Which Alice?

The Gryphon and the Mock Turtle
"Where did you get it?" asked Alice.
"I made it up myself—it's the one I was going to tell you before."
"Oh, good!" said Alice.
WHO IS OLDER? "The puzzle is about the March Hare and the
Hatter. One of them was born in the year 1842, but I won't tell you
which one. The other one was born either in 1843 or 1844; but
again, I won't tell you which. Also, the March Hare was born in
March—did you know that?"
"No," said Alice, "but I'm not surprised."
"Neither am I," said the Mock Turtle.
"Anyway," continued the Gryphon, "the March Hare has a watch
that . . ."
"Oh yes," interrupted Alice, "a very funny watch that tells the day
of the month instead of the hour of the day. I've seen it."
"Not that watch," cried the Gryphon, "he has another watch that
tells the hour of the day like ordinary watches do. The Hatter also
has his own watch. Neither watch keeps perfect time; the Hatter's
watch gains ten seconds every hour and the March Hare's watch
loses ten seconds every hour.
"One day in January they put both watches right at exactly twelve
o'clock noon. 'You realize,' said the Hatter, 'that our watches won't
be together again until your next birthday—the day you will be
twenty-one.'
"'Quite right,' replied the March Hare.
"Who is older, the March Hare or the Hatter?"
"Beats me!" said the Mock Turtle, who slowly walked away.
"Now really!" exclaimed Alice. "This puzzle can actually be
solved?"
"Oh, yes!" replied the Gryphon.
What is the solution?
51