How did the phrase mad as a hatter come about?

The earliest documented use of the phrase "mad as a hatter" appears in Blackwood's Edinburgh Magazine, January-June 1829. It appears in a section of the magazine headed Noctes Ambrocianæ. No. XL1V:

TICKLER (aside to SHEPHERD.): He's raving.

SHEPHERD (to TICKLER.): Dementit.

ODOHERTY (to both.): Mad as a hatter. Hand me a segar.

So the term is at least one hundred and eighty years old.

It is believed to have come about because hatters in the eighteenth and nineteenth century frequently suffered from Mercury poisoning. Mercury is a chemical which used to be used in the production of felt hats. It is extremely toxic and can cause symptoms which appear to be similar to 'madness'.

Hatters in Danbury, Conneticut, USA are known to have suffered the ill effects of mercury poisoning, the symptoms of which were known locally as "the Danbury shakes." It is also claimed that the Danbury hatmakers were known as "the mad hatters," but evidence is unavailable as to whether this predates the appearance of the phrase in Blackwood's.

Apparently in New Zealand the name "hatter" was given to miners /prospectors who work alone. It was thought that they frequently went mad from the solitude of their claim away in the bush although it is more likely that they were named "hatters" after the phrase, rather than the phrase being named after them.

There also is a theory that the phrase is a corruption of the term 'as mad as an adder', which is roughly equivalent to 'as angry as a rattle-snake'.

The phrase has of course been immortalised by the Hatter in Lewis Carroll's Alice's Adventures in Wonderland, who was named "the Mad Hatter" in Disney's 1951 adaptation.