[1] Law was appointed Mayor of Madison in late 1932 to complete the unexpired term of Albert G. Schmedeman, who had been elected Governor of Wisconsin in the 1932 general election.
[2] During his mayorship, he was named to an advisory board to aid the federal government in preparing legislation that would affect municipalities.
[3] He also joined 32 other US mayors in co-signing a 1938 message to the International Peace Campaign expressing "horror and indignation" at bombing violence happening in other parts of the world.
[4] After serving as mayor, Law served as the chair of Wisconsin's state highway commission, and briefly ran for Governor of Wisconsin in the 1946 Republican primary, but didn't make the ballot.
Incumbent Walter Samuel Goodland was renominated and went on to win re-election.