The following is a lightly-edited version of messsages on the AUSTEN-L list. (In my own opinion, while it is possible that Willoughby may not have known that Eliza Williams's protector was Col. Brandon when he ran away with her at Bath, he almost certainly did know it after he had lived with her for a time, which was before his coming back to Devon and meeting Marianne.)
I have noticed what I call (to myself) the "small world phenomenon", and I have discovered it in almost all of Jane Austen's novels.
(I can't think of anything at all in this one, other than the usefulness of Mr. Crawford's having an admiral for an uncle, giving him an opportunity of helping out William Price and looking good in Fanny's eyes.)
There are similar things found in the writings of the Brontës (in Jane Eyre, perhaps the least believable of all: The Rivers being Jane Eyre's long-lost cousins). I find that some of these circumstances require a leap of faith, and yet I think the technique is quite interesting. I was wondering if it is merely a way of making the plot work out just right, or if it is indeed a technique to intrigue the reader. I've been writing a little fiction myself, and I'm not sure I'd have the nerve to use such coincidences.
Remember that it was a fairly small and constricted world Jane Austen lived in: England's population was less, and further limited by the fact that she's writing about only one class, the lower gentry. Transportation was also limited, and the people she writes about go to the same places for the most part, and the men attend the same university. It's likely that people ran into acquaintances of acquaintances all the time.
I agree, to a certain extent, that it was literally a small world in Jane Austen's day -- only most responders mean it more literally than I did.
For example, of all the aspiring clergymen -- the Henry Tilneys, the Edmund Bertrams, the Edward Ferrars's, and yes, the Dr. Grants -- "chance" recommended Mr. Collins to a "supposedly" clever woman like Lady Catherine. Though he suited her better than any of the above-named might have, by his pompous humility, I still think it a lucky coincidence for Elizabeth and Darcy. I don't claim it is a preposterous circumstance, but a particularly clever twist which is integral to the story -- at least, imagine what the book would be without it.
I have come up with an analogy which I would like to share. Suppose a person is set the task of typing a stream of purely randomly-chosen digits (0-9) on their computer. Donald E. Knuth (Art of Computer Programming), for one, has noticed that this is a very hard thing to do -- our brains try to avoid certain patterns which are in fact likely to occur in nature. For example a sequence of two identical digits (e.g. "44" or "77"), should occur about once every ten digits in a random stream, but people asked to type "random" digits will almost always include seemingly-significant combinations such as this at a lower rate -- thus they will more strongly avoid typing "222" or "123", though if the stream is long enough, even patterns like this ought to occur. Call these patterns "coincidences". A novice will go out of his way to avoid such sequences, while an experienced person might try to include them -- but it is hard to know the perfect rate at which to do so, in order to pass Knuth's battery of tests on truly random number generators.
I'm certainly not claiming that life is a random stream of events, or even that literature should model real life. The point is that the novice (like me) might go overboard trying to avoid plots with coincidences, for fear of them seeming too contrived. But Jane Austen, as an experienced writer and shrewd observer of life, has the appropriate balance between realistic occurrences and interesting plot twists. My claim is that she knew when to include "222" and "123".