Etymology always fascinates me.
In sewing, the armscye is the armhole, the fabric edge to which the sleeve is sewn. The length of the armscye is the total length of this edge; the width is the distance across the hole at the widest point.
While the expression “arm’s eye” was used in older sewing texts (e.g. Gynametry by M. V. Coleman, published in 1887 by Byrd & Pattillo) it appears that in poor prints the apostrophe and the crossbar of the lower case “e” were indistinct. The neologism “armscye” was created by readers who concatenated the orphaned fragments “arm” and “s” with the corrupt “cye”.
Until the beginning of the 20th century writers favoured the original term or at least a more logical variation (e.g. “armeye” in The Perfect Dressmaking System by Ella A. Bennett, published in 1914). However, as self-proclaimed experts copied each other, the term “armscye” eventually became widely enough used by home sewers to gain general acceptance.