How does Charles Dickens use Madame Defarge to represent the idea of fate?A Tale of Two Cities by Charles Dickens

Perhaps the most salient reminder of the presence of fate
with the character of Madame Defarge is in her persistent knitting, "to be registered,
as doomed to destruction." In Chapter XV of Book the Second, entitled "Knitting," Ernest
Defarge tells a Jacques that the entire Evremonde family is registered.  When Jacques
Two worries that the coded knitting might be discovered or Madame Defarge may not
remember all the names, Defarge responds to him,

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“Jacques,” returned Defarge, drawing himself up,
“if madame my wife undertook to keep the register in her memory alone, she would not
lose a word of it—not a syllable of it. Knitted in her own stitches and her own symbols,
it will always be as plain to her as the sun. Confide in Madame Defarge. It would be
easier for the weakest poltroon that lives to erase himself from existence, than to
erase one letter of his name or crimes from the knitted register of Madame
Defarge.”

That Madame Defarge
is the agent of fate is also evident in the next chapter which is entitled "Still
Knitting."  For, after John Barsad has come into the wine-shop, Madame Defarge
registers the English spy's name in her knitting.  Then, she counts the coins of their
money and begins to knot the coins in her handerchief in a chain of separate knots.  M.
Defarge complains that "it is a long time" since they have begun their plans for
revolution.  Mme. Defarge retorts that is takes a long time for an earthquake, yet it
comes.  She tells her husband, 

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"Vengeance and retribution require a long time;
it is the rule....But when it is ready, it takes place, and grinds to pieces everything
before it."...She tied a knot with flashing eyes, as if it throttled a
foe.

“I tell thee,” said madame, extending her right hand,
for emphasis, “that although it is a long time on the road, it is on the road and
coming.

"I tell thee it never retreats, and never stops. I
tell thee it is always advancing. Look around and consider the lives of all the world
that we know, consider the faces of all the world that we know, consider the rage and
discontent to which the Jacquerie addresses itself with more and more of certainty every
hour. Can such things last? Bah! I mock you....I believe with all my soul, that we shall
see the triumph.  But even if not, even if I knew certainly not, show me the neck of an
aristocrat and tyrant, and still I
would---"

When Defarge, who
was the servant of Dr. Manette, says that he wishes that Manette and Darnay would stay
out of France, Mme. Defarge remarks that their names are already registered and that
Darnay's "destiny...will take him where he is to go, and will lead him to the end that
is to end him. That is all I know."

In the evening, all the
women of St. Antoine knit; Mme. Defarge moves from group to group, the agent of fate, as
darkness surrounds them.  Dickens foreshadows the coming of the revolution and its
guillotine,

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Another darkness was closing in as surely‚ when
the church bells‚ then ringing pleasantly in many an airy steeple over France‚ should be
melted into thundering cannon; when the military drums should be beating to drown a
wretched voice‚ that night all potent as the voice of Power and Plenty‚ Freedom and
Life. So much was closing in about the women who sat knitting‚ knitting‚ that they their
very selves were closing in around a structure yet unbuilt‚ where they were to sit
knitting‚ knitting‚ counting dropping
heads.