In my (ame) experience, the phrase is ambiguous and can mean any of the first week containing a date in april, the first week in which more days are in april than aren't, or the first week entirely contained … In english, wikipedia says these started out as superscripts: 1 st, 2 nd, 3 rd, 4 th, but during the 20 th century they migrated to the baseline:

So the practice started during the roman …