It was three years later before the Ursulines and their pupils took possession of a massive convent of stone, built for them on the site which they still occupy.
Previously in The Jesuits in North America in the Seventeenth Century.
Our special project presenting the definitive account of France in Canada by Francis Parkman, one of America’s greatest historians.
On the fourth of May, 1639, Madame de la Peltrie, Marie de l’Incarnation, Marie de St. Bernard, and another Ursuline, embarked at Dieppe for Canada. In the ship were also three young hospital nuns, sent out to found at Quebec a Hôtel Dieu, endowed by the famous niece of Richelieu, the Duchesse d’Aiguillon.  Here, too, were the Jesuits Chaumonot and Poncet, on the way to their mission, together with Father Vimont, who was to succeed Le Jeune in his post of Superior. To the nuns, pale from their cloistered seclusion, there was a strange and startling novelty in this new world of life and action, — the ship, the sailors, the shouts of command, the flapping of sails, the salt wind, and the boisterous sea. The voyage was long and tedious. Sometimes they lay in their berths, sea-sick and woe-begone; sometimes they sang in choir on deck, or heard mass in the cabin. Once, on a misty morning, a wild cry of alarm startled crew and passengers alike. A huge iceberg was drifting close upon them. The peril was extreme. Madame de la Peltrie clung to Marie de l’Incarnation, who stood perfectly calm, and gathered her gown about her feet that she might drown with decency. It is scarcely necessary to say that they were saved by a vow to the Virgin and St. Joseph. Vimont offered it in behalf of all the company, and the ship glided into the open sea unharmed.
[1 Juchereau, Histoire de l’Hôtel-Dieu ae Québec, 4.]
They arrived at Tadoussac on the fifteenth of July; and the nuns ascended to Quebec in a small craft deeply laden with salted codfish, on which, uncooked, they subsisted until the first of August, when they reached their destination. Cannon roared welcome from the fort and batteries; all labor ceased; the storehouses were closed; and the zealous Montmagny, with a train of priests and soldiers, met the new-comers at the landing. All the nuns fell prostrate, and kissed the sacred soil of Canada.  They heard mass at the church, dined at the fort, and presently set forth to visit the new settlement of Sillery, four miles above Quebec.
[2 Juchereau, 14; Le Clerc, II. 33; Ragueneau, Vie de Catherine de St. Augustin, “Epistre dédicatoire;” Le Jeune, Relation, 1639, Chap. II.; Charlevoix, Vie de Marie de l’Incarnation, 264; “Acte de Reception,” in Les Ursulines de Québec, I. 21.]
Noel Brulart de Sillery, a Knight of Malta, who had once filled the highest offices under the Queen Marie de Médicis, had now severed his connection with his Order, renounced the world, and become a priest. He devoted his vast revenues — for a dispensation of the Pope had freed him from his vow of poverty — to the founding of religious establishments.  Among other endowments, he had placed an ample fund in the hands of the Jesuits for the formation of a settlement of Christian Indians at the spot which still bears his name. On the strand of Sillery, between the river and the woody heights behind, were clustered the small log-cabins of a number of Algonquin converts, together with a church, a mission-house, and an infirmary, — the whole surrounded by a palisade. It was to this place that the six nuns were now conducted by the Jesuits. The scene delighted and edified them; and, in the transports of their zeal, they seized and kissed every female Indian child on whom they could lay hands, “without minding,” says Father Le Jeune, “whether they were dirty or not.” “Love and charity,” he adds, “triumphed over every human consideration.” 
[4 See Vie de l’Illustre Serviteur de Dieu Noel Brulart de Sillery; also Études et Recherches Bioqraphiques sur le Chevalier Noel Brulart de Sillery, and several documents in Martin’s translation of Bressani, Appendix IV.]
[4 “. . . sans prendre garde si ces petits enfans sauvages estoient sales ou non; . . . la loy d’amour et de charité l’emportoit par dessus toutes les considerations humaines.” — Relation, 1639, 26 (Cramoisy).]
The nuns of the Hôtel-Dieu soon after took up their abode at Sillery, whence they removed to a house built for them at Quebec by their foundress, the Duchesse d’Aiguillon. The Ursulines, in the absence of better quarters, were lodged at first in a small wooden tenement under the rock of Quebec, at the brink of the river. Here they were soon beset with such a host of children, that the floor of their wretched tenement was covered with beds, and their toil had no respite. Then came the small-pox, carrying death and terror among the neighboring Indians. These thronged to Quebec in misery and desperation, begging succor from the French. The labors both of the Ursulines and of the hospital nuns were prodigious. In the infected air of their miserable hovels, where sick and dying savages covered the floor, and were packed one above another in berths, — amid all that is most distressing and most revolting, with little food and less sleep, these women passed the rough beginning of their new life. Several of them fell ill. But the excess of the evil at length brought relief; for so many of the Indians died in these pest-houses that the survivors shunned them in horror.
But how did these women bear themselves amid toils so arduous? A pleasant record has come down to us of one of them, — that fair and delicate girl, Marie de St. Bernard, called, in the convent, Sister St. Joseph, who had been chosen at Tours as the companion of Marie de l’Incarnation. Another Ursuline, writing at a period when the severity of their labors was somewhat relaxed, says, “Her disposition is charming. In our times of recreation, she often makes us cry with laughing: it would be hard to be melancholy when she is near.”
[Lettre de la Mrre Ste Claire ŕ une de ses Seurs Ursulines de Paris, Québec, 2 Sept., 1640. — See Les Ursulines de Québec, I. 38.]
It was three years later before the Ursulines and their pupils took possession of a massive convent of stone, built for them on the site which they still occupy. Money had failed before the work was done, and the interior was as unfinished as a barn.  Beside the cloister stood a large ash-tree; and it stands there still. Beneath its shade, says the convent tradition, Marie de l’Incarnation and her nuns instructed the Indian children in the truths of salvation; but it might seem rash to affirm that their teachings were always either wise or useful, since Father Vimont tells us approvingly, that they reared their pupils in so chaste a horror of the other sex, that a little girl, whom a man had playfully taken by the hand, ran crying to a bowl of water to wash off the unhallowed influence. 
[5 The interior was finished after a year or two, with cells as usual. There were four chimneys, with fireplaces burning a hundred and seventy-five cords of wood in a winter; and though the nuns were boxed up in beds which closed like chests, Marie de l’Incarnation complains bitterly of the cold. See her letter of Aug. 26, 1644.]
[6 Vimont, Relation, 1642, 112 (Cramoisy).]
Now and henceforward one figure stands nobly conspicuous in this devoted sisterhood. Marie de l’Incarnation, no longer lost in the vagaries of an insane mysticism, but engaged in the duties of Christian charity and the responsibilities of an arduous post, displays an ability, a fortitude, and an earnestness which command respect and admiration. Her mental intoxication had ceased, or recurred only at intervals; and false excitements no longer sustained her. She was racked with constant anxieties about her son, and was often in a condition described by her biographers as a “deprivation of all spiritual consolations.” Her position was a very difficult one. She herself speaks of her life as a succession of crosses and humiliations. Some of these were due to Madame de la Peltrie, who, in a freak of enthusiasm, abandoned her Ursulines for a time, as we shall presently see, leaving them in the utmost destitution. There were dissensions to be healed among them; and money, everything, in short, to be provided. Marie de l’Incarnation, in her saddest moments, neither failed in judgment nor slackened in effort. She carried on a vast correspondence, embracing everyone in France who could aid her infant community with money or influence; she harmonized and regulated it with excellent skill; and, in the midst of relentless austerities, she was loved as a mother by her pupils and dependents. Catholic writers extol her as a saint.  Protestants may see in her a Christian heroine, admirable, with all her follies and her faults.
[7 There is a letter extant from Sister Anne de Ste Claire, an Ursuline who came to Quebec in 1640, written soon after her arrival, and containing curious evidence that a reputation of saintship already attached to Marie de l’Incarnation. “When I spoke to her,” writes Sister Anne, speaking of her first interview, “I perceived in the air a certain odor of sanctity, which gave me the sensation of an agreeable perfume.” See the letter in a recent Catholic work, Les Ursulines de Québec, I. 38, where the passage is printed in Italics, as worthy the especial attention of the pious reader.]
The traditions of the Ursulines are full of the virtues of Madame de la Peltrie, — her humility, her charity, her penances, and her acts of mortification. No doubt, with some little allowance, these traditions are true; but there is more of reason than of uncharitableness in the belief, that her zeal would have been less ardent and sustained, if it had had fewer spectators. She was now fairly committed to the conventual life, her enthusiasm was kept within prescribed bounds, and she was no longer mistress of her own movements. On the one hand, she was anxious to accumulate merits against the Day of Judgment; and, on the other, she had a keen appreciation of the applause which the sacrifice of her fortune and her acts of piety had gained for her. Mortal vanity takes many shapes. Sometimes it arrays itself in silk and jewels; sometimes it walks in sackcloth, and speaks the language of self-abasement. In the convent, as in the world, the fair devotee thirsted for admiration. The halo of saintship glittered in her eyes like a diamond crown, and she aspired to outshine her sisters in humility. She was as sincere as Simeon Stylites on his column; and, like him, found encouragement and comfort in the gazing and wondering eyes below.
[Madame de la Peltrie died in her convent in 1671. Marie de l’Incarnation died the following year. She had the consolation of knowing that her son had fulfilled her ardent wishes, and become a priest.]
– The Jesuits in North America in the Seventeenth Century, Chapter 14 by Francis Parkman
The below is from Francis Parkman’s Introduction.
If, at times, it may seem that range has been allowed to fancy, it is so in appearance only; since the minutest details of narrative or description rest on authentic documents or on personal observation.
Faithfulness to the truth of history involves far more than a research, however patient and scrupulous, into special facts. Such facts may be detailed with the most minute exactness, and yet the narrative, taken as a whole, may be unmeaning or untrue. The narrator must seek to imbue himself with the life and spirit of the time. He must study events in their bearings near and remote; in the character, habits, and manners of those who took part in them, he must himself be, as it were, a sharer or a spectator of the action he describes.
With respect to that special research which, if inadequate, is still in the most emphatic sense indispensable, it has been the writer’s aim to exhaust the existing material of every subject treated. While it would be folly to claim success in such an attempt, he has reason to hope that, so far at least as relates to the present volume, nothing of much importance has escaped him. With respect to the general preparation just alluded to, he has long been too fond of his theme to neglect any means within his reach of making his conception of it distinct and true.