United State Note!

As I understand the system, the amount of money able to be issued in the form of United States notes is capped by Congress, at $346,681,016. This level was set way back in 1878. Of this amount, about $239,000,000 already exists in the form of notes that are unaccounted for - in circulation, or hiding in vaults and collections, or notes lost and destroyed without Treasury being informed of this fact. So they are only authorized to print $107,000,000 worth of notes - a paltry amount compared to the total amount of Federal Reserve notes in circulation (about a trillion dollars), not to mention non-physical (electronic) money.

As for the logical explanation of why they switched from notes issued direct by Treasury to the arms-length quasi-federal FRNs, the explanation usually given is that politicians can't be trusted with direct control of the money supply, because they'd simply try to print their way out of poor electoral prospects. The Federal Reserve, in theory, puts the needs of the economy before the needs of the politicians.