. bias on wikipedia, and since we couldn't balance it out with e.g. info on Diplomatic relations with Tunisia, it might be best to remove it unless the relationship with the U.S. is contentious.  Maybe not the best decision, but that was what we decided & why we decided it.  Maybe I can find the actual discussion somewhere.  Koyaanis Qatsi 16:21 Feb 16, 2003 (UTC)

 * The whole encyclopaedia is biased towards America anyway, what with all the Rambot city articles and so on, but I'm not complaining. I don't think we should remove information about one country just because there isn't a corresponding amount of information on other countries. People add what they know, and leave what they don't know to other people. That seems pretty sensible to me. This Wikipedia thing is continually growing, and eventually it'll all fill out nicely, I think. -- Oliver P. 16:34 Feb 16, 2003 (UTC)
 * That makes sense. we decided that before the rambot came through, so I guess it's kind of a Sysyphean task now to correct the bias, but still one I'd undertake if we decided to.  Koyaanis Qatsi

 * I'm all for correcting the bias. But by adding more stuff, not taking it away. :) Oh yes, and welcome back, by the way. :) -- Oliver P. 17:17 Feb 16, 2003 (UTC)

I could not disagree more. In this instance I believe it would be a fundamental mistake to leave the US stuff in.

 * 1) Who is the ambassador to which country is irrelevant to a piece on any country. Naming prime ministers, governments, etc makes sense, but knowing who is an ambassador is quite frankly useless information, not least because it changes so often, (as other info in this article is pre-2000, these names probably date from the Clinton administration and are out of date!) this information is only going to be of interest to 0.000001 of Wikipedia users. Even diplomats aren't going to need that information and if they do, they will look to government publications for that information. You won't find Enclopædia Brittanica or the World Book listing the British ambassador to Brazil, the French ambassador to Australia or the American Ambassador to Ireland. It isn't just space considerations, it is because they would see it as utterly irrelevant to an article on a country. About the only place it would be relevant is in an article on [United States Ambassadors] or [Ambassadors to the United States].

 * 1) Wikipedia is heavily biased in its information. Saying that can be corrected when at some stage in the future someone adds in non-US information is mis-informed. The more of a US bias there is, the less likely people are to correct it because they will see Wikipedia as in effect Americapedia, only of use to and read by Americans. I've just finished talking to a friend of mine on this very topic and he said he doesn't use Wikipedia because so many sites he consulted were so heavily American-orientated it seemed to him written by Americans for Americans. When he mentioned the sites and what they contained, I could understand his argument.

For example, we wouldn't accept an article on abortion that was exclusively pro-life or pro-choice, on the basis that someone from the other side at some undetermined time in the future might put in the alternative argument. We'd start from day one trying to create a balance, which either side can flesh out while maintaining that balance. Adding in consular information that is exclusively American is the same.

''Putting in largely irrelevant information such as this risks damaging Wikipedia by giving the impression that it is American-orientated (and thus only of interest to Americans), all through including information that in any case is probably out of date and irrelevant to almost anyone who might read this article. That makes no logical sense whatsoever. Either put in all the information on all consular offices to and from T&T (or at least a lot), or none. Or if you think this sort of technical minutæ is required, keep the American stuff separate on this page until you have other information on other diplomatic missions, so as to keep the balance and avoid needlessly re-inforcing the impression that Wikipedia is really only Ameripedia. Putting in only American stuff (especially when it is so irrelevant to the article) is too big a risk, in terms of the longterm damage it on its own can do to the whole project.'' JTD 17:58 Feb 16, 2003 (UTC)

 * Please don't shout at me... Look, I haven't put the US information back into this article: I've relocated it to Diplomatic representation of Trinidad and Tobago in the United States. Are you happy with that? The title makes it clear that it's a US-oriented article, and people not interested in the US don't have to look at it. I do think we should include lists of all the ambassadors ever, as it happens, as it would make a great reference source. I sort of started back in November last year, and made an ambassadors page, but that particular project is rather dormant at the moment. I'm going to put some more effort into it later, and see if we can build it up into a truly international list. I hope you won't object too much to it... -- Oliver P. 18:12 Feb 16, 2003 (UTC)

Shout??? Sorry, I wasn't, or didn't mean to. Apart from anything else I have too much respect for you to do that. If you thought I was doing that I unreservatively apologise. I was simply trying to highlight my opinion. As to the idea of an ambassadors page, an excellent idea! If can help I will. JTD 18:22 Feb 16, 2003 (UTC)

 * Ah, that's okay, then. Apology accepted. :) The word "respect" there might be going a bit far, though... ;) -- Oliver P. 18:25 Feb 16, 2003 (UTC)

I think that the info on USA representation was an artifact of the first version of the article (as was true of articles of many nations) being taken from the P.D. CIA World fact book site, which are sometimes usefull starter articles but which wikipedia really should go beyond. I agree it's inappropriate to only list USA diplomatic representation in other nations-- unless of course the USA diplomats play a major and unique role in the politics of the country. -- Infrogmation

 * I'm the one that pasted almost all of those country articles in originally; and if I had thought ahead I would have left out the U.S. diplomatic info to begin with. Anyway, yes, they are all originally from the CIA Factbook, and about 2/3 of them have been supplemented (also by me) with info from the U.S. Dept. of State site, which has its own bias which I should have more aggressively corrected.  Koyaanis Qatsi

no problem. Working on Wiki is a learning experience for all of us. :) JTD 18:40 Feb 16, 2003 (UTC)

Need for updates
A number of "time-related" statements need updating by someone who is familiar with the current situation:

>In recent months a new political presence has emerged...< : that "recent" was added in September 2006 (!)

>with recent time [...] elections [...] fast approaching on the 5th November, 2007..< : added in October 2007 (the elections in question have, presumably, approached and long gone past by now)

Other amendments need making to this section -- ("defunked" --> defunct, although "lapsed" or "former" would probably be better; possessive "it's" --> its) -- but the time-frame needs adjusting first. -- Picapica (talk) 16:17, 23 February 2008 (UTC)

Important notice
The government section of the "Outline of Trinidad and Tobago" needs to be checked, corrected, and completed -- especially the subsections for the government branches.

When the country outlines were created, temporary data (that matched most of the countries but not all) was used to speed up the process. Those countries for which the temporary data does not match must be replaced with the correct information.

Please check that this country's outline is not in error.

If you have any questions or comments, please contact The Transhumanist.

Thank you.

Question on this
So, I'm no expert and that's why I have to ask... What is former supposed to refer to in this line from the 4th paragraph: "Led by former Winston Dookeran, the majority?"--UESPArules (talk) 02:40, 22 November 2011 (UTC)

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title: Talk:Politics of Trinidad and Tobago


text:
Great Central Railway

The Great Central Railway in England was formed when the Manchester, Sheffield and Lincolnshire Railway changed its name in 1897, anticipating the opening in 1899 of its London Extension. On 1 January 1923, the company was grouped into the London and North Eastern Railway.

New name
On assuming its new title, the Great Central Railway had a main line from Manchester London Road Station via Penistone, Sheffield Victoria, Brigg and Grimsby to Cleethorpes. A second line left the line at Penistone and served Barnsley, Doncaster and Scunthorpe, before rejoining the Grimsby line at Barnetby. Other lines linked Sheffield to Barnsley (via Chapeltown) and Doncaster (via Rotherham) and also Lincoln and Wrawby Junction. Branch lines in north Lincolnshire ran to Barton-upon-Humber and New Holland and served ironstone quarries in the Scunthorpe area. In the Manchester area, lines ran to Stalybridge and Glossop.

In the 1890s, the MS&LR began constructing its Derbyshire lines, the first part of its push southwards. Leaving its east–west main line at Woodhouse Junction, some 5½ miles south-east of Sheffield, the line headed towards Nottingham, a golden opportunity to tap into colliery traffic in the north of the county before reaching the city. A loop line was built to serve its station in Chesterfield.

Coat of arms
The Great Central Railway was the first railway granted a coat of arms. It was granted on 25 February 1898 by the Garter, Clarenceux and Norroy Kings of Arms as: "Argent on a cross gules voided of the field between two wings in chief sable and as many daggers erect, in base of the second, in the fesse point a morion winged of the third, on a chief also of the second a pale of the first thereon eight arrows saltirewise banded also of the third, between on the dexter side three bendlets enhanced and on the sinister a fleur de lis or. And for the Crest on a Wreath of the Colours A representation of the front of a locomotive engine between two wings Or as the same are in the margin hereof more plainly depicted to be borne and used for ever hereafter by the said Corporation of the Great Central Railway Company on seals, shields, banners or otherwise according to the Laws of Arms." The design included elements representing Manchester (gules ... three bendlets enhanced ... or); Sheffield (eight arrows saltirewise banded); Lincoln (gules ... a fleur de lis or); Leicester (two wings); and London (Argent ... a cross gules ... daggers erect). Also represented was Mercury (a morion winged [sable]). It was used on locomotives and coaches.

The London and North Eastern Railway and the British Transport Commission, successors of the GCR, were granted arms of their own incorporating the GCR motto Forward.

The Great Central Railway (1976) Company Limited applied to the College of Arms as the successors to British Transport Commission (Loughborough to Birstall Light Railway) for permission to utilise the coat of arms of the GCR. A new design incorporating the same armorial components, updated in the modern style was proposed, but was rejected in favour of the original.

The "London extension"
The MS&LR obtained an act of Parliament, the Manchester, Sheffield and Lincolnshire Railway Act 1893 (56 & 57 Vict. c. lxxix), giving approval for its extension to London. On 1 August 1897, the railway's name was changed to Great Central Railway by the  (60 & 61 Vict. c. liv). Building work started in 1895, and the new line, 92 miles (147 km) in length, opened for coal traffic on 25 July 1898, for passenger traffic on 15 March 1899, and for goods traffic on 11 April 1899. It was designed for high-speed running throughout.

It is a commonly held myth that the nomenclature for the direction of travel on the new line was the opposite of standard UK railway practice, in that trains travelling to London were referred to as "down" trains, and those travelling away from the capital as "up" trains. It is supposed that it was a result of the GCR's headquarters at the time being in Manchester. The mileposts on the Great Central did start at zero at Manchester London Road and increase down the main line via Woodhead, Sheffield Victoria, Woodhouse, and then down the London Extension to Marylebone, 205 route miles from Manchester.

However, official documents dated 21 July 1898, detailing the method of working of mineral trains on the London Extension (used to help consolidate the new earthworks before passenger traffic began in March 1899), clearly show that the direction of travel on the new line was conventional – up to London, down to Annesley. Furthermore, contemporary descriptions in newspapers of the trains running on the new line are explicit that up trains ran to London and down trains away from it. That made the Great Central unusual amongst British railways in that its down trains went towards its "milepost zero" and up trains went away from it, but the convention of up and down trains in relation to London was retained.

The new line was built from Annesley in Nottinghamshire to join the Metropolitan Railway (MetR) extension to Quainton Road, where the line became joint MetR/GCR owned (after 1903), and returned to GCR tracks at Canfield Place, near Finchley Road, for the final section to Marylebone. In 1903, new rails were laid parallel to the Metropolitan Railway from Harrow to the junction north of Finchley Road, enabling more traffic to use Marylebone.

Later history
In 1902, the company introduced an express service from Bournemouth and Southampton to York and Newcastle upon Tyne. A year later, it began a through running express from Dover and Folkestone to Leicester, Nottingham, Sheffield, Leeds, Huddersfield, Halifax, Bradford and Manchester, avoiding London and opening up the South Coast to the Midlands and the North. The route from Banbury to Reading was over Great Western track and from there it traversed South Eastern Railway track via Aldershot and Guildford to Redhill and on to Folkestone and Dover. At the same time, the Great Central was gaining a reputation for fast services to and from London. In May 1903, the company promoted its services as Rapid Travel in Luxury, and Sheffield without a stop, adopted on 1 July 1903, became a trademark for the company, with 163.75 mi run in three hours, an average of nearly 55 mph. Slip coaches were provided for passengers for Leicester and Nottingham.

On 2 April 1906, an "alternative main line" route from Grendon Underwood Junction near Aylesbury to Neasden in north-west London opened. The line was joint GCR/GWR between Ashendon Junction and Northolt Junction. It was built to increase traffic on the GCR by overcoming capacity constraints on the Metropolitan extension and as a result of disagreements between the MetR and GCR after the resignation of Sir Edward Watkin due to poor health. By the time the line was built, the companies had settled their differences.

On 1 January 1923, under the terms of the Railways Act 1921, the GCR amalgamated with several other railways to create the London and North Eastern Railway.

The GCR line was the last complete mainline railway to be built in Britain until section one of High Speed 1 opened in 2003 and was also one of the shortest-lived intercity railway lines. Yet in its early years, its steam-hauled Sheffield expresses were the fastest in the country.

Closure
The express services from London to destinations beyond Nottingham were withdrawn in 1960. The line was closed to passenger trains between Aylesbury and Rugby on 3 September 1966. A diesel multiple-unit service ran between Rugby Central and Nottingham Arkwright Street until withdrawal on 3 May 1969.

Line retention
Since 1996, Chiltern Railways has used the Great Central lines south of Aylesbury for local services into London, including the alternative route south of Haddenham and widened lines south of Neasden for its intercity main line from Birmingham to London. In 2008, in a scheme partly funded by the Department for Transport, about three miles of line north of Aylesbury as far as Aylesbury Vale Parkway was brought back into passenger use. None of these lines are currently electrified.

Work started in 2019 on developing East West Rail, which will extend passenger services north of Aylesbury Vale Parkway through Quainton Road to meet a renewed Bicester Village to Bletchley section of the old 'Varsity Line' just beyond the site of the former Great Central station at Calvert. Services are expected to start in the mid-2020s.

Acquisitions

 * The Lancashire, Derbyshire and East Coast Railway (LD&ECR) opened in 1897, to link the coalfields with deep-water ports, and was intended to run from Sutton-on-Sea in Lincolnshire to Warrington in Lancashire. In the event only the section between Pyewipe Junction, near Lincoln and Chesterfield Market Place station and some branch lines were built. It was purchased by the GCR on 1 January 1907, to provide a better link between the London main line and the east coast.
 * Wrexham, Mold and Connah's Quay Railway was purchased 1 January 1905.
 * North Wales and Liverpool Railway was acquired at the same time.
 * Wigan Junction Railway was bought on 1 January 1906, as was the Liverpool, St Helens and South Lancashire Railway
 * North Lindsey Light Railway Scunthorpe to Whitton opened throughout on 1 December 1910 and was worked by the GCR. It carried passengers, although its main freight was ironstone.

Joint working
Apart from the three branches in the Liverpool area, the GCR lines in the north of England were all east of Manchester but GCR trains could run from coast to coast by means of joint working with other railways. The largest of those utilized in this way were those under the Cheshire Lines Committee: the other participants were the Midland Railway and the Great Northern Railway, taking in both Liverpool and Southport. Other joint undertakings were (west to east):
 * Manchester, South Junction and Altrincham Railway (GCR/LNWR)
 * Oldham, Ashton and Guide Bridge Railway (GCR/LNWR)
 * Macclesfield, Bollington and Marple Railway (GCR/NSR); including its Hayfield branch
 * South Yorkshire Joint Railway (GCR, GNR, Lancashire and Yorkshire Railway, MR and North Eastern Railway)
 * Sheffield District Railway(GCR and MidR)
 * West Riding and Grimsby Joint Railway (GCR/GNR) - giving access to Wakefield and thence to Leeds
 * Hull and Barnsley and Great Central Joint Railway - opened 1916 for freight traffic only.

There were also joint lines in the south:
 * Aylesbury Station Joint Committee
 * Great Western and Great Central Joint Railway
 * Banbury Junction Railway
 * Metropolitan and Great Central Joint Railway
 * Watford Joint Railway

Key officers
For those in position before 1899, dates are as served for the MS&LR.

General Managers

 * 1886–1902 Sir William Pollitt (knighted 1899, later Lord Stuart of Wortley)
 * 1902–1922 Sir Samuel Fay (knighted 1912)

Locomotive Engineer

 * 1894–1900 Harry Pollitt
 * 1900–1902 John George Robinson

Chief Mechanical Engineer

 * 1902–1922 John George Robinson, for whom the post was created

GCR locomotives
These could generally be divided into those intended for passenger work, especially those used on the London Extension and those for the heavy freight work.

 * See Locomotives of the Great Central Railway

Pollitt's locomotives
Taken over from the MS&LR, mainly of class F2, 2-4-2 tank locomotives, and also classes D5 and D6 4-4-0 locomotives.

Robinson locomotives
During Robinson's tenure, many of the larger express passenger engines came into being:
 * Classes B1-B9: 4-6-0 tender locomotives
 * Classes C4/5: 4-4-2 tender locomotives
 * Classes D9-11: 4-4-0 tender locomotives
 * Class J13: 0-6-0T
 * Classes L1/L3: 2-6-4T
 * Classes O4/5: 2-8-0, heavy freight locos, including ROD engines
 * GCR Class 8A (LNER Class Q4) 0-8-0 heavy freight locomotive
 * GCR Class 8H (LNER Class S1) 0-8-4T used at Wath marshalling yard

Preserved locomotives
Only two GCR locomotives are preserved:

In 2019 there were plans to build a replica steam locomotive - a GCR Class 2 (known as the LNER D7 Class) Numbered 567 at Ruddington.

Coaching stock
The following GCR coaches are preserved.

Major stations

 * London Marylebone
 * Manchester London Road
 * Nottingham Victoria
 * Sheffield Victoria
 * Leicester Central
 * Rugby Central

Wath marshalling yard
The marshalling yard at Wath-upon-Dearne opened in November 1907. It was designed to cope with coal trains, full and empty; it was worked with electro-pneumatic signalling.

Accidents and incidents

 * On 30 March 1889, an excursion train was derailed at Penistone, Yorkshire due to a failure of an axle on the locomotive hauling it. A mail train ran into the wreckage at low speed. One person was killed and 61 were injured.
 * On 17 November 1899, GCR goods guard, Charles Harry Bennion was stationed at Staveley Town Railway station, Derbyshire. At approximately 08.30 am his goods train from Staveley to Frodingham was working through the thick fog when it hit two ‘light engines’ due to a 'signalling error'. Charles’ injuries were fatal and he died instantly.
 * On 23 December 1904, an express passenger train was derailed at Aylesbury, Buckinghamshire due to excessive speed on a curve. Another express passenger train ran into the wreckage at low speed. Four people were killed.
 * On 2 February 1908, the driver of a freight train sneezed, his head collided with that of his fireman, knocking both of them out. Due to excessive speed, a van in the train derailed approaching Notton and Royston station, Yorkshire and the train overran signals there. It derailed completely at Ryhill.
 * On 13 December 1911, a freight train ran away and was derailed at Wombwell Central station, Yorkshire. Both locomotive crew were killed.
 * About 1913, a coal train was derailed at Torside, Derbyshire. The crew of the locomotive may have been overcome by fumes in the Woodhead Tunnel.

Grimsby docks
Grimsby, dubbed the "largest fishing port in the world" in the early 20th century, owed its prosperity to the ownership by the GCR and its forebear, the MS&LR. Coal and timber were among its biggest cargoes. The port had two main docks: the Alexandra Dock (named for Queen Alexandra) and the Royal Dock which was completed in 1852, linked by the Union Dock. The total area of docks was 104.25 acres (42 ha).

Immingham Dock
Completed in 1912, this dock covered 71 acre and was mainly concerned with the movement of coal. On 22 July 2012, the docks held an open day to celebrate 100 years of operation.

Ships
The Great Central Railway operated a number of ships.

Immingham museum
Immingham museum, which portrays the role of the Great Central Railway in the building of the docks and construction of the local rail network is home to the Great Central Railway Society archive. The museum is located in the Civic Centre, Pelham Road, Immingham and is open from 1pm to 4pm, Wednesday to Saturday from March through to November.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Great Central Railway


text:
Talk:Stress

Untitled
I want to add a page describing geological stress. Should I add a redirect, or edit this page directly and remove the stuff about disambiguation? cferrero — Preceding undated comment added 16:15, 16 February 2003
 * I haven't looked at what CF eventually did on the accompanying main-namespace page, but just for the record geological stress does not exist, and the answer is "No, neither of those possibilities you mention." --Jerzy•t 02:15, 18 December 2007 (UTC)

Removals
None of these are what someone looking at Stress should expect, even tho the list may be useful to editors adding useful lks to articles on the pages they should expect.

 * Tensile stress
 * Compressive stress
 * Shear stress
 * Extensional stress term for normal stress in rheology
 * Longitudinal stress term for normal stress in acoustics
 * Flexural strength

 * == See also ==

 * Stress management, techniques for coping with personal stress
 * Critical Incident Stress Management

I'm not taking the time to thoroughly clean up the page; some others probably deserve similary treatment. --Jerzy•t 02:15, 18 December 2007 (UTC)

— Preceding unsigned comment added by 98.86.147.178 (talk) 23:43, 6 February 2012 (UTC)

Biology
I wnt abut effects of preesure on strees and strain Sattucharan (talk) 04:49, 25 June 2017 (UTC)

wrong category
Stress (Swiss musician) should be moved to Arts, entertainment, and media - Music--Sun-kid (talk) 20:05, 2 March 2022 (UTC)
 * I've moved Stress (musician) and Stress (record producer) to Groups and musicians. Thanks for pointing this out. —Bruce1eetalk 21:01, 2 March 2022 (UTC)

title: Talk:Stress


text:
René Goblet

René Goblet (26 November 1828 – 13 September 1905) was a French politician, Prime Minister of France for a period in 1886–1887.

He was born at Aire-sur-la-Lys, Pas-de-Calais and was trained in law. Under the Second Empire, he helped found a Liberal journal, Le Progrès de la Somme, and in July 1871 he was sent by the département of the Somme to the National Assembly, where he took his place on the extreme left, as a member of the Republican Union parliamentary group (Union républicaine). Having failed to secure election in 1876, he was returned for Amiens the following year. He held a minor government office in 1879, and in 1882 became minister of the interior in the Freycinet cabinet. He was minister of education, fine arts and religion in Henri Brisson's first cabinet in 1885, and again under Freycinet in 1886, when he greatly increased his reputation by an able defence of the government's education proposals.

Meanwhile, his independence and outspokenness had alienated him from many of his party, and throughout his life he was frequently in conflict with his political associates, from Léon Gambetta downwards. On the fall of the Freycinet cabinet in December he formed a cabinet in which be reserved for himself the portfolios of the interior and of religion. The Goblet cabinet was unpopular from the outset, and it was with difficulty that anybody could be found to accept the ministry of foreign affairs, which was finally given to Gustave Flourens.

Then came what is known as the Schnaebele incident, the arrest on the German frontier of a French official named Schnaebele, which caused immense excitement in France. For some days Goblet took no definite decision, but left Flourens, who stood for peace, to fight it out with General Boulanger, the minister of war, who urged the despatch of an ultimatum. Although he finally intervened on the side of Flourens, and peace was preserved, his weakness in the face of Boulangist propaganda became a national danger. Defeated on the budget in May 1887, his government resigned; but he returned to office next year as foreign minister in the radical administration of Charles Floquet. He was defeated at the polls by a Boulangist candidate in 1889, and sat in the senate from 1891 to 1893 when he returned to the popular chamber. In association with Édouard Locroy, Ferdinand Sarrien and Paul Peytral he drew up a republican programme which they put forward in La Petite République française. At the elections of 1898 he was defeated, and from then on took little part in public affairs. He died in Paris.

Goblet's Ministry, 16 December 1886 – 30 May 1887

 * René Goblet – President of the Council, Minister of the Interior, and Minister of Worship
 * Émile Flourens – Minister of Foreign Affairs
 * Georges Boulanger – Minister of War
 * Albert Dauphin – Minister of Finance
 * Ferdinand Sarrien – Minister of Justice
 * Théophile Aube – Minister of Marine and Colonies
 * Marcellin Berthelot – Minister of Public Instruction and Fine Arts
 * Jules Develle – Minister of Agriculture
 * Édouard Millaud – Minister of Public Works
 * Félix Granet – Minister of Posts and Telegraphs
 * Édouard Lockroy – Minister of Commerce and Industry

title: René Goblet


text:
Gustave Flourens

Gustave Flourens (4 August 1838 in Paris – 3 April 1871) was a French Revolutionary leader and writer, son of the physiologist Jean Pierre Flourens (who was Professor at the Collège de France and deputy in 1838-1839). He was also the elder brother of Émile Flourens, who became minister of foreign affairs under the Third Republic.

At 25 years of age Flourens undertook in 1863, on behalf of his father, a course of lectures at the Collège de France, on the subject of the history of humankind. His theories as to the manifold origin of the human race gave offence to the clergy, and he was prevented from delivering further lectures. He then went to Brussels, where he published his lectures under the title of Histoire de l'homme (1863). Gustave Flourens then visited Constantinople and Athens and took part in the Cretan insurrection of 1866-1868; he was one of those chosen for a difficult mission to Athens on behalf of the Cretan Revolutionary Assembly. He attempted to convince influential people, such as Victor Hugo, to support the Cretan insurrection. Gustave Flourens then spent some time in Italy, where an article of his in the Fe polo d'Italia caused his arrest and imprisonment, and finally, having returned to France, nearly lost his life in a duel with Paul de Cassagnac, editor of the Pays. In Paris he devoted his time to the cause of "red republicanism", and begin writing articles in the La Marseillaise weekly newspaper. At length, having failed in an attempt to organize a revolution at Belleville on 7 February 1870, was compelled to flee from France. Returning to Paris on the downfall of Napoleon III, placed himself at the head of a body of 500 tirailleurs (sharpshooters). Because of his insurrectionary proceedings (he was one of the organizers of the October 1870 uprising against the provisional government's moderate policy) he was taken prisoner at Créteil, near Vincennes, by the provisional government, and confined at Mazas on 7 December 1870, but was released by his men on the night of 21–22 January. On 18 March he joined the population's uprising, was elected a member of the revolutionary Commune by the 20th arrondissement, and was named general. Gustave Flourens was one of the most active leaders of the insurrection, and after a sortie against the Versailles troops in the morning of 3 April, he fled into an inn near the bridge that separates Chatou and Rueil. There, after he was captured and disarmed by the Gendarmerie, he was murdered by Captain Jean-Marc Démaret. Besides his Science de l'homme (Paris, 1869), Flourens was also the author of numerous fugitive pamphlets.

Possible influence on Jules Verne
In his notes to modern editions of some of Jules Verne's works William Butcher, citing the Sunday Times of 5 March 1978, has suggested that one of Verne's most famous characters, Captain Nemo, is based on Gustave Flourens. This view has been challenged by Leonidas Kallivretakis.

Friendship with Sarah Bernhardt
In her autobiography, My Double Life (p. 220), the actress Sarah Bernhardt described him as follows: "I also knew and frequently saw a mad sort of fellow, full of dreams and Utopian follies. His name was Flourens, and he was tall and nice-looking. He wanted every one to be happy and every one to have money, and he shot down the soldiers without reflecting that he was commencing by making one or more of them unhappy. Reasoning with him was impossible, but he was charming and brave. I saw him two days before his death. He came to see me with a very young girl who wanted to devote herself to dramatic art. I promised him to help her. Two days later the poor child came to tell me of the heroic death of Flourens. He had refused to surrender, and, stretching out his arms, had shouted to the hesitating soldiers, 'Shoot, shoot! I should not have spared you!' And their bullets killed him."

title: Gustave Flourens


text:
Infinitesimal strain theory

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.

With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made.

The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in the design of such structures is to minimize their deformation under typical loads. However, this approximation demands caution in the case of thin flexible bodies, such as rods, plates, and shells which are susceptible to significant rotations, thus making the results unreliable.

Infinitesimal strain tensor
For infinitesimal deformations of a continuum body, in which the displacement gradient tensor (2nd order tensor) is small compared to unity, i.e. $$\|\nabla \mathbf u\| \ll 1 $$, it is possible to perform a geometric linearization of any one of the finite strain tensors used in finite strain theory, e.g. the Lagrangian finite strain tensor $$\mathbf E$$, and the Eulerian finite strain tensor $$\mathbf e$$. In such a linearization, the non-linear or second-order terms of the finite strain tensor are neglected. Thus we have

$$\mathbf E = \frac{1}{2} \left(\nabla_{\mathbf X}\mathbf u + (\nabla_{\mathbf X}\mathbf u)^T + (\nabla_{\mathbf X}\mathbf u)^T\nabla_{\mathbf X}\mathbf u\right)\approx \frac{1}{2}\left(\nabla_{\mathbf X}\mathbf u + (\nabla_{\mathbf X}\mathbf u)^T\right)$$ or $$E_{KL}= \frac{1}{2} \left(\frac{\partial U_K}{\partial X_L} +\frac{\partial U_L}{\partial X_K}+ \frac{\partial U_M}{\partial X_K} \frac{\partial U_M}{\partial X_L}\right)\approx \frac{1}{2}\left(\frac{\partial U_K}{\partial X_L}+\frac{\partial U_L}{\partial X_K}\right)$$ and $$\mathbf e =\frac{1}{2} \left(\nabla_{\mathbf x}\mathbf u + (\nabla_{\mathbf x}\mathbf u)^T - \nabla_{\mathbf x}\mathbf u(\nabla_{\mathbf x}\mathbf u)^T\right)\approx \frac{1}{2}\left(\nabla_{\mathbf x}\mathbf u + (\nabla_{\mathbf x}\mathbf u)^T\right)$$ or $$e_{rs}=\frac{1}{2} \left(\frac{\partial u_r}{\partial x_s} +\frac{\partial u_s}{\partial x_r} -\frac{\partial u_k}{\partial x_r} \frac{\partial u_k}{\partial x_s}\right)\approx \frac{1}{2}\left(\frac{\partial u_r}{\partial x_s} +\frac{\partial u_s}{\partial x_r}\right)$$

This linearization implies that the Lagrangian description and the Eulerian description are approximately the same as there is little difference in the material and spatial coordinates of a given material point in the continuum. Therefore, the material displacement gradient tensor components and the spatial displacement gradient tensor components are approximately equal. Thus we have $$\mathbf E \approx \mathbf e \approx \boldsymbol \varepsilon = \frac{1}{2}\left((\nabla\mathbf u)^T + \nabla\mathbf u\right) $$ or $$ E_{KL}\approx e_{rs}\approx\varepsilon_{ij} = \frac{1}{2} \left(u_{i,j}+u_{j,i}\right)$$ where $$\varepsilon_{ij}$$ are the components of the infinitesimal strain tensor $$\boldsymbol \varepsilon$$, also called Cauchy's strain tensor, linear strain tensor, or small strain tensor.

$$\begin{align} \varepsilon_{ij} &= \frac{1}{2}\left(u_{i,j}+u_{j,i}\right) \\ &= \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13} \\ \varepsilon_{21} & \varepsilon_{22} & \varepsilon_{23} \\ \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33} \\ \end{bmatrix} \\ &= \begin{bmatrix} \frac{\partial u_1}{\partial x_1} & \frac{1}{2} \left(\frac{\partial u_1}{\partial x_2}+\frac{\partial u_2}{\partial x_1}\right) & \frac{1}{2} \left(\frac{\partial u_1}{\partial x_3}+\frac{\partial u_3}{\partial x_1}\right) \\ \frac{1}{2} \left(\frac{\partial u_2}{\partial x_1}+\frac{\partial u_1}{\partial x_2}\right) & \frac{\partial u_2}{\partial x_2} & \frac{1}{2} \left(\frac{\partial u_2}{\partial x_3}+\frac{\partial u_3}{\partial x_2}\right) \\ \frac{1}{2} \left(\frac{\partial u_3}{\partial x_1}+\frac{\partial u_1}{\partial x_3}\right) & \frac{1}{2} \left(\frac{\partial u_3}{\partial x_2}+\frac{\partial u_2}{\partial x_3}\right) & \frac{\partial u_3}{\partial x_3} \\ \end{bmatrix} \end{align} $$ or using different notation: $$\begin{bmatrix} \varepsilon_{xx} & \varepsilon_{xy} & \varepsilon_{xz} \\ \varepsilon_{yx} & \varepsilon_{yy} & \varepsilon_{yz} \\ \varepsilon_{zx} & \varepsilon_{zy} & \varepsilon_{zz} \\ \end{bmatrix} = \begin{bmatrix} \frac{\partial u_x}{\partial x} & \frac{1}{2} \left(\frac{\partial u_x}{\partial y}+\frac{\partial u_y}{\partial x}\right) & \frac{1}{2} \left(\frac{\partial u_x}{\partial z}+\frac{\partial u_z}{\partial x}\right) \\ \frac{1}{2} \left(\frac{\partial u_y}{\partial x}+\frac{\partial u_x}{\partial y}\right) & \frac{\partial u_y}{\partial y} & \frac{1}{2} \left(\frac{\partial u_y}{\partial z}+\frac{\partial u_z}{\partial y}\right) \\ \frac{1}{2} \left(\frac{\partial u_z}{\partial x}+\frac{\partial u_x}{\partial z}\right) & \frac{1}{2} \left(\frac{\partial u_z}{\partial y}+\frac{\partial u_y}{\partial z}\right) & \frac{\partial u_z}{\partial z} \\ \end{bmatrix} $$

Furthermore, since the deformation gradient can be expressed as $$\boldsymbol{F} = \boldsymbol{\nabla}\mathbf{u} + \boldsymbol{I}$$ where $$\boldsymbol{I}$$ is the second-order identity tensor, we have $$\boldsymbol\varepsilon = \frac{1}{2} \left(\boldsymbol{F}^T+\boldsymbol{F}\right)-\boldsymbol{I}$$

Also, from the general expression for the Lagrangian and Eulerian finite strain tensors we have $$ \begin{align} \mathbf E_{(m)}& =\frac{1}{2m} (\mathbf U^{2m}-\boldsymbol{I}) = \frac{1}{2m} [(\boldsymbol{F}^T\boldsymbol{F})^m - \boldsymbol{I}] \approx \frac{1}{2m} [\{\boldsymbol{\nabla}\mathbf{u}+(\boldsymbol{\nabla}\mathbf{u})^T + \boldsymbol{I}\}^m - \boldsymbol{I}]\approx \boldsymbol{\varepsilon}\\ \mathbf e_{(m)}& = \frac{1}{2m} (\mathbf V^{2m}-\boldsymbol{I})= \frac{1}{2m} [(\boldsymbol{F}\boldsymbol{F}^T)^m - \boldsymbol{I}]\approx \boldsymbol{\varepsilon} \end{align} $$

Geometric derivation
Consider a two-dimensional deformation of an infinitesimal rectangular material element with dimensions $$dx$$ by $$dy$$ (Figure 1), which after deformation, takes the form of a rhombus. From the geometry of Figure 1 we have

$$\begin{align} \overline {ab} &= \sqrt{\left(dx+\frac{\partial u_x}{\partial x}dx \right)^2 + \left( \frac{\partial u_y}{\partial x}dx \right)^2} \\ &= dx\sqrt{1+2\frac{\partial u_x}{\partial x}+\left(\frac{\partial u_x}{\partial x}\right)^2 + \left(\frac{\partial u_y}{\partial x}\right)^2} \\ \end{align}$$

For very small displacement gradients, i.e., $$\|\nabla \mathbf u\| \ll 1 $$, we have $$\overline {ab} \approx dx + \frac{\partial u_x}{\partial x} dx$$

The normal strain in the $$x$$-direction of the rectangular element is defined by $$\varepsilon_x = \frac{\overline {ab}-\overline {AB}}{\overline {AB}}$$ and knowing that $$\overline {AB}= dx$$, we have $$\varepsilon_x = \frac{\partial u_x}{\partial x}$$

Similarly, the normal strain in the $y$-direction, and $z$-direction, becomes $$\varepsilon_y = \frac{\partial u_y}{\partial y} \quad, \qquad \varepsilon_z = \frac{\partial u_z}{\partial z}$$

The engineering shear strain, or the change in angle between two originally orthogonal material lines, in this case line $$\overline {AC}$$ and $$\overline {AB}$$, is defined as $$\gamma_{xy}= \alpha + \beta$$

From the geometry of Figure 1 we have $$\tan \alpha = \frac{\dfrac{\partial u_y}{\partial x}dx}{dx + \dfrac{\partial u_x}{\partial x} dx} = \frac{\dfrac{\partial u_y}{\partial x}}{1+\dfrac{\partial u_x}{\partial x}} \quad, \qquad \tan \beta=\frac{\dfrac{\partial u_x}{\partial y} dy}{dy+\dfrac{\partial u_y}{\partial y} dy}=\frac{\dfrac{\partial u_x}{\partial y}}{1+\dfrac{\partial u_y}{\partial y}}$$

For small rotations, i.e., $$\alpha$$ and $$\beta$$ are $$\ll 1$$ we have $$\tan \alpha \approx \alpha \quad, \qquad \tan \beta \approx \beta$$ and, again, for small displacement gradients, we have $$\alpha=\frac{\partial u_y}{\partial x} \quad, \qquad \beta=\frac{\partial u_x}{\partial y}$$ thus $$\gamma_{xy}= \alpha + \beta = \frac{\partial u_y}{\partial x} + \frac{\partial u_x}{\partial y}$$ By interchanging $$x$$ and $$y$$ and $$u_x$$ and $$u_y$$, it can be shown that $$\gamma_{xy} = \gamma_{yx}$$.

Similarly, for the $$y$$-$$z$$ and $$x$$-$$z$$ planes, we have $$\gamma_{yz} = \gamma_{zy} = \frac{\partial u_y}{\partial z} + \frac{\partial u_z}{\partial y} \quad, \qquad \gamma_{zx} = \gamma_{xz} = \frac{\partial u_z}{\partial x} + \frac{\partial u_x}{\partial z}$$

It can be seen that the tensorial shear strain components of the infinitesimal strain tensor can then be expressed using the engineering strain definition, $\gamma$, as $$ \begin{bmatrix} \varepsilon_{xx} & \varepsilon_{xy} & \varepsilon_{xz} \\ \varepsilon_{yx} & \varepsilon_{yy} & \varepsilon_{yz} \\ \varepsilon_{zx} & \varepsilon_{zy} & \varepsilon_{zz} \\ \end{bmatrix} = \begin{bmatrix} \varepsilon_{xx} & \gamma_{xy}/2 & \gamma_{xz}/2 \\ \gamma_{yx}/2 & \varepsilon_{yy} & \gamma_{yz}/2 \\ \gamma_{zx}/2 & \gamma_{zy}/2 & \varepsilon_{zz} \\ \end{bmatrix}$$

Physical interpretation
From finite strain theory we have $$d\mathbf{x}^2 - d\mathbf{X}^2 = d\mathbf X \cdot 2\mathbf E \cdot d\mathbf X \quad\text{or}\quad (dx)^2 - (dX)^2 = 2E_{KL}\,dX_K\,dX_L$$

For infinitesimal strains then we have $$d\mathbf{x}^2 - d\mathbf{X}^2 = d\mathbf X \cdot 2\mathbf{\boldsymbol \varepsilon} \cdot d\mathbf X \quad\text{or}\quad (dx)^2 - (dX)^2 = 2\varepsilon_{KL}\,dX_K\,dX_L$$

Dividing by $$(dX)^2$$ we have $$\frac{dx-dX}{dX}\frac{dx+dX}{dX}=2\varepsilon_{ij}\frac{dX_i}{dX}\frac{dX_j}{dX}$$

For small deformations we assume that $$dx \approx dX$$, thus the second term of the left hand side becomes: $$\frac{dx+dX}{dX} \approx 2$$.

Then we have $$\frac{dx-dX}{dX} = \varepsilon_{ij}N_iN_j = \mathbf N \cdot \boldsymbol \varepsilon \cdot \mathbf N$$ where $$N_i=\frac{dX_i}{dX}$$, is the unit vector in the direction of $$d\mathbf X$$, and the left-hand-side expression is the normal strain $$e_{(\mathbf N)}$$ in the direction of $$\mathbf N$$. For the particular case of $$\mathbf N$$ in the $$X_1$$ direction, i.e., $$\mathbf N = \mathbf I_1$$, we have $$e_{(\mathbf I_1)}=\mathbf I_1 \cdot \boldsymbol \varepsilon \cdot \mathbf I_1 = \varepsilon_{11}.$$

Similarly, for $$\mathbf N=\mathbf I_2$$ and $$\mathbf N=\mathbf I_3$$ we can find the normal strains $$\varepsilon_{22}$$ and $$\varepsilon_{33}$$, respectively. Therefore, the diagonal elements of the infinitesimal strain tensor are the normal strains in the coordinate directions.

Strain transformation rules
If we choose an orthonormal coordinate system ($$\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3$$) we can write the tensor in terms of components with respect to those base vectors as $$ \boldsymbol{\varepsilon} = \sum_{i=1}^3 \sum_{j=1}^3 \varepsilon_{ij} \mathbf{e}_i\otimes\mathbf{e}_j $$ In matrix form, $$\underline{\underline{\boldsymbol{\varepsilon}}} = \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13} \\ \varepsilon_{12} & \varepsilon_{22} & \varepsilon_{23} \\ \varepsilon_{13} & \varepsilon_{23} & \varepsilon_{33} \end{bmatrix} $$ We can easily choose to use another orthonormal coordinate system ($$\hat{\mathbf{e}}_1,\hat{\mathbf{e}}_2,\hat{\mathbf{e}}_3$$) instead. In that case the components of the tensor are different, say $$  \boldsymbol{\varepsilon} = \sum_{i=1}^3 \sum_{j=1}^3 \hat{\varepsilon}_{ij} \hat{\mathbf{e}}_i\otimes\hat{\mathbf{e}}_j \quad \implies \quad \underline{\underline{\hat{\boldsymbol{\varepsilon}}}} = \begin{bmatrix} \hat{\varepsilon}_{11} & \hat{\varepsilon}_{12} & \hat{\varepsilon}_{13} \\ \hat{\varepsilon}_{12} & \hat{\varepsilon}_{22} & \hat{\varepsilon}_{23} \\ \hat{\varepsilon}_{13} & \hat{\varepsilon}_{23} & \hat{\varepsilon}_{33} \end{bmatrix} $$ The components of the strain in the two coordinate systems are related by $$ \hat{\varepsilon}_{ij} = \ell_{ip}~\ell_{jq}~\varepsilon_{pq} $$ where the Einstein summation convention for repeated indices has been used and $$\ell_{ij} = \hat{\mathbf{e}}_i\cdot{\mathbf{e}}_j$$. In matrix form $$  \underline{\underline{\hat{\boldsymbol{\varepsilon}}}} = \underline{\underline{\mathbf{L}}} ~\underline{\underline{\boldsymbol{\varepsilon}}}~ \underline{\underline{\mathbf{L}}}^T $$ or $$ \begin{bmatrix} \hat{\varepsilon}_{11} & \hat{\varepsilon}_{12} & \hat{\varepsilon}_{13} \\ \hat{\varepsilon}_{21} & \hat{\varepsilon}_{22} & \hat{\varepsilon}_{23} \\ \hat{\varepsilon}_{31} & \hat{\varepsilon}_{32} & \hat{\varepsilon}_{33} \end{bmatrix} = \begin{bmatrix} \ell_{11} & \ell_{12} & \ell_{13} \\ \ell_{21} & \ell_{22} & \ell_{23} \\ \ell_{31} & \ell_{32} & \ell_{33} \end{bmatrix} \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13} \\ \varepsilon_{21} & \varepsilon_{22} & \varepsilon_{23} \\ \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33} \end{bmatrix} \begin{bmatrix} \ell_{11} & \ell_{12} & \ell_{13} \\ \ell_{21} & \ell_{22} & \ell_{23} \\ \ell_{31} & \ell_{32} & \ell_{33} \end{bmatrix}^T $$

Strain invariants
Certain operations on the strain tensor give the same result without regard to which orthonormal coordinate system is used to represent the components of strain. The results of these operations are called strain invariants. The most commonly used strain invariants are $$ \begin{align} I_1 & = \mathrm{tr}(\boldsymbol{\varepsilon}) \\ I_2 & = \tfrac{1}{2}\{[\mathrm{tr}(\boldsymbol{\varepsilon})]^2 - \mathrm{tr}(\boldsymbol{\varepsilon}^2)\} \\ I_3 & = \det(\boldsymbol{\varepsilon}) \end{align} $$ In terms of components $$ \begin{align} I_1 & = \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33} \\ I_2 & = \varepsilon_{11}\varepsilon_{22} + \varepsilon_{22}\varepsilon_{33} + \varepsilon_{33}\varepsilon_{11} - \varepsilon_{12}^2 - \varepsilon_{23}^2 - \varepsilon_{31}^2 \\ I_3 & = \varepsilon_{11}(\varepsilon_{22}\varepsilon_{33} - \varepsilon_{23}^2) - \varepsilon_{12}(\varepsilon_{21}\varepsilon_{33}-\varepsilon_{23}\varepsilon_{31}) + \varepsilon_{13}(\varepsilon_{21}\varepsilon_{32}-\varepsilon_{22}\varepsilon_{31}) \end{align} $$

Principal strains
It can be shown that it is possible to find a coordinate system ($$\mathbf{n}_1,\mathbf{n}_2,\mathbf{n}_3$$) in which the components of the strain tensor are $$  \underline{\underline{\boldsymbol{\varepsilon}}} = \begin{bmatrix} \varepsilon_{1} & 0 & 0 \\ 0 & \varepsilon_{2} & 0 \\ 0 & 0 & \varepsilon_{3} \end{bmatrix} \quad \implies \quad \boldsymbol{\varepsilon} = \varepsilon_{1} \mathbf{n}_1\otimes\mathbf{n}_1 + \varepsilon_{2} \mathbf{n}_2\otimes\mathbf{n}_2 + \varepsilon_{3} \mathbf{n}_3\otimes\mathbf{n}_3 $$ The components of the strain tensor in the ($$\mathbf{n}_1,\mathbf{n}_2,\mathbf{n}_3$$) coordinate system are called the principal strains and the directions $$\mathbf{n}_i$$ are called the directions of principal strain. Since there are no shear strain components in this coordinate system, the principal strains represent the maximum and minimum stretches of an elemental volume.

If we are given the components of the strain tensor in an arbitrary orthonormal coordinate system, we can find the principal strains using an eigenvalue decomposition determined by solving the system of equations $$ (\underline{\underline{\boldsymbol{\varepsilon}}} - \varepsilon_i~\underline{\underline{\mathbf{I}}})~\mathbf{n}_i = \underline{\mathbf{0}} $$ This system of equations is equivalent to finding the vector $$\mathbf{n}_i$$ along which the strain tensor becomes a pure stretch with no shear component.

Volumetric strain
The volumetric strain, also called bulk strain, is the relative variation of the volume, as arising from dilation or compression; it is the first strain invariant or trace of the tensor: $$\delta=\frac{\Delta V}{V_0} = I_1 = \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33}$$ Actually, if we consider a cube with an edge length a, it is a quasi-cube after the deformation (the variations of the angles do not change the volume) with the dimensions $$a \cdot (1 + \varepsilon_{11}) \times a \cdot (1 + \varepsilon_{22}) \times a \cdot (1 + \varepsilon_{33})$$ and V0 = a3, thus $$\frac{\Delta V}{V_0} = \frac{\left ( 1 + \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33} + \varepsilon_{11} \cdot \varepsilon_{22} + \varepsilon_{11} \cdot \varepsilon_{33}+ \varepsilon_{22} \cdot \varepsilon_{33} + \varepsilon_{11} \cdot \varepsilon_{22} \cdot \varepsilon_{33} \right ) \cdot a^3 - a^3}{a^3}$$ as we consider small deformations, $$1 \gg \varepsilon_{ii} \gg \varepsilon_{ii} \cdot \varepsilon_{jj} \gg \varepsilon_{11} \cdot \varepsilon_{22} \cdot \varepsilon_{33} $$ therefore the formula.

In case of pure shear, we can see that there is no change of the volume.

Strain deviator tensor
The infinitesimal strain tensor $$\varepsilon_{ij}$$, similarly to the Cauchy stress tensor, can be expressed as the sum of two other tensors:
 * 1) a mean strain tensor or volumetric strain tensor or spherical strain tensor, $$\varepsilon_M\delta_{ij}$$, related to dilation or volume change; and
 * 2) a deviatoric component called the strain deviator tensor, $$\varepsilon'_{ij}$$, related to distortion.

$$\varepsilon_{ij}= \varepsilon'_{ij} + \varepsilon_M\delta_{ij}$$ where $$\varepsilon_M$$ is the mean strain given by $$\varepsilon_M = \frac{\varepsilon_{kk}}{3} = \frac{\varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33}}{3} = \tfrac{1}{3}I^e_1$$

The deviatoric strain tensor can be obtained by subtracting the mean strain tensor from the infinitesimal strain tensor: $$\begin{align} \ \varepsilon'_{ij} &= \varepsilon_{ij} - \frac{\varepsilon_{kk}}{3}\delta_{ij} \\ \begin{bmatrix} \varepsilon'_{11} & \varepsilon'_{12} & \varepsilon'_{13} \\ \varepsilon'_{21} & \varepsilon'_{22} & \varepsilon'_{23} \\ \varepsilon'_{31} & \varepsilon'_{32} & \varepsilon'_{33} \\ \end{bmatrix} &=\begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \varepsilon_{13} \\ \varepsilon_{21} & \varepsilon_{22} & \varepsilon_{23} \\ \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33} \\ \end{bmatrix} - \begin{bmatrix} \varepsilon_M & 0 & 0 \\ 0 & \varepsilon_M & 0 \\ 0 & 0 & \varepsilon_M \\ \end{bmatrix} \\ &=\begin{bmatrix} \varepsilon_{11}-\varepsilon_M & \varepsilon_{12} & \varepsilon_{13} \\ \varepsilon_{21} & \varepsilon_{22}-\varepsilon_M & \varepsilon_{23} \\ \varepsilon_{31} & \varepsilon_{32} & \varepsilon_{33}-\varepsilon_M \\ \end{bmatrix} \\ \end{align}$$

Octahedral strains
Let ($$\mathbf{n}_1, \mathbf{n}_2, \mathbf{n}_3$$) be the directions of the three principal strains. An octahedral plane is one whose normal makes equal angles with the three principal directions. The engineering shear strain on an octahedral plane is called the octahedral shear strain and is given by $$ \gamma_{\mathrm{oct}} = \tfrac{2}{3}\sqrt{(\varepsilon_1-\varepsilon_2)^2 + (\varepsilon_2-\varepsilon_3)^2 + (\varepsilon_3-\varepsilon_1)^2} $$ where $$\varepsilon_1, \varepsilon_2, \varepsilon_3$$ are the principal strains.

The normal strain on an octahedral plane is given by $$ \varepsilon_{\mathrm{oct}} = \tfrac{1}{3}(\varepsilon_1 + \varepsilon_2 + \varepsilon_3) $$

Equivalent strain
A scalar quantity called the equivalent strain, or the von Mises equivalent strain, is often used to describe the state of strain in solids. Several definitions of equivalent strain can be found in the literature. A definition that is commonly used in the literature on plasticity is $$ \varepsilon_{\mathrm{eq}} = \sqrt{\tfrac{2}{3} \boldsymbol{\varepsilon}^{\mathrm{dev}}:\boldsymbol{\varepsilon}^{\mathrm{dev}}} = \sqrt{\tfrac{2}{3}\varepsilon_{ij}^{\mathrm{dev}}\varepsilon_{ij}^{\mathrm{dev}}} ~; \boldsymbol{\varepsilon}^{\mathrm{dev}} = \boldsymbol{\varepsilon} - \tfrac{1}{3}\mathrm{tr}(\boldsymbol{\varepsilon})~\boldsymbol{I} $$ This quantity is work conjugate to the equivalent stress defined as $$ \sigma_{\mathrm{eq}} = \sqrt{\tfrac{3}{2} \boldsymbol{\sigma}^{\mathrm{dev}}:\boldsymbol{\sigma}^{\mathrm{dev}}} $$

Compatibility equations
For prescribed strain components $$\varepsilon_{ij}$$ the strain tensor equation $$u_{i,j}+u_{j,i}= 2 \varepsilon_{ij}$$ represents a system of six differential equations for the determination of three displacements components $$u_i$$, giving an over-determined system. Thus, a solution does not generally exist for an arbitrary choice of strain components. Therefore, some restrictions, named compatibility equations, are imposed upon the strain components. With the addition of the three compatibility equations the number of independent equations are reduced to three, matching the number of unknown displacement components. These constraints on the strain tensor were discovered by Saint-Venant, and are called the "Saint Venant compatibility equations".

The compatibility functions serve to assure a single-valued continuous displacement function $$u_i$$. If the elastic medium is visualised as a set of infinitesimal cubes in the unstrained state, after the medium is strained, an arbitrary strain tensor may not yield a situation in which the distorted cubes still fit together without overlapping.

In index notation, the compatibility equations are expressed as $$\varepsilon_{ij,km}+\varepsilon_{km,ij}-\varepsilon_{ik,jm}-\varepsilon_{jm,ik}=0$$

In engineering notation,
 * $$\frac{\partial^2 \epsilon_x}{\partial y^2} + \frac{\partial^2 \epsilon_y}{\partial x^2} = 2 \frac{\partial^2 \epsilon_{xy}}{\partial x \partial y}$$
 * $$\frac{\partial^2 \epsilon_y}{\partial z^2} + \frac{\partial^2 \epsilon_z}{\partial y^2} = 2 \frac{\partial^2 \epsilon_{yz}}{\partial y \partial z}$$
 * $$\frac{\partial^2 \epsilon_x}{\partial z^2} + \frac{\partial^2 \epsilon_z}{\partial x^2} = 2 \frac{\partial^2 \epsilon_{zx}}{\partial z \partial x}$$
 * $$\frac{\partial^2 \epsilon_x}{\partial y \partial z} = \frac{\partial}{\partial x} \left ( -\frac{\partial \epsilon_{yz}}{\partial x} + \frac{\partial \epsilon_{zx}}{\partial y} + \frac{\partial \epsilon_{xy}}{\partial z}\right)$$
 * $$\frac{\partial^2 \epsilon_y}{\partial z \partial x} = \frac{\partial}{\partial y} \left ( \frac{\partial \epsilon_{yz}}{\partial x} - \frac{\partial \epsilon_{zx}}{\partial y} + \frac{\partial \epsilon_{xy}}{\partial z}\right)$$
 * $$\frac{\partial^2 \epsilon_z}{\partial x \partial y} = \frac{\partial}{\partial z} \left ( \frac{\partial \epsilon_{yz}}{\partial x} + \frac{\partial \epsilon_{zx}}{\partial y} - \frac{\partial \epsilon_{xy}}{\partial z}\right)$$

Plane strain
In real engineering components, stress (and strain) are 3-D tensors but in prismatic structures such as a long metal billet, the length of the structure is much greater than the other two dimensions. The strains associated with length, i.e., the normal strain $$\varepsilon_{33}$$ and the shear strains $$\varepsilon_{13}$$ and $$\varepsilon_{23}$$ (if the length is the 3-direction) are constrained by nearby material and are small compared to the cross-sectional strains. Plane strain is then an acceptable approximation. The strain tensor for plane strain is written as: $$\underline{\underline{\boldsymbol{\varepsilon}}} = \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & 0 \\ \varepsilon_{21} & \varepsilon_{22} & 0 \\ 0     &     0       & 0 \end{bmatrix}$$ in which the double underline indicates a second order tensor. This strain state is called plane strain. The corresponding stress tensor is: $$\underline{\underline{\boldsymbol{\sigma}}} = \begin{bmatrix} \sigma_{11} & \sigma_{12} & 0 \\ \sigma_{21} & \sigma_{22} & 0 \\ 0     &     0       & \sigma_{33} \end{bmatrix}$$ in which the non-zero $$\sigma_{33}$$ is needed to maintain the constraint $$\epsilon_{33} = 0$$. This stress term can be temporarily removed from the analysis to leave only the in-plane terms, effectively reducing the 3-D problem to a much simpler 2-D problem.

Antiplane strain
Antiplane strain is another special state of strain that can occur in a body, for instance in a region close to a screw dislocation. The strain tensor for antiplane strain is given by $$\underline{\underline{\boldsymbol{\varepsilon}}} = \begin{bmatrix} 0 & 0 & \varepsilon_{13} \\ 0 & 0 & \varepsilon_{23}\\ \varepsilon_{13} & \varepsilon_{23} & 0 \end{bmatrix}$$

Relation to infinitesimal rotation tensor
The infinitesimal strain tensor is defined as $$ \boldsymbol{\varepsilon} = \frac{1}{2} [\boldsymbol{\nabla}\mathbf{u} + (\boldsymbol{\nabla}\mathbf{u})^T]$$ Therefore the displacement gradient can be expressed as $$ \boldsymbol{\nabla}\mathbf{u} = \boldsymbol{\varepsilon} + \boldsymbol{W}$$ where $$ \boldsymbol{W} := \frac{1}{2} [\boldsymbol{\nabla}\mathbf{u} - (\boldsymbol{\nabla}\mathbf{u})^T]$$ The quantity $$\boldsymbol{W}$$ is the infinitesimal rotation tensor or infinitesimal angular displacement tensor (related to the infinitesimal rotation matrix). This tensor is skew symmetric. For infinitesimal deformations the scalar components of $$\boldsymbol{W}$$ satisfy the condition $$|W_{ij}| \ll 1$$. Note that the displacement gradient is small only if the strain tensor and the rotation tensor are infinitesimal.

The axial vector
A skew symmetric second-order tensor has three independent scalar components. These three components are used to define an axial vector, $$\mathbf{w}$$, as follows $$ W_{ij} = -\epsilon_{ijk}~w_k ~; w_i = -\tfrac{1}{2}~\epsilon_{ijk}~W_{jk} $$ where $$\epsilon_{ijk}$$ is the permutation symbol. In matrix form $$ \underline{\underline{\boldsymbol{W}}} = \begin{bmatrix} 0 & -w_3 & w_2 \\ w_3 & 0 & -w_1 \\ -w_2 & w_1 & 0\end{bmatrix} ~; \underline{\mathbf{w}} = \begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $$ The axial vector is also called the infinitesimal rotation vector. The rotation vector is related to the displacement gradient by the relation $$ \mathbf{w} = \tfrac{1}{2}~ \boldsymbol{\nabla} \times \mathbf{u} $$ In index notation $$ w_i = \tfrac{1}{2}~\epsilon_{ijk}~u_{k,j} $$ If $$\lVert\boldsymbol{W}\rVert \ll 1 $$ and $$\boldsymbol{\varepsilon} = \boldsymbol{0}$$ then the material undergoes an approximate rigid body rotation of magnitude $$|\mathbf{w}|$$ around the vector $$\mathbf{w}$$.

Relation between the strain tensor and the rotation vector
Given a continuous, single-valued displacement field $$\mathbf{u}$$ and the corresponding infinitesimal strain tensor $$\boldsymbol{\varepsilon}$$, we have (see Tensor derivative (continuum mechanics)) $$\boldsymbol{\nabla}\times\boldsymbol{\varepsilon} = e_{ijk}~\varepsilon_{lj,i}~\mathbf{e}_k\otimes\mathbf{e}_l = \tfrac{1}{2}~e_{ijk}~[u_{l,ji} + u_{j,li}]~\mathbf{e}_k\otimes\mathbf{e}_l $$ Since a change in the order of differentiation does not change the result, $$u_{l,ji} = u_{l,ij}$$. Therefore $$ e_{ijk} u_{l,ji} = (e_{12k}+e_{21k}) u_{l,12} + (e_{13k}+e_{31k}) u_{l,13} + (e_{23k} + e_{32k}) u_{l,32} = 0 $$ Also $$ \tfrac{1}{2}~e_{ijk}~u_{j,li} = \left(\tfrac{1}{2}~e_{ijk}~u_{j,i}\right)_{,l} = \left(\tfrac{1}{2} ~ e_{kij}~u_{j,i}\right)_{,l} = w_{k,l} $$ Hence $$ \boldsymbol{\nabla} \times \boldsymbol{\varepsilon} = w_{k,l}~\mathbf{e}_k\otimes\mathbf{e}_l = \boldsymbol{\nabla}\mathbf{w} $$

Relation between rotation tensor and rotation vector
From an important identity regarding the curl of a tensor we know that for a continuous, single-valued displacement field $$\mathbf{u}$$, $$ \boldsymbol{\nabla}\times(\boldsymbol{\nabla}\mathbf{u}) = \boldsymbol{0}. $$ Since $$\boldsymbol{\nabla}\mathbf{u} = \boldsymbol{\varepsilon} + \boldsymbol{W}$$ we have $$ \boldsymbol{\nabla}\times\boldsymbol{W} = -\boldsymbol{\nabla}\times\boldsymbol{\varepsilon} = - \boldsymbol{\nabla} \mathbf{w}. $$

Strain tensor in cylindrical coordinates
In cylindrical polar coordinates ($$r, \theta, z$$), the displacement vector can be written as $$ \mathbf{u} = u_r~\mathbf{e}_r + u_\theta~\mathbf{e}_\theta + u_z~\mathbf{e}_z $$ The components of the strain tensor in a cylindrical coordinate system are given by: $$\begin{align} \varepsilon_{rr} & = \cfrac{\partial u_r}{\partial r} \\ \varepsilon_{\theta\theta} & = \cfrac{1}{r}\left(\cfrac{\partial u_\theta}{\partial \theta} + u_r\right) \\ \varepsilon_{zz} & = \cfrac{\partial u_z}{\partial z} \\ \varepsilon_{r\theta} & = \cfrac{1}{2} \left(\cfrac{1}{r}\cfrac{\partial u_r}{\partial \theta} + \cfrac{\partial u_\theta}{\partial r} - \cfrac{u_\theta}{r}\right) \\ \varepsilon_{\theta z} & = \cfrac{1}{2} \left(\cfrac{\partial u_\theta}{\partial z} + \cfrac{1}{r} \cfrac{\partial u_z}{\partial \theta}\right) \\ \varepsilon_{zr} & = \cfrac{1}{2} \left(\cfrac{\partial u_r}{\partial z} + \cfrac{\partial u_z}{\partial r}\right) \end{align}$$

Strain tensor in spherical coordinates
In spherical coordinates ($$r, \theta, \phi$$), the displacement vector can be written as $$ \mathbf{u} = u_r~\mathbf{e}_r + u_\theta~\mathbf{e}_\theta + u_\phi~\mathbf{e}_\phi $$ The components of the strain tensor in a spherical coordinate system are given by $$\begin{align} \varepsilon_{rr} & = \cfrac{\partial u_r}{\partial r} \\ \varepsilon_{\theta\theta} & = \cfrac{1}{r}\left(\cfrac{\partial u_\theta}{\partial \theta} + u_r\right) \\ \varepsilon_{\phi\phi} & = \cfrac{1}{r\sin\theta}\left(\cfrac{\partial u_\phi}{\partial \phi} + u_r\sin\theta + u_\theta\cos\theta\right)\\ \varepsilon_{r\theta} & = \cfrac{1}{2}\left(\cfrac{1}{r}\cfrac{\partial u_r}{\partial \theta} + \cfrac{\partial u_\theta}{\partial r}- \cfrac{u_\theta}{r}\right) \\ \varepsilon_{\theta \phi} & = \cfrac{1}{2r}\left(\cfrac{1}{\sin\theta}\cfrac{\partial u_\theta}{\partial \phi} + \cfrac{\partial u_\phi}{\partial \theta} - u_\phi\cot\theta\right) \\ \varepsilon_{\phi r} & = \cfrac{1}{2}\left(\cfrac{1}{r\sin\theta}\cfrac{\partial u_r}{\partial \phi} + \cfrac{\partial u_\phi}{\partial r} - \cfrac{u_\phi}{r}\right) \end{align} $$

title: Infinitesimal strain theory


text:
Talk:Isaac Deutscher

[Untitled]
The chronology of the section on Deutscher's anti-Stalinist activity, his expulsion and the publication of "The Danger of Barbarism over Europe" needs clarifying. We need dates for each of these three deveopments. Tamara Deutscher's preface to "The Non-Jewish Jew & Other Essays" is unclear on the sequence and contradicts Marxists.org's entry for Deutcher (see http://www.marxists.org/glossary/people/d/e.htm#deutscher-isaac ). We don't know when exactly "The Danger of Barbarism over Europe" began to appear in the underground CP papers. It was unlikely to have been in 1933 because it seems the KPP had expelled Deutcher by this stage and he'd likely be denied access to the underground presses from which the "The Danger of Barbarism" was published. It appears that "The Danger of Barbarism" was Deutscher's reaction to, rather than a cause of, his expulsion from KPP.

58.172.104.13 (talk) 01:05, 9 March 2011 (UTC)

Untitled
Copyright violation?

http://www.spartacus.schoolnet.co.uk/RUSdeutscher.htm

Dze27 16:39 Feb 16, 2003 (UTC)

Enemies
This looks like a person who made a lot of enemies both at the left as at the right side of politics, people and countries. Was his sudden death ever investigated? How did he die? — Preceding unsigned comment added by 93.125.148.175 (talk) 20:17, 16 November 2013 (UTC)
 * We certainly need information as to why he died.--Jack Upland (talk) 22:28, 9 October 2016 (UTC)

Israeil and Judaism
Why is there so much information on this?--Jack Upland (talk) 22:28, 9 October 2016 (UTC)

Stalin biog & evolution of views
I read his Stalin biog in my youth and I recall that there were a series of introductions which showed the evolution of his views over the years (all of which were printed, but it was in an edition after his death so I've no idea if he would have approved). Might be worth a note if somebody has a copy to hand.Paulturtle (talk) 01:32, 7 March 2020 (UTC)
 * As far as I know, from the time Deutscher wrote his Stalin biography till the day he (Deutscher) died, his view of Stalin remained fundamentally the same. His 1966 preface to the second edition states "I have seen no reason to alter my narrative or interpretation of Stalin's career." --Ismail (talk) 10:27, 19 February 2022 (UTC)

title: Talk:Isaac Deutscher


text:
Talk:Caraș-Severin County

This appears to be a copyright violation with sentences copied from parts of

http://www.clubromania.ro/romania/counties/caras/

Dze27 16:44 Feb 16, 2003 (UTC)

I re-wrote almost the entire page, so all the copyright violations should be gone. I didn't check the page, but if there are any more, let me know. But you won't, because you left this message a year and a half ago, so for anyone else who sees this post, and the page, there may still be some copyright stuff, but I doubt it.

Whew.

--TheGrza 17:57, Sep 16, 2004 (UTC)

Soviets arrived
The sentence "When the Soviets arrived in 1949, it brought enormous upheavel to the area, leading to newly communist state to declare the nationalization of the industries and specifically the Sovietization of UDR." looks dubious.

Who exactly arrived and why in 1949 and w/o them there would be no nationalization? Pavel Vozenilek 18:18, 27 Jan 2005 (UTC)

The sovietization of the area resulted in nationalization. Whether it would or could have happened without them is a moot point; it did happen as a direct result of their actions. --The Grza 21:44, Jan 27, 2005 (UTC)

Wikipedia:Naming conventions (geographic names)
in accordance with Naming conventions (geographic names) page,

paragraph 2. ''The lead: The title can be followed in the first line by a list of alternative names in parenthesis: {name1, name2, name3, etc.}. Any archaic names in the list (including names used before the standardization of English orthography) should be clearly marked as such, i.e.: (name1 arch.). Relevant foreign language names[3] are permitted and should be listed in alphabetic order of their respective languages, i.e.: (Armenian: name1, Belarusian: name2, Czech: name3). Alternatively, all alternative names can be moved to and explained in a names section immediately following the lead. In this case, the redundant list of the names in the article's first line should be replaced with the following text: (known also by several alternative namesNames). Once such a section or paragraph is created, the alternative English or foreign names should not be moved back to the first line.''

Definition

^ The geographic location is considered to have a single widely accepted English name in modern context (swaEn) if the following two conditions are satisfied simultaneously: The English-language encyclopedias (Encyclopedia Britannica, Columbia Encyclopedia and Encarta) consistently use this name in all articles where the corresponding location is mentioned in modern context. ''This name obtains the largest number (75% or more of total hits considering all possible variants) of Google Scholar and Google Books hits (count only articles and books, not number of times the world is used in them) when searched over English language articles and books where the corresponding location is mentioned in modern context. If the name of the location coincides with the name of another entity, care should be taken to exclude inapropriate pages from the count.''

internet hits returned 11.800 results of "Hargita county" and 154 000 results of "Harghita county". English encyclopedias consistently use the name "Harghita county"

there was a voting meant to settle this problem, concluded with 5 votes in favour of providing the HU names against 2. the relevancy of that vote is reduced to 7 people voting,

considering the relevancy of English Encyclopedias and Wikipedia naming conventions

i here by remove the names of hungarian administrative divisions provided as alternates for names of romanian administrative divisions from the lead of the article. refer to Naming conventions (geographic names) for any debate on this matter Criztu 08:10, 10 July 2006 (UTC)criztu

hungarian names for Counties of Romania are not alternative names in english sources
for the editors that keep reverting to lead section formulation with a hungarian name for the administrative divisions of Romania, please consult the currently under development Naming conventions (geographic names). Dispute resolution: Avoid revert wars: If there is a dispute regarding the naming convention in the contents of the article, to prevent revert wars the name from the title of the relevant article should be used in all occurrences until a consensus is reached on the relevant talk page(s).. I have explained my view on providing hungarian names for administrative divisions and geographic places in Romania that are not shared by Romania with Hungary. the situation is similar to providing a hungarian name for London. since Britannica does not ofer hungarian names for administrative divisions of ROmania, i will object to providing the hungarian names in the english wikipedia in the lead section. i will move these names to Demographics, or to a Names section according to the same Wikipedia under development guide Criztu 21:19, 7 August 2006 (UTC)

External links modified
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title: Talk:Caraș-Severin County


text:
JBuilder

JBuilder is a discontinued integrated development environment (IDE) for the programming language Java from Embarcadero Technologies. Originally developed by Borland, JBuilder was spun off with CodeGear which was eventually purchased by Embarcadero Technologies in 2008.

Oracle had based the first versions of JDeveloper on code from JBuilder licensed from Borland, but it has since been rewritten from scratch.

Versions
JBuilder 1 through 3 are based on the Delphi IDE. JBuilder 3.5 through 2006 are based on PrimeTime, an all-Java IDE framework. JBuilder 2007 "Peloton" is the first JBuilder release based on the eclipse IDE framework.

title: JBuilder


text:
Volvocaceae

The Volvocaceae are a family of unicellular or colonial biflagellates, including the typical genus Volvox. The family was named by Ehrenberg in 1834, and is known in older classifications as the Volvocidae. All species are colonial and inhabit freshwater environments.

Description
The simplest of the Volvocaeans are ordered assemblies of cells, each similar to the related unicellular protist Chlamydomonas and embedded in a gelatinous matrix. In the genus Gonium, for example, each individual organism is a flat plate consisting of 4 to 16 separate cells, each with two flagella. Similarly, the genera Eudorina and Pandorina form hollow spheres, the former consisting of 16 cells, the latter of 32 to 64 cells. In these genera each cell can reproduce a new organism by mitosis.

Other genera of Volvocaceans represent another principle of biological development as each organism develops differented cell types. In Pleodorina and Volvox, most cells are somatic and only a few are reproductive. In Pleodorina californica a colony normally has either 128 or 64 cells, of which those in the anterior region have only a somatic function, while those in the posterior region can reproduce; the ratio being 3:5. In Volvox only very few cells are able to reproduce new individuals, and in some species of Volvox the reproductive cells are derived from cells looking and behaving like somatic cells. In V. carteri, on the other hand, the division of labor is complete with reproductive cells being set aside during cell division, and they never assume somatic functions or develop functional flagella.

Thus, the simplest Volvocaceans are colonial organisms but others are truly multicellular organisms. Larger volvocaceans have evolved a specialized form of heterogamy called oogamy, the production of small motile sperm by one mating type and relatively larger immotile eggs by another. Among the Volvocaceans are thus the simplest organisms with distinguishable male and female members. In all Volvocaceans, the fertilization reaction results in the production of a dormant diploid zygote (zygospore) capable of surviving in harsh environments. Once conditions have improved the zygospore germinates and undergoes meiosis to produce haploid offspring of both mating types.

Colony inversion
Colony inversion during development is a special characteristic of this order that results in new colonies having their flagella facing outwards. During this process reproductive cells first undergo successive cell divisions to form a concave-to-cup-shaped embryo or plakea composed of a single cell layer. Immediately after, the cell layer is inside out compared with the adult configuration—the apical ends of the embryo protoplasts from which flagella are formed, are oriented toward the interior of the plakea. Then the embryo undergoes inversion, during which the cell layer inverts to form a spheroidal daughter colony with the apical ends and flagella of daughter protoplasts positioned outside. This process enables appropriate locomotion of spheroidal colonies of the Volvocaceae. The mechanism of inversion has been investigated extensively at the cellular and molecular levels using a model species, Volvox carteri.

Spheroidal colony inversion evolved twice during evolution of the Chlamydomonadales. In the Volvocaceae inversion first occurred when the Volvocaceae diverged from the closely related Goniaceae (see figure). It also occurred during evolution of Astrephomene. Inversion differs between the two lineages: rotation of daughter protoplasts during successive cell divisions in Astrephomene, and inversion after cell divisions in the Volvocaceae.

title: Volvocaceae


text:
Jean Pierre Flourens

Marie Jean Pierre Flourens (13 April 1794 – 6 December 1867), father of Gustave Flourens, was a French physiologist, the founder of experimental brain science, and a pioneer in anesthesia.

Biography
Flourens was born at Maureilhan, near Béziers, in the département of Hérault. At fifteen he began studying medicine at Montpellier, where he received the degree of doctor in 1813. In the following year he went to Paris, carrying an introduction from A. P. de Candolle, the botanist, to Georges Cuvier, who received him kindly, and took an interest in him. In Paris, Flourens engaged in physiological research, occasionally contributing to publications; and, in 1821, at the Athénée, he gave a course of lectures on the physiological theory of the sensations, which attracted much attention amongst men of science.

In 1815, Flourens pioneered the experimental method of carrying out localized lesions of the brain in living rabbits and pigeons and carefully observing their effects on motricity, sensibility and behavior. His intention was to investigate localisationism, i.e., whether different parts of the brain had different functions, as the Austrian physician Franz Joseph Gall, the founder of phrenology, was proposing. The trouble was that Gall did not use a proper scientific approach to his affirmations. In 1825, Flourens was elected as a member to the American Philosophical Society.

Flourens was able to demonstrate convincingly for the first time that the main divisions of the brain were indeed responsible for largely different functions. By removing the cerebral hemispheres, for instance, all perceptions, motricity, and judgment were abolished. The removal of the cerebellum affected the animal's equilibrium and motor coordination, while the destruction of the brainstem (medulla oblongata) caused death. These experiments led Flourens to the conclusion that the cerebral hemispheres are responsible for higher cognitive functions, that the cerebellum regulates and integrates movements, and that the medulla controls vital functions, such as circulation, respiration and general bodily stability. On the other hand, he was unable (probably because his experimental subjects have relatively primitive cortex) to find specific regions for memory and cognition, which led him to believe that they are represented in a diffuse form around the brain. So, different functions could indeed be ascribed to particular regions of the brain, but a finer localization was lacking.

Flourens, by destroying the horizontal semicircular canal of pigeons, noted that they continue to fly in a circle, showing the purpose of the semicircular canals.

Flourens was chosen by Cuvier in 1828 to deliver a course of lectures on natural history at the Collège de France, and in the same year became, in succession to LAG Bosc, a member of the Institute, in the division "Economic rurale." In 1830 he became Cuvier's substitute as lecturer on human anatomy at the Jardin du Roi, and in 1832 was elected to the post of titular professor, which he vacated for the professorship of comparative anatomy created for him at the museum of the Jardin the same year. In 1833 Flourens, in accordance with the dying request of Cuvier, was appointed a perpetual secretary of the Academy of Sciences; and in 1838 he was returned as a deputy for the arrondissement of Béziers. In 1840 he was elected, in preference to Victor Hugo, to succeed Jean François Michaud at the French Academy; and in 1845 he was created a commander of the légion d'honneur, and in the next year a peer of France. In 1841, he was elected a foreign member of the Royal Swedish Academy of Sciences.

In March 1847 Flourens drew the attention of the Academy of Sciences to the anesthetic effect of chloroform on animals.

On the revolution of 1848 he withdrew completely from political life; and in 1855 he accepted the professorship of natural history at the Collège de France. He died at Montgeron, near Paris on 6 December 1867.

Opposition to Darwinism
Flourens was an opponent of Darwinism and criticized the idea of natural selection. In 1864, he authored Examen du livre du M. Darwin sur l'Origine des Espèces. He refuted the arguments of spontaneous generation.

He was a creationist and defended the fixity of species. Flourens criticized Charles Darwin for personifying nature. He argued that natural selection is a contradictory term as nature does not select. Flourens' book was never translated into English and no reviewers attempted to refute his arguments in detail. However, Thomas Henry Huxley took issue with his criticism of Darwinism, noting that "his objections to details are of the old sort, so battered and hackneyed on this side of the Channel, that not even a Quarterly Reviewer could be induced to pick them up for the purpose of pelting Mr. Darwin over again."

title: Jean Pierre Flourens