If the hat is a good one it would be advisable to send it to a competent cleaner.
But if it is desired to do it at home make a thin paste of petrol and powdered block magnesia or French chalk.
Rub this paste into the hat all over with a soft brush, such as a shaving brush, leave it in a few hours, then brush the powder out of the hat with a perfectly clean white brush.
Source: WOMEN’S COLUMN. (1921, February 26). Queensland Times (Ipswich) (Qld. : 1909 – 1954), p. 5 (DAILY.).