Research on anatomy and physiology of the umbilical cord
Ligation of the umbilical cord came into use as a means to prevent bleeding.  Spivack
(1946) studied the structure and physiology of the umbilical cord, and its blood
vessels; the infant's heart pumps blood through the umbilical arteries to the placenta,
which delivers oxygen and nutrients to the baby via the umbilical vein.  Spivack
observed that the umbilical arteries close quickly after onset of respiration, and
commented:

    "Oxygenation of the newborn's blood after establishment of its pulmonary
    respiration is the main factor in bringing about closure of the umbilical arteries…

    …Experience  since long ago has taught some clinicians that ligation of the cord
    is not paramount in the care of the stump." [1, p398]

Spivack cited Engelmann (1883), who noted that the umbilical arteries have an
intrinsic capacity to check their bleeding in unaided labor, and Rachmanow's (1914)
series of several thousand cases in which the cords were not tied, and not a single
newborn died of hemorrhage.  Rachmanow warned however, that spontaneous
cessation of pulsation of the cord and establishment of respiration are essential
conditions before severance of the cord.
Reference
  1. Spivack M. The anatomic peculiarities of the human umbilical cord and
    their clinical significance. Am J Obstet Gynecol 1946 Sep; 52(3):387-401.