Welcome to L&T, Michael. Have you seen the response to your Newcomer's post?

] How were such settlements or fortunes advertised?

Mercenary lot, were they not? It does seem apparent that when a young lady was avaiable for marriage, her financial status was usually spread about, as bait for those who were interested. Servants seem to have been pretty instrumental in this. Public gossip also played its part. However, it was all speculative.

How did people know that Miss Mary King had ten thousand pounds?

Gossip.

how can he assure himself of the truth of this, prior to becoming engaged?

That was why he applied to the father for her hand in marriage, not to the the girl herself. That was the first step in serious discussion and truth-telling.

it would seem to be very much to the advantage of a lady with three thousand pounds to have it generally believed that she had ten thousand.

You bet it did. It was up to the suitor to investigate the truth of such statements. But don't forget that an engagement was a formal affair, and wouldn't be announced until all parties were satisfied as to such details. There couild be a period of negotiations between the father and the suitor.

Unless her suitors are so gauche as to discuss such matters with her, she may even be able to disclaim knowledge of the inflated fortune attributed to her.

Yet, it is often touched upon in conversation. Wealth wasn't a hidden thing- it conveyed power and authority, and was used as such. You might like to look at P&P, where Lizzy has a conversation with Col Fitz...and where she believes that she's been given a subtle hint to acknowledge the fact that he is attracted to her, but needs to marry a rich woman, and that she shouldn't hold out any unrealistic hopes in the matter. So Lizzy dutifully puts all romantic thoughts of the Dear Colonel out of her mind.

] There are aspects of all this in Northanger Abbey, where the Moreland family's fortune is variously mis-estimated.

Actually, in all of the books, the relative wealth of the heroine(s)is a major factor in the story. The Dashwoods don't know how much they are going to have to live on, and their needs are pretty obviously and callously discussed. The Bennet girls' lack of fortune is an obstacle they have to overcome by other assets. The eligibility and self-confidence of the Bertram girls is tied tightly to their fortunes. Emma Woodhouse doesn't feel the need to get married, ever, because she is independently wealthy. And General Tilney makes some big faux pas in his intelligence gathering. Catherine is pretty much aware of how much she is worth all along... but nobody bothers to ask her. However, Henry knows, presumably becasue he's wangled it out of her in a way that she doesn't notice.

For that matter, how is it that everyone is so knowlegable about the fortunes of the young men?

A young man moving into an area would bring with him letters of credit from his bank, from sponsors, and occasionally lawyers. They used these to establish their eligibility for credit in shops, inns, etc. Mr Phillips in Meryton has a good trade in asessing the honesty and credit of the militia officers, for example. Sometimes financial status would be noted in almanacs, newspapers etc, also, just as it is today. Who ever writes about Bill Gates without mentioning his net worth? Thus financial status of men would be pretty common knowledge.

E.g. it is common knowledge that Mr. Bingley has one hundred thousand pounds

And common knowledge that he achieved it by inheriting a fortune from trade. People just liked to know these things about the strangers in their midst.

Money is what made the world go round, Michael. Everyone cared about it. And deceptions were practiced, too. That's why the concept of gentlemanly behaviour included honesty. That's why reputation was so important.