When James Thomson died on 12 January 1849 during a cholera epidemic, the chair of mathematics at Glasgow became vacant. Blackburn was appointed to the chair, with a strong recommendation from Cayley, and took up his duties on 23 April 1849.
Kapag James Thomson namatay sa 12 Enero 1849 sa panahon ng kolera epidemya, ang upuan ng matematika at Glasgow ay naging laman. Blackburn ay hihirangin upang angkinin ang upuan, na may isang malakas na rekomendasyon mula sa Cayley, at kinuha ang kanyang tungkulin sa 23 Abril 1849.