St. Patrick is the patron saint of engineers. This is one of the buttons made for the St Patrick's Day celebration which was a big thing when I attended Univesity of Missouri in the 50's. As you might guess, "taming the atom" was on a lot of people's minds only a few years after WWII ended. St Pat tries it with his animal-tamer's whip on this student designed button.
Erin go braugh is a phonetic version of "Éirinn go brách," which in Irish (Gaelic) means "Ireland Forever."