Some little time later a compatriot of his came down to stay with him.

Monsieur Dessin, who I know cherished ill feeling against Sir William for the insult which his son had passed upon his daughter, and for various belittling words respecting that young lady which Sir William had in his anger permitted himself to use in public, took occasion when he was riding through the streets of Derby, accompanied by his friends, Lord Pomeroy and Sir John Hawkes, gentlemen of fashion and repute, to accost him.

Sir William swore at him as a French dancing master; whereupon Monsieur Dessin at once challenged him to a duel.
Sir William refused with many scornful words to meet a man of such kind, whereupon Monsieur Dessin, drawing Lord Pomeroy to him, in confidence disclosed his name and quality, to which his compatriot--also a French nobleman--testified, and of which he offered to produce documents and proofs.

They did then adjourn to a tavern, where they called for a private room, to talk the matter over out of earshot of the crowd; and after examining the proofs, Lord Pomeroy and Sir John Hawkes declared that Sir William Brownlow could not refuse the satisfaction which Monsieur Dessin demanded.
"It has always been suspected that Sir William was a man of small courage, though of overbearing manner, and he was mightily put to when he heard that he must fight with a man whom he justly regarded as being far more than his match.

So craven did he become, indeed, that the gentlemen with him did not scruple to express their disgust loudly.