Are you getting confused by the many Hamiltons you encounter on this site? There's the infamous Emma; Douglas and Elizabeth from the very beginning; and recently, Elizabeth Gunning. It's almost as if every other Scottish person in the 18th century was a Hamilton, but they scurry around so fast causing scandal here and there that it is difficult to keep track of them! Well for both your and my convenience I've arranged a sort of Dummy's Guide to Aristocratic Hamiltons of the 18th Century. Hold on to your hats folks, this could get complicated.
Let's begin with the lady who is responsible for most of the spawning. Yes, lady. Anne Hamilton, 3rd Duchess of Hamilton (1631-1716). Anne was a Duchess of Hamilton in her own right, that is she was given the title through birth rather than marriage. Her father bequeathed her the title because he knew his time was near and he had no heirs. Normally the Duchy of Hamilton would just go extinct during his death but this happened during a messy time with the uprooting of the crown, etc. etc. so the 1st Duke of Hamilton took advantage and gave his daughter the peerage he worked so hard to earn. That also meant all of his minor peerages followed with the duchy making her also the Marchioness of Clydesdale, Countess of Arran, Lanark and Cambridge, the Lady Aven, Innerdale, Machanshire and Polmont. As you can guess, Anne had no problem finding a husband after that. She married William Douglas (those Douglases get around too!) 1st Earl of Selkirk and they had a litter of children. But for sanity's sake we will only follow two, the eldest surviving and the youngest.
Let's begin with the youngest since that line is slightly less complicated. Anne's youngest son was Lord Archibald Hamilton (1673-1754). He didn't do anything of real notoriety excepting the fact that he married three times, two of his wives having the last name of Hamilton. I told you they breed like rabbits! His third and surviving wife, Jane (oh I hope I don't make this any more confusing!) bore him the heirs he wanted and some daughters too. His youngest daughter, Jane was the mother of the Beautiful Mary Graham.
Archibald's third son was named Sir William Hamilton (1730-1803) who became very successful as an ambassador to Naples and was known for his love of antiques. He married Catherine Barlow who gave him no heirs and left him a lonely widower in 1782. William fell in love and married again nine years later to a woman much younger than him, who was better at giving Horatio Nelson children than she was with her own husband, Lady Emma Hamilton (1761?-1815).
Now back to the eldest of Anne's brood, James 4th Duke of Hamilton (1658-1712) was, ah never mind, not important. But his grandson is of some interest, for it was James the 6th Duke of Hamilton (1724-1758) who fell in love with Elizabeth Chudleigh and then madly in love with Elizabeth Gunning, whom he quickly married. At James' death the title passed to his two year old son, James George who died in his teens leaving the duchy to his younger brother, Douglas 8th Duke of Hamilton (1756-1799). A portrait of the dashing Douglas and his stunning wife, Elizabeth by Joshua Reynolds is one of my personal favourites, unfortunately it was destroyed and we only have (luckily) a black and white image of it. The couple divorced in 1794 and Douglas died five years later without an heir.
The last 18th century Duke of Hamilton I will speak of briefly (goodness there were so many!) was Douglas' cousin who was Alexander 10th Duke of Hamilton (1767-1852) was said to be quite the dandy. He also had a keen interest in ancient Egypt. So interested, in fact, that he willed himself mummified and buried in a sarcophagus.
That about does it for Hamiltons in the 18th Century 101, believe me, there has got to be at least one I'm forgetting. And no, it's not that Hamilton on that we see on US currency!