The White Sphinx is the first thing the Time Traveller sees in the future, and it's also the key to getting him out of the future (since that's where the Morlocks hide his Time Machine). So the White Sphinx seems pretty important. How important? So important that we've decided to give you two totally different theories about it.
Theory #1 says that the White Sphinx is important because of its mythological meaning. If you remember your Greek mythology, the Sphinx...well, there are several versions, but the important thing to keep in mind is that the Sphinx asked a riddle and ate people who failed to answer it correctly. So the first thing the Time Traveller sees upon arriving in the future is the statue of the White Sphinx. Soon his Time Machine disappears into the Sphinx, which kind of sets up a riddle that the Time Traveller has to solve: what the heck is going on? Not only that, but if he doesn't figure out the riddle, there's a chance the Morlocks will eat him. In other words, the Sphinx might be there to indicate to the reader that the Time Traveller has to solve the riddle or die.
Now here's another interesting connection: in most versions of the myth, the Sphinx's riddle is something like, "What walks on four legs in the morning, two legs in the afternoon, and three legs in the evening?" Think about it for a second before we give you the answer....
Give up? The answer is Man. You crawl as a baby, walk on two legs as an adult, and use a cane (or walking stick) when you get old. (Although maybe that last part should involve a motorized wheelchair these days. Ah, technology!) So check this out: every once in a while the Time Traveller will say something like, "It seemed to me that I had happened upon humanity upon the wane. The ruddy sunset set me thinking of the sunset of mankind" (4.24). It seems like there's something of a connection between the riddle of the Sphinx (about the aging of man) and the Time Traveller observing (in fast-forward) the aging of the human race.
OK, on to Theory #2, which is that the Sphinx is an important symbol because many people in Wells's time (roughly speaking) used "Sphinx" to refer to the sort of class division that, in The Time Machine, leads to the Eloi-Morlock split. Here's an example:
In Edward Bellamy's novel Looking Backward (1888), a Bostonian goes forward in time to the year 2000 and finds a utopia, or perfect society. This is one of the books Wells is probably thinking of when he has the Time Traveller talk about utopian books. (Check out the "Allusions" section for more.) Interested in how they created this utopia, the Bostonian asks his hosts, "what solution, if any, have you found for the labor question? It was the Sphinx's riddle of the nineteenth century, and when I dropped out the Sphinx was threatening to devour society, because the answer was not forthcoming."
So that's one example of someone using "Sphinx" to indicate that the problem of class seemed unsolvable to many people in the 19th century. There are others, like Thomas Carlyle's Past and Present, which has a chapter called "The Sphinx."
Do you think these two theories about what the Sphinx represents are compatible? Can they both be helpful in understanding the book?