To unknown recipient
London Decr: 13th: 1800Dear Sir,I am truly sensible of all the obligations I owe you, for the trouble you have been so obliging to take regarding my lost Diamond, I have reason to believe that it is not worth £200 and I have bought another therefore I will decline all farther trouble about it. Again I beg leave to thank you for your goodness and to assure you that I feel myself your obligedNelson[Dreweatts and Bloomsbury auctioneers, sold 09/06/16]
The auctioneer transcribed the word 'lost' as 'last', and newspaper articles speculated on whether the diamond was a present for Nelson's wife, Frances, or his mistress, Emma Hamilton. However, the truth is more interesting, as the good people at the Nelson and his World forum (especially Mark Barrett) discovered.
In 1800, Nelson travelled overland from Naples to England with the Hamiltons. Along the way, in October, they stayed at Hamburg, where a lavish ball and banquet was held in Nelson's honour. Unfortunately for Nelson, at some point during the course of the evening a diamond fell out of the extravagantly blingy gold and diamond-encrusted sword given to him by the Queen of Naples. Despite searching high and low (presumably including the recipient of this letter), and offering a reward of £500, the diamond was never recovered.
The letter is also interesting for Nelson signing his name simply as "Nelson", and letters with this signature are rare. Towards the end of 1800, he experimented with different signatures, such as Bronte Nelson of the Nile. But 'Bronte' was a title that went along with the dukedom of Bronte awarded to him by the King of Naples, and as it was a foreign title could not be held above his British viscountcy. In Nicolas' The Dispatches and Letters of Lord Nelson there are only a handful of letters with the signature "Nelson". But the dukedom of Bronte meant too much to him for him to fashion a signature without it.
Around the same time he was deciding between signatures, he was deciding between women. "Bronte" was inextricably linked with Naples and with Emma, and there lay his happiness. He'd always felt more appreciated by Emma and the Neapolitans than he ever did by his wife and the British establishment. In January 1801, Emma gave birth to their daughter, Horatia, and so, having settled on Emma, he settled on Bronte, and by the end of February he was signing his letters "Nelson & Bronte", and would do so consistently until his death. The diamond he lost from the sword given to him in Naples probably had some sentimental value to him, too.
Considering the story behind it, and the rare signature, whoever bought the letter for £1700 got quite a bargain.
More information can be found on this thread at Nelson and his World. Thanks to Mark Barrett for allowing me to use his research for this article.