With the massive arrangement of hair at the back of the head in the late 1860s and early 1870s, bonnets had to be worn further forward, the front curving fronijust above the hair-line to behind the ears where the ribbons were attached, the back cut away to allow the hair to flow freely. At this time hats were also perched on the forehead; a pillbox shape is sometimes referred to as a casquette, a name also applied to a hat following the lines of the Scotch glengarry cap.
1812, Costumes Parisiens. 1. Hat of silk and plush. 2. Hats of "Virginie." 3. Caps of cotton and tulle. 4. Hats of single velvet. 5. Hat of plush. 6. Hats of curly (crimped? shaggy?) velvet.
fashion plate 1801-02 from the collection of the Bibliothèque des Arts Décoratifs, on flickr by SceneInThePast