In chapter six of my book, Behold the Mother of My Lord: Towards a Mormon Mariology, "Devotions and Apparitions" (pp. 157-175) I discuss examples of approved Marian apparitions (Fatima and The Lady of All Nations) and examples of prayers to Mary.
One common expression of Marian devotion is the Rosary. The following, from two Traditionalist Catholics who affirm the efficacy of the practice, shows the function of the Rosary in Catholic piety and devotion to Mary:
The Blessed Virgin Mary gave the Rosary to St. Dominic in 1214 as a spiritual weapon to combat the Albigensian heresy and to rekindle the Catholic Faith. She told Blessed Alan de la Roche: “When you say the Rosary the angels rejoice, the Blessed Trinity delights in it, my Son finds joy in it too and I myself am happier than you can possibly guess. After the Holy Sacrifice of the Mass, there is nothing in the Church that I love as much as the Rosary” (St. Louis Marie de Montfort, The Secret of the Rosary, p. 120) . . . The Rosary is, according to Pope Pius XII, “A synthesis of the whole Gospels: meditation on the mysteries of the Lord, an evening sacrifice, a garland of roses, a hymn of praise, a family prayer, a compendium of Christian life, a sure pledge of heavenly favors, a defense while we await our expected salvation” (Letter to Philippinas Insulas, July 31, 1946) . . . In 1917, Our Lady of Fatima, known as “the Lady of the Rosary,” told Catholics to amend their lives and pray the Rosary in order to avert spiritual and temporal calamities. One of the visionaries, Sr. Lucia dos Santos, remarked:
The Most Holy Virgin in these last times in which we live has given a new efficacy to the recitation of the Rosary to such an extent that there is no problem, no matter how difficult it is, whether temporal or above all, spiritual, in the personal life of each one of us, of our families, of the families of the world, or of the religious communities, or even of the life of peoples and nations that cannot be solved by the Rosary.
There is no problem I tell you, no matter how difficult it is, that we cannot resolve by the prayer of the Holy Rosary. With the Holy Rosary, we will save ourselves. We will sanctify ourselves. We will console Our Lord and obtain the salvation of many souls. (Frere Michel de la Trinite, The Whole Truth About Fatima, Vol. I, p. 508) (Francisco Radecki and Dominic Radecki, Tumultuous Times: The Twenty General Councils of the Catholic Church and Vatican II and its Aftermath [Wayne, Mich.: St. Joseph’s Media, 2004], 507-8)
Under the section “Meditation on the Mysteries of the Rosary,” we read:
We learn and understand the chief mysteries of the Faith through the recitation of the Rosary. It strengthens our souls, confirms our faith, and protects us from error . . . The Rosary has a special efficacy to aid in living a Christian life, acquiring the spirit of prayer and avoiding the corrupting influence of the world. It is said that one cannot persevere in a habit of mortal sin, and in the daily recitation of the Rosary: One must give up on or the other.
This prayer offers an easy way to impress the chief doctrines of Catholicism upon the mind . . . Pope Pius XI wrote:
We must not, then, despair at the sight of present evils, or even of greater that may come. We must pray to God with confidence, and take as our intermediary and patroness the Blessed Virgin, through whom it is His will we should have all. We must say her Rosary, and by meditation on its mysteries obtain the true, serene, perspective view of life, death, and eternity which they present. Especially the ‘family Rosary’ is to be maintained. (Ingravescentibus malis, September 29, 1937) (Ibid., 508, 509)
Finally, under the heading “15 Promises of Mary to Christians who Recite the Rosary,” we read:
If you are not yet convinced of the great benefits attached to praying the Rosary, consider the 15 promises which Our Blessed Mother has graciously attached to its recitation:
1) Whoever will faithfully serve me by the recitation of the Rosary will receive signal graces.
2) I promise my special protection and greatest graces to those who will recite my Rosary.
3) The Rosary shall be a powerful armor against Hell: it shall destroy vice, decrease sin, and defeat heresy.
4) I will cause virtue and good works to flourish; it shall obtain for souls the abundant mercy of God; it shall withdraw the hearts of men from the love of the world and its vanities and shall lift them to the desire of eternal things. Oh, that souls would sanctify themselves by this means!
5) The soul that recommends itself to me by the meditation of the Rosary shall not perish.
6) Whoever will recite the Rosary devoutly applying himself to the consideration of its sacred mysteries, shall never be conquered by misfortune. God will not chastise him in His justice; he shall not perish by an unprovided death; if he shall be just he shall remain in the grace of God and become worthy of eternal life.
7) Whoever will have a true devotion for the Rosary shall not die without the sacraments of the Church.
8) Those who faithfully recite the Rosary shall have during their life and at their death the light of God and the plenitude of His graces; at the moment of death they shall participate in the merits of the saints in paradise.
9) I will deliver from purgatory those who have been devoted to the Rosary.
10) The faithful children of the Rosary shall merit a high degree of glory in heaven.
11) You shall obtain all that you ask of me by the recitation of the Rosary.
12) All those who propagate the holy Rosary shall be aided by me in their necessities.
13) I have obtain from my Divine Son that all the advocates of the Rosary shall have for intercessors the entire celestial court during their life and at the hour of death.
14) All who recite the Rosary are my son, and brothers of my only Son, Jesus Christ.
15) Devotion to the Rosary is a great sign of predestination. (John Johnson, The Rosary in Action, p. 33) (Ibid., 594)
Such efficacy, both temporal and eschatological, imputed to the Rosary shows the very problematic nature of approved forms of Marian devotion within Catholicism, all the more heightened by the fact that the dogmas about Mary (perpetual virginity; Immaculate Conception; Bodily Assumption) are without any meaningful biblical support and support from anything that could conceivably be called "apostolic tradition" (see my book and blog posts addressing Mariology for documentation).
