In his book The White Knight, A. L. Taylor reports that on May 4, 1862, there was exactly two days’ difference between the lunar and calendar months. This, Taylor argues, suggests that the Mad Hatter’s watch ran on lunar time and accounts for his remark that his watch is “two days wrong.” If Wonderland is near the earth’s center, Taylor points out, the position of the sun would be useless for time-telling, whereas phases of the moon remain unambiguous.
Lewis Carroll; Martin Gardner. The Annotated Alice, The Definitive Edition. New York, W. W. Norton & Company, 2000. Chapter VII: A Mad Tea-Party; note 6 (p. 73).