Thomas Aquinas

“ The priest does not divulge the confession by imposing such a penance, though people may suspect the penitent of having committed some great sin. For a man is not certainly taken to be guilty, because he is punished, since sometimes one does penance for another: thus we read in the Lives of the Fathers of a certain man who, in order to incite his companion to do penance, did penance together with him. And if the sin be public, the penitent, by fulfilling his penance, shows that he has been to confession. ”

“ Although Penance cancels all deficiencies, by restoring man to his former state of grace, yet it does not always restore him to his former dignity. Hence women after doing penance for fornication are not given the veil, because they do not recover the honor of virginity. In like manner, after doing public penance, a sinner does not recover his former dignity so as to be eligible for the clerical state and a bishop who would ordain such a one ought to be deprived of the power of ordaining, unless perhaps the needs of the Church or custom require it. ”

“ The final reconciliation is reserved to the bishop, who alone can impose solemn penance" [*Cap. lxiv, dist. 50] .
This penance can be imposed on men and women; but not on clerics, for fear of scandal. Nor ought such a penance to be imposed except for a crime which has disturbed the whole of the city.
On the other hand public but not solemn penance is that which is done in the presence of the Church, but without the foregoing solemnity, such as a pilgrimage throughout the world with a staff. A penance of this kind can be repeated, and can be imposed by a mere priest, even on a cleric. ”