How did the Hatter try to repair his watch?

In the "Mad Tea-Party" chapter of Carroll's Alice's Adventures in Wonderland, the Hatter, the March Hare, and the Dormouse are all crowded at one part of the table when Alice approaches. When the Hatter's watch is first mentioned, he shakes it and seems puzzled that it does not work:

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 (68).

The Hatter obviously does not know what is wrong with his watch and also does not know what to do to fix it. When the March Hare takes the watch, he has a silly potential solution:

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 (68).

Alice is astounded to find that the watch tells the day of the month but not the hour. The Hatter claims to know time instinctively. The Hatter tells Alice that it's always six o'clock; therefore, it is always tea time. The members of the tea party simply move to the next place settings when they are finished with each cup of tea and plate of bread and butter. The entire scene is nonsensical, as is much of what happens in Wonderland, so we should not expect the Hatter or the March Hare to have a good solution to the broken watch.