The Office of Readings is part of the Divine Office, but not of the Liturgy of the Hours, interestingly enough. The "Hours" are assigned to actual "hours" (more or less) of the day: morning, noon, evening, whereas the Office of Readings, which originated (and in monastic communities is still celebrated) as a nocturnal vigil service, can now be prayed at any time of day. It is, you could say, the liturgical setting for mental prayer (meditation), and consists of three psalms (or, more likely, one rather long psalm divided into three parts) and two readings (one Scriptural, one from the Church's vast library--the Fathers and Doctors of the Church, writings by or about the saint of the day, official Church teachings...).
The second reading in the OR for today's feast of St. Polycarp features one of the most astounding and edifying texts in the whole Christian tradition outside of the Bible itself. It is the eye-witness account of the martyrdom of the elderly bishop of Smyrna, and includes his last words (spoken as he was tied to a stake to be burned to death). I invite you to read them slowly. This dates to a time in the Church's liturgical history when the presider at Mass would pray the Eucharistic prayer more or less spontaneously, without a set script. But you can see from Polycarp's last prayer that the "pattern" for the Eucharistic prayer became the pattern for his own life. Would that the Eucharistic prayer would become the way we interpreted (and lived) our own life, too!
Lord, almighty God, Father of your beloved and blessed Son Jesus Christ, through whom we have come to the knowledge of yourself, God of angels, of powers, of all creation, of all the race of saints who live in your sight, I bless you for judging me worthy of this day, this hour, so that in the company of the martyrs I may share the cup of Christ, your anointed one, and so rise again to eternal life in soul and body, immortal through the power of the Holy Spirit. May I be received among the martyrs in your presence today as a rich and pleasing sacrifice. God of truth, stranger to falsehood, you have prepared this and revealed it to me and now you have fulfilled your promise.
I praise you for all things, I bless you, I glorify you through the eternal priest of heaven, Jesus Christ, your beloved Son. Through him be glory to you, together with him and the Holy Spirit, now and for ever. Amen.
BTW: The little responsory following this reading is another liturgical gem. It is taken from the book of Revelation, chapter 2--the letter "to the angel of the Church in Smyrna." Read that passage in the light of today's saint: Polycarp is said to have been a disciple of St. John. Was he the "angel" of the Church in Smyrna at the time the seer wrote to give advance warning of persecution?
For the full eye-witness account given in today's OR, go to Universalis and scroll down....