Did these considerations prevent him from confessing his sins, and
induce him to cover his transgressions? They were mostly arguments for
his proclaiming his repentance, had his sins been public.

By his sins he had countenanced wickedness, and set the example of it
in a dignified station. By his confession he would condemn it, and
justify the law of God, which forbids it; and by his return to duty,
do every thing then in his power, to repair the injury he had done and
prevent or remove the bad effects of his example. Why then had
he neglected it?

There was only one consideration which could excuse him--that, we
apprehend, justified him. His sins in this affair were not public. It
appears from several circumstances that they were kept out of sight
till the prophet was sent to reprove and publish them, and his
repentance of them. Joab knew indeed that the king wished the death of
Uriah. It is not certain that he knew the cause. If he did, it is not
probable that he had divulged it.

That these matters were not transacted openly, or generally known,
maybe inferred from two considerations, namely, from Bathsheba's going
into mourning for Uriah, and from Nathan's declaration, when he
foretold the evils which would come on David and his family, to punish
his sins on this occasion, notwithstanding his repentance. Mournings
were very short among the Hebrews; but this adulteress would not have
put on mourning, or David delayed to take her to his house, to be his
wife, till her mourning was ended, had this affair been public. But,
that it was not so, is put out of doubt by the language of the prophet
in his address to the king--"Thou didst it secretly."