The herald of 'Don't be late' is well known to most of us who grew up on the tale of Alice in Wonderland. He is after all the catalyst for the story, as it is his rabbit hole that Alice falls into, beginning her adventures.
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The White Rabbit is a fictional character in Lewis Carroll's book Alice's Adventures in Wonderland. He appears at the very beginning of the book, in chapter one, wearing a waistcoat, and muttering "Oh dear! Oh dear! I shall be too late!" Alice follows him down the rabbit hole into Wonderland. Alice encounters him again when he mistakes her for his housemaid Mary Ann and she becomes trapped in his house after growing too large. The Rabbit shows up again in the last few chapters, as a herald-like servant of the King and Queen of Hearts.
In the Disney version of the book, the Rabbit seems to have the most logic out of all the Wonderland characters. Thus, he is often the straight man for their zany antics; when he asks the Dodo for help on getting the "monster" (Alice) out of his house, Dodo's ultimate solution is to burn the house down, to which the White Rabbit is greatly opposed. At the Mad Tea Party, the Mad Hatter and the March Hare try to "fix" his watch, proclaiming it "exactly two days slow". Through various food they put in the watch (butter, tea, jam, and lemon), the two cause it to go mad, and the Hare smashes it with his mallet. The Rabbit was perhaps most famous for the little ditty he sang at the beginning - "I'm late! I'm late! For a very important date! No time to say hello, goodbye! I'm late, I'm late, I'm late!". The Rabbit was voiced by Bill Thompson.
Some believe the rabbit was late for the announcement of the Queen to the royal garden. The panic the rabbit showed was his fear of losing his head. Upon her arrival (where Alice has been helping to paint the roses red) the cards finish their song and the rabbit blows his trumpet (which he had been carrying for most of his lines) royally introducing the king and queen.