When Sherlock says "This is low tar", Mycroft replies "
Well, you barely knew her".
This reenforces the idea that the cigarette is a way of coping with the loss - he didn't know her that well, so he doesn't need a strong cigarette.
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I presumed that it was just Mycroft and John Watson's way of telling whether Sherlock was badly affected by the news of her death.
I think in the original A.C.D. stories, Sherlock Holmes does seem to have a tendency to fall into what we would now call depression and even that he has tendencies towards manic-depression.
In the original stories he is also a user of drugs including opiates (which were not illegal at the time) when depressed.
I thought that (modern) Sherlock does not routinely smoke, therefore if he accepts the cigarette then he is going to be bad.
I don't think it was just a way of helping him relax.
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I can't be certain this is the right answer, but some of episode 2 makes it look like Sherlock's serious addiction is cigarettes not something a little more risque.
So cigarettes are the modern stand-in for his need for cocaine.
Letting him have one is an admission that he has had to deal with something serious (like the loss of Adler).
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Mycroft and Watson mentioned a "danger night.
" I assume Mycroft gave him the stick to be nice when seeing his brother emotionally falling down.
Tobacco has also completely replaced the morphine use, but he did refer to his 7% cocaine solution in one episode.
It was just a treat.
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Actually, if you paid attention to the episode he reveals his use of the Nicotine patches, he says its next to impossible to keep a smoking habit in London "nowadays" this is likely due to some form of legislation limiting areas where one can smoke or additional taxes on them.
While Mycroft most likely extends this due to the loss of Irene Addler as well, it is also because of some form of restriction to smokers in London.
At least, that is my analysis without checking in on British law.
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It was a way of testing how upset Sherlock was.
In the Hounds of Baskerville, Sherlock is extremely stressed out because he doesn't have a case to work on, and can be seen trashing the flat looking for a pack of cigarettes.
When someone comes with a case, Sherlock begs him to smoke (since the person smoked) and then sniffs out all the smoke.
So, since Sherlock was upset, he took the cigarette.
That's why John swears when he finds out.
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I saw it as a test to see how upset he was about Irene.
When he took it and Mycroft spoke to John, he was worried about it being a 'danger night' and Sherlock taking the cigarette provided him with the proof that that night could potentially be one.
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Read Arthur Conan Doyle's first two books, or get his complete works.
Sherlock was a heavy smoker of a pipe.
The three patch problem is reference to a three pipe problem in the original.
In all the books, he only uses cocaine for one stretch of time; Watson said he used it three times a day for the three months he witnessed it.
He was once in an opium den when he was in disguise and saw Watson.
He said that if were identified there, he would be killed.
So we'll assume he didn't smoke opium or it would have blown his disguise.
Watson said in the first book he does seem distant, like on some narcotic.
So the cigarettes replace a pipe.
He's a heavy smoker and the only reference to using cocaine is in the books!
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Mycroft Holmes, gives a cigarette to Sherlock and says  "Merry Christmas" . Then in the following scene, Dr. Watson asks Mycroft if he gave the cigarette to Sherlock.  So, it seems to me that the cigarette has some significance. Although it might also seem like  Sherlock  was just suffering from the  supposed  loss of Irene Adler, and his brother just thought the nicotine patches weren't good enough to help him relax. Any thoughts?
What is the significance of the cigarette in 'Sherlock: A Scandal in Belgravia'?
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<plot-explanation><props><sherlock>
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In the episode he say's that it's next to impossibile to keep a smoking habit in London ''Nowadays'' this is likely due to some form of legislation limiting areas where one can smoke or additional taxes on them.  While Mycroft most likely extends this due to the loss of Irene Addler. it is also because of some form of restriction to smokers in London.
It is also because of some form of restriction to smokers in London. Since it was impossible to keep a smoking habit in London "nowadays" as this is likely due to some form of legislation limiting areas where one can smoke or additional taxes on them.