The Securities Exchange Act of 1934 sets forth certain requirements for companies to register their shares with the S.E.C.
Specifically, Section 12(g) requires that a company register its securities with the S.E.C. if it “has total assets exceeding $1,000,000 and a class of equity security … held of record by five hundred or more … persons…”
Sounds to me like this law has been around for a while.
That statement might mean, "The Securities Exchange Act of 1934 as amended," because laws are often named by their original date of enactment, but amended subsequently.