This Custom is traced (in part to Medieval England, and later it traveled to The New World). It was believed in the 12th Century (forward), that once a child was born, it's Mother needed to swaddle it in her own clothes (when not attending the child). This was because IF the child died before it could be baptized, it's “Soul” could still achieve Heaven. 30 to 50 Percent was considered an accurate number for “Infant Mortality” during this Period – so the “Custom” WAS popular. It was also thought that Mother's clothing could also ward off MANY Fairies and Demons from trying to take the child (or steal it's Soul).
