Note : In 1981, chapters 56, 57 and 58 were given constitutional status [M9GA, 9-65, #6, p. 137]

56-6. Then the minister is to pray for a blessing to attend this ordinance, after which, calling the child by name, he shall say:
I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.
As he pronounces these words, he is to baptize the child with water, by pouring or sprinkling it on the head of the child, without adding any other ceremony; and the whole shall be concluded with prayer.

DIGEST :

BACKGROUND AND COMPARISON :
PCA 1975, adopted text for Directory for Worship, 57-5, Minutes of General Assembly, 3-70, p. 85
PCA 1973, text of DfW 10-7, as printed in the Appendix of the Minutes of General Assembly, p. 158
Continuing Presbyterian Church 1973, Proposed BCO text, Directory for Worship, 10-7, p. 70
PCUS, 1933, DfW, X, §349
Then the minister is to pray for a blessing to attend this ordinance, after which, calling the child by name, he shall say;
"I baptize thee in the name of the Father, and of the Son, and of the Holy Ghost."
As he pronounces these words, he is to baptize the child with water, by pouring or sprinkling it on the head of the child, without adding any other ceremony; and the whole shall be concluded with prayer.

PCUS 1894, IX-6, p. 114
Then the minister is to pray for a blessing to attend this ordinance; after which, calling the child by name, he shall say,
"I baptize thee into the name of the Father, and of the Son, and of the Holy Ghost."
As he pronounces these words, he is to baptize the child with water, by pouring or sprinkling it on the face of the child, without adding any other ceremony; and the whole shall be concluded with prayer.
Although it is proper that baptism be administered in the presence of the congregation, yet there may be cases when it will be expedient to administer this ordinance in private houses; of which the minister is to be the judge.

PCUS 1885, Third Revision of the Directory of Worship, III-4-3
3. Then the minister is to pray that what is signified and sealed in this sacrament may be accomplished by the Spirit in the child; after which, calling it by its name, he shall say, ―I baptize thee in the name of the Father, and of the Son, and of the Holy Ghost, Amen. As he pronounces these words he is to baptize the child with water, by pouring or sprinkling, without adding any other ceremony, and the whole shall be concluded with prayer.

PCUSA, 1789, VII-5, p. 194-195.
Then the Minister is to pray for a blessing to attend this ordinance, after which, calling the child by it's name, he shall say :
'I baptize thee, in the name of the Father, and of the Son, and of the Holy Ghost.'
As he pronounces these words, he is to baptize the Child with water; by pouring or sprinkling it on the face of the Child, without adding any other ceremony : and the whole shall be concluded with prayer.
Although it is proper, that baptism be administered in the presence of the Congregation : yet there may be cases, when it will be expedient to administer this ordinance in private houses; of which the Minister is to be the Judge.

PCUSA, 1786 draft, ¶-8-15, p. 78-79.
Then the Minister is to pray for a blessing to attend this ordinance, in the following or like manner :
'Most merciful, holy, and eternal God, we pray for thy blessing upon these parents and their child. The souls of parents and the souls of children are thine. Enable these parents, in faith and love, to offer up their child to thee, at this time, in this holy ordinance of baptism. Sanctify this child by thy grace. May its original guilt be done away, through the blood of the Lamb, that was slain. Wash this child in the laver of regeneration. Ingraft it into Christ; and make it an heir of glory. Join the inward baptism of the Spirit with the outward baptism of water. Graciously bless and sanctify this holy ordinance to the spiritual benefit of this child. Ratify in heaven what we now do upon earth. Hear us, O our God, accept and answer us, only for the sake of our divine Redeemer. Amen.'
Then the Minister, either taking the Child in his arms, or leaving it in the arms of the parent, shall call the child by its name, and say ;
'I baptize thee, in the name of the Father, and of the Son, and of the Holy Ghost.'
As he pronounces these words, he is to baptize the Child with water, by pouring or sprinkling it on the face of the Child, without adding any other ceremony.
This being performed he shall pray to this or the like purpose :
'O thou most glorious, condescending, and gracious God, Father, Son, and Holy Ghost; we give thee hearty thanks, for the covenant of grace, and for all the institutions of thy mercy. Follow with thy blessing this holy ordinance of baptism, which has now been administered in thy name. O Lord, enable these parents to live in the faithful discharge of every Christian duty, towards this Child. Receive it into thy fatherly care and protection. May it live and grow up before thee, and do worthily in its day and generation. Sanctify it by thy Spirit; uphold it by thy power. May it be a useful member of thy Church here; and be kept, by faith, unto salvation, through Jesus Christ our Lord. Amen.'
This will form a part of the concluding prayer of public worship.

COMMENTARY:
Morton H. Smith, Commentary on the Book of Church Order, 6th edition, 2007, p. 433.
This chapter has been given full constitutional authority, and should be followed carefully by the minister in administering baptism. The questions set forth in this chapter should always be used, not those which appear in the Book of Common Worship, or other Presbyterian books of church order.
The first question calls for a clear understanding of the Biblical doctrine of original sin. The second question makes it explicit that the parent or guardian presenting the child must be a Christian. The third question includes the phrase, "Do you now unreservedly dedicate your child to God . . ." The idea of dedication of the child to God is not explicitly found in the command to baptize in the New Testament, or to circumcise in the Old Testament. The remaining portion of this question calling for the promise to set a godly example, and to teach the faith to the child is certainly Biblical. The reference to dedication of the child should never be used to merely "dedicate children" and not baptize them. Jesus commanded that we baptize, not that we dedicate our children. To substitute "dedication" for baptism is totally unconstitutional, and any Session or minister involved in such should be subject to the discipline of the Presbytery.