Translations for disk in French

Here are paragraphs from public domain books translated:
Sherlock Holmes laughed. "Here is the foresight," said he, putting his finger upon the little disk and loop of the hat-securer. "They are never sold upon hats. If this man ordered one, it is a sign of a certain amount of foresight, since he went out of his way to take this precaution against the wind. But since we see that he has broken the elastic, and has not troubled to replace it, it is obvious that he has less foresight now than formerly, which is a distinct proof of a weakening nature. On the other hand, he has endeavored to conceal some of these stains upon the felt by daubing them with ink, which is a sign that he has not entirely lost his self-respect." Sherlock Holmes sourit. — Voici l’explication de sa prévoyance, dit-il, en posant son doigt sur le petit disque et l’anneau destinés au cordon du chapeau, ceci ne se place que sur commande, et si cet homme a fait mettre ce cordon par précaution contre le vent, c’est bien la preuve qu’il est doué d’une certaine prévoyance. Cependant, je constate que le caoutchouc s’étant cassé, il ne s’est pas donné la peine de le remplacer, d’où j’affirme qu’il a moins de prévoyance maintenant qu’autrefois, preuve d’un affaiblissement de ses facultés. Mais il lui reste encore un certain respect des convenances parce qu’il a cherché à dissimuler les taches de son chapeau en les barbouillant d’encre.
The Adventures of Sherlock Holmes, by Arthur Conan Doyle Les Aventures de Sherlock Holmes, de Arthur Conan Doyle