Go back to article: Ventriloquised voices: the Science Museum and the Hartree Differential Analyser

Origins of the object

In 1933 Douglas Hartree (Beyer Chair of Applied Mathematics at the University of Manchester) visited Vannevar Bush at the Massachusetts Institute of Technology to see his newly developed ‘differential analyser’. The MIT differential analyser was one of many that Bush had designed to mechanise the arithmetic processes of addition, subtraction, multiplication, and division (Crank, 1947, p 1). With eight integrating units, Bush’s differential analyser also mechanised the processes of calculus alongside these arithmetical functions, allowing the machine to numerically solve differential equations for which there was no formal solution (Crank, 1947, p 2). Observing the various gearing components, shafts, and wheels of this new mechanical computer, Hartree commented that the machine looked as if ‘someone had been enjoying himself with an extra-large Meccano set’ (Froese Fischer, 2003). On his return to the United Kingdom, Hartree immediately set about working with his research student, Arthur Porter, to develop their own version of the differential analyser. The Hartree Differential Analyser – created using the children’s construction toy Meccano – helped to reduce the complexity of differential equations that Hartree had researched during the First World War with his father, William Hartree.[3] After completing their differential analyser, Hartree and Porter used it to mechanise the process of integrating equations related to Hartree’s work on the Self-Consistent Field Theory.[4]

Figure 2

Black and white portrait photograph of Douglas Hartree

Douglas Hartree during his time at the University of Manchester. His work on analogue and digital computing systems at both Manchester and Cambridge made him a very influential figure after the Second World War. Hartree was born 27 March 1897 and died 12 February 1958

In contrast to Bush’s analyser, Hartree built his version with a single integrating unit (later increased to three and then four integrators). He described the Hartree Differential Analyser as having ‘exceeded all expectations’, increasing the accuracy rate of resolving equations compared to previously hand-computed processes (Hartree and Porter, 1935). The Meccano analyser could be configured to resolve a variety of differential equations.[5] It provided solutions to these equations — relating to fluid mechanics — through explaining changes in the momentum of an object as it moved through a space that contained different pressure levels and viscosities.[6] In comparison to the methodology of hand-computed equations, the Differential Analyser translated equations mechanically through the units of the machine from the input table to the wheel-and-disk integrating unit and through the torque amplifier, before automatically drawing the solutions as a curved line on the output table. Despite being created as a model to demonstrate this new methodology, the Hartree Differential Analyser ultimately ‘...turned out to be more than a demonstration model… [it was] capable of solving many equations with a considerable degree of accuracy’ (Hawks, 1934, p 441). The analyser initially had one, then three, then four integrating units, and was used by Porter for his MSc Thesis in 1935, calculating the atomic wave functions of Chromium atoms. The success of this Meccano model led Hartree to construct a larger differential analyser — the Manchester Machine, with eight integrating units — in 1935 with Metropolitan Vickers Ltd. However, instead of using Meccano, the pieces of the Manchester Machine were made to Hartree’s specifications by Metropolitan Vickers Ltd., helping to increase the mechanical accuracy of the machine, which was applied to many problems in the final years before the Second World War. The problems that the machine was used to resolve in these years related to the Control Theory, Heat-Flow Thermodynamics, and Fluid Dynamics, as well as being used to resolve more straightforward calculations that related to railway timetables.

While the original Meccano model analyser was stored in Hartree’s study, he and other members of the Servo Panel used the Manchester Machine at the Ministry of Supply throughout the Second World War. A number of these analogue machines were built in England and America in the years before the Second World War, and the increased requirement of computation and processing power during the war led to their use to resolve a number of equations relating to anti-aircraft and ballistics trajectories.[7]

Figure 3

Colour photograph of a differential analyser machine on display

The Manchester Machine was built in 1935 after the success of the Meccano Model Hartree Differential Analyser. Half of the analyser is on display at the Science and Industry Museum in Manchester, with the other half residing in the Mathematics gallery at the Science Museum, London

Hartree’s focus shifted from analogue to digital computing methods as the war progressed, leading to his move to the Mathematics Section at the National Physical Laboratory. Working with a number of contemporaries, including John Womersley, Alan Turing, and John von Neumann, Hartree helped to develop the Colossus computer, the ENIAC, and the EDVAC in the final years of the war, advising and lecturing countries and governments on the benefits of this new system. His move away from the analogue computing and the Servo Panel meant that the running of the Manchester Machine shifted to his research students, Nicholas Eyres, Phyllis Nicholson, Jack Howlett, and Jack Michel, who continued to use it throughout the war. It remained in use at the National Physical Laboratory after the war, becoming available for collection in 1973, when half of it was collected by Jane Pugh at the Science Museum, with the other half collected by the Science and Industry Museum in Manchester. 

Figure 4

Black and white photograph of a number of people working on a differential analyser machine

Hartree and his team using the non-Meccano Manchester Machine during the Second World War at the Ministry of Supply. Douglas Hartree is the figure centre-right, observing one of the output tables of the machine with Phyllis Nicholson, while (from front-to-back) Jack Howlett, Nicholas Eyres, and Jack Michel work to program the machine through its various input tables

After the Second World War, Hartree resumed his academic career at the University of Manchester, before being appointed Plummer Professor of Mathematical Physics at the University of Cambridge in 1946. His inaugural lecture ‘Calculating Machines: Recent and Prospective Developments and their impact on Mathematical Physics’, focused on his experiences in developing both analogue and digital computing systems. As part of his move to Cambridge, the original Meccano differential analyser that he had built with Arthur Porter was dismantled. Although his work increasingly focused on digital computing, Hartree salvaged some Meccano parts from the differential analyser and used them to rebuild a portion of the original model. He removed the input and output tables, turning this new version of the machine into a device that could be programmed with a single differential equation to demonstrate the mechanical methodology of integration. He made these changes so that he could easily transport the machine around the country to demonstrate the principles of mechanical integration in his public lectures, which he did between 1947 and 1949. The equation that he chose to pre-program into this new version measured tractive force as applied to railways, which led it (along with the glass case that Hartree transported it around in) to be nicknamed the ‘Trainbox’. Initially loaned to the Science Museum in 1949, it is the Trainbox version of the Hartree Differential Analyser that forms the subject of this paper.

Figure 5

Colour photograph of a single integrator meccano model built in 1947

The Single Integrator ‘Trainbox’ model rebuilt by Douglas Hartree in 1947 using Meccano parts taken from his original 1934 Differential Analyser. This object currently sits in the Web Exhibit of the Information Age gallery

Component DOI: http://dx.doi.org/10.15180/181005/002