A desideratum is something desired as essential, an aspiration that has not yet been fulfilled.
In this excerpt, the "great desideratum" that Madison is referring to is the first one:
"to sacrifice self-interest for the common good"
Madison thinks that by sacrificing self interests for the greater good, the Government will leave behind the cause of reproach or disgrace under which it has been for so long.
Third person omniscent can read the thoughts and feelings if the charecters while third person limited can only see them and what they are doing/saying
