Manchester Years
In 1929, Hartree was appointed to the Beyer Chair of Applied Mathematics at the University of Manchester. In 1933, he visited Vannevar Bush at the Massachusetts Institute of Technology and learned at first hand about his differential analyser. Immediately on his return to Manchester, he set about building his own analyser from Meccano. Seeing the potential for further exploiting his numerical methods using the machine he prevailed on Sir Robert McDougall to fund a more robust machine, which was built in collaboration with Metropolitan-Vickers.
The first application of the machine reflected Hartree's enthusiasm for railways in calculating timetables for the London, Midland and Scottish Railway. He spent the rest of the decade applying the differential analyzer to the solution of differential equations arising in physics. These included control theory and laminar boundary layer theory in fluid dynamics making significant contributions to each of the fields.
The differential analyzer was not suitable for the solution of equations with exchange. When Fock’s publication pre-empted Hartree’s work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton-Hartree equation. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognized the importance of configuration interaction that he referred to as "superposition of configurations". The first multiconfiguration Hartree-Fock results were published by father, son, and Bertha Swirles (later Lady Jeffreys) in 1939.
At Hartree’s suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation in 1935. With Hartree’s advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay.
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