One of the earlier descriptive names of that form of a hoop-skirted dress known as a farthingale (which see), roundabout was obviously coined with particular reference to the encircling lower part of that garment.
Later, in extension of the same sense, it became applied to garments which encircled the body completely, such as a greatcoat, as well as a woman’s dressing gown.
Finally, early in the nineteenth century (and the use has persisted into the twentieth), American clothiers effected a major shift of emphasis with respect to the area surrounded by adopting the same word, roundabout, as the name of a short jacket reaching no lower than the waist, such as is worn by small boys.