During this time he worked on his habilitation and, immediately after being appointed to Halle in 1869, he presented his thesis, again on number theory, and received his habilitation.
Sa mga panahong ito ay nagtrabaho siya sa kanyang habilitation at, pagkatapos ay hihirangin upang angkinin Halle sa 1,869, he itinanghal sa kanyang sanaysay, muli sa bilang teorya, at nakatanggap ng kanyang habilitation.