It has always been the praiseworthy habit of Catholics to have recourse to Mary in danger and in troublous times, and to take refuge in her maternal goodness.

 
T he supreme Apostolic office which we discharge and the exceedingly difficult condition of the present times, daily exhort and almost compel Us to watch all the more carefully over the integrity of the Church, the greater the calamities from which she suffers. […] To this end, We deem that there could be no surer and more efficacious means than, by religion and piety, to obtain the favour of the great Virgin Mary, the Mother of God. […] Therefore, now that the annual commemoration of the manifold and exceedingly great favours obtained by the Christian people through the prayer of the Rosary is at hand, We desire that, this year, the same prayer be offered by the whole Catholic world with the greatest earnestness to the Blessed Virgin, so that by her intercession, we may be blessed to see her Divine Son appeased and moved to compassion by the evils which afflict us. […]

Outstanding defender of the Church of God

It has always been the praiseworthy habit of Catholics to have recourse to Mary in danger and in troublous times, and to take refuge in her maternal goodness. This demonstrates the firm hope – indeed, the complete confidence – that the Catholic Church has always rightly placed in the Mother of God. And truly the Immaculate Virgin, chosen to be the Mother of God, and for this very reason made the Co-redemptrix of the human race, enjoys such great favour and power with her Son that no human or angelic creature has ever obtained, or could ever attain any greater. […] This most ardent and trusting devotion to the august Queen of Heaven has never shone forth with such brilliancy as when the militant Church of God has seemed to be endangered by the violence of widespread heresy, or by an overwhelming moral corruption, or by the attacks of powerful enemies. Ancient and modern history and the sacred annals of the Church attest to the public and private prayers and petitions addressed to the Mother of God, and to the help She has granted in return, as well as the peace and tranquillity obtained from God through her intercession. This has given rise to the illustrious titles with which Catholic people attribute to Her of Helper of Christians, Benefactor and Consoler, mighty in war, Lady of victories, and peace-giver. Among these titles is specially to be commemorated that of the Rosary, under which the signal benefits She has gained for the whole of Christendom have been solemnly perpetuated. […]

Victory obtained by the recitation of the Rosary

Our Lady of the Rosary of Lepanto - Church of St. Dominic, Granada (Spain)
The efficacy and power of this devotion was also wondrously exhibited in the sixteenth century, when the immense forces of the Turks threatened to impose on nearly the whole of Europe the yoke of superstition and barbarism. Amidst those circumstances, the Supreme Pontiff, St. Pius V, after rousing the Christian princes to the defence of a cause common to all, applied his zeal to obtain for Christendom the favour of the most powerful Mother of God, invoked through the recitation of the Holy Rosary. And the response was the marvellous event which then took place in the sight of Heaven and earth […]. And thus Christ’s faithful warriors, prepared to sacrifice their lives and shed their blood for the deliverance of their religion and their country, proceeded undauntedly to meet their foe near the Gulf of Corinth, while those not invested with arms formed, for their part, a pious band of supplicants calling upon Mary and saluting Her in unison, again and again, in the formula of the Rosary, imploring Her to grant victory to those engaged in battle. And our Sovereign Lady, moved by those prayers, did come to their assistance; for in the naval battle by the Echinades Islands, without sustaining any great loss, the Christian fleet gained a magnificent victory, in which the enemy were routed with great slaughter. Accordingly, to preserve the memory of this great favour, the Holy Pontiff decreed that a feast in honour of Our Lady of Victories should celebrate the anniversary of so memorable a struggle, a feast which Gregory XIII later dedicated under the title of “The Holy Rosary.” […]

Exhortation to pray for the Holy Church

Moved by these thoughts and by the examples of Our Predecessors, We have deemed it most opportune to institute solemn prayers to the August Virgin in the recital of the Rosary, so as to obtain from her Son Jesus Christ a similar aid against present dangers. You have before your eyes, Venerable Brethren, the grave trials to which the Church is incessantly exposed. Christian piety, public morality, and even faith itself, the supreme good and fundament of all the other virtues, are daily menaced with ever greater perils. […] However, the most painful and grievous fact is that so many souls, redeemed by the Blood of Christ, snatched from salvation by the whirlwind of an age of error, precipitated into the abyss of eternal death. […] For these reasons, we not only earnestly exhort all Christians to apply themselves tirelessly to the pious devotion of the Rosary, whether publicly or privately in their home and with their family, but we also desire that the whole of the month of October in this year should be consecrated to the Holy Queen of the Rosary. […] The heavenly Patroness of the human race will kindly receive these prayers and supplications, and will easily obtain a growth in virtue for the good, and that the erring may come to their senses and repent; and that God, the avenger of crime, moved to merciful clemency, may deliver Christendom and civil society from all danger, restoring to them that peace so greatly desired. ◊

Excerpts from: LEO XIII. Supremi apostolatus officio, 1/9/1883