The question is whether the baptism has been solemnized, according to the divine command, in the name of the Father, and of the Son, and of the Holy Ghost.  St. Cyprian in his controversy with Stephen, Bp. of Rome, represented the sterner view that heretical baptism was invalid.  But, with some exceptions in the East, the position ultimately prevailed that baptism with water, and in the prescribed words, by whomsoever administered, was valid.  So St. Augustine, “Si evangelicus verbis in nomine Patris et Filii et Spiritus Sancti Marcion baptismum consecrabat, integrum erat Sacramentum, quamvis ejus fides sub eisdem verbis aliud opinantis quam catholica veritas docet non esset integra.”  (Cont. Petil. de unico bapt. § 3.)  So the VIII. Canon of Arles (314), “De Afris, quod propria lege sua utuntur ut rebaptizent, placuit, ut, si ad ecclesiam aliquis de hæresi venerit, interrogent eum symbolum; et si perviderint eum in Patre, et Filio et Spiritu Sancto, esse baptizatum, manus ei tantum imponantur, ut accipiat spiritum sanctum.  Quod si interrogatus non responderit hanc Trinitatem, baptizetur.”  So the VII. Canon of Constantinople (381) by which the Eunomians who only baptized with one immersion, and the Montanists, here called Phrygians, and the Sabellians, who taught the doctrine of the Fatherhood of the Son, were counted as heathen.  Vide Bright’s notes on the Canons of the Councils, p. 106.  Socrates, v. 24, describes how the Eunomi-Eutychians baptized not in the name of the Trinity, but into the death of Christ.