"The hatter broke the silence. 'What day of the month is it ?' he said,
turning to Alice: he had taken his watch out of his pocket, and was looking at
it uneasily, shaking it every now and then and holding it to his ear.
Alice considered a little, and then said, 'The fourth'
'Two days wrong!' sighed the hatter. 'I told you butter wouldn't suit the works!' he added angrily at the March Hare.
'It was the best butter,' the March Hare meekly replied.
'Yes, but some crumbs must have got in as well,' the hatter grumbled: 'you shouldn't have put it in with the bread knife.'
The March Hare took the watch and looked at it gloomily: then he dipped it into his cup of tea, and looked at it again: but he could think of nothing to say than his first remark, 'It was the best butter you know.'
Alice had been looking over his shoulder with some curiosity. 'What a funny watch!' she remarked. it tells the day of the month, and doesn't tell what o'clock it is!'
'Why should it?' muttered the hatter. 'Does your watch tell you what year it is?'
'Of course not,' Alice replied very readily: 'but that's because it stays the same year for such a long time together.'
'Which is just the case with mine,' said the hatter."
From this and other clues, it can be deduced that Alice's adventure takes place on May 4th 1862. Alice Liddell (for whom the story was written) was 10 on May 4th 1862, and this was her age when the story was first told to her by The rev. Charles Dodgson (who used the pseudenym "Lewis Carroll"). On May 4th 1862, there was exactly two days' difference between the lunar and calendar months. It has been argued from this that the 'lunatic' Mad Hatter's watch ran on Lunar time (hence the two day error).
If Wonderland is near the earth's centre, then the sun would be useless for telling the time of day, but the phase of the moon would be unambiguous. However, other evidence suggests that Alice was 7 in "Alice's adventures in Wonderland" This was taken from "The annotated Alice" which is "Alice in Wonderland" and "Alice through the looking glass", with all the jokes explained (the twentieth century reader can miss a lot) + lots of insights into the mind of the author.