markham was elected to the senate in 1926. previously, he had been an alderman, city attorney and mayor of horicon, wisconsin. during the united states senate elections, 1928, markham was an independent candidate, losing to incumbent robert m. la follette jr.. in 1936, he ran for the wisconsin progressive party nomination for attorney general of wisconsin, losing to orland steen loomis. he was then an unsuccessful candidate for dodge county, wisconsin judge in 1938. in 1948, markham ran for the republican nomination for secretary of state of wisconsin, losing to incumbent fred r. zimmerman.