"You assign greater consequence to the clergyman than one has been used to hear given, or than I can quite comprehend. One does not see much of this influence and importance in society, and how can it be acquired where they are so seldom seen themselves? How can two sermons a week, even supposing them worth hearing, supposing the preacher to have the sense to prefer Blair's to his own, do all that you speak of? govern the conduct and fashion the manners of a large congregation for the rest of the week? One scarcely sees a clergyman out of his pulpit."
It's just a side-mention. It is also a mention by Mary Crawford, and because of that association some people have concluded that Austen -- who read sermons extensively -- was not a fan of Blair.
However, I wonder if there is more to the matter than might seem to be the case at first. Mansfield Park crosses themes with several of Blair's sermons. One that is quite noticeable is that Blair's sermons are a work Austen certainly would have read that uses the word 'constancy' in a sense much like that in which Austen uses it in the novel. Indeed, one of his sermons, Sermon XV of Volume I, is entitled, "On the Motives to Constancy in Virtue".
In the sermon, Blair imagines a man who has decided to devote himself to virtue. However, it turns out to be quite difficult:
The peace which he hoped to enjoy, is interrupted, either by his own frailties, or by the vices of others. Passions, which had not been thoroughly subdued, struggle for their accustomed gratification. The pleasure which he expected to find in devotion, sometimes fails him; and the injustice of the world often sours and frets him. Friends prove ungrateful; enemies misrepresent, rivals supplant him: And part, at least, of the mortifications which he suffers, he begins to ascribe to virtue.
Blair's purpose in the sermon is to argue that, despite occasional appearances, the difficulties of life never provide a sufficient reason to be "weary in well-doing". He raises several points to back this up. (1) Every state of life has its difficulties, so if the aim is to avoid having a difficult life, it's an aim that can't be guaranteed, no matter what one does. (2) More importantly, vice actually increases the difficulty of life even when it isn't obvious that it is doing so. Contrary to what we usually think, self-denial is not the exclusive province of virtue; self-denial, in fact, is common to both virtue and vice. Disorder in one's passions mean that some of your desires will go unmet, and whenever you are doing something wrong you are denying yourself some kind of good. (3) Difficulties associated with virtue, on the other hand, since virtue is linked with moderation of passions, are more bearable, because moderation of passion itself can ease the pain and hardship. Virtue, in other words, better prepares us for when things do not go our own way -- which, inevitably, they sometimes will. Virtue gives its bearer an independence of fortune:
It is the peculiar effect of virtue, to make a man's happiness arise from himself and his own conduct. A bad man is wholly the creature of the world. He hangs upon its favour, lives by its smiles, and is happy or miserable, in proportion to his success. But to a virtuous man, success, in worldly undertakings, is but a secondary object. To discharge his own part with integrity and honour, is his chief aim. If he has done properly what was incumbent on him to do, his mind is at rest; to Providence he leaves the event.
At the same time, while virtue may seem at first to restrict the enjoyments you can have, the truth is actually the opposite: genuine virtue allows worldly pleasures, in proper moderation and place, and adds to them its own pleasures. (4) Those who sow in tears shall reap in joy, due to the future life.
Another of the sermons in Volume I is Sermon XI, "On the Duties of the Young", in which we also find a connection with constancy:
Too many of the pretended friendships of youth, are mere combinations in pleasure. They are often founded on capricious likings; suddenly contracted, and as suddenly dissolved. Sometimes they are the effect of interested complaisance and flattery on the one side, and of credulous fondness on the other. Beware of such rash and dangerous connections, which may afterwards load you with dishonour. Remember that by the character of those whom you choose for your friends, your own is likely to be formed, and will certainly be judged of by the world. Be slow, therefore, and cautious in contracting intimacy; but when a virtuous friendship is once established, consider it as a sacred engagement. Expose not yourselves to the reproach of lightness and inconstancy, which always bespeak, either a trifling, or a base mind. Reveal none of the secrets of your friend. Be faithful to his interests. Forsake him not in danger. Abhor the thought of acquiring any advantage by his prejudice or hurt.
The whole of Sermon XI is worth reading, actually, in this respect, since a large number of themes in the sermon are shared with Mansfield Park. It's true, of course, that the moral dangers of youth are fairly universal, so it's possible that convergence rather than interaction explains the resemblances. But it is suggestive nonetheless.
