Fathers unknown

Jurjentje Rauwerda, the lady who ran the largest and most luxurious brothel in Amsterdam ‘Maison Weinthal’ in the second half of the 19th century, also had children. Before she met Mr. Weinthal with whom she got one child, she already had four, whose fathers were unknown. Two of them sadly passed away early, but the other two are whispered about. Daughter Jacoba (born 1835) is ascribed to the wealthy Mr. Lejeune, a powerful porcelain manufacturer from France. But the story about son Willem (born 1842, Leeuwarden) is even more telling. It is said of him that his father is none other than King Willem III. That is of course very interesting. But how do I find out if this is really true?